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John Baez has been shared in 321 public circles

You can see here the 50 latest shared circles.
If this is your profile, you can check your dashboard to see all shared circles you have been included.

AuthorFollowersDateUsers in CircleCommentsReshares+1Links
EDZUL FREDY KRISNAWAN0Meet the People who WILL...Take This Circle To The TopLet 'er Rip! You guys and gals are SUPERSTARS!!!Want to be added to the #hyperadd?1) Add me to your circles.2) Share, +1, and Comment This Share3) Reshare anything that interests you on my stream (profile) from today or the rest of this week.#circlesharing   #sharedcircles   #circles   #circlemaster  2014-08-29 11:28:104858410CC G+
Wendy Thanh Hồng43GOOGLE FRIENDS! -  RESHARE if you want to be included *'"*:•:••:*:•-:¦:*  *SHARE AND BE  SHARED*  *:¦:-•:*:••-:•:''''*  This is a super Circle and in it I put together a group of really interesting and active people on Google Plus to add in your circles.I'm talking about the top   Google + users that share unique and original contents.Follow   this advice and grow your G+ community with people that share amazing content that will surprise you:boost   visibility on Google+ - Share the circle!If you want to be added to the next Circle you have to do these simple steps:1 - Include me in your circles 3 - Share the circle (Publicly) 4 - Add +1 to the post 5 - Follow  your dreams and smile to life.More you share More you get! :)I will thankful if you plus and share this circle!#circles #shared #share #add #friends #circle #share #sharecircle #circleshare2014-08-25 05:58:2348610214CC G+
Kieu Trinh0GOOGLE FRIENDS! -  RESHARE if you want to be included *'"*:•:••:*:•-:¦:*  *SHARE AND BE  SHARED*  *:¦:-•:*:••-:•:''''*  This is a super Circle and in it I put together a group of really interesting and active people on Google Plus to add in your circles.I'm talking about the top   Google + users that share unique and original contents.Follow   this advice and grow your G+ community with people that share amazing content that will surprise you:boost   visibility on Google+ - Share the circle!If you want to be added to the next Circle you have to do these simple steps:1 - Include me in your circles 3 - Share the circle (Publicly) 4 - Add +1 to the post 5 - Follow  your dreams and smile to life.More you share More you get! :)I will thankful if you plus and share this circle!#circles #shared #share #add #friends #circle #share #sharecircle #circleshare2014-08-25 05:34:0348612518CC G+
Cableicous2,902Thanks for all teh cablezThanks muchly to all those who have contributed their #Cableicous  imagery for another grand week of beautaliciousness.And a new week begins...#photography #cables #cableicous #circleshare #2014 #cableriacirculus2014-08-09 22:10:58406119CC G+
Richard Green77,832Engagers Showcase Circle, August 7, 2014If I sent you a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares.Everyone mentioned below is also included in the circle.Our cat, Chesterhttps://plus.google.com/101584889282878921052/posts/ToxRHsMHytsFibonacci numbers and corridors of width 4https://plus.google.com/101584889282878921052/posts/gCTyaSV4ugzWalk in the rainhttps://plus.google.com/101584889282878921052/posts/gVPzuv7aKHALenticular cloud (reshared from +Sean R. Heavey)https://plus.google.com/101584889282878921052/posts/giTgt4PUd1GGlass Paperweight by Paul Stankardhttps://plus.google.com/101584889282878921052/posts/fLfKWxFj3f2“Mathematistan” by Martin Kuppehttps://plus.google.com/101584889282878921052/posts/AcUBb8Y9uBjCat's back on the menu, boys!https://plus.google.com/101584889282878921052/posts/aP3cZEnaqquWaterfall (reshared from +Keith Boone)https://plus.google.com/101584889282878921052/posts/S2pmsTTyiZzOak tree at “The Pig”https://plus.google.com/101584889282878921052/posts/cv8pi2ffX1NThe Bargate, Southamptonhttps://plus.google.com/101584889282878921052/posts/LsYSEpUS1bLCosmos flowerhttps://plus.google.com/101584889282878921052/posts/KqvLW32KyXfThe Ashton Memorialhttps://plus.google.com/101584889282878921052/posts/aK1E3XqWWSSThrough the castle windowhttps://plus.google.com/101584889282878921052/posts/MT7uBM2SUt7Friedman numbershttps://plus.google.com/101584889282878921052/posts/32tzjfB8NnMThe Norfolk Knifehttps://plus.google.com/101584889282878921052/posts/DHf4jfSkUKKThe lake at Wyresdale Parkhttps://plus.google.com/101584889282878921052/posts/3xFACaympiNCastle of the Clouds2014-08-07 21:46:51451198123234CC G+
Nick Warner645Check out these awesome Crowdfunders2014-08-07 16:05:31470001CC G+
Refurio Anachro4,492This july engagers circle comes packed with curiosity, brought to life by questions and answers, and people sharing their enthusiasm. Take your chance, get acquainted to this party of very nice people and deep thinkers, add it now!+John Baez had asked for an inside view of a mirror ellipsoid i was happy to provide. The result's actually a spheroid because it has a symmetry axis. Since then, i did quite some staring at ellipsoids, see below... https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/5zcrptKx3C3This reshare of +Xah Lee's "math is programing" rant got me into ugly. Gracefully handling distractions would be nice to have more of. If you must know, i heard one can retrieve deleted comments using the search...https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/TZpAUuQfzSn“Mathematistan” by Martin Kuppe offers innocuous glances aside from the popular maths mainstream. Thanks +Richard Green for sharing and noting similarities to the all time favorite "Hitchikers guide to the galaxy"!https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/UnXikyENJo1A raytraced perspective down a mirror cylinder showing quite a lot about billiard trajectories on a bunch of elliptic tables. Learn what Birkhoff, Poincare, and Poncelet had to do with it...https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/Vmrx7GMRe2iReshare of 6d toroid animations, thanks +Owen Maresh and +Cornus Ammonis for sharing!https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/gSma1ksKFeiThis ellipsoid glossary and coordinate system came with puzzles! Special thanks to +Bruce Elliott for taking part in the fun. Apparently i didn't add a clean solution putting everything together at the end... More to come, stay tuned!https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/L6C4Kob2bNeLast june's engagers circlehtt2014-08-03 23:22:2311314310CC G+
Marius Kiupelis279 If you received this notification you are in this circle♚♚  If you want to be shared in this circle ♚♚♚♚♚♚♚ Then just keep sharing! ♚♚♚♚♚2014-08-03 19:05:53201036CC G+
Lynda Chervil890Add this circle of excellent engagers, thinkers, innovators, and future tech leaders. My ++Solar Power++ Circle will provide you with the latest and greatest from the world of tech innovations, especially in the renewable energy sector. Simply add this circle and then share it!If you'd like to be added to this circle, please comment below, share and add the circle. Only those who qualify with content and expertise will be added. Thanks! #Tesla   #nikolatesla   #elonmusk   #solarenergy   #innovation   #technology   #solarpower   #hydroelectric   #science   #STEM   #research   #education   #futuretech   #futuretechnology  2014-07-31 14:24:32343024CC G+
Peter Edenist31,0152014 Super Sci-FI Circle : No, the Sky is not Falling!!! Also the Gravity is not sucking you in... please +1 this post to support it or you may have to take a trip in Snowpiercer, no need to thank me. Please reshare if you think this is a worthwhile circle. If you have been notified, you are in the circle!All the people in this circle are linked to our community (see link further down). As usual, please tag and recommend anyone who you think should be in this circle. Live long and prosper!Sci-FI Community here: http://goo.gl/s1NVd  Science Fiction Pics: http://goo.gl/sOSPK5Mighty Shiny Browncoats : http://goo.gl/9osg1tDoctor Who : http://goo.gl/z3uWX3Ultimate Star Wars : http://goo.gl/Wu8bv6Ultimate Star Trek : http://goo.gl/JJPql9Science on G+ community here: http://goo.gl/46uFH #sciencefiction #sf #scifi  2014-07-24 12:58:0746211961146CC G+
Becky Collins13,434Mobile Operator Circle:Circle of very #social #engagerspeople and companiesTo be included in my shares (#sharedcircle), be so kind to:1 - Do +1 t the post2 - Comment the post and specify your "category" (job or interest) Ex: Fashion, SEO, Companies, Social Media Marketing, Sailing, Photography, Bloggers/Writers, Web graphics and design, Italy, Artists, Sport, Finance/Economy ...3 - include the circle among your circles4 - share the circle (include yourself)Improve your popularity, be social be cool !Keep yourself updated, enjoy the Shared Circles Hellenic Alliance, you can share your shared circles inside the upcoming Community:https://plus.google.com/communities/112552559573595396104  #socialmedia  #media  #circles   #circleshare   #circlesharing  #circlecircle   #beckyscircle   #sharedcircles   #sharedpubliccircles  #sharedcircleoftheday  +Becky Collins ?2014-07-24 05:16:124763112CC G+
Able Lawrence100,166100K Engagers Celebration Circle Thank you all those who have followed me and engaged with my posts and taking me to the milestone of 100,000 followers. Goolge+ has been an exhilarating journey of 3 years and I would like to thank all those who have followed me and engaged on my posts whether they were on Science or Birds or Technology. The circle has been created using  * +Circloscope * which is the work of +Ehsan Ahmadi Gharacheh All of you are free to share your favorite posts in the comments and also reshare this circle. If you are included in the circle, you will get a notification.  2014-07-17 17:22:18340491787CC G+
Doug Hyatt5,196THIS IS MEGA CIRCLE 5    #DOUGHYATTCIRCLESHARING IT ADDED 1,000+ FOLLOWERS FOR ME IN A WEEK.1) ADD THE CIRCLE2) RESHARE THE CIRCLE AND BE SURE TO REMEMBER TO CHECK THE BOX WHICH INCLUDES YOURSELF.3)RESHARE TO PUBLIC EVERY DAY!BE SURE TO COPY THE HASHTAG LIST AND ADD IN YOUR COMMENTS LIKE I HAVE!  IT WILL GIVE YOU MAXIMUM RESULTS#doughyattcirclesharing#circles   #circlemania   #circletoday   #circleplus   #circleshare   #circlesharing   #CircleSharing   #sharecircle   #sharecirclethis   #worldsharecircle   #pleasecircleaddme   #circleoftheday   #newgenerationcircle  #monstercircle   #usacircle   #bestofthecircle   #shareofthecircle   #pleasecircle   #newbestcircl  add circle add circle * best share circle * share please pleaseplease add circle * best share circle * share please please#add #circle   #addcircle   #pleasecircle   #bestcircle   #mostcircle  #bestsharecircle   #newcircle   #top100circle   #best500circle   #top500circle   2014-07-16 15:49:10477151421CC G+
Richard Green74,896Engagers Showcase Circle, July 12, 2014If I sent you a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares.Everyone mentioned below is also included in the circle.Thistlehttps://plus.google.com/101584889282878921052/posts/CKB7ks1VWZ3“Star Gate” by +Gary Matthews https://plus.google.com/101584889282878921052/posts/ean83YFix7sBubble (reshared from +Ann-Marie Jurek)https://plus.google.com/101584889282878921052/posts/PkybKJfXv14Gabriel's Hornhttps://plus.google.com/101584889282878921052/posts/MXNTuq8ZEBPHibiscus flowerhttps://plus.google.com/101584889282878921052/posts/Xsmw62v98CHStackable 12-sided dicehttps://plus.google.com/101584889282878921052/posts/5mLoukdZAA5Astronomical book priceshttps://plus.google.com/101584889282878921052/posts/S15LTNxJA9GPyritohedral symmetryhttps://plus.google.com/101584889282878921052/posts/XQUYMrKGiAQSt Stephen's Basilica (reshared from +Laura Orange)https://plus.google.com/101584889282878921052/posts/ApnSMBsUWFeCircular Pascal Arrays and Fibonacci numbershttps://plus.google.com/101584889282878921052/posts/NVqYKoRVnHg“Fungi tree” by +Tom Beddardhttps://plus.google.com/101584889282878921052/posts/J6S4bDc6QwQAs always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!2014-07-12 05:31:36476209130224CC G+
Refurio Anachro4,312June engagers circle: Say hello to almost 200 nice people who joined in to participate in math topics. If you're intelligent, curious, like well written posts and engaged discussion - these people will not dissappoint. Go on and add them now!Last month's posts:Spin story continues (part 3): Angular velocity and tilings in spin space. While i locked myself in a cycle, struggling to follow, +wendy krieger blew the bubble and lifted the party up to dimension 4! I couldn't resist but to guest post this gem. Next time i'll find a picture first, promised!:https://plus.google.com/115434895453136495635/posts/6F9sxQxiqEaClifford Algebra (part 1): Into Clifford algebra. Because with those one can easily describe spin in any dimension.https://plus.google.com/115434895453136495635/posts/1CtiDXou6RqUnicode math cheat sheet: ⁵√7+x² – ℵ₀ – ℝⁿ – x̅ ≟ x*⊕x⁎ – αβ ≺ ∇ϕhttps://plus.google.com/115434895453136495635/posts/GNoCEmBxSWSClifford Algebra (part 2): Multiplication in geometric algebra.https://plus.google.com/115434895453136495635/posts/NKqs5BwsCqqCardioid gears, a reshare of +Rob Kook's very unexpected video find:https://plus.google.com/115434895453136495635/posts/UMBXJihPgcaCan we get anything faster than light that way? While arguing below +John Baez' cool post i suddenly started hearing vikings...https://plus.google.com/115434895453136495635/posts/jjYu4KhHaCTClifford Algebra (part 3): Cayley graphs and a strange clock. My first attempt to quickly put my thoughts down for you to see. I guess i'll have to practice a bit to make it more appealing on shorter glance, so more people can benefit.https://plus.google.com/115434895453136495635/posts/bkHQAZLzpt8Last may's engagers circle:https://plus.google.com/115434895453136495635/posts/hGPebLWRcU2You're in this circle because you reshared, plussed or commented on one of my posts (possibly via +Spherical Reflections), or got into a discussion with me. Thank you!#engagers #engagerscircle #engagersshowcasecircle  #circleshare #circlesharing #circl2014-07-02 13:23:15194659CC G+
Peter Edenist30,747TESLA Super Science Circle 2014 - June Edition!!!! : A quality circle curated carefully and tended since 2011. Who is in this circle?  people who are either involved in science, love science or are active on the Science on G+ community. Community link is here http://goo.gl/46uFH and the Page is +Science on G+!Have you wondered where one can meet with like-minded people who love science and like to read about the real stuff? This is the ultimate SUL on science.... add and share to keep it alive.--------------------------------------------------------------------------------------------------Want to nominate someone? Please do so in comments. If you want to recommend something let us know. People who are notified are part of the circle.#science #tesla #scienceongplus #scienceeveryday 2014-06-19 13:39:49342755693CC G+
David Wees4,496This is a circle of 346 math educators. If you are interested in following the work of innovative mathematics educators, this circle is for you.If you are a mathematics educator, and I have not included you in this circle, let me know.2014-06-11 16:24:03346010CC G+
Dina Tika0Here is a group of Active Engagers, Circle Sharers, Awesome Plus Oners, and Cool People on Google Plus!   Circle Sharing is an awesome way to increase your followers and active engagers on your profile. Some of my favorite people that I've met here on Google + through Circle Sharing.    Want to be in the next Circle of Awesomeness? Follow the Steps Below!  ☛ Add the circle ☛ Share in the Public ☛ Plus 1 the Post. ☛ Comment. 2014-06-10 05:53:52479001CC G+
Refurio Anachro4,141May engagers circle: Meet the people who made the fabulous cheer of this week's spin party. Many curious people, all of them worth to add!Diagram 18: rotations and spinorshttps://plus.google.com/b/115434895453136495635/115434895453136495635/posts/dpPMfoH6zc5This is actually part two, but got posted earlier (see below). You just made my first +100, thank you! Stay tuned for more on spinning and spinors.https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/TLkA6tCNwEeIf you want to know what an earlier stage of Diagram 18 looked like, see here. I posted 2/3rd of the final post with a question marking my progess. Also note the discussion below, thanks to everybody who helped me out!https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/THePbpcPnqDYou're in this circle because you reshared, plussed or commented on one of my posts (possibly via +Spherical Reflections), or got into a discussion with me. Thank you!Last april's engagers circlehttps://plus.google.com/b/115434895453136495635/115434895453136495635/posts/RFMY2aYscJJ#engagers #engagerscircle #engagersshowcasecircle  #circleshare #circlesharing #circle #circleoftheday  #addcircle #findcircles #publicsharedcircles  #addpeople #plussers #awesomepeople #sciencecircle  #commenterscircle #mathematicians #friends 2014-06-02 11:57:02158447CC G+
John Nuntiatio37,49330k+ Circle - A circle worth adding and followingThe people from this circle have more than 30,000 followers.2014-06-02 08:54:46140496CC G+
Becky Collins10,282Mobile Circle :Circle of very #social #engagerspeople and companiesTo be included in my shares (#sharedcircle), be so kind to:1 - Do +1 t the post2 - Comment the post and specify your "category" (job or interest) Ex: Fashion, SEO, Companies, Social Media Marketing, Sailing, Photography, Bloggers/Writers, Web graphics and design, Italy, Artists, Sport, Finance/Economy ...3 - include the circle among your circles4 - share the circle (include yourself)Improve your popularity, be social be cool !Keep yourself updated, enjoy the Shared Circles Hellenic Alliance, you can share your shared circles inside the upcoming Community:https://plus.google.com/communities/112552559573595396104  #socialmedia   #media   #circles   #circleshare   #circlesharing   #circlecircle   #beckyscircle   #sharedcircles   #sharedpubliccircles   #sharedcircleoftheday  +Becky Collins ?2014-05-28 05:03:174777219CC G+
Jasmina Brozović53,426Notification CircleThis is a circle of people I don't wanna miss any new posts from!Great Circle idea by +Zvonimir FrasRead more :https://plus.google.com/u/0/+ZvonimirFras/posts/VsZjS7H7vJf#circles #circlethis #circleyoushare #sharedcircles #addcircle #sharedpubliccircles #circleshare #publicsharedcircles #circleoftheweek #circlesharing #publiccircle #sharedcircle #circleshare   #circle     #motivateme 2014-05-20 16:26:14179271031CC G+
Daniel Zawadzki7,897This #circle is #great, #amazing, #wonderful,Boost your visibility on Google+ - Share the circle!#1 - Click add people and create your circle#2 - share the circle (include yourself)#3 - add +1 to the post#circle   #circleshare   #circlesharing   #circleoftheday   #circleoftheweek   #share   #sharedcircles   #sharedpubliccircles   #sharedcircleoftheday   #engagers   #engagerscircle   #engagerspeople   2014-05-19 20:33:554709446123CC G+
Refurio Anachro4,070April engagers circle, a ball of intelligent, nice, and responsive people. Have a look!You're in this circle because you reshared, plussed or commented on one of my posts (possibly via +Spherical Reflections), or got into a discussion with me. Thank you!The following has been classic april fool's, of course. Works best on kids %-]https://plus.google.com/115434895453136495635/posts/SA2aNCZPrQkNot being a big fan of synchronous communication, i will try and challenge you in case you do want to hang out. That's a rather new ploy of my character, and it seems i still have to learn a lot on how to do this nicely...https://plus.google.com/115434895453136495635/posts/fM8DtSPKL2MI have been seen spreading rumours with +David Roberts, speculating that this year's Fields medal might go to Manjul Bhargava. Here for the fullest explanation, thanks again David:https://plus.google.com/115434895453136495635/posts/KUbagU2C7C7A raytraced landscape featuring two spherical mirrors. It's about dynamical billiards (chaos theory).https://plus.google.com/115434895453136495635/posts/BCduuGFS75LWhen i saw +Richard Green's post about Coxeter-Conway friezes i couldn't resist to divert my readers to have fun counting paths with +DrJamesTanton. Fibonacci inside:https://plus.google.com/115434895453136495635/posts/gKBcK1HNdMvEverybody should have played at least once with an interactive IFS demo! If you haven't, or want to try again - here's a nice one by +Felix Woitzel:https://plus.google.com/115434895453136495635/posts/N9HeysDgTzi #engagers   #engagerscircle   #engagersshowcasecircle   #circleshare   #circlesharing   #circle   #circleoftheday   #addcircle   2014-05-16 11:46:1281867CC G+
Richard Green68,138Engagers Showcase Circle, May 12, 2014If you received a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares.Everyone mentioned below is also included in the circle.Peruvian glacier (reshared from +Irina Tcherednichenko)https://plus.google.com/101584889282878921052/posts/Z6NR7zaZa5qGrape hyacinthshttps://plus.google.com/101584889282878921052/posts/GZoHH2bnRUiSymmetries of a regular octagonhttps://plus.google.com/101584889282878921052/posts/bFcGcsurF5HHappy Easter!https://plus.google.com/101584889282878921052/posts/YkWFA9WmxVAPerfect Squared Squareshttps://plus.google.com/101584889282878921052/posts/HDU4mWD3wptOur dog Rexhttps://plus.google.com/101584889282878921052/posts/5JtEcnt5MpPPerrott's Follyhttps://plus.google.com/101584889282878921052/posts/8DzXHLn6fe4The Lonely Runner Conjecturehttps://plus.google.com/101584889282878921052/posts/YHJkEdKg3jz“Owl” by Andrea Mininihttps://plus.google.com/101584889282878921052/posts/12uh9J9MjMXPenrose nanotileshttps://plus.google.com/101584889282878921052/posts/7PZPSLaFkAx“Interlaced Stars” by Magnenauthttps://plus.google.com/101584889282878921052/posts/5vNjv1yjVMqBlack Forest View (reshared from +Ralph Reichert)https://plus.google.com/101584889282878921052/posts/YKPsvCFDyUv“Hippie Bus Apartments” by +Richie Montgomeryhttps://plus.google.com/101584889282878921052/posts/iCMXCBVzjd2Not crazy enoughhttps://plus.google.com/101584889282878921052/posts/d5EeDSoHe5u“Impossible Sphere” by Alexey Ermushevhttps://plus.google.com/101584889282878921052/posts/J2yUMw6YASqBeethoven, high on 2014-05-12 05:07:06489214129230CC G+
Cindy Wilson02014-05-10 14:34:25371700CC G+
Pamela Baskett02014-05-10 13:35:433711505CC G+
DRESS3,901If you want to be added to the next Circle you have to do these simple steps:1 - Include me in your circles 2 - Share this post3 - Add +1 to the post 4 - Leave a comment if you have done the 3 steps above#circle   #circleshare  #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare #circle #circleshare 2014-05-05 12:20:413723411CC G+
Graeme McRae24,994Graeme's Circle of Active GooglePlussers! . . . This is a curated circle of active people on Google+* If you add this circle, you will see hundreds of new posts per day in your stream from this circle alone. It's a circle of people I started following a few months ago, and who have consistently posted something at least once a week during all of weeks since then. If you want an interesting stream, you should add this circle. If you're interested in how I curated this circle, and why I think it makes for a really great stream, read on. . .How did these people get in the circle?. . . They must have posted something interesting, at least once, because I don't follow people unless they post something interesting. By now, you're probably not surprised by the number of people on G+ whose pages are full of repeated posts, videos without comments, "what's up" and other uninteresting things. I don't follow those people.How did they stay in the circle since they were added?. . . After I add someone, I keep them in the circle of people I added around the same time. Then, several times a week, I go through all my circles and delete people who haven't posted (something visible to me) in the last 7 days. So the people who are left in the circle are consistent posters. That says something important about them, because consistency is a proxy for quality.Wait. What? Why is consistency is a proxy for quality?. . . I'll admit it: I don't have the science to back up that wild statement, but I'll tell you why I believe it to be true. People who post crap don't get a lot of followers, and the few followers they have don't bother to engage. After a while, the crappy-posting people start to think G+ is a ghost town, and they lose interest. On the other hand, the people who share (or re-share) interesting things get followers and engagement, slowly at first, but ever increasing, and this outpouring of love is what keeps them going. That's what I think anyway, and I'm sticking to it.People who share interesting things get lots of followers. . . This is another half-baked theory of mine, but hear me out. You might think this makes sense: Google+ offers suggestions of people to follow, especially to new users. Google+'s only source of names to suggest are other G+ers like yourself. The G+ers who have the most engagement are the ones Google+ knows will be good to follow, so these people get put out as suggestions more often, and some percentage of those suggestions are taken up. So the more engagement you have, the more Google+ will suggest you as a person to follow, and so the more followers you'll get. Completing the theory: the more interesting the stuff you share (or reshare), the more engagement you'll get, and hence the more followers you'll get.How can I get in your circle?. . . Don't bother trying to "get into" this circle. This circle isn't for you to get into. Think of it the other way around. This circle is for you to add, so you can follow a bunch of interesting and consistent people. The stream from this one circle will be chock-full of fascinating content for you to reshare. People will start to notice your reshares, and they will engage with you, and then Google+ will "notice" (it's a computer, but let's anthropomorphise, shall we?) you and suggest you to others, who will then follow you.No, really. How can I get in your circle?. . . First, unfollow me, then wait, oh, about a week. Spend that week posting a shitload of interesting things. Then follow me. Since you're so interesting, Google+ will notify me that you followed me (G+ doesn't notify me about every follower). I'll look at your posts, find one interestin2014-05-04 21:03:52371111319CC G+
nicholas syahputra821. Plus The Post2. Comment3. Add People To Circles4. Share The Circle!#circlesharing #circleshare #circles #circle #googleplustips #googleplus #indonesia #artists #artist #artistphotographeramateurorprofessional2014-04-30 07:03:1548531642CC G+
Ryan Johnson3,346My new some cool, fun & interesting people CirclePlease reshare it#circles           #circlescirclescircles           #circleshare         #circleshare2014-04-25 06:14:362357820CC G+
Becky Collins8,289Engagers Showcase Circle :Circle of very #social #engagerspeople and companiesTo be included in my shares (#sharedcircle), be so kind to:1 - Do +1 t the post2 - Comment the post and specify your "category" (job or interest) Ex: Fashion, SEO, Companies, Social Media Marketing, Sailing, Photography, Bloggers/Writers, Web graphics and design, Italy, Artists, Sport, Finance/Economy ...3 - include the circle among your circles4 - share the circle (include yourself)Improve your popularity, be social be cool !Keep yourself updated, enjoy the Shared Circles Hellenic Alliance, you can share your shared circles inside the upcoming Community:https://plus.google.com/communities/112552559573595396104  #socialmedia  #media  #circles   #circleshare   #circlesharing  #circlecircle   #beckyscircle   #sharedcircles   #sharedpubliccircles  #sharedcircleoftheday  +Becky Collins ?2014-04-23 05:59:02400201526CC G+
Circlemania !!!2,173in this circle you can find people keen to publish, share, track and unr to good communities. see and discover new friends and circles that may interest you. Do not forget to follow me as: +Andres Aguilar  #circle   #circleshare   #circlemaina   #circlemeup  2014-04-19 15:48:55498262034CC G+
Richard Green64,997Engagers Showcase Circle, April 17, 2014If you received a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares. Two of the posts below attracted too much engagement to be usable for the circle, but I am including links to them for completeness.Everyone mentioned below is also included in the circle.Adding cubeshttps://plus.google.com/101584889282878921052/posts/WqimoVTZWL3Flower and snail shell (reshared from +Ralph Reichert)https://plus.google.com/101584889282878921052/posts/5st1n4VBMh5April Fools' Dayhttps://plus.google.com/101584889282878921052/posts/Mxa1TNjYo4r“Trinity” by Jen Starkhttps://plus.google.com/101584889282878921052/posts/gfRheBovSZUHyperbolic honeycombs (reshared from +Roice Nelson)https://plus.google.com/101584889282878921052/posts/59yPx8yoFbuCoxeter—Conway friezeshttps://plus.google.com/101584889282878921052/posts/4XvYb9biaLpTriple helix staircase (reshared from +Romain Brasselet)https://plus.google.com/101584889282878921052/posts/SRJ7CqGNrtLWhich airport is closest to you?https://plus.google.com/101584889282878921052/posts/FxxdDb6orPy“Spinning Cosmos” by Paul Friedlanderhttps://plus.google.com/101584889282878921052/posts/RjnVfRhBPmZStrč prst skrz krkhttps://plus.google.com/101584889282878921052/posts/h87PZWs2MSbMersenne primes and perfect numbershttps://plus.google.com/101584889282878921052/posts/cLWBTddiSyy“Urge to fly” by Hermin Abramovitchhttps://plus.google.com/101584889282878921052/posts/j2K97AvLvAoKeeper of Time (reshared from +Michael Quinn)https://plus.google.com/101584889282878921052/posts/QnaHrgKjsUUSeven mutual2014-04-17 04:49:32487185132233CC G+
Ryan Johnson2,352sharedcircle   #publiccircleshare     #circleshare     #circleoftheday  #circleshares     #circlesharing     #circlesshare    #publicsharedcircle   #publicsharedcircles   #sharedcircleoftheday   #sharedcircleoftheweek     #sharedcircles     #sharedpubliccircle   #todayspublicsharedcircle  #todayssharedcircle     #publiccircle   #circle     #circles    #awesome   #awesomeness   #awesomepeople   #shareyourcircle     #bestengagers   #followers   #followback     #awesomecircles  #topsharedcircle   #topsharedcircle     #myseoissocial     #besocial     #socializethesocial     #trust   #circles   #sharedcircle     #followers      #social     #socialnetworking     2014-04-16 05:12:352629212CC G+
Adam Black6,732Transhumans CircleBy popular Demand,  I am sharing some of my Circles. This is +Mark Bruce  Transhumans Circle  Plus Others Ive been adding.If you are tagged,  you are in it.Web Link for Mobile https://plus.google.com/u/0/+AdamBlack/posts/6iQmLpEj1Zm #sharedcircles   #GeekCulture   #ScienceSunday #Transhumans #Transhumanism #HumanPlus  2014-04-13 06:25:0424522733CC G+
John Nuntiatio33,101#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport #health #tennis #europe   #asia   #america   #africa   #australia   #football   #golf   #basketball   #news  2014-04-09 06:25:5632961213CC G+
Refurio Anachro3,603You're in this march engagers circle because you reshared, plussed or commented on one of my posts (possibly via +Spherical Reflections), or got into a discussion with me. It's been fun being with you and i'm looking forward to more of it soon! Thank you!Mar 4, 2014 - links a couple of my favorite videos featuring John Conway on the occasion of +Numberphile posting a new one:https://plus.google.com/115434895453136495635/posts/AHpMJ79biC3Mar 12, 2014 - reshared an excellent post by +Gerald Stuhrberg about Richard Couranthttps://plus.google.com/115434895453136495635/posts/CzMomxKK2HzMar 18, 2014 - Diagram 17: Bratteli diagram about C★ algebrashttps://plus.google.com/115434895453136495635/posts/6EiftoFjkxmMar 19, 2014 - reshared a four dimensional platonic covered with gears by Greg Egan, thanks +John Baezhttps://plus.google.com/115434895453136495635/posts/NeaNS4XDBXNMar 22, 2014 - linked a blog post by keegan, an animated quiascrystal with a simple recipe to get one. Don't miss the link to Roger Penroses latest public lecture video in the commentshttps://plus.google.com/115434895453136495635/posts/8RUh6oQzMdpMar 31 - a link to +Vladimir Voevodsky's latest public lecture, and to an implementation of the addictive 2048 game in Coq!https://plus.google.com/115434895453136495635/posts/9bnhXDeH1UXIf you're looking for even more, please have a look at my trusty +Spherical Reflections's page. I reshare interesting circles there, and occasionally post mandelbrot beach pictures. #engagers   #circle , #circles   #circleshare   #circlesharing   #sharedcircles   #publiccircle   2014-04-03 11:25:3978165CC G+
John Nuntiatio32,205#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport #health2014-04-03 06:40:30128164CC G+
Jean-Marc Luna36,938My buddies (432/1)of the G+ villageI am happy to share (finally) my first big circles (432/1 and 432/2) with you. It is also a way to thank you and to inform you of my consideration.You will find in these two circles all the people I follow regularly since my first steps on Google+ and which accompany me for soon two years in this beautiful adventure, bringing every day, by their sympathy, their humor, their knowledge, their generosity and their open-mindedness, a bit extra to my everyday life.I do not know everybody, I have crossed the path with some, I communicate more with some and many people became friends, thing which I did not expect by landing here.When I began, I was lucky enough to discover new interesting people, thanks to the system of circles sharing, and I hope that these both will be for you of the same utility.If you add a “plus”, maybe it will have an impact on climate change,if you share this circle, maybe Putin is going to get married with an ukrainian women in 2014,if you include me in your circles, maybe it will solve the problem of hunger in the world,Maybe ... but in fact, nothing is sure ;)A good day to all :)With a special thought for #dirktalamasca   #sharedcircles   #circles   #circlesharing  2014-03-31 15:25:36432622658CC G+
Daniel Zawadzki6,461Very soccial Circle#specialcircle      #topengagers   #circleoftheday     #saturdaycircle #weekendcircleHi friends! This is very imoprtant circle, most of top g+ pplif you want to add this circle:1 - include all circle in your circles 3 - shared the circle (include yourself) 4 - add +1 to the post More you share more you are great.2014-03-22 09:41:38472571572CC G+
Enrico Altavilla5,522I'm sharing with you my Science circle. It's focused mainly on physics, astrophysics and math but it also contains subjects (both people and pages) who share news about other scientific fields. Enjoy! 2014-03-21 06:45:031031015CC G+
Richard Green61,119Engagers Showcase Circle, March 20, 2014If you received a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares. I ran out of room, so my most recent posts will be included next time instead.Everyone mentioned below is also included in the circle.Michelangelo and the Jordan curve theoremhttps://plus.google.com/101584889282878921052/posts/UN8TetdX48VThe Kelpieshttps://plus.google.com/101584889282878921052/posts/M6aWXwu6zESAntoine's necklacehttps://plus.google.com/101584889282878921052/posts/4anPfBNTyjXThe Farey-Ford tessellationhttps://plus.google.com/101584889282878921052/posts/GrZP3ajnRGUAlien Garden (reshared from +Kevin Clift)https://plus.google.com/101584889282878921052/posts/j55RpNfocNABetween a rock and a hard placehttps://plus.google.com/101584889282878921052/posts/WGNdNFneW1uAlan Turing: a universal Turing machine?https://plus.google.com/101584889282878921052/posts/MUjAnVtL7hbVisual artist Aliza Razellhttps://plus.google.com/101584889282878921052/posts/hbd3e6U1fhSBeet it (reshared from +Laura Ockel)https://plus.google.com/101584889282878921052/posts/U7RjV31mM7WChess played on a sphere... and other animalshttps://plus.google.com/101584889282878921052/posts/LGXUE73Z3MoPass 'Em Onhttps://plus.google.com/101584889282878921052/posts/iFCQcXfhNdDArizona sunset (reshared from +Debashish Samaddar)https://plus.google.com/101584889282878921052/posts/CR1yJ48g8CWThe inside of my fridge, through Glasshttps://plus.google.com/101584889282878921052/posts/SQK6KoFL2rmBatmobile 1?https://plus.google.com/101584889282878921052/posts/aV43AZenAd9Mary O'Malley ceramics (reshared from 2014-03-20 19:09:36469199157230CC G+
John Nuntiatio30,154#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport2014-03-18 08:53:47471025CC G+
John Nuntiatio30,154#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport2014-03-18 08:53:18471001CC G+
John Nuntiatio30,154#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport2014-03-18 08:52:50471125CC G+
John Nuntiatio30,154#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport2014-03-18 08:52:22471002CC G+
John Nuntiatio30,154#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport2014-03-18 08:51:36471313CC G+
John Nuntiatio29,767#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport2014-03-14 19:46:45475126CC G+
John Nuntiatio29,767#circles #sharedcircles #circlesharing #circle #circleoftheday #bestofcircles #bestcircleshare #share #tech #business #sport2014-03-14 19:46:00475125CC G+

