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Artur Popławski has been at 1 events

HostFollowersTitleDateGuestsLinks
NASA1,687,975Join us for a live Google+ Hangout on observing the Earth while in orbit and the importance of Earth science observations from space. The astronauts living aboard the International Space Station get a unique view of planet Earth. In a single 90-minute orbit, they can see weather systems like hurricanes, man-made developments like cities and geological phenomena like volcanoes. Of all the planets NASA has explored, none yet have matched the dynamic complexity of our own Earth. Luckily for us here on the ground, astronauts like Rick Mastracchio and Koichi Wakata have documented and shared their views from the orbiting laboratory 250 miles above the Earth. Both Mastracchio and Wakata tweeted during their 188 days in orbit, sharing photos of auroras, islands, lakes, bridges, glaciers, cities, deserts, mountains, clouds, and more. Photos like theirs give us a new perspective on our planet. A fleet of NASA satellites also monitor the Earth’s vital signs every day. One example is the joint US-Japan Global Precipitation Measurement (GPM) mission, which launched while Mastracchio and Wakata were living on ISS. The astronauts briefed President Obama on GPM in April, describing it as “a groundbreaking satellite that is changing how we measure rain and snowfall from space.”Mastracchio and Wakata will be joined by Eric Holthaus, a meteorologist who writes about weather and climate for Slate’s Future Tense blog, and Gail Skofronick Jackson, a GPM scientist at NASA’s Goddard Space Flight Center. You may submit questions on Twitter and Google+ in advance and during the Hangout using the hashtag #askNASA .Observing Earth from Space2014-09-17 20:30:001675 

Artur Popławski has been shared in 121 public circles

You can see here the 50 latest shared circles.
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AuthorFollowersDateUsers in CircleCommentsReshares+1Links
Richard Green81,215Engagers Showcase Circle, September 14, 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. I skipped over one post because it received too much engagement, but I'm including a link to it for completeness.Everyone mentioned below is also included in the circle.Do nuclear physicists have half life crises?https://plus.google.com/101584889282878921052/posts/ayw6WPGGaFESt Peter's Church, Heyshamhttps://plus.google.com/101584889282878921052/posts/9DEtmbdz15zSmiling cow?https://plus.google.com/101584889282878921052/posts/9NuqPpsgtBkThe look-and-say sequence and Conway's Cosmological Theoremhttps://plus.google.com/101584889282878921052/posts/jEQ7zxFpJt4Cordyline australis, the “cabbage tree”https://plus.google.com/101584889282878921052/posts/hktDAgyo6mA“Maurits, stop picking at it. You'll only make it worse.” by David Swarthttps://plus.google.com/101584889282878921052/posts/gj327Ywh33T“Phyllotactic Portrait of Fibonacci” by Robert Boschhttps://plus.google.com/101584889282878921052/posts/8LykdvHpRvPFountain in Williamson Parkhttps://plus.google.com/101584889282878921052/posts/HzZTLQaQ9RT“Youth” by Silvia Cordeddahttps://plus.google.com/101584889282878921052/posts/T2Lo3c2zLxvThe arithmetic derivative, the Goldbach conjecture, and the twin prime conjecturehttps://plus.google.com/101584889282878921052/posts/9nY35Ma1pbUGlobe Thistlehttps://plus.google.com/101584889282878921052/posts/i8mtiyVikWhTallinn (reshared from +Paul Harper)https://plus.google.com/101584889282878921052/posts/U4DAQxK5fkxCubes passing in the night (reshared from +Sean Walker)https://plus.google.com/101584889282878921052/posts/32JKvAFqP9SThe graph of arctanhttps://plus.google.com/101584889282878921052/posts/FLvyDupud1z“Hopf Knott” by Peter Sittner2014-09-14 15:25:57463224129234
Becky Collins15,950Dance Related 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 ?2014-09-02 05:00:4347130935
Kukuh Malindo2322014-08-02 10:20:4450015218
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 15:49:10477151421
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 05:31:36476209123224
Greg Strandberg942Sci-Fi and Fantasy Readers CircleWant to connect with #fantasyauthor  and #scifiauthor  ?This #circleshare  has those folks and chances are you'll get some interesting things in your feed. #circlesharing   #googleshare   #circleoftheday   #sharedcircles   #fantasywriters   #sciencefictionfantasy   #scifi  2014-07-10 23:13:52173000
Doug Hyatt3,234MANY NEW PEOPLE #2 THAT WILL PLUS 1 and RESHARESimply ADD yourself to this circle, copy the #HASHTAGS, and REPOST#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   #circleoftheday   #circledaily   #nicecircle   2014-06-29 10:59:0549119415
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 05:53:52479001
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 05:07:06489214128231
Bakerson, LLC287This Circle is Amazing! If you want more likes, shares, and +1's, you will want to join and add this circle! To be added to this circle of Super Engagers simply +1, reshare, and comment!! You will be added to the next go around soon. Boost your social status quickly!2014-05-01 15:52:48479121014
Krzysztof Skomra5,314*PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the who said thanks to my last circle#sharedcircle #publiccircleshare   #circleshare   #circleoftheday #circleshares   #circlesharing   #circlesshare   #publicsharedcircle #publicsharedcircles   #sharedcircleoftheday #sharedcircleoftheweek #sharedcircles   #sharedpubliccircle #todayspublicsharedcircle #todayssharedcircle   #publiccircle #circle   #circles   #awesome #awesomeness #awesomepeople #shareyourcircle   #bestengagers #followers   #followback #paulaawesomecircle   #awesomecircles #paulateshima #topsharedcircle #topsharedcircle   #myseoissocial #besocial   #socializethesocial   #trust #circles #shar2014-04-19 06:31:05377139
Krzysztof Skomra5,314*PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the who said thanks to my last circle#sharedcircle #publiccircleshare   #circleshare   #circleoftheday #circleshares   #circlesharing   #circlesshare   #publicsharedcircle #publicsharedcircles   #sharedcircleoftheday #sharedcircleoftheweek #sharedcircles   #sharedpubliccircle #todayspublicsharedcircle #todayssharedcircle   #publiccircle #circle   #circles   #awesome #awesomeness #awesomepeople #shareyourcircle   #bestengagers #followers   #followback #paulaawesomecircle   #awesomecircles #paulateshima #topsharedcircle #topsharedcircle   #myseoissocial #besocial   #socializethesocial   #trust #circles #shar2014-04-19 06:30:35377116
Krzysztof Skomra5,314*PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the who said thanks to my last circle#sharedcircle #publiccircleshare   #circleshare   #circleoftheday #circleshares   #circlesharing   #circlesshare   #publicsharedcircle #publicsharedcircles   #sharedcircleoftheday #sharedcircleoftheweek #sharedcircles   #sharedpubliccircle #todayspublicsharedcircle #todayssharedcircle   #publiccircle #circle   #circles   #awesome #awesomeness #awesomepeople #shareyourcircle   #bestengagers #followers   #followback #paulaawesomecircle   #awesomecircles #paulateshima #topsharedcircle #topsharedcircle   #myseoissocial #besocial   #socializethesocial   #trust #circles #shar2014-04-19 06:29:49377335
Krzysztof Skomra5,314*PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the who said thanks to my last circle#sharedcircle #publiccircleshare   #circleshare   #circleoftheday #circleshares   #circlesharing   #circlesshare   #publicsharedcircle #publicsharedcircles   #sharedcircleoftheday #sharedcircleoftheweek #sharedcircles   #sharedpubliccircle #todayspublicsharedcircle #todayssharedcircle   #publiccircle #circle   #circles   #awesome #awesomeness #awesomepeople #shareyourcircle   #bestengagers #followers   #followback #paulaawesomecircle   #awesomecircles #paulateshima #topsharedcircle #topsharedcircle   #myseoissocial #besocial   #socializethesocial   #trust #circles #shar2014-04-19 06:29:03377157
Krzysztof Skomra5,201PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the who said thanks to my last circle#sharedcircle #publiccircleshare   #circleshare   #circleoftheday #circleshares   #circlesharing   #circlesshare   #publicsharedcircle #publicsharedcircles   #sharedcircleoftheday #sharedcircleoftheweek #sharedcircles   #sharedpubliccircle #todayspublicsharedcircle #todayssharedcircle   #publiccircle #circle   #circles   #awesome #awesomeness #awesomepeople #shareyourcircle   #bestengagers #followers   #followback #paulaawesomecircle   #awesomecircles #paulateshima #topsharedcircle #topsharedcircle   #myseoissocial #besocial   #socializethesocial   #trust #circles #sharedcircle 2014-04-15 11:37:45501006
Krzysztof Skomra5,201PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the who said thanks to my last circle#sharedcircle #publiccircleshare   #circleshare   #circleoftheday #circleshares   #circlesharing   #circlesshare   #publicsharedcircle #publicsharedcircles   #sharedcircleoftheday #sharedcircleoftheweek #sharedcircles   #sharedpubliccircle #todayspublicsharedcircle #todayssharedcircle   #publiccircle #circle   #circles   #awesome #awesomeness #awesomepeople #shareyourcircle   #bestengagers #followers   #followback #paulaawesomecircle   #awesomecircles #paulateshima #topsharedcircle #topsharedcircle   #myseoissocial #besocial   #socializethesocial   #trust #circles #sharedcircle 2014-04-15 11:36:23501012
Krzysztof Skomra5,201PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the who said thanks to my last circle#sharedcircle #publiccircleshare   #circleshare   #circleoftheday #circleshares   #circlesharing   #circlesshare   #publicsharedcircle #publicsharedcircles   #sharedcircleoftheday #sharedcircleoftheweek #sharedcircles   #sharedpubliccircle #todayspublicsharedcircle #todayssharedcircle   #publiccircle #circle   #circles   #awesome #awesomeness #awesomepeople #shareyourcircle   #bestengagers #followers   #followback #paulaawesomecircle   #awesomecircles #paulateshima #topsharedcircle #topsharedcircle   #myseoissocial #besocial   #socializethesocial   #trust #circles #sharedcircl2014-04-15 11:35:35501011
Julek Maciejewski0PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the 411  who said thanks to my last circle, and 88 new #thankyou members entering this circle for the first time. All of these people I observed over the last week taking a second to say "thanks". I was so pleased, I created a circle of 500 of you. I am amazed every day what a fun group of people have been accumulating here on Google+. I continue to be impressed with quality, the professionalism,  and the sincerity of everyone I am meeting. This circle is for YOU  (Click on this #thankyoumagic to see my other 2014 circles) #Circlemagic #Magiccircle   PLEASE VISIT the "The Magic of Circles" hosted by +Circle Magic Each day I am gathering the most active Circles I can find. Circles are #Magic , and if you love them, they will love you back.   PLEASE SHARE A #CIRCLE  Do you want to Grow your ? Get started now, add or share a Circle and watch your  grow.  Sharing circles benefits everyone, Sharing circles helps you by getting you added to their next circle and it helps the "Circle Master" by getting them recognized and promoted as active circle distributors. The more shares he/she gets THIS WEEK the more people that follow you NEXT WEEK.THE MAGIC OF CIRCLEShttps://plus.google.com/u/1/b/103678492966360900254/communities/110533309056060602888SPECIAL THANK YOU FROM +Circle Magic  - I just wanted to take a second to thank all the best of the best circle promoters, who probably mostly go un-noticed, but without them, the success of the circle sharing would be much more challenging. These SPECIAL people have all dropped by my community "The Magic of Circles" and shared someone else's circle. #TIPHAT to .....+Logan Lynn Roberts+Michael Q Todd+Sandra Deichmann...SPECIAL THANK YOU TO THE CIRCLE MASTERS - I cannot forget you either. without your  thankless hard work, building, maintaining, auditing, promoting these lists in the first place, none of us would have anything to promote.+Selected Circles 2014...Here are some of the most amazing circles I have seen released in the last seven days, each of these amazing people have worked really hard to deliver a specialize list just for you+Chad Hart...FAVOR TO ASK - As if all of you are not already doing TOO much work already. I was  hoping to ask, that when you drop of your circles each day, that you take an extra  minute to SHARE a a couple other peoples circles too. My team tries to give each and every circle between 7-12 shares to every circle dropped off in my community "The Magic of Circles" but as we become more and more successful we find we are getting  20-30 new circles listed each day, and it is getting harder and harder to keep up with everyone, and already I am starting to have to pick and choose which circles I  can afford to run #Empireavenue   missions on to get that extra 5-6 shares on the most active  circles..I know we are all doing this for free, with no real idea of why we are doing this,  except that it feels li2014-04-14 01:08:56501016
Julek Maciejewski0PEOPLE WHO SAY "THANK YOU"  This circle is to show appreciation to the 411  who said thanks to my last circle, and 88 new #thankyou members entering this circle for the first time. All of these people I observed over the last week taking a second to say "thanks". I was so pleased, I created a circle of 500 of you. I am amazed every day what a fun group of people have been accumulating here on Google+. I continue to be impressed with quality, the professionalism,  and the sincerity of everyone I am meeting. This circle is for YOU  (Click on this #thankyoumagic to see my other 2014 circles) #Circlemagic #Magiccircle   2014-04-14 01:05:48501112
Circle Connection570The Mix it Up Circle! #circleconnection  2014-04-10 20:22:45481723035
Richard Green62,178Engagers Showcase Circle, March 29, 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. My most recent post will be included next time.Everyone mentioned below is also included in the circle.Happy Pi Day!https://plus.google.com/101584889282878921052/posts/74oomcTuJoVSierpinski sponge (reshared from +David Roberts)https://plus.google.com/101584889282878921052/posts/ZKUreVJfWxoCloud Gate (reshared from +Christian Cable)https://plus.google.com/101584889282878921052/posts/XGRNqbbBjgEContinued fractionshttps://plus.google.com/101584889282878921052/posts/2mbZvUrewmCFood mapshttps://plus.google.com/101584889282878921052/posts/BKMgJ6WzfiyNeptune's Lament (reshared from +Paul Haworth)https://plus.google.com/101584889282878921052/posts/1AHZMatxm8JEscher's “Ascending and Descending”... in Legohttps://plus.google.com/101584889282878921052/posts/9XJsanAguNCDead Horse Point State Park (reshared from +Tom Malloy)https://plus.google.com/101584889282878921052/posts/edKVZ8NqAW4It's the Chicken from Hell! (reshared from +Chad Haney)https://plus.google.com/101584889282878921052/posts/2tc9WchRABJDerangements, or how everyone got the wrong homework backhttps://plus.google.com/101584889282878921052/posts/Bjb3CvDYBwxSnowy La Sal Mountains (reshared from +Tom Malloy)https://plus.google.com/101584889282878921052/posts/8tiW4gbzVrXMultimove chess2014-03-29 04:30:56482209161234
Bob Mulholland20,590Haven't done a  #FollowFriday  in a while. Beam these mofos into your Circles , Scotty!Nothin' but a buncha  #StarTrek  nerds in here.... #SharedCircles  2014-03-07 20:06:14486519
Artur M.35,611circle of people, with active life position in Google+2014-01-19 04:03:28438251674
Richard Green52,056Engagers Showcase Circle, January 9, 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 waited too long to share the circle, so I ran out of room. As a consequence, several of my recent posts will be included next time instead.Everyone mentioned below is also included in the circle.50,000 followershttps://plus.google.com/101584889282878921052/posts/CXAHuH8epQaHyperbolic honeycombs (reshared from +Roice Nelson)https://plus.google.com/101584889282878921052/posts/XkTecGK6CghMarie Antoinette: Let Them Eat Niphttps://plus.google.com/101584889282878921052/posts/hu9YeJxPVPmMy daughter jugglinghttps://plus.google.com/101584889282878921052/posts/F38QyMXs7YDBridge photography (reshared from +Eric Larson)https://plus.google.com/101584889282878921052/posts/XQsEw9CtLjSWhite-throated Kingfisher (reshared from +Anuradha Goyal)https://plus.google.com/101584889282878921052/posts/H6zMhGj3aS5What's up with 163?https://plus.google.com/101584889282878921052/posts/7enyPxZW3RBSeascape (reshared from +Paul Haworth)https://plus.google.com/101584889282878921052/posts/3XxHeKz61wcLittlewood's Law of Miracleshttps://plus.google.com/101584889282878921052/posts/gLmKu3vPXhsKnot theorists of the world untie!https://plus.google.com/101584889282878921052/posts/HLmx56CSPDEMelted crayon artwork (reshared from +Laura Ockel)https://plus.google.com/101584889282878921052/posts/FkeBeRvtnRR5-dimensional hypercubehttps://plus.google.com/101584889282878921052/posts/9soBKs4TtRmAs alwa2014-01-09 22:16:33499193142241
Richard Green50,191Engagers Showcase Circle, December 27 2013If 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 skipped two of the posts below because they attracted low-quality engagement, but I'm listing them here for completeness.Everyone mentioned below is also included in the circle.Seven cylinders a-touchinghttps://plus.google.com/101584889282878921052/posts/FGZHF7kqaWkLeaves in Water (reshared from +Marjolein Caniels)https://plus.google.com/101584889282878921052/posts/bQvdz7yL82FElf on the Shelf (on a Reindeer)https://plus.google.com/101584889282878921052/posts/DvXFqZ89andIridescent Cloudshttps://plus.google.com/101584889282878921052/posts/S2izLcENvjnSpear Lodge Manhttps://plus.google.com/101584889282878921052/posts/DUWKF4CG3XHLaser Christmas decorationshttps://plus.google.com/101584889282878921052/posts/B7ngNnfdQ6bRadial Normals (by +Patrick Honner) https://plus.google.com/101584889282878921052/posts/34zwPWe3cD2Rainbow photography (reshared from +James Wheeler)https://plus.google.com/101584889282878921052/posts/Ph8JSPXWAEnCornwall seascape painting (reshared from +Paul Haworth) https://plus.google.com/101584889282878921052/posts/BypBhhkPzMcMulticultural Santa (reshared from +Mike Stay)https://plus.google.com/101584889282878921052/posts/Uk9AreT7eC5Temari ballshttps://plus.google.com/101584889282878921052/posts/E5UibQyB1rjThe Eagle Catcherhttps://plus.google.com/101584889282878921052/posts/BXayNs16RdKChristmas lights in Boulder2013-12-27 07:02:36454179145235
Chill Ideaz Jay Beek Rocksuperstar0Another round of #topengagers  !(Be sure to click READ MORE, it is important if you want to be included in this circle next time)These people shareThese people +1These people create original contentThese people make G+ BetterIf you add this circle, you will, without a doubt, see your engagement soar through the roof.  Guaranteed.  If you were notified, you guessed it, you are already in.To be included in the NEXT top engagers circle this week is easier than ever.1.) Follow me2.) Share this post3.) Keep engaging#sharedcircle   #sharedcircles   #sharecircle   #publiccircle   #publiccircles   #publicsharedcircles   #topengagers   #engagers   #snowballcircle   #snowball   #circles   #circleshare   #circlemasters   #circlemaster   #circlequeen   #crazycircles   #circlehub   #morefollowers #ghosttown 2013-11-25 00:30:29405006
Chill Ideaz Jay Beek Rocksuperstar0Another round of #topengagers  !(Be sure to click READ MORE, it is important if you want to be included in this circle next time)These people shareThese people +1These people create original contentThese people make G+ BetterIf you add this circle, you will, without a doubt, see your engagement soar through the roof.  Guaranteed.  If you were notified, you guessed it, you are already in.To be included in the NEXT top engagers circle this week is easier than ever.1.) Follow me2.) Share this post3.) Keep engaging#sharedcircle   #sharedcircles   #sharecircle   #publiccircle   #publiccircles   #publicsharedcircles   #topengagers   #engagers   #snowballcircle   #snowball   #circles   #circleshare   #circlemasters   #circlemaster   #circlequeen   #crazycircles   #circlehub   #morefollowers #ghosttown 2013-11-24 16:58:13405007
Chill Ideaz Jay Beek Rocksuperstar0Another round of #topengagers  !(Be sure to click READ MORE, it is important if you want to be included in this circle next time)These people shareThese people +1These people create original contentThese people make G+ BetterIf you add this circle, you will, without a doubt, see your engagement soar through the roof.  Guaranteed.  If you were notified, you guessed it, you are already in.To be included in the NEXT top engagers circle this week is easier than ever.1.) Follow me2.) Share this post3.) Keep engaging#sharedcircle   #sharedcircles   #sharecircle   #publiccircle   #publiccircles   #publicsharedcircles   #topengagers   #engagers   #snowballcircle   #snowball   #circles   #circleshare   #circlemasters   #circlemaster   #circlequeen   #crazycircles   #circlehub   #morefollowers #ghosttown 2013-11-24 08:00:39405105
Chill Ideaz Jay Beek Rocksuperstar0#sharedcircle   #sharedcircles   #sharecircle   #publiccircle   #publiccircles   #publicsharedcircles   #topengagers   #engagers   #snowballcircle   #snowball   #circles   #circleshare   #circlemasters   #circlemaster   #circlequeen   #crazycircles   #circlehub   #morefollowers #ghosttown2013-11-24 06:33:32405005
Chill Ideaz Jay Beek Rocksuperstar0This group will follow back !#sharedcircle   #sharedcircles   #sharecircle   #publiccircle   #publiccircles   #publicsharedcircles   #topengagers   #engagers   #snowballcircle   #snowball   #circles   #circleshare   #circlemasters   #circlemaster   #circlequeen   #crazycircles   #circlehub   #morefollowers #ghosttown2013-11-24 01:22:28405104