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Top posts in the last 50 posts

Most comments: 216

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2014-08-03 09:59:26 (216 comments, 70 reshares, 243 +1s)

My last post on the NASA "quantum vacuum plasma thruster" was mainly about the shoddy theory behind it - like how there's no such thing as a "quantum vacuum plasma".

But you could argue: hey, if the gizmo actually works, isn't that good enough?   

Unfortunately, the experiment has problems too.  In brief:

1.  They tested a device that was designed to work and one that was designed not to work.  They both worked.

2.  They tested the devices in a "vacuum chamber", but they didn't take the air out.

3.  They didn't carefully study all possible causes of experimental error... like their devices heating the air.

In a bit more detail:

1.  Their device, called the Cannae drive, was invented by a guy named Guido Fetta.  You can see a picture below.  It's not complicated! It's a... more »

Most reshares: 671

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2014-08-10 02:51:19 (169 comments, 671 reshares, 548 +1s)

Both rectangles are moving at constant speed

At least that's what the creator of this illusion says!  It looks like the yellow and blue rectangles are taking turns going forward - one step at a time.

This is an illusion that's so good it's hard to believe it's an illusion. When the black and white lines disappear, it's easy to see the rectangles are moving at constant speed.  But before that they seem to be taking turns, and pausing when they reach each new line.

Could the creator of this illusion be cheating - fooling you into thinking there's an illusion?   How can you tell, except by making your own version of this animated gif?

Hide one rectangle with your hand.  Then look closely at the other.  Try not to look at the black and white lines.  I think you'll see the rectangle is moving at constant speed.

Butif you... more »

Most plusones: 596

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2014-08-13 03:16:36 (53 comments, 247 reshares, 596 +1s)

Maryam Mirzakhani won the Fields medal yesterday.

As a child in Tehran, she didn't intend to become a mathematician - she just wanted to read every book she could find!  She also watched television biographies of famous women like Marie Curie and Helen Keller.  She started wanting to do something great... maybe become a writer.

She finished elementary school while the Iran-Iraq war was ending, and took a test that got her into a special middle school for girls.  She did poorly in math her first year, and it undermined her confidence.  “I lost my interest in math," she said.

But the next year she had a better teacher, and she fell in love with the subject.  She and a friend became the first women on Iranian math Olympiad team.  She won a gold medal the first year, and got a perfect score the next year.

After getting finishing her undergraduate workat Shar... more »

Latest 50 posts

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2014-09-02 00:41:09 (43 comments, 29 reshares, 83 +1s)

Hyperreal numbers: infinities and infinitesimals

When Newton invented calculus, he used infinitesimals - numbers that are bigger than zero but smaller than 1/2, 1/3, 1/4, ... and so on.  Many people were uncomfortable with these, so they figured out how to do calculus without infinitesimals.   That's how it's usually taught now.

But it turns out you can do calculus with infinitesimals in a perfectly rigorous way... and in some ways, it's easier!   Here's a free online textbook that teaches calculus this way:

• H. Jerome Keisler, Elementary Calculus,  http://www.vias.org/calculus/

The picture here is from this book.  There's a tiny little infinitesimal number ε, pronounced epsilon.  And 1/ε is infinitely big!  These aren't 'real numbers' in the usual sense.  Sometimes they're calledhyperreal ... more »

Hyperreal numbers: infinities and infinitesimals

When Newton invented calculus, he used infinitesimals - numbers that are bigger than zero but smaller than 1/2, 1/3, 1/4, ... and so on.  Many people were uncomfortable with these, so they figured out how to do calculus without infinitesimals.   That's how it's usually taught now.

But it turns out you can do calculus with infinitesimals in a perfectly rigorous way... and in some ways, it's easier!   Here's a free online textbook that teaches calculus this way:

• H. Jerome Keisler, Elementary Calculus,  http://www.vias.org/calculus/

The picture here is from this book.  There's a tiny little infinitesimal number ε, pronounced epsilon.  And 1/ε is infinitely big!  These aren't 'real numbers' in the usual sense.  Sometimes they're called hyperreal numbers.

You can calculate the derivative, or rate of change, of a function f by doing

(f(x+ε) - f(x)) / ε

and then at the end throwing out terms involving ε.  For example, suppose

f(x) = x²

Then to compute its derivative we do

((x+ε)² - x²) / ε

Working this out, we get

(x² + 2εx + ε² - x²) / ε = (2εx + ε²) / ε  = 2x + ε

At the end, we throw out the term involving ε.  So, we get 2x.  This is the rate of change of the function x².

The book will teach you calculus this way, from scratch.  If you had trouble understanding 'limits' in calculus, you might prefer this way.  Or, you might just enjoy seeing another approach.

The details of this subject are infinitely interesting, but I'll just say an infinitesimal amount.  In 1961 the logician Abraham Robinson showed that hyperreal numbers are just as consistent as ordinary real numbers, and that the two systems are compatible in a certain precise sense.  In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers.  

Now it's free, with a Creative Commons copyright! ___

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2014-09-01 04:02:12 (12 comments, 40 reshares, 149 +1s)

A sunflower at infinity

This picture by +Roice Nelson shows the 'view at infinity' of a honeycomb in hyperbolic space.

A honeycomb is a way of chopping space into polyhedra.  For example, we can chop ordinary 3d space into cubes.  This is called the {4,3,4} honeycomb.  Why?

• a square has 4 sides so its symbol is {4}

• a cube has 3 squares meeting at each corner so its symbol is {4,3}

• the cubical honeycomb has 4 cubes meeting at each edge so its symbol is {4,3,4}

The picture here is a view of the {3,3,7} honeycomb.  This is defined in the same sort of way, but it doesn't fit into ordinary Euclidean space.  It fits into a curved space called hyperbolic space!   The honeycomb extends forever, and it forms this pattern where it meets the 'plane at infinity' of hyperbolic space.
For ... more »

A sunflower at infinity

This picture by +Roice Nelson shows the 'view at infinity' of a honeycomb in hyperbolic space.

A honeycomb is a way of chopping space into polyhedra.  For example, we can chop ordinary 3d space into cubes.  This is called the {4,3,4} honeycomb.  Why?

• a square has 4 sides so its symbol is {4}

• a cube has 3 squares meeting at each corner so its symbol is {4,3}

• the cubical honeycomb has 4 cubes meeting at each edge so its symbol is {4,3,4}

The picture here is a view of the {3,3,7} honeycomb.  This is defined in the same sort of way, but it doesn't fit into ordinary Euclidean space.  It fits into a curved space called hyperbolic space!   The honeycomb extends forever, and it forms this pattern where it meets the 'plane at infinity' of hyperbolic space.

For links to related pictures, visit my +American Mathematical Society blog Visual Insight:

http://blogs.ams.org/visualinsight/2014/09/01/intersection-of-337-honeycomb-and-the-plane-at-infinity/

#geometry  ___

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2014-08-30 06:59:03 (29 comments, 54 reshares, 168 +1s)

The Klein bottle has just one side!  

A mathematician named Klein
Thought the Möbius strip was divine
Said he, "If you glue
The edges of two
You get a weird bottle like mine."

The Möbius strip has just one side and one edge.  So if you glue the edges of two, you get a surface with one side and no edge... which happens to be a Klein bottle!

But here's an even cooler way to get a Klein bottle.  Consider black-and-white images that are 3×3 pixels in size.  It takes 9 numbers to describe such an image.  So, the set of all possible images like this is a 9-dimensional cube.  

But if you go through actual black-and-white photos and keep track of the 3×3-pixel images that show up, you'll find they aren't evenly distributed in this 9-dimensional cube!  Most of them lie near acertain sur... more »

The Klein bottle has just one side!  

A mathematician named Klein
Thought the Möbius strip was divine
Said he, "If you glue
The edges of two
You get a weird bottle like mine."

The Möbius strip has just one side and one edge.  So if you glue the edges of two, you get a surface with one side and no edge... which happens to be a Klein bottle!

But here's an even cooler way to get a Klein bottle.  Consider black-and-white images that are 3×3 pixels in size.  It takes 9 numbers to describe such an image.  So, the set of all possible images like this is a 9-dimensional cube.  

But if you go through actual black-and-white photos and keep track of the 3×3-pixel images that show up, you'll find they aren't evenly distributed in this 9-dimensional cube!  Most of them lie near a certain surface.  

And this surface is a Klein bottle!

Puzzle 1: Why?

If you get stuck, look at this picture:

http://math.ucr.edu/home/baez/mathematical/klein_bottle_carlsson.jpg

If that doesn't give it away, do this:

Puzzle 2: Start with a square of paper.  Glue the top and bottom together without a twist.  Glue the left and right sides together with a twist.  What do you get?

If you actually try this, you'll find it a bit hard.  I prefer to just visualize it.  This is a good way to build your powers of visualization.

Here's the paper where the Klein bottle was found in the space of 3×3 images:

• Gunnar Carlsson, Tigran Ishkhanov, Vin de Silva and Afra Zomorodian, On the local behavior of spaces of natural images, International Journal of Computer Vision 76 (2008), 1-12.  Available at http://comptop.stanford.edu/u/preprints/mumford.pdf.

They show as you study n×n pixel images for larger and larger n, the space of most likely images eventually stops being a Klein bottle - more complicated image features start showing up.

I thank my friend the physicist +Igor Khavkine for pointing out this paper.  I got the animated gif from the webpage of Dr. Christian Salas:

http://www.drchristiansalas.org.uk/sidepage4.htm

but I don't know its original source.  Do you?

#spnetwork doi:10.1.1.121.9768 #computerVision #topology___

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2014-08-28 15:40:07 (0 comments, 6 reshares, 71 +1s)

Goodbye, it was nice knowing you.

Goodbye, it was nice knowing you.___

posted image

2014-08-27 06:01:31 (67 comments, 72 reshares, 218 +1s)

Did you ever feel your brain is about to break?  It happens not just to beginners in math, but to everyone! 

So, in case you feel frustrated with math, let me share one of my own frustrations.  You'll see you're not alone!

Right now I'd love to understand something a logician tried to explain to me at lunch a while back.  His name is Boris Zilber.  He's studying what he calls 'logically perfect' theories - that is, lists of axioms that almost completely determine the structure they're trying to describe.  He thinks that we could understand physics better if we thought harder about these logically perfect theories.

Now, Gödel's incompleteness theorem means our usual theory of natural numbers

0, 1, 2, 3, ...

together with addition and multiplication is far from 'logically perfect' in this sense.   In fact,only fi... more »

Did you ever feel your brain is about to break?  It happens not just to beginners in math, but to everyone! 

So, in case you feel frustrated with math, let me share one of my own frustrations.  You'll see you're not alone!

Right now I'd love to understand something a logician tried to explain to me at lunch a while back.  His name is Boris Zilber.  He's studying what he calls 'logically perfect' theories - that is, lists of axioms that almost completely determine the structure they're trying to describe.  He thinks that we could understand physics better if we thought harder about these logically perfect theories.

Now, Gödel's incompleteness theorem means our usual theory of natural numbers

0, 1, 2, 3, ...

together with addition and multiplication is far from 'logically perfect' in this sense.   In fact, only finite-sized mathematical structures can be completely determined by finite lists of axioms in ordinary logic (so-called 'first-order logic').

If we've got an infinite-sized structure, the most we can hope for is that after we specify the size of the structure, the axioms completely determine it. 

And this actually happens sometimes.  It happens for the complex numbers!  Zilber believes this has something to do with why the complex numbers show up so much in physics.

More precisely, say λ is some size - that is, some cardinal, which could be finite or infinite.  A list of axioms in first-order logic is called λ-categorical if it's obeyed by a unique structure of size λ.   And a guy named Morley showed that if a list of axioms is λ-categorical for some uncountable λ, it's also λ-categorical for all uncountable λ.   I have no idea why this is true.  But such lists of axioms are called uncountably categorical.