Chill Ideaz Jay Beek Rocksuperstar0Here's the latest update of my Engagers circle. The last version of this circle was close to full, so I started it again from scratch. This circle includes people who have recently engaged with one of my posts in the form of +1s, comments and public reshares.I might have missed some people because of limitations of the Google+ interface. Fortunately, the next release of +Circloscope on June 28 is likely to include new features that make circles like this one much easier to create.I've included 100 guest members in this circle, taken from my Favourites circle, which I haven't shared in a while.Like my previous circle share, this is a Showcase circle! What this means is that everyone is invited to leave a comment on (the original post of) this circle share containing a link to one of your own posts. Ideally, this should be something that you posted recently and that you are particularly pleased with. (Don't post spam though; I will delete it.)2013-11-24 00:22:24405014
Silvio De Rossi3,801It's dance time! #saturdaynight  Circle! :DThis is my first #sharedcircle of #topengagers, a group of interesting people who share unique and original content.What are you waiting to add them to your circles? :)To be included in my shares (#sharedcircle), be so kind to:1) Do +1 t the post2) Comment the post and specify your "category" (ex: fashion, photography, seo, social media marketing)3) Include the circle among your circles4) Share the circle (include yourself)5) Smile to life, sun in sunshine.Special thanks my dear #friends and #followers:+Raffaele Romeo Arena  +Tancredi Matranga +Alessandro Folghera +Christine DeGraff +Viktor Mulin +Cesare Riccardo Have a good life!#topsharedcircle   #facciamolastoria   #leonardo   #deroplus   #circleoftheday   #sharedcircle   #topsharedcircle   #sharedcircleoftheday   #myseoissocial   #besocial   #socializethesocial  #trust #circles  #circleshare  #sharedcircle   2013-10-26 19:28:02457531239
Raffaele Romeo Arena5,311Welcome my dear #friends and #follower this is #thursdaycircle #topengagers  This circle is very important because it's composed of many important peolple, that often #interact with me and our community.You remember that #social  is   #sharedlife  and #follow is #friendship  . And so:-include me in your circles-create a large network-shared the circle (include yourself)-add +1 to the post-interact will allow you to enter the great circle that soon will share-happy life and sun is sunshine.Special thanks, to my #friends  and #followers  :+Alessandro Folghera +Mario Falcetti +Cesare Riccardo +Edith Kukla +Dominique Keller +Viktor Mulin +Silvio De Rossi +Tancredi Matranga +Tazein Mirza Saad +Fashion Circles #circles   #circleshare   #sharedcircle 2013-10-24 09:20:30459623468
Circle Construct is for communication561A little room to add yourself. Please public share, because if you are not in this circle, that is how you will get included into future circles somewhere. 2013-10-22 08:23:1946613833
Refurio Anachro1,560Mochizuki club circle Here's everyone who showed interest (posted) when Shinichi Mochizuki announced he had proof for the abc- conjecture. It's been great fun to read the impressions from back then.I have seen especially interesting posts by +John Baez, who gave very accessible first fragmentary impressions. Just search for his name and "mochizuki" and don't forget to read the comments!Also, i urge you to look at +lieven lebruyn's profile, who may be the one who got deepest into explaining it. And look: Colored, hand drawn diagrams! He's been posting MinuteMochizuki on his blog until mid of june and i think he'll be back!http://matrix.cmi.ua.ac.be/ For more here's the polymath page which, among many other interesting links, lists quite a reaction here on google+. +Jordan Ellenberg +Timothy Gowers +Terence Tao  also made it into this circle.http://michaelnielsen.org/polymath1/index.php?title=ABC_conjectureAs for where matters stand, it may be that Mochizuki is currently giving private lectures to Go Yamashita, a colleague, who might be inclined to do the travelling to explain it to others. Or so... that's what this blog post by Caroline Chen suggests:http://projectwordsworth.com/the-paradox-of-the-proof/Minhyong Kim, a friend of Mochizuki at Oxford, has been posting on mathoverflow an early attempt to give some overview from a closer vantage point:http://mathoverflow.net/questions/106560/philosophy-behind-mochizukis-work-on-the-abc-conjectureAnd, as i must say, i stole the following taglist from +Rusty Ferguson's latest circle share. You wrote some appealing stuff, your tags must be good:https://plus.google.com/112078832938393562132/posts/WvqYjBrKiir #sharedcircles   #publicsharedcircles   #circleshare   #sharedpublicricle   #circlesharing   #circle   2013-10-18 00:17:00125145
Richard Green32,670Engagers Showcase Circle, October 16 2013If 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. In the last two weeks, I discussed mathematical aspects of the art of M.C. Escher, as well as the fractal known as the Sierpinski triangle. I also posted about a sign with a typo on it, and a set of tea mugs for the kind of people who would be annoyed by such a mistake. I posted some original photography; one of my photo posts got into What's Hot, so I skipped over it when compiling this circle. I also reshared posts by +John Baez, +Arnold Hayes, +Jason Hill, and +Bo Insogna, all of whom are included in the circle.Google's persistent domain name bug has meant that I wasn't able to include everyone I wanted to in this circle. The bug is now even worse than before, and has stripped certain people out of all of my circles because of my attempt to add them to this one! I hope they fix this soon, because it's really annoying.As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!2013-10-16 17:57:37418246152238
Raffaele Romeo Arena4,418#mondaysharedcircle in your #circle #seocircle #fashioncircle This #circle includes important followers to affirm a strong #community getting bigger. Join the community and shareTo 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)If you come accross Google error messages, incorporating my circles, please provide me the error, I'm classifying these errors. Have a wonderful Monday and all week; and a better popularityMost important: Keep yourself updated, enjoy the Shared Circles Hellenic Alliance, you can share your shared circles inside the upcoming Community:https://plus.google.com/communities/112552559573595396104Special thaks to my friend and special follower:+Alessandro Folghera+Viktor Mulin+Fashion Circles+Scott Buehler+Sam Stormborn Ormandy+Владимир Самсонов+Ludovic Moreeuw+Dominique Keller+Tancredi Matranga+Silvio De Rossi+Edith Kukla2013-10-14 20:44:30460211238
Raffaele Romeo Arena3,803Astonishing #topengagers   Happy  #Tuesday my #friends , and you are welcome in my #tuesdaycircle A nice group of people who I found to share and comment my posts, and have as a goal to grow our #community.And so, after difficult day on #Monday we are to enjoy on Tuesday in #fashionstyle To 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, photography, seo, social media marketing)3 - include the circle among your circles4 - share the circle (include yourself)5 - Plus and share the new important #fashionprofile https://plus.google.com/u/0/b/101905178080519621345/101905178080519621345/posts5 - smile to life, sun in sunshine.Thanks to all of you who are part of my circles and those who will be part of, in particular, I thank my #friends and #followers :+Alessandro Folghera+Alfredo Torres+Dirk Talamasca+Viktor Mulin+Cesare Riccardo+Mario Falcetti+Владимир Самсонов+Dominique KellerHave a wonderful weekend and increasing your #popularity and your #circles#topsharedcircle   2013-10-08 08:07:37463571660
Circle Construct is for communication561To You, When you are not comfortable with circles here is exactly what to do....1. Name the Circle and save the #circle .2. Give the circle creator credit #circleconstruct   3. Give credit to who shared the circle with you #circleconstruct   4. Add yourself to the circle. 5. Share the circle public, all your circles, or specific people who would      benefit from the people in the circle. 6. Say thank you in the stream. (comments)7. Let me know if you don’t wish to be in shared circles, we have          circles marked for that here so you can still receive page member  information.#circleconstruct  says you are welcome in advance.... #queenpld   #circleconstruct   #vipcirclemember    #highnumbers   #samepeople   #everycircle  2013-09-29 10:08:244681835
Richard Green27,236Engagers Showcase Circle, September 21 2013If 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. This week, I posted about the union-closed sets conjecture in mathematics, and I shared some of my original photography and some artwork from my daughter. I also reshared posts by +Paul Haworth, +Tiffany Lykins, +Jeni Ong, +Pauline Taylor and +Rupert Wood. I ran out of room on this circle because I waited too long to share it, so I excluded some people who didn't have me in their circles. However, everyone who reshared the last version of the circle should be included, provided that they have a profile picture. I did not include the engagers on my two most recent posts, but I will include them next time. I apologise to +Azure Tackert and +Eng UNG, who are supposed to be in this circle, but Google will not let me circle them back because of the annoying domain restriction bug.As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!2013-09-21 16:59:27473241168250
Raffaele Romeo Arena2,188Welcome in my #weekendcircle .You remember that #social  is  #sharedlife  and #follow is #friendship  . And so:-include me in your circles-create a large network-shared the circle (include yourself)-add +1 to the post-happy lifeSpecial thanks, to my #friends  and #followers  :+Alessandro Folghera +Mario Falcetti +Cesare Riccardo  #circles   #circleshare  #sharedcircle #circlesharing   #follower #socialnetworking   #social   #followme   #follow4followback  2013-09-13 17:59:23468472555
Richard Green26,219Engagers Showcase Circle, September 13 2013If 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.This week, I have been mostly posting about: Ramsey theory in mathematics; oddly comprehensible sentences; the wave/particle nature of light; and the mathematics of electrical networks. I've also posted some original photography and reshared posts from +Marjolein Caniels, +AyJay Schibig and +Debashish Samaddar.As always, reshares of this circle are appreciated, and I look forward to seeing everyone's links. Thanks for reading my posts!2013-09-13 15:31:32467212117223
Raffaele Romeo Arena991#happycircleWelcome   in my #sharedcircles  in #wednesday and happy #sharedweek  Special thanks to +Yaiza Pozo Vara +Mario Falcetti +Alessandro Folghera You remember that #social  is #sharedlife  and #follow  is #friendship And so:-Include me in your circles-create a large network-share the circle (include yourself)-add +1 to the post-happy life#Wednesdaysharedcircle   #topsharedcircle   #circleoftheday   #sharedcircle #trustinme  #circlesharing   #circleshare        #circles        #circleoftheday   #sharedpubliccircles     #sharedcircles    #share  #vipsnowballcircle #sharedcircleoftheday        #sharewithyou        #circlefriday   #circlethursday  #followme     #followers #followback #circle #g2013-08-21 13:32:27446632681
Kai Saffron14,954Mathematician +Richard Green's shared circle of highly engaged Plussers!  Consider adding to liven up your stream-  Remember: "nothing ventured, nothing gained". #SharedCircles   #GooglePlus   #GhostTown   2013-08-07 16:37:49446582266
Leo Walsh3,691Richard Green originally shared:Engagers Showcase Circle, August 5 2013 If 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 may have missed some people due to limitations of the G+ interface, but as usual, everyone who reshared last week's version of the circle has been included this time.As always, reshares are appreciated. And, if you have been, thanks for reading my posts!2013-08-06 00:51:27447521360
Richard Green20,938Engagers Showcase Circle, August 5 2013 If 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 may have missed some people due to limitations of the G+ interface, but as usual, everyone who reshared last week's version of the circle has been included this time.As always, reshares are appreciated. And, if you have been, thanks for reading my posts!2013-08-05 23:36:22446267123229
Michael Q Todd37,249A circle of active engagersHave a great weekend hanging out with these people on Google Plus! #circleshare #circlesharing #circles  2013-08-02 21:35:0746914268170
Christy Sandhoff12,031Here's a great fresh circle started by +Daniel Mihai Popescu. It's called Showcase Circle.  This circle will help your attract some engaging people to your circles . Follow the simple steps below:Daniel Mihai Popescu originally shared:I have to name this fresh circle Showcase, because it's based on +Richard Green's recently shared "showcase engagers" circle plus my Invincible, of course. I liked his idea, to let you promote yourself if you feel in the mood, so I go further and mention that any sort of link is welcomed (except links to adult sites or affiliate links of any kind, Amazon, whatever, you know exactly what I'm talking about), not only links to google+ posts.It has a round number, and I saw some very nice engagement too!You'll receive a notification as much as I hate to send it."Based" doesn't mean "identical", but merely inspired. I have noticed in any shared circle, especially in my friends' shared circles that at least 100 or more are already in my circles. So it's not a big deal anymore to assume a circle paternity without being considered a plagiarist, not for me, anyway. I'm not at all annoyed when someone adds a circle pro bono and shares it without mentioning my name. Sometimes is better to not do it. It's just networking and I can understand that as long as the sharer is not annoying. But my dear friends and future friends, I put some soul in my circles, and I like to share them after they "stabilized", because they are my humble homage to you!Already showcased are the people on the circle's cover, as you see, that's a happy coincidence because I never look out on how to arrange it. There are a lot of things I don't know yet :). I'm too blunt sometimes, I can hurt easily by showing a lack of flexibility on human flaws. It's not my intention. I don't want to hurt anybody, when expressing my opinion on a comment. Sometimes I'm wrong, which is only human. I'll admit it with no remorse, because it's just fair, but I have to know myself I'm wrong. I have to be conscious of it, I'm not going to show mea culpa with any superficial "open mouth" who attends to put me down!This is a way to show my appreciation for +Richard Green, +Cesare Riccardo, +Scott Buehler, +Ludovic Moreeuw, +Marlo Angelo Tito, +Jasmina Brozović, +Linda Dee, +Dirk Talamasca, +Steven Krohn, +Jan Schellenberger, +Katherine Vucicevic, +Mark HELM, +Robert van Koesveld, +César Bustíos Benites, +Laurent Jean Philippe, +Zbynek Kysela, +Jack C Crawford, +kirthika M, +Morgan Abbou, +Tazein Mirza Saad, +Miguel Ricardo, +Andreas Levi, +Randy Culler, +Michael Bennett, +AyJay Schibig, +Jean-Marc Luna, +Rinus Bakker,  +Adriana Popovici, and many more who know themselves better than my memory helps me now, and do the spine of all my public circles!2013-07-09 03:18:45334481658
Steven Krohn3,647Here's a great fresh circle started by +Daniel Mihai Popescu. It's called Showcase Circle.  This circle will help your attract some engaging people to your circles . Follow the simple steps below:Daniel Mihai Popescu originally shared:I have to name this fresh circle Showcase, because it's based on +Richard Green's recently shared "showcase engagers" circle plus my Invincible, of course. I liked his idea, to let you promote yourself if you feel in the mood, so I go further and mention that any sort of link is welcomed (except links to adult sites or affiliate links of any kind, Amazon, whatever, you know exactly what I'm talking about), not only links to google+ posts.It has a round number, and I saw some very nice engagement too!You'll receive a notification as much as I hate to send it."Based" doesn't mean "identical", but merely inspired. I have noticed in any shared circle, especially in my friends' shared circles that at least 100 or more are already in my circles. So it's not a big deal anymore to assume a circle paternity without being considered a plagiarist, not for me, anyway. I'm not at all annoyed when someone adds a circle pro bono and shares it without mentioning my name. Sometimes is better to not do it. It's just networking and I can understand that as long as the sharer is not annoying. But my dear friends and future friends, I put some soul in my circles, and I like to share them after they "stabilized", because they are my humble homage to you!Already showcased are the people on the circle's cover, as you see, that's a happy coincidence because I never look out on how to arrange it. There are a lot of things I don't know yet :). I'm too blunt sometimes, I can hurt easily by showing a lack of flexibility on human flaws. It's not my intention. I don't want to hurt anybody, when expressing my opinion on a comment. Sometimes I'm wrong, which is only human. I'll admit it with no remorse, because it's just fair, but I have to know myself I'm wrong. I have to be conscious of it, I'm not going to show mea culpa with any superficial "open mouth" who attends to put me down!This is a way to show my appreciation for +Richard Green, +Cesare Riccardo, +Scott Buehler, +Ludovic Moreeuw, +Marlo Angelo Tito, +Jasmina Brozović, +Linda Dee, +Dirk Talamasca, +Steven Krohn, +Jan Schellenberger, +Katherine Vucicevic, +Mark HELM, +Robert van Koesveld, +César Bustíos Benites, +Laurent Jean Philippe, +Zbynek Kysela, +Jack C Crawford, +kirthika M, +Morgan Abbou, +Tazein Mirza Saad, +Miguel Ricardo, +Andreas Levi, +Randy Culler, +Michael Bennett, +AyJay Schibig, +Jean-Marc Luna, +Rinus Bakker,  +Adriana Popovici, and many more who know themselves better than my memory helps me now, and do the spine of all my public circles!2013-07-08 20:23:30333411955
Daniel Mihai Popescu6,546I have to name this fresh circle Showcase, because it's based on +Richard Green's recently shared "showcase engagers" circle plus my Invincible, of course. I liked his idea, to let you promote yourself if you feel in the mood, so I go further and mention that any sort of link is welcomed (except links to adult sites or affiliate links of any kind, Amazon, whatever, you know exactly what I'm talking about), not only links to google+ posts.It has a round number, and I saw some very nice engagement too!You'll receive a notification as much as I hate to send it."Based" doesn't mean "identical", but merely inspired. I have noticed in any shared circle, especially in my friends' shared circles that at least 100 or more are already in my circles. So it's not a big deal anymore to assume a circle paternity without being considered a plagiarist, not for me, anyway. I'm not at all annoyed when someone adds a circle pro bono and shares it without mentioning my name. Sometimes is better to not do it. It's just networking and I can understand that as long as the sharer is not annoying. But my dear friends and future friends, I put some soul in my circles, and I like to share them after they "stabilized", because they are my humble homage to you!Already showcased are the people on the circle's cover, as you see, that's a happy coincidence because I never look out on how to arrange it. There are a lot of things I don't know yet :). I'm too blunt sometimes, I can hurt easily by showing a lack of flexibility on human flaws. It's not my intention. I don't want to hurt anybody, when expressing my opinion on a comment. Sometimes I'm wrong, which is only human. I'll admit it with no remorse, because it's just fair, but I have to know myself I'm wrong. I have to be conscious of it, I'm not going to show mea culpa with any superficial "open mouth" who attends to put me down!This is a way to show my appreciation for +Richard Green, +Cesare Riccardo, +Scott Buehler, +Ludovic Moreeuw, +Marlo Angelo Tito, +Jasmina Brozović, +Linda Dee, +Dirk Talamasca, +2013-07-07 19:19:58333933572

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Most comments: 20

2014-10-09 17:03:08 (20 comments, 0 reshares, 14 +1s)Open 

Teleturniej "Jeden z 10" (dziś, jeszcze trwa). Sznuk pyta: "Jak się nazywa jedyna karta w danym kolorze otrzymana w jednym rozdaniu. Dla ułatwienia, tak określa się osobę samotną, nie posiadającą partnera". Gracz: "Lewa" :)

Most reshares: 3

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2014-10-12 19:30:21 (1 comments, 3 reshares, 5 +1s)Open 

Manuel Blum suggests a cryptographic hash function that a human can carry out mentally but that computers cannot break.

Update: The video of his talk is available online http://www.heidelberg-laureate-forum.org/blog/video/lecture-monday-september-22-2014-manuel-blum/

Most plusones: 29

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2014-07-31 20:10:59 (7 comments, 2 reshares, 29 +1s)Open 

Latest 50 posts

2014-10-18 19:19:32 (5 comments, 0 reshares, 17 +1s)Open 

Byłem dzisiaj na "Bogowie". Jeden z lepszych polskich filmów, może zresztą i filmów w ogóle, jakie widziałem ostatnio. Absolutnie polecam. Duża rzecz.

Byłem dzisiaj na "Bogowie". Jeden z lepszych polskich filmów, może zresztą i filmów w ogóle, jakie widziałem ostatnio. Absolutnie polecam. Duża rzecz.___

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2014-10-18 05:20:18 (0 comments, 0 reshares, 6 +1s)Open 

The Gods of the World: A group called "The 40 Foundation" put together this rather extraordinary infographic of the world's religions and how they're (historically) related to one another. It's a phylogenetic tree of the gods.

I can't say that this diagram is complete, nor that it shows every possible cross-pollination; it would be very hard to do so, given just how intricate this aspect of history is. Likewise, it's hard to define the boundaries between various sects, at times; while the Protestants are very famous for each sect having its own name and being firmly opposed to those schismatics from the Popular Front of Judea, many other religious divisions have been more subtle, two groups simply moving away from each other over time, or one group simply adopting a radically different theology without telling anyone. But the image is detailed enough that you can... more »

The Gods of the World: A group called "The 40 Foundation" put together this rather extraordinary infographic of the world's religions and how they're (historically) related to one another. It's a phylogenetic tree of the gods.

I can't say that this diagram is complete, nor that it shows every possible cross-pollination; it would be very hard to do so, given just how intricate this aspect of history is. Likewise, it's hard to define the boundaries between various sects, at times; while the Protestants are very famous for each sect having its own name and being firmly opposed to those schismatics from the Popular Front of Judea, many other religious divisions have been more subtle, two groups simply moving away from each other over time, or one group simply adopting a radically different theology without telling anyone. But the image is detailed enough that you can clearly see phenomena like the Protestant Reformation, the emergence of Islam, and quite a few other historical events very visually. And to nitpick a work this complex feels almost petty.

You can view single images at the link, or a zoomable version (with an admittedly crappy UI) at http://funki.com.ua/ru/portfolio/lab/world-religions-tree/ . 

h/t +Alex Fink for finding this.___

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2014-10-15 18:34:13 (4 comments, 1 reshares, 12 +1s)Open 

Nie wiem jak artykuł, ale ciacho - ekstra.

Why Google+ is the place for passions

The single biggest controversy about social media, and one that has persisted for two or three years now without resolution, is whether Google+ is a dying wasteland of non-activity, or a hive of conversation and engagement.

It can't be both. So which is it? And why can't this fundamental question be answered?

I believe I have the key to the puzzle, and I'll attempt to solve it once and for all.

Here what the Twitter people and the Facebook people don't understand about the Google+ people: 

http://www.computerworld.com/article/2824613/why-google-is-the-place-for-passions.html

#googleplus

(Pic props: http://goo.gl/K75VYX )___Nie wiem jak artykuł, ale ciacho - ekstra.

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2014-10-12 19:30:21 (1 comments, 3 reshares, 5 +1s)Open 

Zaznaczam sobie do obejrzenia

Manuel Blum suggests a cryptographic hash function that a human can carry out mentally but that computers cannot break.