According to Zilber - and I'm sure he knows what he's talking about here - the axioms for the complex numbers together with addition and multiplication are uncountably categorical.

Zilber likes lists of axioms that are uncountably categorical so much that he calls them logically perfect theories.  And he writes:

There are purely mathematical arguments towards accepting the above for a defi nition of perfection. First, we note that the theory of the field of complex numbers (in fact any algebraically closed fi eld) is uncountably categorical. So, the fi eld of complex numbers is a perfect structure, and so are all objects of complex algebraic geometry by virtue of being de finable in the fi eld.

It is also remarkable that Morley's theory of categoricity (and its extensions) exhibits strong regularities in models of categorical theories generally. First, the models have to be highly homogeneous [....] Moreover, a notion of dimension (the Morley rank) is applicable to defi nable subsets in uncountably categorical structures, which gives one a strong sense of working with curves, surfaces and so on in this very abstract setting. A theorem of the present author states more precisely that an uncountably categorical structure M is either reducible to a 2-dimensional "pseudo-plane" with at least a 2-dimensional family of curves on it (so is non-linear), or is reducible to a linear structure like an (infinite dimensional) vector space, or to a simpler structure like a G-set for a discrete group G.

Somehow 'logical perfection' in Zilber's sense connects logic to some concepts from geometry!  But I don't understand any of the details.  And when I start studying them, I feel like Gollum here.

• Boris Zilber, Perfect infinities and finite approximation, in Infinity and Truth, World Scientific, Singapore, 2014,
https://people.maths.ox.ac.uk/zilber/inf-to-finite.pdf.

#spnetwork #logic___

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2014-08-26 02:52:51 (73 comments, 11 reshares, 91 +1s)

The latest news is getting people upset. +David Brin writes:

This is what we had all feared.  The possible tipping point.  Methane plumes are emanating from at least 570 seafloor cold seeps on the outer continental shelf and the continental slope, Mississippi State University reported.  A potential disaster that I warned about in EARTH (1989), accelerating ocean acidification and turning the greenhouse into a runaway.

http://www.hngn.com/articles/40189/20140825/methane-leaking-from-sea-floor-could-change-ocean-acidity-oxygen-content.htm

"Warming of ocean temperatures on seasonal, decadal or much longer time scales can cause gas hydrate to release its methane, which may then be emitted at seep sites," said Carolyn Ruppel, study co-author and chief of the USGS Gas Hydrates Project.  "Such continental slope seeps have previously been recognized inthe... more »

The latest news is getting people upset. +David Brin writes:

This is what we had all feared.  The possible tipping point.  Methane plumes are emanating from at least 570 seafloor cold seeps on the outer continental shelf and the continental slope, Mississippi State University reported.  A potential disaster that I warned about in EARTH (1989), accelerating ocean acidification and turning the greenhouse into a runaway.

http://www.hngn.com/articles/40189/20140825/methane-leaking-from-sea-floor-could-change-ocean-acidity-oxygen-content.htm

"Warming of ocean temperatures on seasonal, decadal or much longer time scales can cause gas hydrate to release its methane, which may then be emitted at seep sites," said Carolyn Ruppel, study co-author and chief of the USGS Gas Hydrates Project.  "Such continental slope seeps have previously been recognized in the Arctic, but not at mid-latitudes.  So this is a first."

To be clear, methane is a far worse greenhouse gas than CO2… and rising ocean temps will cause icy methane hydrates to fizz, all over the globe, possibly causing a runaway effect.

Which leaves me with this to say to you wretched, monstrous, science-hating fools, with your “hypnotize-me!” Fox-Nuremberg rallies and neo-confederate rant-fests against all big-city-university “smartypants” types. 

No evidence will change your opposition to negotiating even moderate, sensible, precautionary interim measures to increase energy efficiency or do basic R&D. You sabotage TWODA (Things We Ought to be Doing Anyway.)  You helped to sabotage the satellites and instruments and research vessels that could have nailed it all down.

You help to denigrate and geld the smartest, most knowledgeable, competitive and wisest human beings whom our species has ever produced, and thereby you declare yourselves to be brave authority questioners and skeptics!  While kneejerk-robotically obeying  the hypnotize-me channels owned by coal and oil barons... and never once sniffing the suspicious irony.

We can expect more of this sort of rhetoric in the decades to come.  However, about this new discovery, it's worth noting:

1) Nobody before has looked very hard for methane venting off the East Coast, so it's hard to tell if it's new.  The guy who found the vents, Adam Skarke, says:

The fact that it is there in the quantities that it is and it is exposed suggests that indeed the processes at these locations have been going on, in a very general sense, on the order of at least 1,000 years.

So we need to monitor the vents and see if they're getting bigger, while meanwhile taking action to limit carbon emissions.  Brin is right about stupid US government cutbacks on climate monitoring.  It's a really shortsighted way to save money!

2) The amount of methane being released from the vents seen in this study is small.  Methane is indeed a very bad greenhouse gas, and we do need to worry about a 'tipping point' where warming oceans release more of the vast amounts of methane stored in sea beds, thus warming the Earth even more.  There are vast amounts of methane stored in hydrates there, and there's evidence that it could have been released during the Paleocene-Eocene Thermal Maximum, an episode when the Earth's temperature rose by 6 °C (11 °F) in about 20,000 years.  However,  there's no evidence that we're already in an unstoppable runaway situation. 

David Archer, an expert on climate and the carbon cycle, says:

In the timescale of centuries to hundreds of thousands of years, it (methane hydrate) is clearly a significant amplifier.  But in terms of the climate of just the coming century, the actual forcing of climate from the rise in atmospheric methane due to this, I think, will be small.

He, like most climate scientists, believes that human CO2 emissions are the main cause of global warming.

3) Let's not just complain, let's do something!  David Brin is talking about US politics, so let me focus on that - just today.  Until there's more action at the federal level in the US, we can act locally.  California has a carbon cap-and-trade system, which is linked with Quebec's:

http://www.arb.ca.gov/cc/capandtrade/capandtrade.htm

Connecticut, Delaware, Maine, Maryland, Massachusetts, New Hampshire, New York, Rhode Island, and Vermont have their own system, the Regional Greenhouse Gas Initiative:

http://www.rggi.org/

Another group, the Midwestern Greenhouse Gas Reduction Accord, includes Illinois, Iowa, Kansas, Michigan, Minnesota, Wisconsin and also Manitoba:

https://en.wikipedia.org/wiki/Midwestern_Greenhouse_Gas_Reduction_Accord

And the Western Climate Initiative includes Arizona, California, Montana, New Mexico, Oregon, Utah and Washington in the US, and British Columbia, Manitoba, Ontario and Quebec in Canada:

http://www.co2offsetresearch.org/policy/WCI.html

So: we should figure out ways to help these initiatives succeed!   The ones that succeed will become the groundwork for a national system!  Ideas? 

The actual paper on methane emissions is here:

• A. Skarke et al, Widespread methane leakage from the sea floor on the northern US Atlantic margin, Nature Geoscience , 24 August 2014, http://www.nature.com/ngeo/journal/vaop/ncurrent/full/ngeo2232.html.

It's not free except for the abstract, so someone should 'liberate' it.  It's absurd to have such important results locked up, while any blogger with a loud mouth (like me) can be read for free.___

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2014-08-25 04:56:35 (35 comments, 71 reshares, 189 +1s)

Why do we have these particles in our Universe?

We understand a lot about physics - and that makes the remaining mysteries even more tantalizing!  For example: why are quarks so much like leptons?

Elementary particles come in two main kinds: the ones that carry forces (gauge bosons) and the ones that make up matter (quarks and leptons).   There's also at least one more... but never mind!  Today's puzzle is about quarks and leptons.  You'll see from the chart that they look sort of similar.   But why?

Maybe a lightning review of particle physics will help, in case you skipped that class in high school.  Most of the matter you see is made of electrons, protons and neutrons.   Protons and neutrons are made of up and down quarks, held together by the strong force.  But electrons are 'leptons', which means they don'tfeel the s... more »

Why do we have these particles in our Universe?

We understand a lot about physics - and that makes the remaining mysteries even more tantalizing!  For example: why are quarks so much like leptons?

Elementary particles come in two main kinds: the ones that carry forces (gauge bosons) and the ones that make up matter (quarks and leptons).   There's also at least one more... but never mind!  Today's puzzle is about quarks and leptons.  You'll see from the chart that they look sort of similar.   But why?

Maybe a lightning review of particle physics will help, in case you skipped that class in high school.  Most of the matter you see is made of electrons, protons and neutrons.   Protons and neutrons are made of up and down quarks, held together by the strong force.  But electrons are 'leptons', which means they don't feel the strong force.

Up quarks, down quarks and electrons - those are 3 of the 4 particles in 'generation 1'.  The 4th is the electron neutrino.  It's also a lepton - it's doesn't feel the strong force.  But it's also has no electric charge!  So, it's very hard to detect - it whizzes easily through ordinary matter.   But we have detected it, and we actually know a  huge amount about it.

We also know that besides 'generation 1' there's a 'generation 2' and 'generation 3' of quarks and leptons.  We're pretty sure there are only 3: people have done experiments that show there can't be more different kinds of neutrinos, unless they are very heavy, or different from all the rest in some other way.  We have no idea why there are only 3 generations.

But our puzzle today is: why do quarks and leptons come in generations at all?    So let's just think about generation 1.

We know that the up and down quark are closely connected.   We also know that the electron and electron neutrino are closely connected.  For example, you can collide an electron and an up quark and have them turn into an electron neutrino and a down quark!  We understand this stuff very well, actually: there's a detailed mathematical theory of it, and it works great.

But there are other things that seem mysterious.   The up quark has charge 2/3, the down quark has charge -1/3, the electron has charge -1 and the electron neutrino has charge 0.   Quarks also come in 3 different kinds, called 'colors' - they change colors when they interact with the strong force.   Leptons have no color.

Are all the 3's in the last paragraph a coincidence?   It seems not.  For example, if quarks came in 4 colors, but had the charges they do now, all hell would break loose!   I could explain why, but that's not my goal today.

My goal is just to say this: there's a theory called the Pati-Salam model that says leptons are secretly just a funny kind of quarks - a 'fourth color of quark'.  This theory unifies quarks and leptons.  And this theory also explains why quarks have charges like 2/3 and -1/3.

This theory has been around since 1974.  It has some problems.  If it didn't, we'd probably all believe it by now!  It's very hard to find theories of elementary particles that fit all the data we have; if you just make up stuff, you'll almost surely run into problems.  But the Pati-Salam model is pretty good, it's not completely ruled out by experiments... and last year something interesting happened.

A famous mathematician named Alain Connes has an approach to physics based on noncommutative geometry, which replaces our usual picture of spacetime by something that's more like algebra than geometry.  His theory predicted the wrong mass for the Higgs boson - that's the extra particle I hinted at near the start of this story.  But last year he came out with a new improved version, that doesn't suffer from this problem.  And it turns out to be a lot like the Pati-Salam model!

What's interesting is how he gets it.  In his earlier work, he laid down a bunch of mathematical axioms, and one of the simplest theories that obeys all these axioms turned out to be very similar to the Standard Model - our usual theory of particles.  

But now, he and some other guys have noticed that if you drop one of the axioms, something like the Pati-Salam model is also allowed.  Moreoever, you can get a Higgs boson with the right mass!

I wish I understood this better.  Alas, I don't have much time for this stuff anymore!  Here is his paper:

• Ali H. Chamseddine, Alain Connes and Walter D. van Suijlekom, Beyond the spectral standard model: emergence of Pati-Salam unification, http://arxiv.org/abs/1304.8050.

and here is an intro to the Pati-Salam model, mainly good for mathematicians and physicists:

• John Baez and John Huerta, The algebra of grand unified theories, http://math.ucr.edu/~huerta/guts/guts.html

Here's the abstract of Connes' paper, which gives a flavor of what he's doing... at least if you know enough jargon:

Abstract. The assumption that space-time is a noncommutative space formed as a product of a continuous four dimensional manifold times a finite space predicts, almost uniquely, the Standard Model with all its fermions, gauge fields, Higgs field and their representations. A strong restriction on the noncommutative space results from the first order condition which came from the requirement that the Dirac operator is a differential operator of order one. Without this restriction, invariance under inner automorphisms requires the inner fluctuations of the Dirac operator to contain a quadratic piece expressed in terms of the linear part. We apply the classification of product noncommutative spaces without the first order condition and show that this leads immediately to a Pati-Salam SU(2)_R x SU(2)_L x SU(4) type model which unifies leptons and quarks in four colors. Besides the gauge fields, there are 16 fermions in the (2,2,4) representation, fundamental Higgs fields in the (2,2,1), (2,1,4) and (1,1,1+15) representations. Depending on the precise form of the order one condition or not there are additional Higgs fields which are either composite depending on the fundamental Higgs fields listed above, or are fundamental themselves. These additional Higgs fields break spontaneously the Pati-Salam symmetries at high energies to those of the Standard Model.

#spnetwork arXiv:1304.8050 #mustread___

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2014-08-24 01:08:06 (53 comments, 87 reshares, 401 +1s)

Head on

Wolves run through the air, hit a glass wall and fall down.  Then they pick themselves up, go back and do it again.

This is just one of the remarkable and unsettling pieces by Chinese artist Cai Guo-Qiang

He recently made the news by creating a kind of Noah's ark with endangered animals and floating it down the river past the main financial district of Shanghai.  The animals aren't real - but they look pretty real, like these wolves.

The boat is now on display in Shanghai, in an exhibit that's become very popular.  You can see more of it here:

http://www.npr.org/blogs/parallels/2014/08/21/342189261/chinas-pollution-crisis-inspires-an-unsettling-art-exhibit

and here:

http://www.emptykingdom.com/featured/cai-guo-qiang/

A piece called 'Silent Ink' features a waterfall of inkplu... more »

Head on

Wolves run through the air, hit a glass wall and fall down.  Then they pick themselves up, go back and do it again.

This is just one of the remarkable and unsettling pieces by Chinese artist Cai Guo-Qiang

He recently made the news by creating a kind of Noah's ark with endangered animals and floating it down the river past the main financial district of Shanghai.  The animals aren't real - but they look pretty real, like these wolves.

The boat is now on display in Shanghai, in an exhibit that's become very popular.  You can see more of it here:

http://www.npr.org/blogs/parallels/2014/08/21/342189261/chinas-pollution-crisis-inspires-an-unsettling-art-exhibit

and here:

http://www.emptykingdom.com/featured/cai-guo-qiang/

A piece called 'Silent Ink' features a waterfall of ink plunging into a 5,300-gallon lake excavated from the museum's floor.  The lake is ringed by mounds of crushed concrete and iron bars.  It looks like a scene from a Chinese landscape painting - made of industrial waste.  It's hard to stay there for very long, because the smell of the ink becomes overpowering. 

But in its own strange way it's beautiful.

Of course, if you don't know the politics of China you'll miss part of the meaning of this wolf pack.  If you don't know that 16,000 dead pigs were found floating down a river in Shanghai last year, you won't fully understand that ark.  If you don't know a bit about the pollution crisis in China and the art of landscape painting, you'll miss some of what's going on in 'Silent Ink'.  But this art is good because it's not merely commentary on politics and the pollution crisis in China.  It's visually stunning, mysterious and tragic.

#art  ___

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2014-08-23 03:45:54 (84 comments, 10 reshares, 94 +1s)

Sub-Roman Britain

I've been a fan of the legends of King Arthur for a long time.  I love how they continue to inspire new versions, from Marion Zimmer Bradley's Tales of Avalon (where Morgaine is recast as a hero in the doomed struggle of the Druids against encroaching Christians) to the goofy but fun TV series Merlin (where a black Guinevere starts as a serving-girl and winds up ruling Camelot).

But I'm only just now poking into the mysterious centuries from 400 to 600 AD in Britain, after the collapse of Roman rule, when Arthur would have lived... if he existed.

It's really cool to imagine life in former Roman towns and villas during these 'dark ages'.  We have some archaeological evidence, but very little written history: mainly just the writings of Saint Patrick and a book called On the Ruin and Conquest of Britain,  written by a guyca... more »

Sub-Roman Britain

I've been a fan of the legends of King Arthur for a long time.  I love how they continue to inspire new versions, from Marion Zimmer Bradley's Tales of Avalon (where Morgaine is recast as a hero in the doomed struggle of the Druids against encroaching Christians) to the goofy but fun TV series Merlin (where a black Guinevere starts as a serving-girl and winds up ruling Camelot).

But I'm only just now poking into the mysterious centuries from 400 to 600 AD in Britain, after the collapse of Roman rule, when Arthur would have lived... if he existed.

It's really cool to imagine life in former Roman towns and villas during these 'dark ages'.  We have some archaeological evidence, but very little written history: mainly just the writings of Saint Patrick and a book called On the Ruin and Conquest of Britain,  written by a guy called Saint Gildas or 'Gildas the Wise'.

This book is a grumpy attack on various kings, including:

• "Constantine, the tyrannical whelp of the unclean lioness of Dumnonia".   The kingdom of Dumnonia was in southwest England, mainly Devon and Cornwall.

• "dragon of the island... Maelgwn".  Maelgwn was one of the kings of Gwynedd, who ruled a chunk of what's now Wales from their base on the Isle of Anglesey.

• "Vortipore... like to the spotted leopard... tyrant of the Demetians."   Vortipore was a king of Demetia, or Dyfed, a small kingdom in south-west Wales.

There were many other kingdoms that Gildas didn't bother to write about.  Gildas is himself rather mysterious; one later biography tells of how he helped mediate a struggle between King Arthur and a king who had abducted and raped Guinevere... but this is all just legend.

'Medieval Bex' has a great blog on medieval matters, and here's what she says about the two biographies of Gildas:

The earlier account, written in the ninth century in Rhuys, Brittany, tells how Gildas son of Caw was born in the north of Britain. He moved to a monastic college to begin his education and then to Iren (probably Ireland) to continue his studies, before returning to north Britain to preach to those naughty heathens. St Brigid (d. 524) asked Gildas for a token so he made her a bell. As you do. After these high-jinks he then travelled around a bit before settling in Rhuys, where he built a monastery and lived out his days preaching and writing epistles about kings that he didn’t like very much. When he died his body was placed in a boat and set adrift according to his wishes. Just a floating corpse; not set aflame or anything. Imagine being the person to find a boat containing a decomposing monk… which someone actually did (the HORROR!!) – his boat washed up a few months later and was found by some men from Rhuys. They did the sensible thing and took his body back to Rhuys and buried it there. Gildas’ corpsified wandering days were over.

The other book, however, depicts Gildas as a sort of monk-cum-Arthurian action hero. It seems like the writer of the twelfth-century biography, Caradoc of Llancarfan, read the earlier book and said ‘Oh ho! I think we can do better than that!’ and essentially pimped the Life of Gildas. The twelfth-century version has Gildas educated in Gaul before settling near Glastonbury… all normal enough so far, if ever-so-slightly at odds with the ninth-century version of events… but then things get a little bit more exciting when Guinevere and Arthur arrive on the scene! That’s right, no floating corpses here!

According to Caradoc’s biography of Gildas, King Melwas abducted Queen Guinevere and Arthur then proceeded to throw a massive wobbly. He stormed over to Melwas’ stronghold in Glastonbury with his knights, ready to attack. It was all getting a bit intense… until Gildas stepped in and saved the day! He happened to be in the neighbourhood and persuaded Melwas to release Guinevere, before unbelievably managing to make the two kings kiss and make up. They probably all went for a beer and a good chortle about it all afterwards. As an interesting aside, this is the first recorded instance of the Guinevere abduction scene, a plot which becomes a recurring motif in subsequent redactions of the Arthurian stories. So a highly imaginative biography of a monk has helped to shape the legend of Arthur as we know it today. Who’d have thought! There is also something in this version about Gildas’ brothers rising up against Arthur, and one of them being killed, and Gildas being rather upset about this. Apparently the large stone in Ruthin town square (north Wales) is the chopping block that was used when Arthur decapitated Gildas’ brother. It’s still there, you can go and see it!

Here is her blog:

http://medievalbex.wordpress.com/2012/10/31/the-arthurian-tradition-gildas/

and here is some other good stuff:

https://en.wikipedia.org/wiki/Sub-Roman_Britain
https://en.wikipedia.org/wiki/Gildas

#history  ___

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2014-08-22 02:42:17 (65 comments, 75 reshares, 179 +1s)

The ostrich effect

Why do people think ostriches stick their heads under the sand when they're scared?  A Roman named Pliny the Elder might be to blame.  He wrote that ostriches "imagine, when they have thrust their head and neck into a bush, that the whole of their body is concealed."  

That would be silly - birds aren't that dumb.  But people will actually pay to avoid learning unpleasant facts.  It seems irrational to avoid information that can help us survive.  But people do it.  It's called information aversion.

Here's a new experiment:

In order to gauge how information aversion affects health care, one group of researchers decided to look at how college students react to being tested for a sexually transmitted disease.

That's a subject a lot of students worry about, according to JoshTasoff,... more »

The ostrich effect

Why do people think ostriches stick their heads under the sand when they're scared?  A Roman named Pliny the Elder might be to blame.  He wrote that ostriches "imagine, when they have thrust their head and neck into a bush, that the whole of their body is concealed."  

That would be silly - birds aren't that dumb.  But people will actually pay to avoid learning unpleasant facts.  It seems irrational to avoid information that can help us survive.  But people do it.  It's called information aversion.

Here's a new experiment:

In order to gauge how information aversion affects health care, one group of researchers decided to look at how college students react to being tested for a sexually transmitted disease.

That's a subject a lot of students worry about, according to Josh Tasoff, an economist at Claremont Graduate University who led the study along with Ananda Ganguly, an associate professor of accounting at Claremont McKenna College.

The students were told they could get tested for the herpes simplex virus. It's a common disease that spreads via contact. And it has two forms: HSV1 and HSV2.

The type 1 herpes virus produces cold sores. It's unpleasant, but not as unpleasant as type 2, which targets the genitals. Ganguly says the college students were given information — graphic information — that made it clear which kind of HSV was worse.

"There were pictures of male and female genitalia with HSV2, guaranteed to kind of make them really not want to have the disease," Ganguly says.

Once the students understood what herpes does, they were told a blood test could find out if they had either form of the virus.

Now, in previous studies on information aversion it wasn't always clear why people declined information. So Tasoff and Ganguly designed the experiment to eliminate every extraneous reason someone might decline to get information.

First, they wanted to make sure that students weren't declining the test because they didn't want to have their blood drawn. Ganguly came up with a way to fix that: All of the students would have to get their blood drawn. If a student chose not to get tested, "we would draw 10 cc of their blood and in front of them have them pour it down the sink," Ganguly says.

The researchers also assured the students that if they elected to get the blood tested for HSV1 and HSV2, they would receive the results confidentially.

And to make triply sure that volunteers who said they didn't want the test were declining it to avoid the information, the researchers added one final catch. Those who didn't want to know if they had a sexually transmitted disease had to pay $10 to not have their blood tested.

So what did the students choose? Quite a few declined a test.

And while only 5 percent avoided the HSV1 test, three times as many avoided testing for the nastier form of herpes.

For those who didn't want to know, the most common explanation was that they felt the results might cause them unnecessary stress or anxiety.

Let's try extrapolating from this.  Global warming is pretty scary.  What would people do to avoid learning more about it?  You can't exactly pay scientists to not tell you about it.  But you can do lots of other things: not listen to them, pay people to contradict what they're saying, and so on.  And guess what?  People do all these things.

So, don't expect that scaring people about global warming will make them take action.  If a problem seems scary and hard to solve, many people will just avoid thinking about it.

Maybe a better approach is to tell people things they can do about global warming.  Even if these things aren't big enough to solve the problem, they can keep people engaged.

There's a tricky issue here.  I don't want people to think turning off the lights when they leave the room is enough to stop global warming.  That's a dangerous form of complacency.  But it's even worse if they decide global warming is such a big problem that there's no point in doing anything about it.  

The quote is from here:

• Shankar Vedantham, Why we think ignorance Is bliss, even when It hurts our health, http://www.npr.org/blogs/health/2014/07/28/333945706/why-we-think-ignorance-is-bliss-even-when-it-hurts-our-health.

Here's the actual study:

• Ananda Ganguly and Joshua Tasoff, Fantasy and dread: the demand for information and the consumption utility of the future, http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2370983.

The photo, probably fake, is from here:

http://www.ostrichheadinsand.com/___

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2014-08-21 02:43:20 (22 comments, 17 reshares, 72 +1s)

A mix of bosonic and fermionic superfluids

Two different kinds of gas, each completely frictionless, can pass through each other as they wiggle back and forth in a magnetic field!

One gas is made of lithium with an even number of electrons, protons and neutrons, so it's called a boson. The other is made of lithium with an odd number of these particles, so it's a fermion.  They act very different. 

If you cool down a gas of bosons enough, it can become a completely frictionless fluid - a superfluid.  It's a lot harder to do this trick for fermions.  This is the first time anyone has made a mixture of bosonic and fermionic superfluids.

Christophe Salomon gave a talk about this here at the +Centre for Quantum Technologies.  He said nobody has been able to make such a mixture with helium.

Helium-4 is the mostcomm... more »

A mix of bosonic and fermionic superfluids

Two different kinds of gas, each completely frictionless, can pass through each other as they wiggle back and forth in a magnetic field!

One gas is made of lithium with an even number of electrons, protons and neutrons, so it's called a boson. The other is made of lithium with an odd number of these particles, so it's a fermion.  They act very different. 

If you cool down a gas of bosons enough, it can become a completely frictionless fluid - a superfluid.  It's a lot harder to do this trick for fermions.  This is the first time anyone has made a mixture of bosonic and fermionic superfluids.

Christophe Salomon gave a talk about this here at the +Centre for Quantum Technologies.  He said nobody has been able to make such a mixture with helium.

Helium-4 is the most common kind of helium.  It has an even number of electrons, protons and neutrons, so it's a boson.  If you cool it down to just 2 degrees above absolute zero it becomes a superfluid, and does amazing things like climb over the walls of a jar.  In a superfluid, all the atoms act like a single thing.

Helium-3 is missing a neutron, so it has an odd number of protons, electrons and neutrons: 5 instead of 6.  This makes it a fermion.  It doesn't become superfluid until it cools down enough for the atoms to pair up, giving an even number of particles.  That happens at about 0.0025 degrees above absolute zero.

Nobody has succeeded in making a mixture of superfluid helium-4 and helium-3.  I don't completely understand why, but Christophe Salomon said the two kinds repel each other.   Theorists believe you can get them to mix if you cool them down to about a nanokelvin - a billionth of a degree above absolute zero!  But nobody has succeeded yet.

Christophe Salomon and his team tried a different idea.  They're using two kinds of lithium, one a boson and one a fermion.  Lithium is a metal, so it's solid at low temperatures.  But a very dilute gas of lithium, held in place by a magnetic field, can become superfluid! 

At 100 nanokelvin, both kinds of lithium become superfluid, and clouds of the two kinds can pass through each other.  That's very cold - but 100 times warmer than you'd need for helium.

In the picture here, each cloud is shown separately, so you can see how they oscillate back and forth, held loosely in place by a magnetic field.  They oscillate at different rates because one kind of lithium is a bit heavier than the other.  The clouds pass through each other, but they interact slightly, so over time they slow down.  The experiment sees just what the theory predicts.

Read more here!

• Igor Ferrier-Barbut, Marion Delehaye, Sebastien Laurent, Andrew T. Grier, Matthieu Pierce, Benno S. Rem, Frédéric Chevy and Christophe Salomon, A mixture of Bose and Fermi superfluids, http://arxiv.org/abs/1404.2548.

#spnetwork arXiv:1404.2548 #superfluids___

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2014-08-19 02:00:21 (47 comments, 94 reshares, 334 +1s)

How to turn space into time - in the lab

Wouldn't it be cool if we could turn one dimension of space into an extra dimension of time?  We can't - but we can fake it!

Einstein showed the only difference between space and time is a minus sign.  So: make a material where light obeys equations with an extra minus sign! 
 
How?  Just take lots of microscopic metal wires and put them in transparent stuff that doesn't conduct electricity.  Line them all up.  You'll get something that conducts electricity like a metal in one direction but not the other two directions! 

It's called a hyperbolic metamaterial.  The video explains why. 

But why is this like converting a dimension of space into a dimension of time? 

Einstein showed that if you have a photon - a particle of light - in a vacuum, it obeys
X² + Y² ... more »

How to turn space into time - in the lab

Wouldn't it be cool if we could turn one dimension of space into an extra dimension of time?  We can't - but we can fake it!

Einstein showed the only difference between space and time is a minus sign.  So: make a material where light obeys equations with an extra minus sign! 
 
How?  Just take lots of microscopic metal wires and put them in transparent stuff that doesn't conduct electricity.  Line them all up.  You'll get something that conducts electricity like a metal in one direction but not the other two directions! 

It's called a hyperbolic metamaterial.  The video explains why. 

But why is this like converting a dimension of space into a dimension of time? 

Einstein showed that if you have a photon - a particle of light - in a vacuum, it obeys

X² + Y² + Z² - T² = 0

where:

X is the momentum of the light in the x direction
Y is the momentum of the light in the y direction
Z is the momentum of the light in the z direction
T is the momentum of the light in the time direction

(Momentum in the time direction is basically just energy.)

Photons in other stuff obey more complicated equations.  In a hyperbolic metamaterial with wires lined up in the z direction, they obey an equation basically like this:

X² + Y² - Z² - T² = 0

So, the z direction is acting like an extra time dimension! And this lets us do very weird things.

A few warnings if you watch the video:

1) A transparent material like glass is called a dielectric, so you'll see that word a lot.

2) Instead of writing X, Y, and Z for momentum in the x, y and z direction, physicists often write the letter k with a little x, y, or z under it.  

3) Particles are also waves!  The momentum of a particle in some direction is basically just how many times its wave wiggles per meter in that direction.  So, k is also called the wave number.

4) Instead of writing T for the momentum in the time direction, physicists write ω.   This is how much the wave wiggles per second, so it's also called the frequency

5) When I say 'basically', it means I'm leaving out numbers that make things look more complicated, but don't change the basic idea.

You can learn more about hyperbolic metamaterials here:

• Prashant Shekhar, Jonathan Atkinson and Zubin Jacob, Hyperbolic metamaterials: fundamentals and applications, http://arxiv.org/ftp/arxiv/papers/1401/1401.2453.pdf.

#spnetwork arXiv:1401.2453 #metamaterials  ___

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2014-08-17 02:06:16 (10 comments, 8 reshares, 25 +1s)

The only thing savin' your life
is that I don't look good in orange and I hate stripes

If you like songs with catchy lyrics and a dark sense of humor, you've got to listen to... Cole Porter.  But he's dead.  For new stuff, try Brandy Clark.

She's been working as a song writer for about 16 years, but she just came out with an album of her own, 12 Stories.    It's about life in small-town America, with all its hilarious and tragic craziness.  I recommend this song here, and also:

"Stripes" - by Brandy Clark

Brandy Clark Get High

Pray To Jesus - Brandy Clark

and

Brandy Clark - Take A Little Pill

which is about the epidemic of prescription painkiller abuse:

Fella down the road
Walks with a limp
He's a decorated soldier
And a pain pillpimp... more »

The only thing savin' your life
is that I don't look good in orange and I hate stripes

If you like songs with catchy lyrics and a dark sense of humor, you've got to listen to... Cole Porter.  But he's dead.  For new stuff, try Brandy Clark.

She's been working as a song writer for about 16 years, but she just came out with an album of her own, 12 Stories.    It's about life in small-town America, with all its hilarious and tragic craziness.  I recommend this song here, and also:

"Stripes" - by Brandy Clark

Brandy Clark Get High

Pray To Jesus - Brandy Clark

and

Brandy Clark - Take A Little Pill

which is about the epidemic of prescription painkiller abuse:

Fella down the road
Walks with a limp
He's a decorated soldier
And a pain pill pimp
Got a loaded gun
And an old pit bull
A black Cadillac
With a whole trunk full.

Says if one don't work
Then another one will
If you got a little hurt
You take a little pill

Lay it on your tongue
Ain't a nerve that can't be numbed
Ain't a buzz that you can't buy
Ain't a low you can't make high
Til it wears off
Like it always will
And when it does
You take a little pill

She tried to sell this this song to major-label artists - and they liked it, but didn't buy.  She says "I'm thankful that no one did bite on it, because it seems to be the song that resonates the strongest with people. I think it's just so real, and kind of a realness that's a little bit ugly."

Other songs are really funny.   Great stuff!

Urbanites have always looked down on country music.  I bet Babylonian city slickers already had a word for 'redneck'.  So you may think it's weird that I like this stuff.  But American pop music seems pretty stale to me right now, and one of the few bright spots is the rise of women country musicians. Brandy Clark has been writing songs for several of them, notably Kacey Musgraves.  For more on this trend, try:

http://www.npr.org/2013/12/26/257362793/quiet-as-kept-women-dominated-country-music-in-2013

(Getting my news on country music from here proves I don't know much about it.)___

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2014-08-16 01:04:37 (15 comments, 8 reshares, 112 +1s)

Reflections at Keppel Bay

There's a big network of trails and parks in Singapore.  You can climb up a huge wooden bridge and suddenly see this futuristic apartment complex amid the jungle.

My friend +Jamie Vicary is visiting the Centre for Quantum Technologies.  He showed Lisa and me how to walk through park land to Vivocity, a fancy shopping mall by the sea.  There are some elevated walkways through the jungle, that really let you see the trees and vines.  There's a World War II museum that shows how the Japanese invaded, and the battles fought around here.  It was open for free because it was National Day - the 49th anniversary of the birth of Singapore as an independent country.   It's weird to be in a country that's younger than I am.

Walking across the Henderson Wave Bridge, we spotted these buildings, called Reflections at KeppelBaymore »

Reflections at Keppel Bay

There's a big network of trails and parks in Singapore.  You can climb up a huge wooden bridge and suddenly see this futuristic apartment complex amid the jungle.

My friend +Jamie Vicary is visiting the Centre for Quantum Technologies.  He showed Lisa and me how to walk through park land to Vivocity, a fancy shopping mall by the sea.  There are some elevated walkways through the jungle, that really let you see the trees and vines.  There's a World War II museum that shows how the Japanese invaded, and the battles fought around here.  It was open for free because it was National Day - the 49th anniversary of the birth of Singapore as an independent country.   It's weird to be in a country that's younger than I am.

Walking across the Henderson Wave Bridge, we spotted these buildings, called Reflections at Keppel Bay, on the horizon near the sea.  They were designed by Daniel Libeskind, who also created the plan for the World Trade Center Memorial. 

Once a Chinese billionaire invited Lisa and me to lunch near those apartments!  He wanted me to work with him on his physics theories.  Alas, I couldn't bring myself to do it. 

When we reached Vivocity, we were really tired - it was a cool day by Singapore standards, but still sweaty after a 4-hour hike.  We watched a crowd of Chinese folks doing country-western dancing outdoors by the mall.   It's fun to see a middle-aged Chinese guy wearing cowboy boots and a hat slowly dancing to country music as if it were some sort of tai chi exercise.  I really wonder how this fad got started.  Then we went to an overpriced restaurant called The Queen and Mangosteen and had beers and dinner by the water.

Life is stranger and more interesting than I'd expected.

Here's a map for this walk:

http://www.nparks.gov.sg/cms/docs/HortPark_and_SouthernRidges_guide.pdf

#singapore  ___

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2014-08-15 01:28:39 (39 comments, 46 reshares, 150 +1s)

{7,3,3} meets the plane at infinity

Maryam Mirzakhani won the Fields medal largely for her work on hyperbolic geometry.  The hyperbolic plane is something we can all enjoy: it's not flat, but curved like a saddle, and triangles have angles that add up to less than 180 degrees.  We can draw it crushed down to a disk, as in this picture by +Roice Nelson.  All the light blue circles should really be the same size - but the ones near the edge have been squashed.

Instead of learning Euclidean geometry in school, you could have learned hyperbolic geometry - it's almost the same, with some big differences.  The main thing is that the parallel postulate is false in hyperbolic geometry: there are many ways to draw a line through a point parallel to another line!  This is how Lobachevsky  discovered hyperbolic geometry in 1823: by seeing what would happen ifyou c... more »

{7,3,3} meets the plane at infinity

Maryam Mirzakhani won the Fields medal largely for her work on hyperbolic geometry.  The hyperbolic plane is something we can all enjoy: it's not flat, but curved like a saddle, and triangles have angles that add up to less than 180 degrees.  We can draw it crushed down to a disk, as in this picture by +Roice Nelson.  All the light blue circles should really be the same size - but the ones near the edge have been squashed.

Instead of learning Euclidean geometry in school, you could have learned hyperbolic geometry - it's almost the same, with some big differences.  The main thing is that the parallel postulate is false in hyperbolic geometry: there are many ways to draw a line through a point parallel to another line!  This is how Lobachevsky  discovered hyperbolic geometry in 1823: by seeing what would happen if you changed the rules this way.

And instead of learning trigonometry, you could have learned hyperbolic trigonometry - it's very similar, but you have identities like

cosh²θ - sinh²θ = 1

The most exciting thing you could do in this alternate universe is take the hyperbolic plane, cut out carefully chosen pieces, and fold them into multi-holed doughnut shapes without wrinkling the paper.  

These shapes were intensively studied by Felix Klein and Henri Poincaré... and Maryam Mirzakhani is carrying on this grand tradition.  They're important in number theory, string theory and many other subjects.

Hyperbolic geometry works in higher dimensions, too.  In my last Visual Insight post, I showed you a 3-dimensional 'hyperbolic honeycomb', a marvelous pattern built of sheets of regular heptagons.  It's called the {7,3,3} honeycomb because each heptagon has 7 sides, the heptagons meet in groups of 3 on each sheet, and 3 sheets meet along each edge of each heptagon.

This is a view of the 'sky' in a 3-dimensional world with a {7,3,3} honeycomb in it.  To understand it, check out my latest Visual Insight post:

http://blogs.ams.org/visualinsight/2014/08/14/733-honeycomb-meets-plane-at-infinity/

and compare the picture there with the previous one:

http://blogs.ams.org/visualinsight/2014/08/01/733-honeycomb/

#geometry  ___

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2014-08-14 03:06:45 (19 comments, 95 reshares, 241 +1s)

The 290 theorem

Manjul Bhargava is another of this year's Fields medalists.  He works on number theory, which in its simplest form is the study of integers:

 ..., -3, -2, -1, 0, 1, 2, 3, ...

So when I say 'number' in this post, I'll always mean one of these!

When Bhargava was a grad student at Princeton, he read a book on number theory by the famous mathematician Gauss.  Gauss was interested in quadratic forms, which are things like this:

x² + 3xy + y²

or this

-3x² + y² + 4xz + yz - 7z²

Gauss was mainly interested in quadratic forms with two variables, but it's also fun to think about more variables.

I can hand you a quadratic form and ask: what numbers can you get if you plug in any numbers you want for the variables?

Start with something reallyeasy.  ... more »

The 290 theorem

Manjul Bhargava is another of this year's Fields medalists.  He works on number theory, which in its simplest form is the study of integers:

 ..., -3, -2, -1, 0, 1, 2, 3, ...

So when I say 'number' in this post, I'll always mean one of these!

When Bhargava was a grad student at Princeton, he read a book on number theory by the famous mathematician Gauss.  Gauss was interested in quadratic forms, which are things like this:

x² + 3xy + y²

or this

-3x² + y² + 4xz + yz - 7z²

Gauss was mainly interested in quadratic forms with two variables, but it's also fun to think about more variables.

I can hand you a quadratic form and ask: what numbers can you get if you plug in any numbers you want for the variables?

Start with something really easy.  For this one



you can only get the perfect squares

0, 1, 4, 9, 16, ...

But what about this one?

x² + y²

Can you find numbers x and y that make x² + y² = 100?  How about x² + y² = 99?  Remember, I'm using 'numbers' to mean numbers like these:

 ..., -3, -2, -1, 0, 1, 2, 3, ...

And what about this quadratic form?

w² + x² + y² + z²

It's a famous fact that for this one, you can get any positive number by plugging in numbers for w, x, y and z. 

What about this?

x² + y² + z²

Now you can't get every positive number.   Do you see why?

We say a quadratic form is positive definite if whenever you plug numbers into it, you get something positive - unless all those numbers were zero.  For example,

x² + y² + z²

is positive definite, but

x² + y² - z²

is not. 

Okay, now you're ready.  Here's something amazing that Manjul Bhargava proved with +Jonathan Hanke in 2005.

Here's how to tell if you can get every positive number by plugging in numbers for the variables in a positive definite quadratic form.  It's enough to check that you can get every number from 1 to 290.

In fact, it's enough to get these numbers:

1, 2, 3, 5, 6, 7, 10, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, 31, 34, 35, 37, 42, 58, 93, 110, 145, 203, 290.

Weird! 

This is just one of many things Bhargava has done.  Most are a bit harder to explain, but I described one here:

https://plus.google.com/u/0/117663015413546257905/posts/VouaWQnthn5

It's about 'elliptic curves', another really popular topic in number theory. 

And in fact, the 290 theorem I just explained is secretly about elliptic curves!  As usual in number theory, the statement of a theorem may sound simple, cute, and pointless... but the proof reveals a very different world, and that's what really matters. 

Here's a nice explanation of the proof:

• Yong Suk Moon, Universal quadratic forms and the 15-theorem and 290-theorem, https://math.stanford.edu/theses/moon.pdf.

The original paper is here:

• Manjul Bhargava and Jonathan Hanke, Universal quadratic forms and the 290-Theorem, to appear in Inventiones Mathematicae,  http://www.wordpress.jonhanke.com/wp-content/uploads/2011/09/290-Theorem-preprint.pdf

There's a lot left to do.  For example, Jonathan Rouse tried to show that a positive definite quadratic form gives all  odd positive numbers if gives the odd numbers from 1 up to 451... but he only succeeded in showing this assuming something called the Generalized Riemann Hypothesis!  Proving this is an extremely hard problem in its own right.

• Jonathan Rouse, Quadratic forms representing all odd positive integers, http://arxiv.org/abs/1111.0979.

#spnetwork arxiv:1111.0979  #fieldsmedal   #numbertheory   #spnetwork  ___

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2014-08-13 03:16:36 (53 comments, 247 reshares, 596 +1s)

Maryam Mirzakhani won the Fields medal yesterday.

As a child in Tehran, she didn't intend to become a mathematician - she just wanted to read every book she could find!  She also watched television biographies of famous women like Marie Curie and Helen Keller.  She started wanting to do something great... maybe become a writer.

She finished elementary school while the Iran-Iraq war was ending, and took a test that got her into a special middle school for girls.  She did poorly in math her first year, and it undermined her confidence.  “I lost my interest in math," she said.

But the next year she had a better teacher, and she fell in love with the subject.  She and a friend became the first women on Iranian math Olympiad team.  She won a gold medal the first year, and got a perfect score the next year.

After getting finishing her undergraduate workat Shar... more »

Maryam Mirzakhani won the Fields medal yesterday.

As a child in Tehran, she didn't intend to become a mathematician - she just wanted to read every book she could find!  She also watched television biographies of famous women like Marie Curie and Helen Keller.  She started wanting to do something great... maybe become a writer.

She finished elementary school while the Iran-Iraq war was ending, and took a test that got her into a special middle school for girls.  She did poorly in math her first year, and it undermined her confidence.  “I lost my interest in math," she said.

But the next year she had a better teacher, and she fell in love with the subject.  She and a friend became the first women on Iranian math Olympiad team.  She won a gold medal the first year, and got a perfect score the next year.

After getting finishing her undergraduate work at Sharif University in Tehran in 1999, she went on to grad school at Harvard.  There she met Curtis McMullen, a Fields medalist who works on hyperbolic geometry and related topics.

Hyperbolic geometry is about curved surfaces where the angles of a triangle add up to less than 180 degrees, like the surface of a saddle.  It's more interesting than Euclidean geometry, or the geometry of a sphere.  One reason is that if you have a doughnut-shaped thing with 2 or more holes, there are many ways to give it a hyperbolic geometry where its curvature is the same at each point.  These shapes stand at the meeting-point of many roads in math.  They are simple enough that we can understand them in amazing detail - yet complicated enough to provoke endless study.

Maryam Mirzakhani took a course from McMullen and started asking him lots of questions.  “She had a sort of daring imagination,” he later said.  “She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, ‘Is it right?’ I was always very flattered that she thought I would know.”

Here's a question nobody knew the answer to.  If an ant walks on a flat Euclidean plane never turning right or left, it'll move along a straight line and never get back where it started.  If it does this on a sphere, it will get back where it started: it will go around a circle.  If it does this on a hyperbolic surface, it may or may not get back where it started.  If it gets back to where it started, facing the same direction, the curve it moves along is called a closed geodesic.  

The ant can go around a closed geodesic over and over.  But say we let it go around just once: then we call its path a simple closed geodesic.    We can measure the length of this curve.  And we can ask: how many simple closed geodesics are there with length less than some number L?

There are always only finitely many - unlike on the sphere, where the ant can march off in any direction and get back where it started after a certain distance.  But how many?

In her Ph.D. thesis, Mirzakhani figured out a formula for how many.  It's not an exact formula, just an 'asymptotic' one, an approximation that becomes good when L becomes large.  She showed the number of simple closed geodesics of length less than L is asymptotic to some number times L to the power 6g-6, where g is the number of holes in your doughnut. 

She boiled her proof down to a 29-page argument, which was published in one of the most prestigious math journals:

• Maryam Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Annals of Mathematics 168 (2008), 97–125, http://annals.math.princeton.edu/wp-content/uploads/annals-v168-n1-p03.pdf.

This is a classic piece of math: simple yet deep.  The statement is simple, but the proof uses many branches of math that meet at this crossroads. 

What matters is not just knowing that the statement is true: it's the new view of reality you gain by understanding why it's true.   I don't understand why this particular result is true, but I know that's how it works.  For example, her ideas also gave here a new proof of a conjecture by the physicist Edward Witten, which came up in his work on string theory!  

This is just one of the first things Mirzakhani did.  She's now a professor at Stanford.

"I don't have any particular recipe," she said.  "It is the reason why doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out."

She has a lot left to think about.  There are problems she has been thinking about for more than a decade. "And still there’s not much I can do about them," she said.

"I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers."

I got some of my quotes from here:

http://www.simonsfoundation.org/quanta/20140812-a-tenacious-explorer-of-abstract-surfaces/

and some from here:

http://www.theguardian.com/science/2014/aug/13/interview-maryam-mirzakhani-fields-medal-winner-mathematician

They're both fun to read.

#spnetwork doi:10.4007/annals.2008.168.97 #geometry #mustread___

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2014-08-11 03:56:02 (44 comments, 40 reshares, 154 +1s)

What is quantum entanglement good for?

Here's a headline from the New York Times in 1935.   Einstein had already done his best work: photons, special relativity and general relativity.  But this year he had 2 good ideas about spooky ways that distant objects could be connected.  He wrote about them in 2 papers with a guy named Rosen. 

One introduced the idea of a 'wormhole': a kind of tunnel connecting distant regions of space.  Another, written with a third guy named Podolsky, argued that quantum theory was 'incomplete'.  Einstein later complained that it allowed 'spooky action at a distance'.

Why?  Because you can't always fully describe a quantum system by fully describing each piece of it.   In fact sometimes you can know as much as possible about the whole system while still knowing nothing about the state of each piece. 
more »

What is quantum entanglement good for?