Update: The video of his talk is available online http://www.heidelberg-laureate-forum.org/blog/video/lecture-monday-september-22-2014-manuel-blum/___Zaznaczam sobie do obejrzenia

2014-10-10 14:37:23 (3 comments, 0 reshares, 16 +1s)Open 

Hehehe... Urocze.

"Pismo Święte uczy nas, że najwyższe szczęście człowieka przed jego upadkiem stanowił zupełny brak jakiejkolwiek pracy. Umiłowanie próżniactwa odszukujemy i w człowieku upadłym. Dziś jednak nie może on pozostać zupełnie bezczynny, nie tylko z powodu klątwy bożej, ciążącej nad nim i skazującej go na pracę w pocie czoła dla zdobycia chleba, ale w ogóle, wskutek całej jego konstrukcji moralnej. Głos tajemniczy, głos sumienia ostrzega go, że staje się występny, oddając się próżniactwu. Gdyby jednak mógł połączyć ciążące na nim obowiązki ze słodką bezczynnością, używałby niezaprzeczenie owego pierwotnego szczęścia w raju Adama i Ewy. W tych mniej więcej warunkach znajduje się jednak cała jedna warstwa ludzkości, mianowicie: wyżsi wojskowi. Ci oddają się częstokroć bezczynnemu życiu niejako z musu. Jest im to nietylko dozwolone, ale prawie nakazane, i stanowi, Bogiem a prawd... more »

Hehehe... Urocze.

"Pismo Święte uczy nas, że najwyższe szczęście człowieka przed jego upadkiem stanowił zupełny brak jakiejkolwiek pracy. Umiłowanie próżniactwa odszukujemy i w człowieku upadłym. Dziś jednak nie może on pozostać zupełnie bezczynny, nie tylko z powodu klątwy bożej, ciążącej nad nim i skazującej go na pracę w pocie czoła dla zdobycia chleba, ale w ogóle, wskutek całej jego konstrukcji moralnej. Głos tajemniczy, głos sumienia ostrzega go, że staje się występny, oddając się próżniactwu. Gdyby jednak mógł połączyć ciążące na nim obowiązki ze słodką bezczynnością, używałby niezaprzeczenie owego pierwotnego szczęścia w raju Adama i Ewy. W tych mniej więcej warunkach znajduje się jednak cała jedna warstwa ludzkości, mianowicie: wyżsi wojskowi. Ci oddają się częstokroć bezczynnemu życiu niejako z musu. Jest im to nie tylko dozwolone, ale prawie nakazane, i stanowi, Bogiem a prawdą, główny urok służby wojskowej."

L.Tołstoj, Wojna i pokój___

2014-10-09 17:03:08 (20 comments, 0 reshares, 14 +1s)Open 

Teleturniej "Jeden z 10" (dziś, jeszcze trwa). Sznuk pyta: "Jak się nazywa jedyna karta w danym kolorze otrzymana w jednym rozdaniu. Dla ułatwienia, tak określa się osobę samotną, nie posiadającą partnera". Gracz: "Lewa" :)

Teleturniej "Jeden z 10" (dziś, jeszcze trwa). Sznuk pyta: "Jak się nazywa jedyna karta w danym kolorze otrzymana w jednym rozdaniu. Dla ułatwienia, tak określa się osobę samotną, nie posiadającą partnera". Gracz: "Lewa" :)___

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2014-10-05 08:52:15 (5 comments, 0 reshares, 0 +1s)Open 

The US has the highest statutory corporate tax rate among developed countries. Laura Tyson outlines what the nation needs to do to attract investment and bring back jobs from abroad:

http://wef.ch/Ybp8H8

The US has the highest statutory corporate tax rate among developed countries. Laura Tyson outlines what the nation needs to do to attract investment and bring back jobs from abroad:

http://wef.ch/Ybp8H8___

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2014-10-04 17:32:45 (8 comments, 0 reshares, 21 +1s)Open 

Ha! Ja stary a nie wiedziałem. Okazuje się, że aparat, w moim telefonie przynajmniej, widzi promieniowanie podczerwone emitowane przez pilota do telewizora. Nie wiem dlaczego, ale mnie to zachwyciło.

Ha! Ja stary a nie wiedziałem. Okazuje się, że aparat, w moim telefonie przynajmniej, widzi promieniowanie podczerwone emitowane przez pilota do telewizora. Nie wiem dlaczego, ale mnie to zachwyciło.___

posted image

2014-10-04 16:43:52 (0 comments, 0 reshares, 2 +1s)Open 

In case you missed it: What the world looks like when measured by internet population. How does your country perform?

In case you missed it: What the world looks like when measured by internet population. How does your country perform?___

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2014-10-03 06:57:15 (1 comments, 2 reshares, 12 +1s)Open 

Krásné páteční ránko přeji všem #morning  

Krásné páteční ránko přeji všem #morning  ___

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2014-10-01 05:53:18 (17 comments, 0 reshares, 16 +1s)Open 

Komunikacja publiczna w Krakowie właśnie upada. Ten tłum, rosnący i z lekka tylko zlizywany przez nadjeżdżające autobusy składa się prawdopodobnie z już spóźnionych. Ja rozumiem, początek roku akademickiego, ale jako wieloletni użytkownik MPK nie łudzę się, że jutro będzie znacząco lepiej.mamy za to w Krakowie drogi i niemal nieużywany stadion obok drugiego, równie wielkiego.

Komunikacja publiczna w Krakowie właśnie upada. Ten tłum, rosnący i z lekka tylko zlizywany przez nadjeżdżające autobusy składa się prawdopodobnie z już spóźnionych. Ja rozumiem, początek roku akademickiego, ale jako wieloletni użytkownik MPK nie łudzę się, że jutro będzie znacząco lepiej.mamy za to w Krakowie drogi i niemal nieużywany stadion obok drugiego, równie wielkiego.___

2014-09-24 16:54:22 (4 comments, 0 reshares, 3 +1s)Open 

Większość dziewcząt z Huty wydaje mi się być do siebie podobna. Jeśli to to, co myślę, to była to kiedyś najbardziej swingująca dzielnica Krakowa (wcześniej miasto - fakt).

Większość dziewcząt z Huty wydaje mi się być do siebie podobna. Jeśli to to, co myślę, to była to kiedyś najbardziej swingująca dzielnica Krakowa (wcześniej miasto - fakt).___

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2014-09-24 15:18:47 (1 comments, 0 reshares, 1 +1s)Open 

"This is one of the intriguing creations of the Festival Pattern Group - a unique project at the 1951 Festival of Britain involving X-ray crystallographers, designers and manufacturers. At the instigation of Dr Helen Megaw (1907-2002) diagrams of atomic structures inspired patterns on curtains, wallpapers, carpets, lace, dress fabrics, ties, plates and ashtrays. Although this pattern has been simplified, the motif in this screen-printed wallpaper is essentially the same as Dorothy Hodgkin’s contour map of insulin. From a distance the pattern resembles floral rosettes. This wallpaper was used in the Regatta Restaurant at the Festival of Britain."

The image and text are from the website dedicated to the exhibition 
From Atoms To Patterns   (2008)
Feel free to explore at 
http://www.wellcomecollection.org/whats-on/exhibitions/from-atoms-to-patterns.aspx
An... more »

"This is one of the intriguing creations of the Festival Pattern Group - a unique project at the 1951 Festival of Britain involving X-ray crystallographers, designers and manufacturers. At the instigation of Dr Helen Megaw (1907-2002) diagrams of atomic structures inspired patterns on curtains, wallpapers, carpets, lace, dress fabrics, ties, plates and ashtrays. Although this pattern has been simplified, the motif in this screen-printed wallpaper is essentially the same as Dorothy Hodgkin’s contour map of insulin. From a distance the pattern resembles floral rosettes. This wallpaper was used in the Regatta Restaurant at the Festival of Britain."

The image and text are from the website dedicated to the exhibition 
From Atoms To Patterns   (2008)
Feel free to explore at 
http://www.wellcomecollection.org/whats-on/exhibitions/from-atoms-to-patterns.aspx

And when you have 44 mins of free time ;-) +The Royal Institution shared a great video today 
A Century of Crystallography: the Braggs Legacy
http://youtu.be/a-jE7BM902Q

Have a great day :-) 

Image downloaded from:
http://www.wellcomecollection.org/whats-on/exhibitions/from-atoms-to-patterns/image-galleries/the-scientists.aspx?view=insulin-827-wallpaper
V&A Images/Victoria and Albert Museum

#sciencehistory  ___

2014-09-23 16:14:29 (10 comments, 0 reshares, 9 +1s)Open 

Firma wynajęła dodatkowe biuro. I oczywiście po 10 latach w poprzednim przenieśli mnie do tego nowego. Dziwnie. Zwłaszcza ze względu na ostentacyjną pogardę dla tradycji europejskiego egalitaryzmu objawiającą się w jednej toalecie dla mężczyzn i dwóch toaletach dla pań - tymczasowo opisanych, jedna jako dla "women" a druga dla "ladies"...

Firma wynajęła dodatkowe biuro. I oczywiście po 10 latach w poprzednim przenieśli mnie do tego nowego. Dziwnie. Zwłaszcza ze względu na ostentacyjną pogardę dla tradycji europejskiego egalitaryzmu objawiającą się w jednej toalecie dla mężczyzn i dwóch toaletach dla pań - tymczasowo opisanych, jedna jako dla "women" a druga dla "ladies"...___

posted image

2014-09-22 14:05:59 (2 comments, 0 reshares, 5 +1s)Open 

Inequality is rising. Or is it? Ton van Schaik on a crucial factor being overlooked:

http://wef.ch/1ucdrdf

Chart: http://wef.ch/1ucdshp

Inequality is rising. Or is it? Ton van Schaik on a crucial factor being overlooked:

http://wef.ch/1ucdrdf

Chart: http://wef.ch/1ucdshp___

2014-09-21 10:04:18 (4 comments, 0 reshares, 17 +1s)Open 

Muszę się zabrać za skończenie prezentacji. Muszę już od siódmej. Odwlekanie przez pięć godzin kosztowało mnie na razie dobrych kilka rozdziałów "Wojny i pokoju", wyjście do sklepu, partyjkę w "Angry birds", dwa zadania z tegorocznej olimpiady matematycznej, artykuł o TAFTA i niniejszy post. Kończą mi się pomysły i chyba w końcu zacznę z tą prezentacją...

Muszę się zabrać za skończenie prezentacji. Muszę już od siódmej. Odwlekanie przez pięć godzin kosztowało mnie na razie dobrych kilka rozdziałów "Wojny i pokoju", wyjście do sklepu, partyjkę w "Angry birds", dwa zadania z tegorocznej olimpiady matematycznej, artykuł o TAFTA i niniejszy post. Kończą mi się pomysły i chyba w końcu zacznę z tą prezentacją...___

2014-09-20 11:59:10 (4 comments, 0 reshares, 17 +1s)Open 

29-ta w Krakowie. Trzy pasy w jedną, trzy w drugą, przez środek betonowa bariera. Ruch duży. Do przejścia dla pieszych ca 100m. Na środku, przy barierze stoi żul i macha ręką. Drugi stoi na przystanku i krzyczy:
-Masz???
-Mam!
- To chodź!
Ten na środku patrzy na sięgającą mu do wysokości krocza barierę z obrzydzeniem i wrzeszczy przekrzykując objeżdżające go samochody:
- Ale mokro!!!! (dziś w Krakowie podlewa rzeczywiście)
- chodź, chodź - pogania ten z przystanku
Ten z ulicy bada dalej wzrokiem barierę, zapewne wyobraża sobie, jak przekraczając moczy spodnie w kroku i w końcu zrezygnowany rusza wzdłuż niej środkiem ulicy w kierunku przejścia... Zarządzanie ryzykiem.

29-ta w Krakowie. Trzy pasy w jedną, trzy w drugą, przez środek betonowa bariera. Ruch duży. Do przejścia dla pieszych ca 100m. Na środku, przy barierze stoi żul i macha ręką. Drugi stoi na przystanku i krzyczy:
-Masz???
-Mam!
- To chodź!
Ten na środku patrzy na sięgającą mu do wysokości krocza barierę z obrzydzeniem i wrzeszczy przekrzykując objeżdżające go samochody:
- Ale mokro!!!! (dziś w Krakowie podlewa rzeczywiście)
- chodź, chodź - pogania ten z przystanku
Ten z ulicy bada dalej wzrokiem barierę, zapewne wyobraża sobie, jak przekraczając moczy spodnie w kroku i w końcu zrezygnowany rusza wzdłuż niej środkiem ulicy w kierunku przejścia... Zarządzanie ryzykiem.___

posted image

2014-09-19 15:41:19 (1 comments, 0 reshares, 1 +1s)Open 

Chess gets little attention or respect these days. Maybe it's because today's computers can beat even the top world champions, or that ordinary folks can't comprehend what's going on in the top games, the way they can follow along in, say, the world series of poker. St. Louis has become the US chess center of gravity, and it just hosted a tournament, the Sinquefield Cup, with the strongest field of players in the world, that yielded an upset by the world's now #2 player, who went undefeated with 7 straight wins and then 3 draws, which was utterly shocking, considering the strength of his competition. But there were only 100 spectators, and the online broadcast world-wide only drew 75k viewers, a joke compared to the 32 million viewers that watched the streamed video game "League of Legends" championship, for example. 

The winner, left below, and now #2 in the... more »

Chess gets little attention or respect these days. Maybe it's because today's computers can beat even the top world champions, or that ordinary folks can't comprehend what's going on in the top games, the way they can follow along in, say, the world series of poker. St. Louis has become the US chess center of gravity, and it just hosted a tournament, the Sinquefield Cup, with the strongest field of players in the world, that yielded an upset by the world's now #2 player, who went undefeated with 7 straight wins and then 3 draws, which was utterly shocking, considering the strength of his competition. But there were only 100 spectators, and the online broadcast world-wide only drew 75k viewers, a joke compared to the 32 million viewers that watched the streamed video game "League of Legends" championship, for example. 

The winner, left below, and now #2 in the world, and my personal favorite player, is 22-year-old Fabiano Caruana, who learned to play chess at a synagogue in Park Slope, Brooklyn. At 14, he became the youngest USA–born grandmaster ever, though he has since relocated to Italy. I am rooting for and expect him to become the world champ pretty soon. On the right, the current 23-year-old world champ and maybe least-nerd-looking, most attractive pretty-boy chess star Magnus Carlsen of Norway, who even has modeling contracts for clothing. He was the favorite, but Caruana ripped him apart, in the biggest blow-out upset ever. The nerd kicked the hottie's ass.

These grandmasters draw their games most of the time, so you get a few important wins or losses and the rest of the games are tied with draws. 7 wins and 3 draws against the best players in the world is unheard of (except for a computer). This Slate article tells of the tournament, and of the retired rich fan, Rex Sinquefield, who grew up an orphan from St. Louis, became hugely successful and rich in the stock market, inventing the first passively managed, market-weighted S&P 500 index fund. Retired, he moved back to St. Louis and poured his wealth into his favorite hobby, chess, and built a 6,000 square foot chess center of playing halls, libraries, and classrooms, with now more than 1,000 dues-paying members, and a World Chess Hall of Fame across the street, making St.Louis the place to be these days for the country's top players. 

I'm just sad I wasn't there to see all this happen, but hey, there's always internet streaming. If I said, "hey, how about a road trip to St. Louis to see the most awesome chess tournament ever," I wouldn't get a single taker, even among my geek board-game-playing friends, This game gets no respect. But it should. I'm not that good at it (a pitiful 1800 rating, which is barely above average for those who play in tournaments), but I like to teach the game, and I'm good enough to follow the games and be awed with how brilliant and beautiful these international grandmasters' games can be. I wish more people were. In any case, great Slate article on the event.

#chess   #boardgames  ___

2014-09-14 20:01:24 (7 comments, 0 reshares, 28 +1s)Open 

Jako samouk w wielu dziedzinach (w sumie zarabiam na życie tym w czym jestem samoukiem, za to czego mnie uczyli nikt mi nie płaci - byłoby to paradoksalne, gdyby nie tak powszechne), może mogę się miarodajnie wypowiedzieć w następującej kwestii: Otóż optymalna książka do nauki czegoś nowego powinna zawierać około 75% materiału znanego i resztę nieznanego . To pozwala zachować efekt zafrapowania materiałem, akcja jest wciągająca i zrozumiała, i oczywiście to w dużej czści powtórka. Nowy materiał w tak wartkiej akcji wchłania się niemal bezboleśnie. A potem następna, ciut znowu trudniejsza książka. Taka obróbka skrawaniem.

Jako samouk w wielu dziedzinach (w sumie zarabiam na życie tym w czym jestem samoukiem, za to czego mnie uczyli nikt mi nie płaci - byłoby to paradoksalne, gdyby nie tak powszechne), może mogę się miarodajnie wypowiedzieć w następującej kwestii: Otóż optymalna książka do nauki czegoś nowego powinna zawierać około 75% materiału znanego i resztę nieznanego . To pozwala zachować efekt zafrapowania materiałem, akcja jest wciągająca i zrozumiała, i oczywiście to w dużej czści powtórka. Nowy materiał w tak wartkiej akcji wchłania się niemal bezboleśnie. A potem następna, ciut znowu trudniejsza książka. Taka obróbka skrawaniem.___

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2014-09-11 17:11:53 (0 comments, 0 reshares, 4 +1s)Open 

Science Museum unveils £5m design for 'world's foremost' mathematics gallery. Centrepiece of gallery will be experimental plane designed using advances in maths of aerodynamics and material stress. http://gu.com/p/4xegf/tw

Science Museum unveils £5m design for 'world's foremost' mathematics gallery. Centrepiece of gallery will be experimental plane designed using advances in maths of aerodynamics and material stress. http://gu.com/p/4xegf/tw___

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2014-09-09 23:31:17 (0 comments, 0 reshares, 1 +1s)Open 

What Do You Believe Is True Even Though You Cannot Prove It?

This is the Dyson Challenge, named after Freeman Dyson, who came up with the challenge in 2005, and also provided a precise mathematical statement that falls, as far as he is concerned, into this category.   The linked blog post gives a nice elucidation of the issue.

What Do You Believe Is True Even Though You Cannot Prove It?

This is the Dyson Challenge, named after Freeman Dyson, who came up with the challenge in 2005, and also provided a precise mathematical statement that falls, as far as he is concerned, into this category.   The linked blog post gives a nice elucidation of the issue.___

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2014-09-09 07:13:28 (0 comments, 1 reshares, 4 +1s)Open 

Science, models, and machine learning

Machine learning is the art of getting computers to learn, so you don't have to explicitly tell them what to do.  People use it in spam filters, search engines that guess what you're trying to find, optical character recognition, cars that drive themselves, and many other things.  But how does it work? 

There are many different approaches, but here +David Tweed explains some of the main ideas:

http://johncarlosbaez.wordpress.com/2014/09/03/science-models-and-machine-learning/

The picture shows one.  Say we're trying to classify dots into two kinds - the kind on the left of the red curve, and the kind on the right.  There are lots of choices of where you could put this red curve.  For the data so far, anything between the dashed curves will work.  Which choice is best?   You'd like amachine ... more »

Science, models, and machine learning

Machine learning is the art of getting computers to learn, so you don't have to explicitly tell them what to do.  People use it in spam filters, search engines that guess what you're trying to find, optical character recognition, cars that drive themselves, and many other things.  But how does it work? 

There are many different approaches, but here +David Tweed explains some of the main ideas:

http://johncarlosbaez.wordpress.com/2014/09/03/science-models-and-machine-learning/

The picture shows one.  Say we're trying to classify dots into two kinds - the kind on the left of the red curve, and the kind on the right.  There are lots of choices of where you could put this red curve.  For the data so far, anything between the dashed curves will work.  Which choice is best?   You'd like a machine to be able to learn this if you teach it with more examples. 

But the red curve is complicated!  Sometimes you can simplify the problem by doing some preprocessing.  That's the function ϕ here.  This takes our problem and changes it to one where the red curve becomes a straight line!  Now the machine can look for the best straight line - with some alternate choices shown as dashed lines.  This is easier, because the formula for a line is simpler.

Of course, all this raises tons of questions.  How do we find the function ϕ in the first place?  In practice there will be lots of choices, none perfect.  Which one is best?   And then, which choice of line is best?  What does "best" even mean here?

Some of these questions have a deep philosophical aspect to them - they're about cognition,  how we can divide the messy world into neat pieces, and what it means to "know" something.  But they're also extremely practical!    And they're not just about machine learning - they're about science and modeling in general.

David Tweed's article is a great introduction.  My little article here is just an introduction to the introduction!

All this is part of the Azimuth Code Project.  The big challenge is to use machine learning to help predict El Niños.  But our strategy is to explain things as we go, so that even if we don't succeed in the end, we'll have educated a lot of people... including ourselves.

#El_Niño___

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2014-09-08 05:05:57 (0 comments, 1 reshares, 4 +1s)Open 

Theorema Egregium. Smacznego!

How a 19th Century Math Genius Taught Us the Best Way to Hold a Pizza Slice

This is why math is awesome: the same principle applies to everything from pizza to architecture to maps to the mantis shrimp: http://goo.gl/DznALh

And also: blades of grass, power plants, fashion design, and why you can't crush an egg if you wrap your fingers around it.

A great read for +ScienceSunday!

http://goo.gl/DznALh

#ScienceSunday  ___Theorema Egregium. Smacznego!

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2014-09-06 20:01:42 (8 comments, 3 reshares, 23 +1s)Open 

Today is the day Marty McFly goes to the future!

#woohoo   #sciencebitch  

Today is the day Marty McFly goes to the future!