Here's a headline from the New York Times in 1935.   Einstein had already done his best work: photons, special relativity and general relativity.  But this year he had 2 good ideas about spooky ways that distant objects could be connected.  He wrote about them in 2 papers with a guy named Rosen. 

One introduced the idea of a 'wormhole': a kind of tunnel connecting distant regions of space.  Another, written with a third guy named Podolsky, argued that quantum theory was 'incomplete'.  Einstein later complained that it allowed 'spooky action at a distance'.

Why?  Because you can't always fully describe a quantum system by fully describing each piece of it.   In fact sometimes you can know as much as possible about the whole system while still knowing nothing about the state of each piece.  

And in this situation, if you measure stuff about the pieces, what you see will be random... but correlated in ways that are impossible according to classical probability theory.   We say the pieces are entangled.

We're now quite sure that entanglement is real.  People routinely see it in the lab.  The way out of the 'paradox' is not spooky action at a distance.  It's that the world is not described by classical probability theory.   It's described by quantum theory.

Here at the Centre for Quantum Technologies, people owe a lot to Einstein's discovery of entanglement.   But they don't regard it as a flaw of quantum theory.  They regard it as a 'resource'.  You can use it to do wonderful things.

Or can you?  Is it really entanglement that lets us do wonderful things with quantum mechanics... or something slightly different?   It turns out there are interesting kinds of quantum information processing that don't use entanglement, and even kinds that don't even work if there's too much entanglement. 

Here at the CQT,  +Valerio Scarani and coauthors wrote a nice article on the state of the art in quantum information processing - the "quantum frontier".  And they say:

Jozsa and Linden show that any quantum algorithm involving only pure states that achieves exponential speed up over classical algorithms must entangle a large numbers of qubits. While entanglement is necessary for an exponential speed up, the existence of entanglement is far from sufficient to guarantee a speed up, and it may turn out that another property better characterizes what enables a speed up. Many entangled systems have been shown to be classically simulable. Indeed, the Gottesman-Knill theorem, as well as results on the classical simulation of match gates, have shown that there exist non-classical computational models that allow for highly entangled states which are efficiently classically simulable. Furthermore, if one looks at query complexity instead of algorithmic complexity, improvements can be obtained with no entanglement whatsoever. Meyer shows that in the course of the Bernstein-Vazirani algorithm, which achieves an N to 1 reduction in the number of queries required, no qubits become entangled. Going beyond quantum computation it becomes more obvious that entanglement is not required to reap benefits. For example, the BB84 quantum key distribution protocol makes no use of entanglement. While measurement-based quantum computation, discussed in Section 6.2, graphically illustrates the use of entanglement as a resource for quantum computation, it turns out that if states are too highly entangled, they are useless for measurement-based quantum computation. In the same paper in which they showed that entanglement is necessary, Jozsa and Linden end their abstract with “we argue that it is nevertheless misleading to view entanglement as a key resource for quantum-computational power.” The reasons for quantum information processing’s power remains mysterious; Vedral refers to “the elusive source of quantum effectiveness”.

There are lots of references here that I've deleted... but you can get those details here:

• Joseph F. Fitzsimons, Eleanor G. Rieffel, Valerio Scarani, The quantum frontier, http://arxiv.org/abs/1206.0785.

#spnetwork arXiv:1206.0785 #quantumcomputing  ___

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2014-08-10 02:51:19 (169 comments, 671 reshares, 548 +1s)

Both rectangles are moving at constant speed

At least that's what the creator of this illusion says!  It looks like the yellow and blue rectangles are taking turns going forward - one step at a time.

This is an illusion that's so good it's hard to believe it's an illusion. When the black and white lines disappear, it's easy to see the rectangles are moving at constant speed.  But before that they seem to be taking turns, and pausing when they reach each new line.

Could the creator of this illusion be cheating - fooling you into thinking there's an illusion?   How can you tell, except by making your own version of this animated gif?

Hide one rectangle with your hand.  Then look closely at the other.  Try not to look at the black and white lines.  I think you'll see the rectangle is moving at constant speed.

Butif you... more »

Both rectangles are moving at constant speed

At least that's what the creator of this illusion says!  It looks like the yellow and blue rectangles are taking turns going forward - one step at a time.

This is an illusion that's so good it's hard to believe it's an illusion. When the black and white lines disappear, it's easy to see the rectangles are moving at constant speed.  But before that they seem to be taking turns, and pausing when they reach each new line.

Could the creator of this illusion be cheating - fooling you into thinking there's an illusion?   How can you tell, except by making your own version of this animated gif?

Hide one rectangle with your hand.  Then look closely at the other.  Try not to look at the black and white lines.  I think you'll see the rectangle is moving at constant speed.

But if you look away, and watch the rectangle with your peripheral vision, it will seem to move in steps.

We don't just "see what's there".  We construct a mental model of reality from sensory data.  We need  to do this.  But people can manipulate this. 

It's not optical illusions we need to worry about.  It's political illusions, economic illusions, social illusions.  We think we're just seeing what's there... but we're actually constructing a model of reality.  And politicians and other people are busy trying to shape your model, so you'll do what they want.  Escaping their illusions is much, much harder than escaping this optical illusion.

You can probably think of many examples of other  people who are fooled by politicians, ideologies, doctrines and dogmas.   Now list the ways in which you are being fooled.

Oh, you think you're better than average?  Join the club.

Puzzle 1: name the biggest way you've been fooled by a cultural, political or religious illusion.

Puzzle 2: name a way you're just starting to realize that you're being fooled by such an illusion.

For Puzzle 2, it should be just as hard to really believe you're being fooled as it is with this optical illusion.  For example: I'm just starting to realize that I've been fooled into wanting to be a 'bigshot': well-known, and seemingly 'important'.  But it's hard to break out of this belief.  Even now, I'm trying to get you to pay attention to me.  I'm sorry - at least I try to make it worth your while.

#illusion  ___

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2014-08-07 02:42:37 (30 comments, 42 reshares, 165 +1s)

Harpooning a comet

After a decade-long chase, the Rosetta spacecraft has now reached a comet!  This photo was taken from just 285 kilometers away.  The comet's gravity is very weak, so Rosetta will move in a triangular orbit under its own power before moving closer. 

On November 11th, Rosetta will send in a probe called Philae, which will harpoon the comet and land on it!  The picture at bottom right shows what that should look like.  Philae will drill into the comet and carry out lots of experiments.

As the comet approaches the Sun, it will heat up.  Gas will start to boil up from the surface, earthquakes will shake it, and I suppose Philae may even be destroyed.  I haven't read any details about what to expect!  But they will try to land Philae far away from places where jets of gas will erupt.  The comet will makes its closestapproach... more »

Harpooning a comet

After a decade-long chase, the Rosetta spacecraft has now reached a comet!  This photo was taken from just 285 kilometers away.  The comet's gravity is very weak, so Rosetta will move in a triangular orbit under its own power before moving closer. 

On November 11th, Rosetta will send in a probe called Philae, which will harpoon the comet and land on it!  The picture at bottom right shows what that should look like.  Philae will drill into the comet and carry out lots of experiments.

As the comet approaches the Sun, it will heat up.  Gas will start to boil up from the surface, earthquakes will shake it, and I suppose Philae may even be destroyed.  I haven't read any details about what to expect!  But they will try to land Philae far away from places where jets of gas will erupt.  The comet will makes its closest approach to the Sun on August 13th, 2015.

Here are the scientific instruments on the lander Philae:

CONSERT, the COmet Nucleus Sounding Experiment by Radiowave Transmission. This will shoot radio waves through the coment, which will be detected on the other side by Rosetta!  It's sort of like taking an X-ray to see what's inside the comet.

APXS, the Alpha Proton X-ray Spectrometer.  This will determine which elements are on the surface below the lander.

COSAC, for COmetary SAmpling and Composition. This is a combination gas chromatograph and time-of-flight mass spectrometer that will perform analysis of soil samples and determine the content of volatile components.

Ptolemy is an instrument used to measure stable isotopic ratios of key volatile compounds on the comet's nucleus.

ÇIVA, the Comet Nucleus Infrared and Visible Analyzer.

ROLIS, the Rosetta Lander Imaging System.

MUPUS, the MUlti-PUrpose Sensors for Surface and Sub-Surface Science.

ROMAP, the Rosetta Lander Magnetometer and Plasma Monitor.

SESAME, the Surface Electric Sounding and Acoustic Monitoring Experiment.

SD2, the sampling, drilling and distribution subsystem.

If you know more about what these do, please tell us!  I'm annoyed that the stuff I've seen doesn't go into much detail.

For more great photos of the comet, go to the European Space Agency website:

http://www.esa.int/spaceinimages/Missions/Rosetta/%28class%29/image___

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2014-08-05 00:52:07 (6 comments, 33 reshares, 122 +1s)

Lost in space

Physicists often use a 'Cartesian coordinate system' - an imaginary grid, like 3d graph paper,  that lets us name any point in space with 3 numbers.  But what if it were real?  You could climb around on it!

That's the idea of this art project by Numen/For Use, the guys who made that expanding and shrinking glowing cube with an infinity of reflections inside.

It's an inflatable structure.   Ropes inside get stretched tight when it inflates.  They form a 3d grid that's strong enough to climb around on.  The inside walls are white, so it seems to go on infinitely. They tested it out in countryside near Vienna at the end of December 2013. 

For more photos, try this:

http://www.numen.eu/installations/string/prototype/

If you didn't see that glowing cube, you missed some fun.  Here itis:
more »

Lost in space

Physicists often use a 'Cartesian coordinate system' - an imaginary grid, like 3d graph paper,  that lets us name any point in space with 3 numbers.  But what if it were real?  You could climb around on it!

That's the idea of this art project by Numen/For Use, the guys who made that expanding and shrinking glowing cube with an infinity of reflections inside.

It's an inflatable structure.   Ropes inside get stretched tight when it inflates.  They form a 3d grid that's strong enough to climb around on.  The inside walls are white, so it seems to go on infinitely. They tested it out in countryside near Vienna at the end of December 2013. 

For more photos, try this:

http://www.numen.eu/installations/string/prototype/

If you didn't see that glowing cube, you missed some fun.  Here it is:

http://tinyurl.com/n-light-membrane

#art  ___

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2014-08-03 09:59:26 (216 comments, 70 reshares, 243 +1s)

My last post on the NASA "quantum vacuum plasma thruster" was mainly about the shoddy theory behind it - like how there's no such thing as a "quantum vacuum plasma".

But you could argue: hey, if the gizmo actually works, isn't that good enough?   

Unfortunately, the experiment has problems too.  In brief:

1.  They tested a device that was designed to work and one that was designed not to work.  They both worked.

2.  They tested the devices in a "vacuum chamber", but they didn't take the air out.

3.  They didn't carefully study all possible causes of experimental error... like their devices heating the air.

In a bit more detail:

1.  Their device, called the Cannae drive, was invented by a guy named Guido Fetta.  You can see a picture below.  It's not complicated! It's a... more »

My last post on the NASA "quantum vacuum plasma thruster" was mainly about the shoddy theory behind it - like how there's no such thing as a "quantum vacuum plasma".

But you could argue: hey, if the gizmo actually works, isn't that good enough?   

Unfortunately, the experiment has problems too.  In brief:

1.  They tested a device that was designed to work and one that was designed not to work.  They both worked.

2.  They tested the devices in a "vacuum chamber", but they didn't take the air out.

3.  They didn't carefully study all possible causes of experimental error... like their devices heating the air.

In a bit more detail:

1.  Their device, called the Cannae drive, was invented by a guy named Guido Fetta.  You can see a picture below.  It's not complicated!  It's a hollow container made of metal, about 11 inches in diameter and 4-5 inches long.  You pump radio waves in one end. At the other end, a copper wire serves as an antenna.  This lets you measure the radio waves bouncing around inside the container, and adjust their frequency until you hit a resonance.  Then this thing is supposed to generate thrust, for some unknown reason.

Fetta thought this device would work if you carve slots on one side of the flat part.  The NASA guys tried a version with slots and one without slots.  They claim both versions generate a thrust of 22-48 micronewtons when they pump 17-28 watts of radio waves into them:

Thrust was observed on both test articles, even though one of the test articles was designed with the expectation that it would not produce thrust. Specifically, one test article contained internal physical modifications that were designed to produce thrust, while the other did not (with the latter being referred to as the "null" test article).

So, basically they found evidence against Fetta's idea: the slots make no difference.  It's like giving someone a placebo and finding it works just as well as the drug you're testing.

They also tried a resistor instead of their device.  They claim this produced no thrust.  This rules out some possibilities of experimental error... but not others. 

For example, if parts of their flat metal can get hot and create air currents, that might create the force they saw.  It's a tiny force, less you'd get from 5 milligrams of mass pushing down due to gravity.

2.  Their paper goes into great detail about the "vacuum chamber" their experiment was done in - but in the abstract to the paper, they say they didn't remove the air.  This is important because of the issue of air currents. 

It's also just weird.  In their paper they say:

To simulate the space pressure environment, the test rig is rolled into the test chamber. After sealing the chamber, the test facility vacuum pumps are used to reduce the environmental pressure down as far as 5x10E-6 Torr. Two roughing pumps provide the vacuum required to lower the environment to approximately 10 Torr in less than 30 minutes. Then, two high-speed turbo pumps are used to complete the evacuation to 5x10E-6 Torr, which requires a few additional days. During this final evacuation, a large strip heater (mounted around most of the circumference of the cylindrical chamber) is used to heat the chamber interior sufficiently to emancipate volatile substances that typically coat the chamber interior walls whenever the chamber is at ambient pressure with the chamber door open. During test run data takes at vacuum, the turbo pumps continue to run to maintain the hard vacuum environment. The high-frequency vibrations from the turbo pump have no noticeable effect on the testing seismic environment.

They're working really hard to get a good vacuum, right?  But in their abstract they say:

Testing was performed on a low-thrust torsion pendulum that is capable of detecting force at a single-digit micronewton level, within a stainless steel vacuum chamber with the door closed but at ambient atmospheric pressure.

At ambient atmospheric pressure?   What's the point of the fancy vacuum chamber?  A sentence in their conclusions gives a clue.  Talking about future plans, they say:

Vacuum compatible RF amplifiers with power ranges of up to 125 watts will allow testing at vacuum conditions which was not possible using our current RF amplifiers due to the presence of electrolytic capacitors.

So it seems they couldn't actually test their device in a vacuum.

3.  If you're trying to find some small effect, checking the ways you could have screwed up is the most important thing.  The device they're testing is simple, but the test apparatus itself is very complicated, and lots of things could go wrong. 

Their paper should have a big section on this, but it doesn't.  Instead it has a section on how if the gizmo works, you could scale it up and do great things:

Figure 23 shows a conservative 300 kilowatt solar electric propulsion roundtrip human exploration class mission to Mars/Deimos. Figure 24 shows a 90 metric ton 2 megawatt (MW) nuclear electric propulsion mission to Mars that has considerable reduction in transit times due to having a thrust to mass ratio greater than the gravitational acceleration of the Sun (0.6 milli-g’s at 1 AU). Figure 25 shows the same spacecraft mass performing a roundtrip mission to the Saturn system spending over a year around two moons of interest, Titan and Enceladus.

This is called 'counting your chickens before the eggs have hatched'.

I would need to be more of an expert than I am to imagine all the things that could go wrong with their experiment.  But just so you see what I mean, here's one thing they do mention:

one visible effect to the seismic environment is the periodic (about one-third to one-quarter Hertz) perturbation created by the waves from the Gulf of Mexico (about 25 miles southeast of Johnson Space Center), especially on windy days.

The thrust they're measuring is so small that waves in the ocean 25 miles away could screw up the experiment!  They tried to deal with this... but it goes to show, you can't revolutionize physics until you carefully check all the sources of error.

I thank Greg Egan and +Matt McIrvin for their help, but of course they're not to blame for any mistakes I made. 

The paper I'm talking about was published here:

• David Brady, Harold White, Paul March, James Lawrence and Frank Davies, Anomalous thrust production from an RF test device measured on a low-thrust torsion pendulum, 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, http://arc.aiaa.org/doi/abs/10.2514/6.2014-4029.  

Unfortunately it's not free except for the abstract.  Luckily someone has liberated the paper and put a free version here:

• http://rghost.net/57230791

Beware: the abstract in the paper is different than the abstract on the NASA technical report server here:

• http://ntrs.nasa.gov/search.jsp?R=20140006052

This is where they say they didn't remove the air from the vacuum chamber.

There's a website about Guido Fetta's company and his device:

• Cannae Drive, http://cannae.com/about

It says:

The Cannae Drive is a resonating cavity with design features that redirect the radiation pressure exerted in the cavity to create a radiation pressure imbalance on the cavity. This differential in radiation pressure generates an unbalanced force that creates thrust. The cavity is accelerated without use of propellant. Don't believe it? Study the theory.  Replicate our numerical models.  Review our experimental results.  And draw your own conclusions.

Unfortunately, when I click on the links to theory, numerical models or experimental results, I get:

404 - Article not found

+Hamilton Carter pointed out another paper by the NASA team, which explains the wild optimism behind this experiment:

• Dr. Harold “Sonny” White, Paul March, Nehemiah Williams, and William O’Neill, Eagleworks Laboratories: advanced propulsion physics research,  http://ntrs.nasa.gov/archive/nasa/casi.ntrs.nasa.gov/20110023492.pdf

They write:

NASA/JSC is implementing an advanced propulsion physics laboratory, informally known as "Eagleworks", to pursue propulsion technologies necessary to enable human exploration of the solar system over the next 50 years, and enabling interstellar spaceflight by the end of the century. This work directly supports the "Breakthrough Propulsion" objectives detailed in the NASA OCT TA02 In-Space Propulsion Roadmap, and aligns with the #10 Top Technical Challenge identified in the report. Since the work being pursued by this laboratory is applied scientific research in the areas of the quantum vacuum, gravitation, nature of space-time, and other fundamental physical phenomenon [sic], high fidelity testing facilities are needed. The lab will first implement a low-thrust torsion pendulum (<1 uN), and commission the facility with an existing Quantum Vacuum Plasma Thruster. To date, the QVPT line of research has produced data suggesting very high specific impulse coupled with high specific force. If the physics and engineering models can be explored and understood in the lab to allow scaling to power levels pertinent for human spaceflight, 400kW SEP human missions to Mars may become a possibility, and at power levels of 2MW, 1-year transit to Neptune may also be possible. Additionally, the lab is implementing a warp field interferometer that will be able to measure spacetime disturbances down to 150nm.  Recent work published by White suggests that it may be possible to engineer spacetime creating conditions similar to what drives the expansion of the cosmos. Although the expected magnitude of the effect would be tiny, it may be a “Chicago pile” moment for this area of physics.

The "Chicago pile" was the experiment that demonstrated a nuclear chain reaction. 

#spnetwork doi:10.2514/MJPC14  #cannae_drive  ___

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2014-08-02 09:33:16 (75 comments, 219 reshares, 469 +1s)

The incredible shrinking force

Around 2000, a guy named Roger Shawyer claimed he could bounce microwaves inside a fancy-shaped can and get them to  push the can forwards, without anything leaving the can. 

This would violate conservation of momentum.  It's like sitting inside a car and making it roll forwards by pushing on the steering wheel.  Standard physics doesn't allow this.  He didn't claim to be using anything other than standard physics. 

So: ho hum, just another guy with a really bad idea.  I get emails like this all the time.

But in 2001, his company got a £45,000 grant from the British government to study this idea.  He built his machine and claimed that with 850 watts of power he could get a force of 0.016 newtons.   That's a bit less than the force of gravity from a penny pushing down on your hand.  It could easilybe an exper... more »

The incredible shrinking force

Around 2000, a guy named Roger Shawyer claimed he could bounce microwaves inside a fancy-shaped can and get them to  push the can forwards, without anything leaving the can. 

This would violate conservation of momentum.  It's like sitting inside a car and making it roll forwards by pushing on the steering wheel.  Standard physics doesn't allow this.  He didn't claim to be using anything other than standard physics. 

So: ho hum, just another guy with a really bad idea.  I get emails like this all the time.

But in 2001, his company got a £45,000 grant from the British government to study this idea.  He built his machine and claimed that with 850 watts of power he could get a force of 0.016 newtons.   That's a bit less than the force of gravity from a penny pushing down on your hand.  It could easily be an experimental error.

Why would people want a machine that uses lots of power to create a pathetically feeble force?   Because - here's the great piece of salesmanship - if it existed, you could use it to build a reactionless drive!  If you had a spaceship with huge amounts of power to spare - like, say, a nuclear reactor - you could use this gizmo to push your spaceship forwards without anything spewing out the back end. 

Again, this is about as plausible as powering a spaceship by having the crew push on it from the inside.   But if you don't know physics, it sounds very exciting. 

The story goes on.  And on.  And on.  It won't die.  In 2012, some Chinese physicists claimed they could get a force of 0.720 newtons from a power of 2,500 watts using some version of Shawyer's device. 

And now NASA is studying it!

They're claiming to see a force one thousandth as big as the Chinese - probably because they are doing the experiment one thousand times more accurately.  And still, some people are excited about this. 

The new device comes with new improved mumbo-jumbo.  Shawyer claimed that thanks to special relativity, classical electromagnetism can violate conservation of momentum.  I took those courses in college, I know that's baloney.  Now the NASA scientists say:

"Test results indicate that the RF resonant cavity thruster design, which is unique as an electric propulsion device, is producing a force that is not attributable to any classical electromagnetic phenomenon and therefore is potentially demonstrating an interaction with the quantum vacuum virtual plasma."

This is baloney too - but now it's graduate-level baloney.  "Quantum vacuum virtual plasma" is something you'd say if you failed a course in quantum field theory and then smoked too much weed.  There's no such thing as "virtual plasma".   If you want to report experimental results that seem to violate the known laws of physics, fine.  But it doesn't help your credibility to make up goofy pseudo-explanations.

I expect that in 10 years the device will be using quantum gravity and producing even less force. 

For an article written by a severely optimistic blogger, see:

http://www.wired.co.uk/news/archive/2014-07/31/nasa-validates-impossible-space-drive

For the NASA report see:

• David Brady, Harold White, Paul March, James Lawrence and Frank Davies, Anomalous thrust production from an RF test device measured on a low-thrust torsion pendulum, 50th AIAA/ASME/SAE/ASEE Joint Propulsion Conference, http://arc.aiaa.org/doi/abs/10.2514/6.2014-4029.  Free version available at http://rghost.net/57230791.

Unfortunately only the abstract is free in the official version.___

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2014-08-02 02:14:22 (11 comments, 14 reshares, 106 +1s)

Fractal madness with heptagons

This picture drawn by +Danny Calegari shows the '{7,3,3} honeycomb' in hyperbolic space.  Hyperbolic space is an infinite space where triangles have angles that add up to less than 180 degrees.  But the mathematician Poincaré figured out how compress it down to a ball so we can see it from the outside, and that's what we see here.

The {7,3,3} honeycomb is built of regular 7-sided shapes - heptagons - in hyperbolic space.  But what does {7,3,3} mean?

The heptagons lie on infinite sheets, which show up as holes here.  If you look at these holes,  you'll see they have three heptagons meeting at each corner.  So, each one is a copy of the {7,3} tiling of the hyperbolic plane.  7 stands for heptagon, 3 stands for three meeting at each corner.

It's impossible to see, but 3 of these {7,3}tilings... more »

Fractal madness with heptagons

This picture drawn by +Danny Calegari shows the '{7,3,3} honeycomb' in hyperbolic space.  Hyperbolic space is an infinite space where triangles have angles that add up to less than 180 degrees.  But the mathematician Poincaré figured out how compress it down to a ball so we can see it from the outside, and that's what we see here.

The {7,3,3} honeycomb is built of regular 7-sided shapes - heptagons - in hyperbolic space.  But what does {7,3,3} mean?