#woohoo   #sciencebitch  ___

2014-09-06 18:18:04 (7 comments, 0 reshares, 19 +1s)Open 

Całą mą wczesną młodość straszyli mnie wojną atomową. W TV, radiu, w szkole itp. W wieku chyba 16 lat w czasie samotnego spaceru po kołosanockich wzgórzach tzw. Glinicach, patrząc na panoramę miasta miałem jakiś straszny atak paniki, gdy wyobraźnia podsunęła mi apokaliptyczne obrazy. Jak się otrząsnąłem po kilkunastu minutach i wrócił mi spokój, stwierdziłem, że to pierdolę i nie mam zamiaru się więcej bać ani dać zastraszać tym gównem.
Choć oczywiście jak teraz straszą, to żal, że w razie czego, nie ma czym oddać.

Całą mą wczesną młodość straszyli mnie wojną atomową. W TV, radiu, w szkole itp. W wieku chyba 16 lat w czasie samotnego spaceru po kołosanockich wzgórzach tzw. Glinicach, patrząc na panoramę miasta miałem jakiś straszny atak paniki, gdy wyobraźnia podsunęła mi apokaliptyczne obrazy. Jak się otrząsnąłem po kilkunastu minutach i wrócił mi spokój, stwierdziłem, że to pierdolę i nie mam zamiaru się więcej bać ani dać zastraszać tym gównem.
Choć oczywiście jak teraz straszą, to żal, że w razie czego, nie ma czym oddać.___

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2014-09-06 13:04:46 (0 comments, 0 reshares, 7 +1s)Open 

Seventeen fake cellphone towers were discovered across the U.S. last week. Owned by mysterious entities, they look like Verizon or AT&T towers etc, but sift and steal messages, texts… anything they want. Interceptor use in the U.S. is much higher than people had anticipated. One of our customers took a road trip from Florida to North Carolina and he found eight different interceptors on that trip.  

http://finance.yahoo.com/news/mysterious-fake-cellphone-towers-intercepting-162645809.html

Seventeen fake cellphone towers were discovered across the U.S. last week. Owned by mysterious entities, they look like Verizon or AT&T towers etc, but sift and steal messages, texts… anything they want. Interceptor use in the U.S. is much higher than people had anticipated. One of our customers took a road trip from Florida to North Carolina and he found eight different interceptors on that trip.  

http://finance.yahoo.com/news/mysterious-fake-cellphone-towers-intercepting-162645809.html___

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2014-09-03 19:01:25 (0 comments, 2 reshares, 9 +1s)Open 

Useful graphic comparing the sizes of various large optical and infrared telescopes (current and planned) around the world.
http://en.wikipedia.org/wiki/Optical_telescope
HT +Catherine Qualtrough 

Useful graphic comparing the sizes of various large optical and infrared telescopes (current and planned) around the world.
http://en.wikipedia.org/wiki/Optical_telescope
HT +Catherine Qualtrough ___

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2014-09-02 04:29:41 (0 comments, 0 reshares, 7 +1s)Open 

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! ___

2014-09-01 16:20:39 (7 comments, 0 reshares, 19 +1s)Open 

Wychodząc z pracy i przechodząc obok boiska piłkarskiego, które sobie firma urządziła (podobnie jak zresztą siatkarskie) przy swoim budynku, natknąłem się na rozgrywki fazy grupowej w naszej wewnętrznej lidze. To, a zwłaszcza widok ubranych w swoje organizacyjne stroje piłkarzy z drużyn czekających na rozgrywkę stanowiących jednocześnie grupę kibiców drużyn aktualnie grających (również organizacyjnie ubranych) sprowokowało mnie do pytania, jak wyglądałby mecz w następującej grze: mamy cztery drużyny, grają na raz i wygrywa strzelająca najwięcej goli? (samobóje są nieuznawane). A co, gdyby wygrywała drużyna która ma największy max(p,q) gdzie p i q to odpowiednio ilość goli zdobytych i straconych? A co jeśli p+|p-q| albo q+|p-q|? A jeśli wtedy dopuścić samobóje? Czy dochodziło by do zawiązywania chwilowych koalicji w którymś wariancie? Bohaterskich obronbramki przeciwnika przed zawodnikami jego drużyny... more »

Wychodząc z pracy i przechodząc obok boiska piłkarskiego, które sobie firma urządziła (podobnie jak zresztą siatkarskie) przy swoim budynku, natknąłem się na rozgrywki fazy grupowej w naszej wewnętrznej lidze. To, a zwłaszcza widok ubranych w swoje organizacyjne stroje piłkarzy z drużyn czekających na rozgrywkę stanowiących jednocześnie grupę kibiców drużyn aktualnie grających (również organizacyjnie ubranych) sprowokowało mnie do pytania, jak wyglądałby mecz w następującej grze: mamy cztery drużyny, grają na raz i wygrywa strzelająca najwięcej goli? (samobóje są nieuznawane). A co, gdyby wygrywała drużyna która ma największy max(p,q) gdzie p i q to odpowiednio ilość goli zdobytych i straconych? A co jeśli p+|p-q| albo q+|p-q|? A jeśli wtedy dopuścić samobóje? Czy dochodziło by do zawiązywania chwilowych koalicji w którymś wariancie? Bohaterskich obron bramki przeciwnika przed zawodnikami jego drużyny? Ktoś by się w ogóle połapał? A gdyby tak jeszcze, zamiast jednej wpuścić dwie piłki, żeby podkreślić element współbieżności?
I jak w takich wariantach wyglądałyby trybuny? Kibole innych drużyn nie zawsze byliby jednoznacznymi wrogami? Ile czasu wytrzymałby sędzia zanim popadłby w szaleństwo?___

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2014-08-29 07:02:57 (2 comments, 0 reshares, 5 +1s)Open 

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2014-08-28 10:05:30 (4 comments, 0 reshares, 10 +1s)Open 

China claims to have moved a step closer to creating a supersonic, supercavitating submarine that could travel from Shanghai to San Francisco in less than two hours.

From: http://www.scmp.com/news/china/article/1580226/shanghai-san-francisco-100-minutes-chinese-supersonic-submarine

Water produces more friction, or drag, on an object than air, which means conventional submarines cannot travel as fast as an aircraft. However, during the cold war, the Soviet military developed a technology called supercavitation, which involves enveloping a submerged vessel inside an air bubble to avoid problems caused by water drag.

A Soviet supercavitation torpedo called Shakval was able to reach a speed of 230 mph or more - much faster than any other conventional torpedoes. In theory, a supercavitating vessel could reach the speed of sound underwater, or about 3600 mph, which would... more »

China claims to have moved a step closer to creating a supersonic, supercavitating submarine that could travel from Shanghai to San Francisco in less than two hours.

From: http://www.scmp.com/news/china/article/1580226/shanghai-san-francisco-100-minutes-chinese-supersonic-submarine

Water produces more friction, or drag, on an object than air, which means conventional submarines cannot travel as fast as an aircraft. However, during the cold war, the Soviet military developed a technology called supercavitation, which involves enveloping a submerged vessel inside an air bubble to avoid problems caused by water drag.

A Soviet supercavitation torpedo called Shakval was able to reach a speed of 230 mph or more - much faster than any other conventional torpedoes. In theory, a supercavitating vessel could reach the speed of sound underwater, or about 3600 mph, which would reduce the journey time for a transatlantic underwater cruise to less than an hour, and for a transpacific journey to about 100 minutes, according to a report by California Institute of Technology in 2001.

However, supercavitation technology has faced two major problems. First, the submerged vessel has needed to be launched at high speeds, approaching 60 mph, to generate and maintain the air bubble.

Second, it is extremely difficult - if not impossible - to steer the vessel using conventional mechanisms, such as a rudder, which are inside the bubble without any direct contact with water. ___

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2014-08-28 07:14:31 (0 comments, 0 reshares, 25 +1s)Open 

Why we should use the Imperial System.

Why we should use the Imperial System.___

2014-08-28 06:19:02 (0 comments, 0 reshares, 11 +1s)Open 

Usiłuję dostać się z Podgórza do pracy. Tragedia. Jeśli chodzi o OPR(*) to są dziś w Europie trzy konkurujące o prymat miasta. Donieck, Ługańsk i Kraków. Dwie pierwsze załatwiły rakiety Grad a trzecie prezydent M.

(*) Ogólny Poziom R..a

Usiłuję dostać się z Podgórza do pracy. Tragedia. Jeśli chodzi o OPR(*) to są dziś w Europie trzy konkurujące o prymat miasta. Donieck, Ługańsk i Kraków. Dwie pierwsze załatwiły rakiety Grad a trzecie prezydent M.

(*) Ogólny Poziom R..a___

2014-08-27 12:21:13 (14 comments, 0 reshares, 12 +1s)Open 

Właśnie sie zorientowałem, że wczoraj, rozmawiając z kolegą mówiliśmy obaj o ulicy Konopnickiej, mając na myśli ulicę Orzeszkowej.
To mi przypomniało zabawną rozmowę sprzed lat z panem taksówkarzem na temat oddziału pewnego banku czynnego, wg strony internetowej, w sobotę, który to oddział, jak podpowiadała mi pamięć tego co przeczytałem, był na ulicy Okulickiego, na której - twierdził pan taksówkarz - żadnego oddziału owego banku nie ma. Oczywiście był, ale na Bora-Komorowskiego w Krokusie i o ten oddział chodziło. Ciekawe, czy gdyby ulice były u nas numerowane zamiast nazywane, rzadziej bym się mylił w ten sposób. Sądzę, że nie. W końu 23 łatwo pomylić z 32 albo np 18 z 24 (bo jedno to 2*3^2 a drugie 3*2^3) 

Właśnie sie zorientowałem, że wczoraj, rozmawiając z kolegą mówiliśmy obaj o ulicy Konopnickiej, mając na myśli ulicę Orzeszkowej.
To mi przypomniało zabawną rozmowę sprzed lat z panem taksówkarzem na temat oddziału pewnego banku czynnego, wg strony internetowej, w sobotę, który to oddział, jak podpowiadała mi pamięć tego co przeczytałem, był na ulicy Okulickiego, na której - twierdził pan taksówkarz - żadnego oddziału owego banku nie ma. Oczywiście był, ale na Bora-Komorowskiego w Krokusie i o ten oddział chodziło. Ciekawe, czy gdyby ulice były u nas numerowane zamiast nazywane, rzadziej bym się mylił w ten sposób. Sądzę, że nie. W końu 23 łatwo pomylić z 32 albo np 18 z 24 (bo jedno to 2*3^2 a drugie 3*2^3) ___

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2014-08-26 07:28:22 (0 comments, 1 reshares, 5 +1s)Open 

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2014-08-25 07:51:26 (2 comments, 1 reshares, 3 +1s)Open 

Co czytamy dziś w gazecie? Ano czytamy:

http://wyborcza.pl/1,75478,16524340,To_nie_kabaret__to_luk_prawicy_w_stolicy.html#BoxSlotIMT

Najbardziej podoba mi się ten Król Duch i OMC premier techniczny, profesor Gliński. Profesor podkreślę.