The heptagons lie on infinite sheets, which show up as holes here.  If you look at these holes,  you'll see they have three heptagons meeting at each corner.  So, each one is a copy of the {7,3} tiling of the hyperbolic plane.  7 stands for heptagon, 3 stands for three meeting at each corner.

It's impossible to see, but 3 of these {7,3} tilings meet along each edge in the picture.  That's why the whole thing is called the {7,3,3} honeycomb.

It sounds wacky and fun, and it is, but it's also part of a deep theory, which I explain on my blog:

http://blogs.ams.org/visualinsight/2014/08/01/733-honeycomb/

For a nice picture of a {7,3} tiling, try this earlier blog article:

http://blogs.ams.org/visualinsight/2014/07/15/73-tiling/

The topology of the {7,3,3} honeycomb is interesting. It is simply connected, since all the holes extend all the way to the edge of the Poincaré ball.  And its ‘boundary’ is a highly distorted copy of the Sierpinski carpet. 

That's why I had a contest to create a nice picture of the Sierpinski carpet a while back!  To see the winning entry and learn more about what makes that fractal special, go here:

http://blogs.ams.org/visualinsight/2014/07/01/sierpinski-carpet/

#fractals #geometry___

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2014-08-01 02:04:52 (4 comments, 21 reshares, 76 +1s)

Citizen Science

The Azimuth Code Project is a friendly gang of hackers and geeks. We're studying a new method of El Niño prediction that uses a "climate network".  We replicated the software used in a paper about this method, and we made it open-source.  Then a statistician named Steven Wenner jumped in and examined the results!  Check it out here:

http://johncarlosbaez.wordpress.com/2014/07/23/el-nino-project-part-6/

Very roughly, when the red curve goes over the horizontal line, the method predicts an El Niño in the following year - a blue spike.  But sometimes it doesn't work, and there are weird borderline cases.

Wenner ran some statistical tests on this method, and then +Jan Galkowski jumped in and ran a bunch more, using sophisticated Bayesian ideas.  You can read about that in the comments. 

There's a lot ofbuzz ab... more »

Citizen Science

The Azimuth Code Project is a friendly gang of hackers and geeks. We're studying a new method of El Niño prediction that uses a "climate network".  We replicated the software used in a paper about this method, and we made it open-source.  Then a statistician named Steven Wenner jumped in and examined the results!  Check it out here:

http://johncarlosbaez.wordpress.com/2014/07/23/el-nino-project-part-6/

Very roughly, when the red curve goes over the horizontal line, the method predicts an El Niño in the following year - a blue spike.  But sometimes it doesn't work, and there are weird borderline cases.

Wenner ran some statistical tests on this method, and then +Jan Galkowski jumped in and ran a bunch more, using sophisticated Bayesian ideas.  You can read about that in the comments. 

There's a lot of buzz about citizen science these days - how ordinary folks can contribute to scientific projects by collecting data or running software.  It's a great trend...  but I'm enjoying how extraordinary folks are joining the Azimuth Project and helping us out with their special skills. 

We need all the help we can get, that's for sure.  Most of all we could use advice from some climate scientists.  But it would also be great if we had more folks who enjoyed explaining techniques from math, statistics, and machine learning.  For example, Dara Shayda just used 'continuous wavelet analysis' to study patterns in the air pressure at two locations important for El Niños.  Since I'm the main writer in the gang, I had to write this up, which required learning about continuous wavelet analysis and figuring out how to explain it - explaining stuff is a big part of the project.  I did it, and I enjoyed it, but there's too much for me to do!  We could go faster with another good writer.___

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2014-07-31 00:12:17 (48 comments, 514 reshares, 386 +1s)

The one you're not looking at turns clockwise

Look at either the red dot or the yellow dot.  The circles near that dot will turn counterclockwise.  The others turn clockwise!

Or: let your eyes bounce back and forth between the two.

Or: look away from both of them.

Puzzle  1: how does it work?

Puzzle 2: who first made this gif?  I can't find the original source.

#illusions  

The one you're not looking at turns clockwise

Look at either the red dot or the yellow dot.  The circles near that dot will turn counterclockwise.  The others turn clockwise!

Or: let your eyes bounce back and forth between the two.

Or: look away from both of them.

Puzzle  1: how does it work?

Puzzle 2: who first made this gif?  I can't find the original source.

#illusions  ___

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2014-07-30 01:44:38 (32 comments, 11 reshares, 110 +1s)

There's a monster in the kitchen!

Not really.  This is a baby aye-aye being weighed at the the Duke Lemur Centre in North Carolina.  

Aye-ayes live in Madagascar.  They're the world's largest nocturnal primate.  They find grubs to eat by tapping on trees.  When an aye-aye finds a good spot, it chews a hole in the wood.  Then it sticks its narrow middle finger in the hole to pull the grubs out.

Since it was founded in 1966, the Duke Lemur Center has collected data on 3600 animals from more than 40 species of prosimians - the group of primates that includes lemurs, lorises, galagos, bushbabies, and tarsiers.  Now they've released the data to the world!  It's available online, for free:

http://lemur.duke.edu/duke-lemur-center-database/

Almost all these animals only live in Madagascar, and most of them are rare,threaten... more »

There's a monster in the kitchen!

Not really.  This is a baby aye-aye being weighed at the the Duke Lemur Centre in North Carolina.  

Aye-ayes live in Madagascar.  They're the world's largest nocturnal primate.  They find grubs to eat by tapping on trees.  When an aye-aye finds a good spot, it chews a hole in the wood.  Then it sticks its narrow middle finger in the hole to pull the grubs out.

Since it was founded in 1966, the Duke Lemur Center has collected data on 3600 animals from more than 40 species of prosimians - the group of primates that includes lemurs, lorises, galagos, bushbabies, and tarsiers.  Now they've released the data to the world!  It's available online, for free:

http://lemur.duke.edu/duke-lemur-center-database/

Almost all these animals only live in Madagascar, and most of them are rare, threatened or endangered.  This rich diversity of life is precious in ways we're still too crude to assign much economic value.  Each of these species is a rich assemblage of strategies and tricks, from their behavior down to their very molecules, finely honed by millions of years of evolution.  But the natural biotechnology they represent is too sophisticated for us to understand or copy yet - or make much money from, except for 'ecotourism'.  For the most part, we count them as worthless trash, while spending millions on canvases cleverly daubed with paint.  Someday we'll regret this.  Let's try to change it sooner rather than later.

Some people are thinking about it:

http://www.capitalinstitute.org/moneyandwealth/can-nature-be-monetized-capital-institute-conversation___

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2014-07-29 02:47:39 (31 comments, 10 reshares, 54 +1s)

Mansion of Wind and Waves

Last night Lisa and I ate at Feng Bo Zhuang on Temple Street in Singapore.  We went there since it had good spicy food from Hunan and Dongbei, a crowd of happy customers, and nice wood decor... but it turned out to have a jiang-hu theme: that's what Chinese call the world of wandering martial artists and swordsmen. 

See that sword on the wall there?

The name of this restaurant means 'Mansion of Wind and Waves' - but 'wind and waves' means the turbulence and fighting that that goes on in the jiang-hu.  There's a poem by the entrance that says "in the jiang-hu you have no choice, you either fight back or die".  This tough world is romanticized in wuxia fiction and movies:

Typically, the heroes in wuxia fiction do not serve a lord, wield military power or belong to theari... more »

Mansion of Wind and Waves

Last night Lisa and I ate at Feng Bo Zhuang on Temple Street in Singapore.  We went there since it had good spicy food from Hunan and Dongbei, a crowd of happy customers, and nice wood decor... but it turned out to have a jiang-hu theme: that's what Chinese call the world of wandering martial artists and swordsmen. 

See that sword on the wall there?

The name of this restaurant means 'Mansion of Wind and Waves' - but 'wind and waves' means the turbulence and fighting that that goes on in the jiang-hu.  There's a poem by the entrance that says "in the jiang-hu you have no choice, you either fight back or die".  This tough world is romanticized in wuxia fiction and movies:

Typically, the heroes in wuxia fiction do not serve a lord, wield military power or belong to the aristocratic class. They are often from the lower social classes of ancient Chinese society. Wuxia heroes are usually bound by a code of chivalry that requires them to right wrongs, fight for righteousness, remove an oppressor, redress wrongs and bring retribution for past misdeeds. The Chinese wuxia traditions can be compared to martial codes from other countries, such as the Japanese samurai's bushido tradition, the chivalry of medieval European knights and the gunslingers of America's Westerns.

We had frog cooked in bamboo, dumplings with hot broth inside called xiaolongbao, spicy sliced cucumber, and an appetizer of roast peanuts.  Very tasty with some Harbin beer!

Back in 2011 this restaurant was quite serious about the jiang-hu theme: the waitresses would wear traditional outfits and chant a poem when you left.  When one reviewer tried to pay by credit card, his waitress said “江湖中只收银两” - "in jiang-hu, we only accept silver ingots".    Luckily it's mellowed out by now; none of this nonsense, just good food.

As usual, most of my expertise on Chinese culture comes from Lisa... but the long quote is from here:

https://en.wikipedia.org/wiki/Wuxia

and the 2011 review is here:

http://rubbisheatrubbishgrow.com/2011/06/11/feng-bo-zhuang-%E9%A3%8E%E6%B3%A2%E5%BA%84-chinatown/

#singapore___

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2014-07-28 01:57:54 (27 comments, 13 reshares, 99 +1s)

Cracked moon

Jupiter's moon Europa is about as big as ours... but its crust is made of water ice, and underneath there seems to be a salty ocean!  

The surface has red cracks.  Spectrographs suggest these are rich in salts like magnesium sulfate left by evaporating water that comes from within.  But why are they red?  Nobody knows.  Maybe it's sulfur.

Why are there cracks?  That's an interesting story.

Europa orbits Jupiter every three and a half days... but it's tidally locked to Jupiter, so there's a place on Europa's surface where Jupiter always hangs directly overhead.  If you looked up, it would be about 24 times as big across as the Sun viewed from Earth.

But all is not calm!  Europa is in resonance with two other moons of Jupiter.   It goes around exactly half as often as the moon Io, and twice asoften as G... more »

Cracked moon

Jupiter's moon Europa is about as big as ours... but its crust is made of water ice, and underneath there seems to be a salty ocean!  

The surface has red cracks.  Spectrographs suggest these are rich in salts like magnesium sulfate left by evaporating water that comes from within.  But why are they red?  Nobody knows.  Maybe it's sulfur.

Why are there cracks?  That's an interesting story.

Europa orbits Jupiter every three and a half days... but it's tidally locked to Jupiter, so there's a place on Europa's surface where Jupiter always hangs directly overhead.  If you looked up, it would be about 24 times as big across as the Sun viewed from Earth.

But all is not calm!  Europa is in resonance with two other moons of Jupiter.   It goes around exactly half as often as the moon Io, and twice as often as Ganymede.

This keeps its orbit from settling down into a perfect circle.   So Jupiter seems to move towards Europa and then back away every 3½ days.  Just a little bit.

When Jupiter comes closer, its gravitational attraction increases more on the near side of Europa.  This causes Europa to stretch towards and away from it - a tidal force.  When Jupiter moves away, Europa relaxes a bit into a more spherical shape. 

This constant stretching and relaxing causes cracks in the surface ice of Europa.  More importantly... for fans of extraterrestrial life... it keeps Europa's oceans warm enough to stay liquid under the ice! 

We've got a lot of evidence for this.  The cracks and 'chaotic terrain' are hard to explain without an ocean under the ice.  The Galileo probe, which took this great photo of Europa, also detected a changing magnetic field that could be due to electric currents flowing through a salty ocean.   And the Hubble telescope has even seen water vapor near Europa's south pole!   This may have come from huge geysers... like the geysers on Saturn's moon Enceladus, but even bigger.

But we don't know how thick the ice crust is.  Some people say 10-30 kilometers, others say just a few.  If it's thin enough, we could send a probe that would melt through the ice and explore the ocean.  What's down there?

In 2012, the European Space Agency (ESA) announced it wants to launch a Jupiter Icy Moon Explorer.  This would includes some flybys of Europa, but is more focused on Ganymede.  In January 2014, the US House Appropriations Committee announced a new bipartisan bill that includes $80 million in funding to keep planning a Europa mission.  One possibility is the Europa Clipper, which would orbit Jupiter and conduct 45 low-altitude flybys of Europa, carrying an ice penetrating radar, short wave infra red spectrometer, topographical imager, and an ion and neutral mass spectrometer.

Puzzle: where does the energy originally come from, that heats Europa?  If something is gaining energy, something else must be losing it.

#astronomy___

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2014-07-27 02:26:25 (10 comments, 13 reshares, 110 +1s)

As if millions of voices cried out in terror and were suddenly silenced

The first report of a fast radio burst appeared in 2007.  An astronomer named Duncan Lorimer found a signal buried in recordings made at the Parkes radio telescope in Australia.  It lasted for less than 5 milliseconds and it seemed to come from outside our galaxy.  It didn't match anything we'd seen in visible light, X-rays or anything else.  A complete mystery! 

Last year people found 4 more.  But all at the Parkes telescope.  Maybe there was an error of some sort?

But now they've seen one at Arecibo, the famous radio telescope in Puerto Rico.  Duncan Lorimer says several more confirmations will soon be announced.

So what causes these fast radio bursts?

We don't know.  But here's one theory: a 'blitzar'.

When a supernovablasts t... more »

As if millions of voices cried out in terror and were suddenly silenced

The first report of a fast radio burst appeared in 2007.  An astronomer named Duncan Lorimer found a signal buried in recordings made at the Parkes radio telescope in Australia.  It lasted for less than 5 milliseconds and it seemed to come from outside our galaxy.  It didn't match anything we'd seen in visible light, X-rays or anything else.  A complete mystery! 

Last year people found 4 more.  But all at the Parkes telescope.  Maybe there was an error of some sort?

But now they've seen one at Arecibo, the famous radio telescope in Puerto Rico.  Duncan Lorimer says several more confirmations will soon be announced.

So what causes these fast radio bursts?

We don't know.  But here's one theory: a 'blitzar'.

When a supernova blasts the outer layers of a big star into space, the remaining core collapses down to a ball of neutronium heavier than our Sun and the size of a small city: a neutron star

If this spins fast enough, like a thousand times a second, it's highly magnetic.  It produces regular pulses of intense radiation - and we call it a pulsar

If it's too heavy, though, the neutron star collapses into a black hole.

But suppose it's spinning really fast!  Then the centrifugal force might pull it out and keep it from collapsing into a black hole! 

Until it slowed down.  Then it would collapse into a black hole.  The magnetic field lines would suddenly get cut by an event horizon.  They don't like that.  WHAM - a blast of radio waves.  A blitzar.

One newspaper headline describes it this way: "as if millions of voices suddenly cried out in terror and were suddenly silenced".  It's good to see that purple prose isn't dead in science journalism.

This is just a theory, so far.  We'll get more evidence as we see more short radio bursts.

For more, read these:

http://arstechnica.com/science/2013/07/mysterious-radio-bursts-come-from-outside-our-galaxy/

http://arstechnica.com/science/2013/07/possible-explanation-for-radio-bursts-meet-the-blitzar/

They're well-written! 

And here's the paper that introduced the blitzar theory.  The calculations are surprisingly sketchy.  It's really hard to calculate what happens when a ball of neutronium suddenly collapses into a black hole, so they use simple estimates:

• Heino Falcke and Luciano Rezzolla, Fast radio bursts: the last sign of supramassive neutron stars, http://arxiv.org/abs/1307.1409.

Abstract. Several fast radio bursts have been discovered recently, showing a bright, highly dispersed millisecond radio pulse. The pulses do not repeat and are not associated with a known pulsar or gamma-ray burst. The high dispersion suggests sources at cosmological distances, hence implying an extremely high radio luminosity, far larger than the power of single pulses from a pulsar. We suggest that a fast radio burst represents the final signal of a supramassive rotating neutron star that collapses to a black hole due to magnetic braking. The neutron star is initially above the critical mass for non-rotating models and is supported by rapid rotation. As magnetic braking constantly reduces the spin, the neutron star will suddenly collapse to a black hole several thousand to million years after its birth. We discuss several formation scenarios for supramassive neutron stars and estimate the possible observational signatures {making use of the results of recent numerical general-relativistic calculations). While the collapse will hide the stellar surface behind an event horizon, the magnetic-field lines will snap violently. This can turn an almost ordinary pulsar into a bright radio "blitzar": Accelerated electrons from the travelling magnetic shock dissipate a significant fraction of the magnetosphere and produce a massive radio burst that is observable out to z > 0.7. Only a few percent of the neutron stars needs to be supramassive in order to explain the observed rate. We suggest that fast radio bursts might trace the solitary formation of stellar mass black holes at high redshifts. These bursts could be an electromagnetic complement to gravitational-wave emission and reveal a new formation and evolutionary channel for black holes that are not seen as gamma-ray bursts. Radio observations of these bursts could trace the core-collapse supernova rate throughout the universe.

#astronomy   #spnetwork arXiv:1307.1409 #mustread  ___

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2014-07-26 02:38:12 (45 comments, 240 reshares, 248 +1s)

The hypersnake versus the moiré eel

This animated gif is cool, but here's something much cooler:

http://wry.me/hacking/moire-eel.html

It starts out intense... and then keeps getting more so. 

You can control the shape of the little rectangles by moving your cursor over the screen.  Try to keep your eye on just one little rectangle!  It moves up and down, not very fast... but sometimes it's impossible to keep your eye on it, because all the rectangles together produce patterns that grab your attention.  These are called moiré patterns. 

I think the 'hypersnake' here is attention-grabbing because your brain has parts that are good at detecting snakes even before you are conscious of it.  Your amygdala is one of these parts:

Information from an external stimulus reaches the amygdala in twodiffere... more »

The hypersnake versus the moiré eel

This animated gif is cool, but here's something much cooler:

http://wry.me/hacking/moire-eel.html

It starts out intense... and then keeps getting more so. 

You can control the shape of the little rectangles by moving your cursor over the screen.  Try to keep your eye on just one little rectangle!  It moves up and down, not very fast... but sometimes it's impossible to keep your eye on it, because all the rectangles together produce patterns that grab your attention.  These are called moiré patterns. 

I think the 'hypersnake' here is attention-grabbing because your brain has parts that are good at detecting snakes even before you are conscious of it.  Your amygdala is one of these parts:

Information from an external stimulus reaches the amygdala in two different ways: by a short, fast, but imprecise route, directly from the thalamus; and by a long, slow, but precise route, by way of the cortex.

It is the short, more direct route that lets us start preparing for a potential danger before we even know exactly what it is. In some situations, these precious fractions of a second can mean the difference between life and death.

Here is an example. Suppose you are walking through a forest when you suddenly see a long, narrow shape coiled up at your feet. This snake-like shape very quickly, via the short route, sets in motion the physiological reactions of fear that are so useful for mobilizing you to face the danger. But this same visual stimulus, after passing through the thalamus, will also be relayed to your cortex. A few fractions of a second later, the cortex, thanks to its discriminatory faculty, will realize that the shape you thought was a snake was really just a discarded piece of garden hose. Your heart will then stop racing, and you will just have had a moment’s scare.

The 'moiré eel' was made by Darius Bacon.  You can see more of his stuff here: 

http://wry.me/blog/

Puzzle: who made the 'hypersnake' here?  I don't know!  A Google image search shows it on many websites, but I haven't found one that credits the inventor.  Naughty!

For more on moiré patterns try this:

https://en.wikipedia.org/wiki/Moiré_pattern

For more on the amygdala, try this:

http://thebrain.mcgill.ca/flash/i/i_04/i_04_cr/i_04_cr_peu/i_04_cr_peu.html

#illusions  ___

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2014-07-25 00:43:43 (36 comments, 66 reshares, 157 +1s)

Twist into the continuum

Can you see what's happening here?

Each square is rotated by some angle compared to the square directly below it.  This angle increases as time passes.

The angle starts out being zero, so the stack is straight.  As the angle increases, the stack of squares starts to twist.  When the angle becomes big, the stack twists so much that it becomes very complicated!  But when the angle reaches 90 degrees, the stack becomes straight again - because when you rotate a square by 90 degrees, it looks exactly the same! 

So, the stack seems to twist more and more... and then straighten out again.

Moral: a symmetry is a way to change something so that it doesn't change. 

This 'paradox' is why symmetry is so powerful.  We see it in action here.  We twist the squares so much they are untwisted.
This ... more »

Twist into the continuum

Can you see what's happening here?

Each square is rotated by some angle compared to the square directly below it.  This angle increases as time passes.

The angle starts out being zero, so the stack is straight.  As the angle increases, the stack of squares starts to twist.  When the angle becomes big, the stack twists so much that it becomes very complicated!  But when the angle reaches 90 degrees, the stack becomes straight again - because when you rotate a square by 90 degrees, it looks exactly the same! 

So, the stack seems to twist more and more... and then straighten out again.

Moral: a symmetry is a way to change something so that it doesn't change. 

This 'paradox' is why symmetry is so powerful.  We see it in action here.  We twist the squares so much they are untwisted.

This gif was created by a mysterious person known only as intothecontinuum.   I'll guess it's a he, because he uses a picture of Erwin Schrödinger as his icon.  He puts his gifs here:

http://intothecontinuum.tumblr.com/

Here's the Mathematica code for this particular gif:

v[x_, y_, z_] =
Flatten[Table[ {(-1)^i*x, (-1)^j*y, (-1)^k*z}, {i, 0, 1}, {j, 0,
1}, {k, 0, 1} ], 2];

f = {{1 , 2 , 4 , 3 }, {1 , 2 , 6 , 5 }, {5 , 6 , 8 , 7 }, { 3, 4 ,
8 , 7 }, { 1, 3 , 7 , 5 }, { 2, 4 , 8 , 6 } };

G[x_, y_, z_, s_, H_ , t_] :=
Table[
Translate[
Rotate[
GraphicsComplex[v[x, y, z], Polygon[f]],
h (Cos[t] + 1) Pi/4, {0 , 0, 1 }],
{0, 0, s*h}],
{h, 1, H}]

Manipulate[
Graphics3D[
G[2, 2, .1, .25, 30, t],
Lighting -> "Neutral", ViewPoint -> Front, ViewAngle -> 35 Degree,
Boxed -> False, ImageSize -> 500],
{t, 0, Pi}]

Puzzle 1: What's the significance of these numbers:

f = {{1 , 2 , 4 , 3 }, {1 , 2 , 6 , 5 }, {5 , 6 , 8 , 7 }, { 3, 4 ,
8 , 7 }, { 1, 3 , 7 , 5 }, { 2, 4 , 8 , 6 } };

?

Puzzle 2: who is "intothecontinuum", really?___

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2014-07-24 04:41:04 (18 comments, 17 reshares, 80 +1s)

Beautiful poison

Cinnabar is a mineral made of mercury - the silver balls - and sulfur - the yellow ones.  It's fascinated people for thousands of years.  When you grind it up, you get vermilion: a brilliant red pigment.

Vermillion was used in murals in Çatalhöyük, one of the world's oldest cities, in Turkey, back around 7000 BC.   It's been used in the art and lacquerware of China since the Han Dynasty!  You'll also find it in the Tomb of the Red Queen built by the Mayans around 650 AD.

It was precious in Rome, used for art and decoration.  Since mercury is poisonous, a term in working in the cinnabar mines was a virtual death sentence.  Pliny the Elder wrote:

Nothing is more carefully guarded. It is forbidden to break up or refine the cinnabar on the spot. They send it to Rome in its natural condition,under sea... more »

Beautiful poison

Cinnabar is a mineral made of mercury - the silver balls - and sulfur - the yellow ones.  It's fascinated people for thousands of years.  When you grind it up, you get vermilion: a brilliant red pigment.

Vermillion was used in murals in Çatalhöyük, one of the world's oldest cities, in Turkey, back around 7000 BC.   It's been used in the art and lacquerware of China since the Han Dynasty!  You'll also find it in the Tomb of the Red Queen built by the Mayans around 650 AD.

It was precious in Rome, used for art and decoration.  Since mercury is poisonous, a term in working in the cinnabar mines was a virtual death sentence.  Pliny the Elder wrote:

Nothing is more carefully guarded. It is forbidden to break up or refine the cinnabar on the spot. They send it to Rome in its natural condition, under seal, to the extent of some ten thousand pounds a year. The sales price is fixed by law to keep it from becoming impossibly expensive, and the price fixed is seventy sesterces a pound.

The Chinese were probably the first to make a synthetic vermilion, back in the 4th century BC. A Greek alchemist named Zosimus of Panopolis mentioned the process around the 3rd century AD. In the early ninth century the alchemist Jabir ibn Hayyan described it in a book - and it then spread to Europe.

The process is pretty simple.   You mix mercury and sulfur together, forming a black compound called Aethiopes mineralis. You heat it in a flask. The compound vaporizes, and recondenses on the top of the flask. Then you break the flask, take out the vermilion, and grind it.  At first the stuff is almost black, but the more you grind it, the redder it gets.

Puzzle 1: Where did they get the mercury in the first place, if not from cinnabar? 

Puzzle 2: If they had cinnabar, why not just grind that to make vermillion?

Puzzle 3: Why does the stuff start out black?

Here's one possible answer to Puzzle 3.  Cinnabar contains one crystal form of mercury sulfide, the so-called alpha form, shown here.  It's a hexagonal crystal, and it's red.  But there's also another form, the beta form, which is black.  This is sometimes called metacinnabar - a cool word if I ever saw one.

In Taoist alchemy in China, cinnabar and gold were used in various potions that were supposed to give long life.  Cinnabar was considered to have a lot of yang and gold a lot of yin.  According to their theories, gold naturally transmutes into cinnabar over time, much as yin becomes yang (and vice versa). The evidence?   Deposits of cinnabar are sometimes found beneath veins of gold. 

Unfortunately, some people got mercury poisoning thanks to these potions! 

Isaac Newton also spent a lot of his later life doing alchemy.  This is not as dumb as it sounds, because at that time alchemy included what we now call 'chemistry', along with more mystical things.  Some hairs from Newton's body have been found to contain 4 times as much lead, arsenic and antimony as normal - and 15 times as much mercury!  This might explain Newton's tremors, severe insomnia, and paranoia.

I love the look of this crystal!  The picture, made by Ben Mills, is on Wikipedia:

https://en.wikipedia.org/wiki/Mercury_sulfide

Some of my text is quoted or paraphrased from these articles:

https://en.wikipedia.org/wiki/Cinnabar
https://en.wikipedia.org/wiki/Vermilion

For the use of cinnabar in Taoist alchemy, see:

http://tinyurl.com/taoist-cinnabar

#chemistry  ___

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2014-07-23 02:58:40 (30 comments, 30 reshares, 92 +1s)

The world is getting old

In the last century the world's population doubled twice.  It probably won't double again this century.  But the number of people over 65 is set to double in just 25 years!  This will affect the world in huge ways, which we barely understand.

There are already 600 million people over 65.  That's impressive: half the humans that old who ever lived are alive now!   And in democracies, old people vote more.  So they are setting the agenda: in the US, for example, spending on the young and poor is getting cut, while spending for the elderly continues to rise. 

Wealth inequality tends to be greater among older people, since the rich keep getting richer as they age.  Also, older people tend to spend less and save more.  All this will have big economic effects.

In 2010, the world had an age dependency ratio ofabout 16.... more »

The world is getting old

In the last century the world's population doubled twice.  It probably won't double again this century.  But the number of people over 65 is set to double in just 25 years!  This will affect the world in huge ways, which we barely understand.

There are already 600 million people over 65.  That's impressive: half the humans that old who ever lived are alive now!   And in democracies, old people vote more.  So they are setting the agenda: in the US, for example, spending on the young and poor is getting cut, while spending for the elderly continues to rise. 

Wealth inequality tends to be greater among older people, since the rich keep getting richer as they age.  Also, older people tend to spend less and save more.  All this will have big economic effects.

In 2010, the world had an age dependency ratio of about 16.  That is, there are 16 people over 65 years old for every 100 people with ages between 25 and 65.  But the UN expects this will rise to about 26 by 2035.

There are more old folks in rich countries, of course. Japan already has an age dependency ratio of 43, and the UN expects it will hit 69 by 2035.  For the US, a much younger country, it's about 23 now, and is expected to reach 44.   For China it's about 15 and may reach 35.

The name "age dependency ratio" suggests that old folks rely on younger ones, and that's true in many ways.  But people are working longer, and more educated people work longer than others.   In the US, for example, only 32% of men with just a high school education and age between 62 and 74 are employed.   But for men with a PhD or professional degree, the figure is about 65%.  So education may be a way to reduce the "dependency" of the old.

Now consider that in China, nearly half the workers between 50 and 64 haven't finished primary school!  And China may eventually surpass the US in the fraction of people over 65, because its birth rate is lower.  This will be a big deal.

Where are we heading?  A very different world than today, that's all we can say for sure.

I got this information mainly from the Economist briefing on "Demography, growth and inequality" from April 26, 2014.  It's not free:

http://www.economist.com/news/briefing/21601248-generation-old-people-about-change-global-economy-they-will-not-all-do-so

On aging in China:

http://www.economist.com/node/21553056

The graph is from here:

http://www.mintpressnews.com/global-study-world-ready-aging-population/169900/___

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2014-07-22 09:31:17 (8 comments, 5 reshares, 55 +1s)

Nanoprofessionals

Want to teach kids organic chemistry?  Have them attach these different 'heads' to a molecule called Nanokid, and create tiny people!

Take a look at Nanokid:

https://en.m.wikipedia.org/wiki/Nanoputian

It's sort of goofy!   James Tour and coworkers at Rice University designed and synthesized these compounds in 2003 to help teach young students.  However, the chemistry is not easy.  Here's one step of building Nanokid:

2,5-Bis(3,3-dimethylbutynyl)-4-bromobenzaldehyde (3). To a solution of 2,5-bis(3,3-dimethylbutynyl)-1,4-dibromobenzene (2.43 g, 6.135 mmol) in THF (30 mL) cooled to -78 °C under nitrogen was added dropwise n-BuLi (2.48 M, 2.72 mL). The reaction mixture was allowed to stir at -78 °C for 1 h. To this mixture was added DMF (0.48 mL, 6.135 mmol) predried over molecular sieves. Thereacti... more »

Nanoprofessionals

Want to teach kids organic chemistry?  Have them attach these different 'heads' to a molecule called Nanokid, and create tiny people!

Take a look at Nanokid:

https://en.m.wikipedia.org/wiki/Nanoputian

It's sort of goofy!   James Tour and coworkers at Rice University designed and synthesized these compounds in 2003 to help teach young students.  However, the chemistry is not easy.  Here's one step of building Nanokid:

2,5-Bis(3,3-dimethylbutynyl)-4-bromobenzaldehyde (3). To a solution of 2,5-bis(3,3-dimethylbutynyl)-1,4-dibromobenzene (2.43 g, 6.135 mmol) in THF (30 mL) cooled to -78 °C under nitrogen was added dropwise n-BuLi (2.48 M, 2.72 mL). The reaction mixture was allowed to stir at -78 °C for 1 h. To this mixture was added DMF (0.48 mL, 6.135 mmol) predried over molecular sieves. The reaction mixture was allowed to stir for another 1 h and then warmed to room temperature for 4 h. It was then diluted with water and extracted with Et2O. The combined organic phases were washed with brine, dried over MgSO4, filtered, and evaporated. Purification by flash chromatography (silica gel, hexanes/CH2Cl21/1) afforded 1.77 g (83% yield) of the title compound as a white solid.

(╯°□°)╯  Yikes!   Maybe I'll just play with dolls.

Here's the original paper, pointed out by Noah Friedman:

• S. H. Chanteau and J. M. Tour, Synthesis of anthropomorphic molecules: the NanoPutians, The Journal of Organic Chemistry 68 (2003), 8750–8766, http://web.pdx.edu/~yanm/Chanteau.pdf.

#spnetwork doi:10.1021/jo0349227 #organic_chemistry___

posted image

2014-07-21 02:45:33 (36 comments, 16 reshares, 107 +1s)

Boron - not boring

Boron is the 5th element in the periodic table, right next to carbon. But we don't hear much about it.  Why not?  Because stars skip boron when building up elements, so it's rather rare! 

It does, however, form interesting molecules, a bit like carbon.  This is borospherene,  a cage of 40 boron atoms.  Earlier this year, a team of Chinese chemists synthesized molecules made of 40 borons and did computer simulations to guess what they'd made.  This is their best guess!

It has a confusing shape.   Each boron atom is connected to 4 or 5 others, and they make 48 triangles, 2 big hexagons - and 4 heptagons, which are on the top, bottom, left and right.

It's a bit like the famous buckyball made of 60 carbons.  But it's much less symmetrical, and it doesn't have any hydrogens hanging off it.  Ithas 8 sym... more »

Boron - not boring

Boron is the 5th element in the periodic table, right next to carbon. But we don't hear much about it.  Why not?  Because stars skip boron when building up elements, so it's rather rare! 

It does, however, form interesting molecules, a bit like carbon.  This is borospherene,  a cage of 40 boron atoms.  Earlier this year, a team of Chinese chemists synthesized molecules made of 40 borons and did computer simulations to guess what they'd made.  This is their best guess!

It has a confusing shape.   Each boron atom is connected to 4 or 5 others, and they make 48 triangles, 2 big hexagons - and 4 heptagons, which are on the top, bottom, left and right.

It's a bit like the famous buckyball made of 60 carbons.  But it's much less symmetrical, and it doesn't have any hydrogens hanging off it.  It has 8 symmetries.   For starters, you can:

1) leave it alone,
2) rotate it 180 degrees around the axis pointing towards you,
3) switch the top and bottom in a certain way, or
4) do first 2) and then 3).

Abstractly this group of symmetries is called the Klein 4-group, because "klein" means "small" in German.

But in fact, as +Layra Idarani pointed out below, there are more symmetries, for a total of 8.

Puzzle 1: spot the joke.

Puzzle 2: explain why it's not just a joke; it's also sort of true.

Puzzle 3: how was most of the boron here on Earth made?

For more on symmetries of objects in 3d space, see:

https://en.wikipedia.org/wiki/Point_groups_in_three_dimensions

The symmetry group of borospherene is called D_{2d}, and you can learn what that means.

Here's the paper, unfortunately not free:

•  Hua-Jin Zhai, Ya-Fan Zhao, Wei-Li Li, Qiang Chen, Hui Bai, Han-Shi Hu, Zachary A. Piazza, Wen-Juan Tian, Hai-Gang Lu, Yan-Bo Wu, Yue-Wen Mu, Guang-Feng Wei, Zhi-Pan Liu, Jun Li, Si-Dian Li & Lai-Sheng Wang, Observation of an all-boron fullerene, Nature Chemistry, http://www.nature.com/nchem/journal/vaop/ncurrent/full/nchem.1999.html.

I thank +Mark Bruce for alerting me to this discovery!

If you ask me if this molecule is useful, I will send a hit man out to kill you.  Someone asks that every time I show you a cool-looking molecule!  But in chemistry you often have to discover things and spend time getting to know them before you can find a use for them.  This discovery is still too new. 

When people first discovered buckyballs they didn't understand their significance, either.  The idea of science is that seeking beauty and understanding is worthwhile for its own sake.  Practical benefits automatically follow.  Not every discovery will have a practical benefit, but enough will to make the whole enterprise worthwhile even if you don't give a damn about beauty and understanding... as long as the experiments are not too expensive.  And chemistry experiments are relatively cheap, unlike huge particle accelerators.

(I put that comment way down here so someone who doesn't read the whole post will say "But is this molecule useful, or just for fun?"  Then the rest of you can say "Read the whole post!")

The picture here, made by 'Materialscientist', is on Wikicommons:

https://en.wikipedia.org/wiki/Borospherene

#spnetwork doi:10.1038/nchem.1999 #chemistry  ___

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2014-07-20 04:24:35 (61 comments, 60 reshares, 136 +1s)

Ten kinds of matter

A cool discovery: substances can be divided into 10 kinds.

The basic idea is pretty simple.  Some substances have time-reversal symmetry: they would look the same, even on the atomic level, if you made a movie of them and ran it backwards.  Some don't - these are more rare, like certain superconductors made of yttrium barium copper oxide!   The substances that do have time reversal symmetry have a symmetry operator T that can square to 1 or to -1: please take my word for this, it's a quantum thing.  So, we get 3 choices, which are listed in the chart under T as 1, -1, or 0 (no time reversal symmetry).

Similarly, some substances have charge conjugation symmetry, meaning a symmetry where we switch particles and holes: places where a particle is missing.  The 'particles' here can be rather abstract things, likeph... more »

Ten kinds of matter

A cool discovery: substances can be divided into 10 kinds.

The basic idea is pretty simple.  Some substances have time-reversal symmetry: they would look the same, even on the atomic level, if you made a movie of them and ran it backwards.  Some don't - these are more rare, like certain superconductors made of yttrium barium copper oxide!   The substances that do have time reversal symmetry have a symmetry operator T that can square to 1 or to -1: please take my word for this, it's a quantum thing.  So, we get 3 choices, which are listed in the chart under T as 1, -1, or 0 (no time reversal symmetry).

Similarly, some substances have charge conjugation symmetry, meaning a symmetry where we switch particles and holes: places where a particle is missing.  The 'particles' here can be rather abstract things, like phonons - little vibrations of sound in a substance, which act like particles - or spinons - little wiggles in the spin of electrons.  Basically any sort of wave can, thanks to quantum mechanics, also act like a particle.  And sometimes we can switch particles and holes, and a substance will act the same way!

The substances that do have charge conjugation symmetry have a symmetry operator C that can square to 1 or to -1.  So again we get 3 choices, listed in the chart under C as 1, -1, or 0 (no charge conjugation symmetry).

So far we have 3 × 3 = 9 kinds of matter.  What is the tenth kind? 

Some kinds of matter don't have time reversal or charge conjugation symmetry, but they're symmetrical under the combination of time reversal and charge conjugation!  You switch particles and holes and run the movie backwards, and things look the same! 

This chart shows a 1 under the S when your matter has this combined symmetry, and 0 when it doesn't.  So, 0 0 1 is the tenth kind of matter (the second row in the chart).

This stuff was first discovered around 1997 by Altland and Zirnbauer.  But it's just the beginning of an amazing story.  Since then people have found substances called topological insulators that act like insulators in their interior but conduct electricity on their surface.   We can make 3-dimensional topological insulators, but also 2-dimensional ones (that is, thin films) and even 1-dimensional ones (wires).  And we can theorize about higher-dimensional ones, though this is mainly a mathematical game.

So we can ask which of the 10 kinds of substance can arise as topological insulators in various dimensions. And the answer is: in any particular dimension, only 5 kinds can show up. This chart shows how it works for dimensions 1 through 8.  The kinds that can't show up are labelled 0. 

(There's more information in this chart, which I'm too lazy to explain now.)

If you look at the chart, you'll see it has some nice patterns.  And it repeats after dimension 8.  In other words, dimension 9 works just like dimension 1, and so on.

There is a huge amount of cool math lurking here, and you can see some more in my blog article:

http://golem.ph.utexas.edu/category/2014/07/the_tenfold_way.html

This math is called the ten-fold way.

The chart here comes from the paper that showed only 5 kinds of topological insulator are possible in each dimension:

• Shinsei Ryu, Andreas P Schnyder, Akira Furusaki, and Andreas W. W. Ludwig,  Topological insulators and superconductors: tenfold way and dimensional hierarchy, New J. Phys. 12 (2010) 065010, http://arxiv.org/abs/0912.2157.

#spnetwork arXiv:0912.2157 #must_read #condensed_matter #topology___

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2014-07-19 00:36:02 (26 comments, 60 reshares, 177 +1s)

This double pendulum is chaotic.  But you can make a machine with pendulums that traces out beautiful orderly curves!  It's called a harmonograph.  My artist friend Anita Chowdry built one, and you can see it here:

http://johncarlosbaez.wordpress.com/2014/07/18/the-harmonograph/

It's an old-fashioned apparatus made of brass and steel - and the story of how Chowdry built it is part of the fun.  She writes:

Today, saturated as we are with the ephemeral intangibility of virtual objects and digital functions, there is a resurgence of interest in the ingenious mechanical contraptions of pre-digital eras, and in the processes of handcraftsmanship and engagement with materials. The solid corporality of analogue machines, the perceivable workings of their kinetic energy, and their direct invitation to experience their science through hands-on interaction bringsus ... more »

This double pendulum is chaotic.  But you can make a machine with pendulums that traces out beautiful orderly curves!  It's called a harmonograph.  My artist friend Anita Chowdry built one, and you can see it here:

http://johncarlosbaez.wordpress.com/2014/07/18/the-harmonograph/

It's an old-fashioned apparatus made of brass and steel - and the story of how Chowdry built it is part of the fun.  She writes:

Today, saturated as we are with the ephemeral intangibility of virtual objects and digital functions, there is a resurgence of interest in the ingenious mechanical contraptions of pre-digital eras, and in the processes of handcraftsmanship and engagement with materials. The solid corporality of analogue machines, the perceivable workings of their kinetic energy, and their direct invitation to experience their science through hands-on interaction brings us back in touch with our humanity.

This is part of what motivates the 'steampunk' movement... so you can think of Anita Chowdry's work as high-end steampunk.

The harmonograph is now on display at the Oxford Museum of the History of Science - and she's giving free public talks about it at 3 pm today on Saturday July 19th, and also Saturday August 16th and Saturday September 20th!

#art___

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2014-07-18 01:07:23 (35 comments, 5 reshares, 48 +1s)

Sailing in outer space, pushed by the sun.   It's been a dream for many years.  What could be more elegant?  LightSail-1 will try it in April 2016.  Watch the movie - it will make you happy!

I want there to be living things in space, like huge moths with mirrored wings, slowly sailing from star to star, powered by light.  If they don't exist, we could make them.... someday.

But we're starting small.  LightSail-1 is a privately funded project run by the Planetary Society.  It starts as a little box, shot into space by an ordinary rocket.  Tucked inside are four ultra-thin mirrored sails.  When the box is in orbit, these unfold!  They'll expand to 32 square meters, so they should be easy to see by naked eye from Earth. 

I hope it works!  Getting into space is not easy.  In 2005, the Planetary Society attempted to send its first solar sail,Cosmos 1, in... more »

Sailing in outer space, pushed by the sun.   It's been a dream for many years.  What could be more elegant?  LightSail-1 will try it in April 2016.  Watch the movie - it will make you happy!

I want there to be living things in space, like huge moths with mirrored wings, slowly sailing from star to star, powered by light.  If they don't exist, we could make them.... someday.

But we're starting small.  LightSail-1 is a privately funded project run by the Planetary Society.  It starts as a little box, shot into space by an ordinary rocket.  Tucked inside are four ultra-thin mirrored sails.  When the box is in orbit, these unfold!  They'll expand to 32 square meters, so they should be easy to see by naked eye from Earth. 

I hope it works!  Getting into space is not easy.  In 2005, the Planetary Society attempted to send its first solar sail, Cosmos 1, into orbit, but the Russian launch vehicle failed to reach orbit.  NASA had their own project, called NanoSail-D.  The first time they tried it, the rocket failed and it crashed into the Pacific.  NASA succeeded in 2011 with NanoSail-D2, which had a light sail 10 square meters in area.  It stayed aloft for 240 days before re-entering the Earth's atmosphere and crashing - as expected.

LightSail-1 is a somewhat more ambitious test.  If it succeeds, then comes LightSail-2, and LightSail-3.   The last should go to the Lagrange point L1, between the Earth and Sun.

The Japanese are further along!  They built a light sail called IKAROS.  It sailed to Venus in 2010, and it's still working!  So far it has gained a total of 400 meters/second of velocity from its solar sail.  This is a technology that requires patience.

For more on solar sails, try:

https://en.wikipedia.org/wiki/Solar_sail
https://en.wikipedia.org/wiki/NanoSail-D
https://en.wikipedia.org/wiki/NanoSail-D2

You can see some technical specs for LightSail-1 here:

http://cubesat.calpoly.edu/images/cubesat/presentations/DevelopersWorkshop2010/1600_lightsail-mattnehrenz-cubesat_conference.pdf

Puzzle:  On page 6 here it seems to say the sails are big enough to accelerate the craft by 0.06 meters per second per second.  But +Nick Parker argues that's impossible - way too much - and I agree.    So what is the acceleration for this craft really?___

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2014-07-17 00:34:34 (33 comments, 94 reshares, 388 +1s)

If you water it, it will grow

This is a mural by Natalia Rak in Białystok, Poland. It reminds me of Alice in Wonderland, and the great Jefferson Airplane song "White Rabbit" with its line

     Ask Alice... when she's ten feet tall.

And that reminds me of this magnificent version of the same song:

Mayssa Karaa - White Rabbit

If you love the original you must listen to this!!!  I can't give away what's so great about it: that would spoil the surprise.  Grace Slick's vocals are so powerful on the original I had thought no other version could be enjoyable, but I was wrong.  As with the mural, good art wants a good idea. 

Here is Natalia Rak's page:

https://www.facebook.com/ArtNataliaRak

I think this piece is more inspired than most of hers.  Having the girl stand ontip-toes ... more »

If you water it, it will grow

This is a mural by Natalia Rak in Białystok, Poland. It reminds me of Alice in Wonderland, and the great Jefferson Airplane song "White Rabbit" with its line

     Ask Alice... when she's ten feet tall.

And that reminds me of this magnificent version of the same song:

Mayssa Karaa - White Rabbit

If you love the original you must listen to this!!!  I can't give away what's so great about it: that would spoil the surprise.  Grace Slick's vocals are so powerful on the original I had thought no other version could be enjoyable, but I was wrong.  As with the mural, good art wants a good idea. 

Here is Natalia Rak's page:

https://www.facebook.com/ArtNataliaRak

I think this piece is more inspired than most of hers.  Having the girl stand on tip-toes is a great idea, since that's all about being barely tall enough.___

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2014-07-13 03:17:24 (17 comments, 16 reshares, 105 +1s)

A rotaxane is a 2-part molecule where one part is a ring that can rotate around the other part... but can't slip off!  

People are starting to make molecular machines with rotaxanes.  That's really cool, but let's talk about something simpler.  How do you make  a rotaxane? 

The first one was made in 1967 by two chemists named Harrison.   They used a simple but clever trick.   Say you have a bunch of molecules that react and stick together in pairs to form a bigger dumbbell-shaped molecule.  Say you let them do this when mixed with copies of some other ring-shaped molecule.  Then a few of them will connect through the ring, forming a rotaxane!

By now there are better tricks:

1) Capping: you let a rod-shaped molecule fit through a ring, and then cap it off with balls that keep the ring from sliding off.

2)Clippi... more »

A rotaxane is a 2-part molecule where one part is a ring that can rotate around the other part... but can't slip off!  

People are starting to make molecular machines with rotaxanes.  That's really cool, but let's talk about something simpler.  How do you make  a rotaxane? 

The first one was made in 1967 by two chemists named Harrison.   They used a simple but clever trick.   Say you have a bunch of molecules that react and stick together in pairs to form a bigger dumbbell-shaped molecule.  Say you let them do this when mixed with copies of some other ring-shaped molecule.  Then a few of them will connect through the ring, forming a rotaxane!

By now there are better tricks:

1) Capping: you let a rod-shaped molecule fit through a ring, and then cap it off with balls that keep the ring from sliding off.

2) Clipping: you let a short C-shaped molecule fit around the middle of a dumbbell, and then get it to close off and form a ring.

3) Slipping: sometimes at high temperatures a ring can stretch and fit around the end of a dumbbell... but at low temperatures it can't slip off.

The picture shows a rotaxane made in 1998.  The paper describing this is not open-access, and I'm too lazy to get ahold of it and find out what trick they used.  The picture was made by James Fraser Stoddart, who was kind enough to put it on Wikicommons.  You can see it here:

https://en.wikipedia.org/wiki/Rotaxane

This article also explains molecular machines made using rotaxanes!___

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2014-07-11 16:16:52 (53 comments, 18 reshares, 148 +1s)

Dumb Romans

Caligula was just insane, I think.  Here's something really dumb.

Compared to the Egyptians and Babylonians, the Romans were traditionally never great at calendars.  The early Roman calendar had 355 days a year...so they'd put in a whole extra month now and then, making the year 377 or 378 days long. 

At first it stayed roughly in line with the seasons.  But the people who ran the calendar were politicians, so if they wanted to make their enemies' terms of office end quicker, they'd refuse to stick in the extra month! 

Eventually things got way out of whack.  The politicians would only announce these extra months at the last minute, and it got really confusing.

So, Julius Caesar called together all his wise men to invent a better calendar.  And they invented a pretty good one, with 365 days a year, and an extraleap d... more »

Dumb Romans

Caligula was just insane, I think.  Here's something really dumb.

Compared to the Egyptians and Babylonians, the Romans were traditionally never great at calendars.  The early Roman calendar had 355 days a year...so they'd put in a whole extra month now and then, making the year 377 or 378 days long. 

At first it stayed roughly in line with the seasons.  But the people who ran the calendar were politicians, so if they wanted to make their enemies' terms of office end quicker, they'd refuse to stick in the extra month! 

Eventually things got way out of whack.  The politicians would only announce these extra months at the last minute, and it got really confusing.

So, Julius Caesar called together all his wise men to invent a better calendar.  And they invented a pretty good one, with 365 days a year, and an extra leap day every four years. 

But when they implemented it, the politicians in charge put in a leap year every three years.  According to a dude named Macrobius, this is because they thought "every four years" meant:

1         2       3       4
Leap  Not   Not   Leap

Dumb.

After 36 years, the emperor Augustus fixed this, and skipped some leap years to bring things back into synch.

Of course, he also got August.

https://en.wikipedia.org/wiki/Julian_calendar#Leap_year_error___

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2014-07-11 04:23:18 (18 comments, 15 reshares, 69 +1s)

El Niño coming?

See how the eastern Pacific has gotten much hotter since May?  That could be the start of an El Niño. 

My friends and I at the Azimuth Code Project are starting to work on El Niño prediction.  Now you can get free software to study a method that uses 'climate networks'.  I'll give you hints on how to modify it and make new discoveries of your own.  If you do, please tell us what you find! 

Here's how to get started:

http://johncarlosbaez.wordpress.com/2014/07/08/el-nino-project-part-4/

This explains how to download climate data and programs to analyze it.   First you go to a website (or ftp site) and get ahold of the Earth's surface air temperatures since 1950.  Then you run a program to get just the temperatures in the Pacific.  Then you run another to see how much temperatures near theequator are ... more »

El Niño coming?

See how the eastern Pacific has gotten much hotter since May?  That could be the start of an El Niño. 

My friends and I at the Azimuth Code Project are starting to work on El Niño prediction.  Now you can get free software to study a method that uses 'climate networks'.  I'll give you hints on how to modify it and make new discoveries of your own.  If you do, please tell us what you find! 

Here's how to get started:

http://johncarlosbaez.wordpress.com/2014/07/08/el-nino-project-part-4/

This explains how to download climate data and programs to analyze it.   First you go to a website (or ftp site) and get ahold of the Earth's surface air temperatures since 1950.  Then you run a program to get just the temperatures in the Pacific.  Then you run another to see how much temperatures near the equator are correlated to those in the rest of the Pacific.  The theory is that when they become strongly correlated, an El Niño is brewing!

The next blog article will about how a complete beginner - me - managed to actually do this stuff.  I didn't write the programs; Graham Jones did that.  But I managed to download the data and run and modify his programs.  I've always avoided programming.  But now I'm actually doing it - so you can too!  Maybe a lot better.___

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2014-07-09 00:45:24 (32 comments, 12 reshares, 111 +1s)

It seems a lot of ultra-high-energy cosmic rays are coming from a patch of the sky near the Big Dipper!  

Cosmic rays are high-energy particles, mainly protons and atomic nuclei, which come from outer space and hit the Earth's atmosphere.  When one hits, it produces a big shower of other particles.  Most cosmic rays are believed to have picked up their energy by interacting with shock waves in the interstellar medium.  But the most energetic ones remain mysterious — nobody knows how they could have acquired such high energies.

The record is a 1994 event seen by a detector in Utah called the Fly's Eye - because that's what it looks like.   It saw a shower of particles produced by a cosmic ray with an energy of about 300 times 10¹⁸ electron volts.   That's an insane amount of energy.  It's about 50 joules: the energy of a one-kilogram mass movingat 10 meters/... more »

It seems a lot of ultra-high-energy cosmic rays are coming from a patch of the sky near the Big Dipper!  

Cosmic rays are high-energy particles, mainly protons and atomic nuclei, which come from outer space and hit the Earth's atmosphere.  When one hits, it produces a big shower of other particles.  Most cosmic rays are believed to have picked up their energy by interacting with shock waves in the interstellar medium.  But the most energetic ones remain mysterious — nobody knows how they could have acquired such high energies.

The record is a 1994 event seen by a detector in Utah called the Fly's Eye - because that's what it looks like.   It saw a shower of particles produced by a cosmic ray with an energy of about 300 times 10¹⁸ electron volts.   That's an insane amount of energy.  It's about 50 joules: the energy of a one-kilogram mass moving at 10 meters/second, all packed into one particle!  

To put it another way: the Large Hadron Collider, our best particle accelerator, speeds up protons to an energy of 7 trillion electron volts.  The cosmic ray seen by the Fly's Eye had an energy of 300,000,000 trillion electron volts.  We're not doing so well compared to nature.  But we don't know how nature does it.

Anyway, now we've got a detector much better than the Fly's Eye: the Telescope Array.  It's also in Utah, because the air is clear and the nights are dark.  It's a jaw-dropping 760 square kilometers in size, because land is cheap.  It consists of about 500 scintillation detectors in a square grid, each 1.2 kilometers away from the next.  Each one is a solar-powered gadget containing plastic that lights up when a shower of particles hits it.  There are also three telescopes that watch the air light up.

So, we can tell where the ultra-high energy cosmic rays are coming from! 

Chart (a) shows where.  Each dot is a cosmic ray with energy more than 57 quintillion eV.  Well, the dot labelled GC is the galactic center, and the dot labelled anti-GC is the 'anti-galactic center': the direction in the sky pointing exactly away from the center of the Milky Way.  GP is the plane of the galaxy, and there's some other stuff. 

But the point is: the dots are clustered in a patch of the northern sky.

The colors in chart (b) show how many of these cosmic rays there are in a 20-degree circle around each point.  This makes it easier to see where they're coming from.  Their paths get bent by magnetic fields, so even if they all originate in one location they'd get smeared out.

What's making them?  We don't know!   That's the cool part: it's still a big mystery.  Here's what the astronomers say:

Assuming the hotspot is real, two possible interpretations are: it may be associated with the closest galaxy groups and/or the galaxy filament connecting us with the Virgo cluster; or if cosmic rays are heavy nuclei they may originate close to the supergalactic plane, and be deflected by extragalactic magnetic fields and the galactic halo field.

What the heck is the supergalactic plane?   It's the curve in chart (a) lablled SGP.  It's major structure in the local universe: nearby galaxy clusters like the Virgo cluster,  the Pisces-Perseus supercluster and the Great Attractor lie roughly in a plane!

Someday we'll figuring out what's really happening.  The paper is here:

• The Telescope Array Collaboration: R.U. Abbasi, M. Abe, T.Abu-Zayyad, M. Allen, R. Anderson, R. Azuma, E. Barcikowski, J.W. Belz, D.R. Bergman, S.A. Blake, R. Cady, M.J. Chae, B.G. Cheon, J. Chiba, M. Chikawa, W.R. Cho, T. Fujii, M. Fukushima, T. Goto, W. Hanlon, Y. Hayashi, N. Hayashida, K. Hibino, K. Honda, D. Ikeda, N. Inoue, T. Ishii, R. Ishimori, H. Ito, D. Ivanov, C.C.H. Jui, K. Kadota, F. Kakimoto, O. Kalashev, K. Kasahara, H. Kawai, S. Kawakami, S. Kawana, K. Kawata, E. Kido, H.B. Kim, J.H. Kim, J.H. Kim, S. Kitamura, Y. Kitamura, V. Kuzmin, Y.J. Kwon, J. Lan, S.I. Lim, J.P. Lundquist, K. Machida, K. Martens, T. Matsuda, T. Matsuyama, J.N. Matthews, M. Minamino, K. Mukai, I. Myers, K. Nagasawa, S. Nagataki, T. Nakamura, T. Nonaka, A. Nozato, S. Ogio, J. Ogura, M. Ohnishi, H. Ohoka, and 59 more authors, Indications of intermediate-scale anisotropy of cosmic rays with energy greater than 57 EeV in the northern sky measured with the surface detector of the Telescope Array experiment, http://arxiv.org/abs/1404.5890.___

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2014-07-08 04:50:35 (5 comments, 6 reshares, 34 +1s)

Now you can apply to attend a workshop on Entropy and Information in Biological Systems.  This is going to be fun!

I'm running it with John Harte at Berkeley, who uses maximum entropy methods to study ecosystems, and +Marc Harper at UCLA, who uses information theory to study evolutionary games.  It's happening on April 8-10, 2015 at the National Institute for Mathematical and Biological Synthesis in Knoxville Tennesee.  There will be financial support for workshop attendees who need it.  We will choose among the best applicants and invite 10-15 of them. 

To apply, go here:

http://www.nimbios.org/workshops/WS_entropy

The idea

Information theory and entropy methods are becoming powerful tools in biology, from the level of individual cells, to whole ecosystems, to experimental design, model-building, and the measurement ofbiod... more »

Now you can apply to attend a workshop on Entropy and Information in Biological Systems.  This is going to be fun!

I'm running it with John Harte at Berkeley, who uses maximum entropy methods to study ecosystems, and +Marc Harper at UCLA, who uses information theory to study evolutionary games.  It's happening on April 8-10, 2015 at the National Institute for Mathematical and Biological Synthesis in Knoxville Tennesee.  There will be financial support for workshop attendees who need it.  We will choose among the best applicants and invite 10-15 of them. 

To apply, go here:

http://www.nimbios.org/workshops/WS_entropy

The idea

Information theory and entropy methods are becoming powerful tools in biology, from the level of individual cells, to whole ecosystems, to experimental design, model-building, and the measurement of biodiversity. The aim of this investigative workshop is to synthesize different ways of applying these concepts to help systematize and unify work in biological systems.  Early attempts at “grand syntheses” often misfired, but applications of information theory and entropy to specific highly focused topics in biology have been increasingly successful.  In ecology, entropy maximization methods have proven successful in predicting the distribution and abundance of species.  Entropy is also widely used as a measure of biodiversity.  Work on the role of information in game theory has shed new light on evolution. As a population evolves, it can be seen as gaining information about its environment.  The principle of maximum entropy production has emerged as a fascinating yet controversial approach to predicting the behavior of biological systems, from individual organisms to whole ecosystems.  This investigative workshop will bring together top researchers from these diverse fields to share insights and methods and address some long-standing conceptual problems.

Our goals

• To study the validity of the principle of Maximum Entropy Production (MEP), which states that biological systems – and indeed all open, non-equilibrium systems – act to produce entropy at the maximum rate.

• To familiarize all the participants with applications to ecology of the MaxEnt method: choosing the probabilistic hypothesis with the highest entropy subject to the constraints of our data. We will compare MaxEnt with competing approaches and examine whether MaxEnt provides a sufficient justification for the principle of MEP.

• To clarify relations between known characterizations of entropy, the use of entropy as a measure of biodiversity, and the use of MaxEnt methods in ecology.

• To develop the concept of evolutionary games as “learning” processes in which information is gained over time.

• To study the interplay between information theory and the thermodynamics of individual cells and organelles.

For more details including a list of invited speakers, go here:

http://johncarlosbaez.wordpress.com/2013/11/02/entropy-and-information-in-biological-systems/___

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2014-07-07 12:15:18 (48 comments, 43 reshares, 121 +1s)

What if famous paintings were photoshopped like models today?

Lauren Wade writes: Whether it’s tucking tummies, contouring jaw lines, enlarging eyes and lips, brushing out cellulite, or full-out head swapping, I’ve seen it all as a photo editor. While the conversation about the media’s portrayal and obsession with an unrealistic and unattainable beauty standard is not a new one, I think it’s crazy how much retouching people don’t notice. Over the last five years, having done many of the quick, subtle fixes that are the industry standard myself, I know that even an image considered to look “natural” is anything but.

So, she changed a bunch of famous paintings.  This is Titian's Danaë With Eros.  You can see the rest here:

http://www.takepart.com/feature/2014/05/15/famous-paintings-photoshopped-to-look-like-fashion-models

What if famous paintings were photoshopped like models today?

Lauren Wade writes: Whether it’s tucking tummies, contouring jaw lines, enlarging eyes and lips, brushing out cellulite, or full-out head swapping, I’ve seen it all as a photo editor. While the conversation about the media’s portrayal and obsession with an unrealistic and unattainable beauty standard is not a new one, I think it’s crazy how much retouching people don’t notice. Over the last five years, having done many of the quick, subtle fixes that are the industry standard myself, I know that even an image considered to look “natural” is anything but.

So, she changed a bunch of famous paintings.  This is Titian's Danaë With Eros.  You can see the rest here:

http://www.takepart.com/feature/2014/05/15/famous-paintings-photoshopped-to-look-like-fashion-models___

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2014-07-06 02:29:38 (73 comments, 199 reshares, 571 +1s)

Warp cube

The N-Light Membrane is a cube of mirrors with fluorescent lights as edges.  3 mirrors are one-way, so you can see inside.   All you can see is reflections of the inside of the cube, extending to infinity!   

The other 3 mirrors are flexible, and the cube is connected to an air tank.  By inflating or deflating the air tank, you can make the cube convex or concave.  The reflections bend in weird ways. The effect is hypnotic.

This cube was created by an art collective called Numen/For Use, and it was displayed in St. Petersburg.   It's fun to watch videos of it shot from different angles:

http://www.numen.eu/installations/n-light/membrane/

What if you did a tetrahedron or octahedron?  There's no need to imagine; you can see them here:

http://www.numen.eu/installations/n-light/objects/
Numen/F... more »

Warp cube

The N-Light Membrane is a cube of mirrors with fluorescent lights as edges.  3 mirrors are one-way, so you can see inside.   All you can see is reflections of the inside of the cube, extending to infinity!   

The other 3 mirrors are flexible, and the cube is connected to an air tank.  By inflating or deflating the air tank, you can make the cube convex or concave.  The reflections bend in weird ways. The effect is hypnotic.

This cube was created by an art collective called Numen/For Use, and it was displayed in St. Petersburg.   It's fun to watch videos of it shot from different angles:

http://www.numen.eu/installations/n-light/membrane/

What if you did a tetrahedron or octahedron?  There's no need to imagine; you can see them here:

http://www.numen.eu/installations/n-light/objects/

Numen/For Use is really three Croatian and Austrian guys, Sven Jonke, Christoph Katzler and Nikola Radeljković. 

Puzzle 1: can you make a mirrored box with warped sides so the reflections make it look like you're in hyperbolic space?  You may have seen the 'hyperbolic honeycombs' in my #geometry series - that's the sort of thing I mean.

Puzzle 2: more generally, what cool effects could you get from a mirrored box? 

If we're in an ellipsoidal mirrored box and we each put one of our eyes at one of the foci of the box, all you should see is the pupil of my eye, and vice versa.

#geometry  ___

posted image

2014-07-05 08:31:48 (21 comments, 26 reshares, 124 +1s)

Water world

Here is weather simulated on an aqua planet: a world like our Earth, but with only ocean!  With no land, the weather becomes simpler.  Here's what happens when you add land:

http://tinyurl.com/NICAM-with-land

The aqua planet simulation was done in 2004, in Japan.   The planet's surface was divided into an icosahedron!   Then each triangle was chopped into smaller triangles with sides 3.5 kilometers long.  These are just barely small enough to simulate clouds, but nobody had simulated the whole planet's atmosphere in such a fine-grained way before.  It required a supercomputer.

By the way, simulating weather is different than simulating climate. When people try to predict the climate 50 years from now, they don't do it by simulating each day's weather for the next 50 years.

This weather simulationproje... more »

Water world

Here is weather simulated on an aqua planet: a world like our Earth, but with only ocean!  With no land, the weather becomes simpler.  Here's what happens when you add land:

http://tinyurl.com/NICAM-with-land

The aqua planet simulation was done in 2004, in Japan.   The planet's surface was divided into an icosahedron!   Then each triangle was chopped into smaller triangles with sides 3.5 kilometers long.  These are just barely small enough to simulate clouds, but nobody had simulated the whole planet's atmosphere in such a fine-grained way before.  It required a supercomputer.

By the way, simulating weather is different than simulating climate. When people try to predict the climate 50 years from now, they don't do it by simulating each day's weather for the next 50 years.

This weather simulation project was called NICAM, the Nonhydrostatic ICosahedral Atmospheric Model.  Later, in 2008, they added land.  You can see how much more interesting it gets!  

I imagine people can do much better now, but I'm not an expert in this subject.  For example, I don't know why the aqua planet doesn't have cyclones!  Is this just a deficiency of the model... or would a world without land really not have cyclones?

You can read more about NICAM here:

http://www.nicam.jp/hiki/?About+NICAM

and the details of the aqua planet are here:

• H. Tomita et al, A global cloud-resolving simulation: Preliminary results from an aqua planet experiment, Geophysical Research Letters 32 (2005), http://onlinelibrary.wiley.com/doi/10.1029/2005GL022459/full.

The paper is free!

The NICAM project is still underway.  They're very interested in the Madden-Julian oscillation, the largest form of variability in the tropical atmosphere on time scales of 30-90 days. It’s a pulse that moves east across the Indian Ocean and Pacific Ocean at 4-8 meters/second.  It gives patches of anomalously high rainfall... and also patches of anomalously low rainfall.

I want to learn more about the Madden-Julian oscillation, since strong Madden-Julian oscillations often hint that 6-12 months later there will be an El Niño.

#El_Niño___

posted image

2014-07-04 02:56:43 (37 comments, 32 reshares, 115 +1s)

Open-access climate science

A recent paper says there's 75% chance of a major climate event called an El Niño by the end of 2014  This would be huge news!  So my friends and I decided to replicate this paper, criticize it, and improve it.

The paper uses a climate network, shown here.  See the little circles?   Every day, scientists measure air temperatures at each of these points.  The red ones are in the El Niño basin.   The paper calculates how temperatures in the El Niño basin are correlated to temperatures at the other points.  When the average correlation gets high enough, they predict an El Niño.

That's a very  rough summary of what the paper does!  I explain exactly what it does here:

http://johncarlosbaez.wordpress.com/2014/07/01/el-nino-project-part-3/

including how they got their data.
+Graha... more »

Open-access climate science

A recent paper says there's 75% chance of a major climate event called an El Niño by the end of 2014  This would be huge news!  So my friends and I decided to replicate this paper, criticize it, and improve it.

The paper uses a climate network, shown here.  See the little circles?   Every day, scientists measure air temperatures at each of these points.  The red ones are in the El Niño basin.   The paper calculates how temperatures in the El Niño basin are correlated to temperatures at the other points.  When the average correlation gets high enough, they predict an El Niño.

That's a very  rough summary of what the paper does!  I explain exactly what it does here:

http://johncarlosbaez.wordpress.com/2014/07/01/el-nino-project-part-3/

including how they got their data.

+Graham Jones downloaded this data and wrote software that does what they do in the paper.  (At least we think so: +Nadja Kutz found a mathematical glitch, where the authors may not have said what they really meant.  Read my article for that.)  Graham's software is on GitHub, and we'll explain it soon.  

This is an experiment in open science.  Not just the final results but the software, the data, the whole process is in public view.  You can read all our discussions here:

http://azimuth.mathforge.org

One of our next steps will be to simplify the method used in this paper.  It's more complicated than it needs to be; Graham has already found one way to make it simpler while keeping its predictive ability just about as good.

What about after that?   Three more programmers have just joined the team - the Azimuth Code Project - but in the next couple of weeks I think we need some strategy sessions.  Personally I want to get a better feel for El Niños.  I want to read more papers, but also I'd love to watch lots of movies of Pacific air temperatures, ocean temperatures, and so on.  Some of these movies exist, but we may want to create more.  It would also be great to write software illustrating simplified models of El Niño, and one of the team wants to do that. 

We are seriously short of actual experts on climate science, but I'm afraid that's inevitable until we publish some papers: the experts are busy doing their own work, and so far there's no big reason for them to take us seriously.  And that's okay, for now: we're on a learning curve.

Puzzle: what is the pink rectangle?

Oh, and by the way: I keep talking about "a paper".   Here it is:

• Josef Ludescher, Avi Gozolchiani, Mikhail I. Bogachev, Armin Bunde, Shlomo Havlin, and Hans Joachim Schellnhuber, Very early warning of next El Niño, PNAS, February 2014, http://www.climatelinc.eu/fileadmin/UG_ADVANCED/Publications/BIU_-_Avi__Halvin__et_al-Very_early_warning_of_next_El_Nino.pdf.

#El_Niño___

posted image

2014-07-03 03:52:05 (48 comments, 22 reshares, 76 +1s)

Puzzle 1: Suppose you have 10 white balls and 10 black balls.  You can distribute them any way between two urns, as long as you put at least one ball in each urn.   Your friend selects an urn at random and randomly selects a ball from that urn.  How can you maximize the chance that your friend picks a white ball?  

This is from Paul Nahin's new book Will You Be Alive 10 Years From Now?   It's a great introduction to probability based on puzzles and history.   I like it because it's fun at many levels.   You need to know some probability theory to follow it.   But it should be okay for beginners - it uses some calculus near the end - and it was also fun for me.  

The use of history is key here.  Some books use 'human interest stories' as a way to placate the reader who is getting bored with the science.  For example, while talking aboutSchrödinger'... more »

Puzzle 1: Suppose you have 10 white balls and 10 black balls.  You can distribute them any way between two urns, as long as you put at least one ball in each urn.   Your friend selects an urn at random and randomly selects a ball from that urn.  How can you maximize the chance that your friend picks a white ball?  

This is from Paul Nahin's new book Will You Be Alive 10 Years From Now?   It's a great introduction to probability based on puzzles and history.   I like it because it's fun at many levels.   You need to know some probability theory to follow it.   But it should be okay for beginners - it uses some calculus near the end - and it was also fun for me.  

The use of history is key here.  Some books use 'human interest stories' as a way to placate the reader who is getting bored with the science.  For example, while talking about Schrödinger's equation, they might digress and tell us how the married Erwin Schrödinger invented his equation during a two-and-a-half-week romantic getaway with a mysterious girlfriend in the Swiss Alps.   But this book uses stories to propel the explanations forward.

For example: I know how to calculate odds of dice doing different things, so that part would be boring for me... except that I didn't know Samuel Pepys, the Brit with the famous diary, had sent Isaac Newton a letter asking him to calculate some odds for gambling purposes!  Nor did I know the mistake Newton made in his reply. 

Now, back to the puzzle.  If you put all 10 white balls in one urn and all 10 black balls in the other, your friend has a 50% chance of picking a white ball.  If you mix them evenly, your friend still has a 50% chance of picking a white ball.   So: can you do better?  And if  so, how much better can you do?

Once you've solved that, try this:

Puzzle 2: Repeat the game with N white balls and N black balls.  What's the biggest you can get for the probability your friend picks a white ball, in the limit N → ∞?

#probability  ___

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