Wczoraj wieczorem, ponieważ kiedyś przeczytałem, że Putin cytuje i powołuje się często na Bierdiajewa, zacząłem czytać "Ideę rosyjską" tegoż Bierdiajewa, licząc, że coś zrozumiem z tego co wyrabiają Rosjanie. Chyba rozumiem.  Jeżeli ktoś serio myśli o polityce w kategoriach wziętych z tej książki, czy szerzej, z podobnego nurtu myśli, w zasadzie kwalifikuje się do łagodnej obserwacji psychiatrycznej. A zdaje sie, że oni tak serio - w księgarni naukowej na Podwalu natknąłem się na książke niejakiej Tatiany Graczowej " Święta Ruś przeciwko Chazarii". Podobnoż pani Tatiana pracujew jakimś "ośrodku studiów strategicznyc... more »

Co czytamy dziś w gazecie? Ano czytamy:

http://wyborcza.pl/1,75478,16524340,To_nie_kabaret__to_luk_prawicy_w_stolicy.html#BoxSlotIMT

Najbardziej podoba mi się ten Król Duch i OMC premier techniczny, profesor Gliński. Profesor podkreślę.

Wczoraj wieczorem, ponieważ kiedyś przeczytałem, że Putin cytuje i powołuje się często na Bierdiajewa, zacząłem czytać "Ideę rosyjską" tegoż Bierdiajewa, licząc, że coś zrozumiem z tego co wyrabiają Rosjanie. Chyba rozumiem.  Jeżeli ktoś serio myśli o polityce w kategoriach wziętych z tej książki, czy szerzej, z podobnego nurtu myśli, w zasadzie kwalifikuje się do łagodnej obserwacji psychiatrycznej. A zdaje sie, że oni tak serio - w księgarni naukowej na Podwalu natknąłem się na książke niejakiej Tatiany Graczowej " Święta Ruś przeciwko Chazarii". Podobnoż pani Tatiana pracuje w jakimś "ośrodku studiów strategicznych" Rosji  czy coś podobnego. Pięknie. Pięknie, że pracuje, pięknie że pisze i pięknie, naprawdę kurwa pięknie, że sprzedaje swoje książki w księgarniach,  naukowych przypominam, w naszym kraju.  Czy tylko mnie się wydaje, że  pogrążamy się w szaleństwie?

Łuk, Król Duch z profesorem Glińskim i żoliborsko-inteligenckim zapleczem intelektualnym komponują mi się z tym  wyjątkowo ładnie. Jak awers i rewers tej samej monety. Czy "Księgi narodu i pielgrzymstwa polskiego" są na liście lektur? Nie? To czuję, że wkrótce będą.___

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2014-08-25 07:28:59 (0 comments, 0 reshares, 4 +1s)Open 

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 14:49:49 (0 comments, 0 reshares, 6 +1s)Open 

The arithmetic derivative, the Goldbach conjecture, and the twin prime conjecture

Can you differentiate a number and get a nonzero answer? You can't with the usual kind of differentiation, but you can with the arithmetic derivative.

The basic version of the arithmetic derivative takes positive integers as inputs. The only requirements are the two shown in the picture: (1) the derivative of a prime number is 1, and (2) the product rule holds. It can be proved fairly easily that there is only one function satisfying these requirements. This function is known as the arithmetic derivative, and a formula for it is given at the bottom of the picture in terms of the factorization of n into prime powers. The table shows the values of the derivatives of the first few positive integers; these values will always be other nonnegative integers.

The first person to... more »

The arithmetic derivative, the Goldbach conjecture, and the twin prime conjecture

Can you differentiate a number and get a nonzero answer? You can't with the usual kind of differentiation, but you can with the arithmetic derivative.

The basic version of the arithmetic derivative takes positive integers as inputs. The only requirements are the two shown in the picture: (1) the derivative of a prime number is 1, and (2) the product rule holds. It can be proved fairly easily that there is only one function satisfying these requirements. This function is known as the arithmetic derivative, and a formula for it is given at the bottom of the picture in terms of the factorization of n into prime powers. The table shows the values of the derivatives of the first few positive integers; these values will always be other nonnegative integers.

The first person to investigate the arithmetic derivative systematically seems to have been E.J. Barbeau in 1961, although the function had previously appeared in 1950 as a question on a Putnam Prize competition. The first known reference to the function seems to have been in a conference talk in June 1911 by the Spanish mathematician José Mingot Shelly.

The arithmetic derivative has a number of interesting properties, as well as close connections to some famous problems in number theory. It also allows for the study of differential equations involving natural numbers, using the arithmetic derivative in place of the usual derivative. For example, the only solution of the differential equation n'=0 is n=1, and the only solution of n'=1 is for n to be prime. Both of these results are easy exercises.

An excellent introduction to this area is the 2003 paper by Victor Ufnarovski and Bo Åhlander entitled How to Differentiate a Number, which builds on Barbeau's work. The paper contains the above two results but proves many others and offers several conjectures. Some of these conjectures relate to famous open problems in number theory, such as the Goldbach conjecture and the twin prime conjecture.

The Goldbach conjecture is the hypothesis that every even integer greater than 2 can be expressed as the sum of two primes. Ufnarovski and Åhlander conjecture that the (arithmetic) differential equation n'=2b has a positive integer solution for any natural number b > 1; in other words, that any even number greater than 2 shows up as the arithmetic derivative of some natural number. They point out that the Goldbach conjecture implies this conjecture; this is because if 2b is the sum of the primes p and q, then the arithmetic derivative of the number n=pq is 2b. (Note that this is a one-way implication, and it does not mean that a proof of this differential equation identity would prove the Goldbach conjecture.)

The twin prime conjecture is the hypothesis that there are infinitely many primes p such that p+2 is also prime. This is still an open problem, although there have been breakthroughs towards proving this in the last year or so, thanks to work of Yitang Zhang, Terence Tao and others. Ufnarovski and Åhlander conjecture that the differential equation n''=1 has infinitely many solutions, and they point out that the twin prime conjecture would imply this. The reason for this is that if p and p+2 are both primes, then n=2p is a solution to the equation n''=1. (As in the case of the other conjecture, this is a one-way implication.)

There are many generalizations of the arithmetic derivative, some of which are discussed in the paper. For example, the derivative can be extended to negative numbers by changing the sign, and to rational numbers by requiring the derivative to satisfy the quotient rule. It can also be extended to unique factorization domains (UFDs), which are algebraic systems in which elements can be factorized into primes in an essentially unique way. An example of a UFD other than the integers is the Gaussian integers, which is the set of all complex numbers of the form a+bi where a and b are integers.

Relevant links

Wikipedia on the arithmetic derivative: http://en.wikipedia.org/wiki/Arithmetic_derivative

The On-Line Encyclopedia of Integer Sequences on the arithmetic derivative: https://oeis.org/A003415

Ufnarovski and Åhlander's paper: https://cs.uwaterloo.ca/journals/JIS/VOL6/Ufnarovski/ufnarovski.html

A paper by +Mike Stay on a version of the arithmetic derivative for finite fields: https://cs.uwaterloo.ca/journals/JIS/VOL8/Stay/stay44.html

The Goldbach conjecture: http://en.wikipedia.org/wiki/Goldbach_conjecture

The twin prime conjecture: http://en.wikipedia.org/wiki/Twin_primes_conjecture

(Found via Evelyn Lamb on Twitter.)

#mathematics #scienceeveryday___

2014-08-22 21:10:06 (19 comments, 2 reshares, 17 +1s)Open 

Czy nie można zrezygnować z tej maniery okraszania zaniepokojenia przymiotnikiem w rodzaju "głębokie", "najgłębsze" itd. Biorąc pod uwagę możliwości stopniowania przymiotników, dyplomaci i rządy, które im płacą tkwią w pułapce - po kilku dniach kryzysu brakuje już możliwości wyrażenia jeszcze większego zaniepokojenia niż ostatnio. Sądzę, że może to wywoływać mylne wrażenie, że zaniepokojenie uległo stabilizacji i już się nie zmienia.
sądzę, że dyplomacja powinna zaadoptować - idąc za językiem młodzieży - sposób stopniowania wzięty z stosowanego w nauce sposobu tworzenia jednostek wyższego rzędu. Tj. Można by mówić, kiedy w jakimś kraju inny wywołuje niepokoje, że jesteśmy zaniepokojeni, kiedy płaci tamtejszym terrorystom, że jesteśmy megazaniepokojeni,, kiedy dostarcza broń i przerzuca żołnierzy, że gigazaniepokojeni,przy otwartej wojnie lub kiedy ktoś wjeżdża w cudze granice... more »

Czy nie można zrezygnować z tej maniery okraszania zaniepokojenia przymiotnikiem w rodzaju "głębokie", "najgłębsze" itd. Biorąc pod uwagę możliwości stopniowania przymiotników, dyplomaci i rządy, które im płacą tkwią w pułapce - po kilku dniach kryzysu brakuje już możliwości wyrażenia jeszcze większego zaniepokojenia niż ostatnio. Sądzę, że może to wywoływać mylne wrażenie, że zaniepokojenie uległo stabilizacji i już się nie zmienia.
sądzę, że dyplomacja powinna zaadoptować - idąc za językiem młodzieży - sposób stopniowania wzięty z stosowanego w nauce sposobu tworzenia jednostek wyższego rzędu. Tj. Można by mówić, kiedy w jakimś kraju inny wywołuje niepokoje, że jesteśmy zaniepokojeni, kiedy płaci tamtejszym terrorystom, że jesteśmy megazaniepokojeni,, kiedy dostarcza broń i przerzuca żołnierzy, że gigazaniepokojeni, przy otwartej wojnie lub kiedy ktoś wjeżdża w cudze granice jak w swoje. można wyrazić terazaniepokojenie, przy okupacji pentazaniepokojenie itd. To się też kończy w jakimś momencie. Wtedy należy przejść na współczynnik numeryczny wyrażony jako potęga dziesiątki. Np, "jesteśmy 10^24-zaniepokojeni" kiedy państwo zostanie wcielone w inne bo tak sobie pożeracz wymyślił.___

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2014-08-20 18:36:54 (3 comments, 0 reshares, 8 +1s)Open 

Coś mi się wydaje, że wkrótce ktoś nam każe płacić za ochronę...

Rusko plánuje stavbu systému na likvidaci asteroidů, komet i kosmického smetí.___Coś mi się wydaje, że wkrótce ktoś nam każe płacić za ochronę...

2014-08-18 16:52:43 (3 comments, 0 reshares, 10 +1s)Open 

Czytam sobie z przyjemnością "Matematykę przy kominku" Michała Szurka. Zbiór esejów i "małych form" na tematy około matematyczne. Część znana mi z dawnych lektur różnych pism w rodzaju "Młodego Technika" dawno temu, ale wg. słów autora opracowana na nowo. Lektura miła, sympatyczna, kulturalna - a przez to "dawno temu" trochę sentymentalna.
Trochę mnie wszak denerwuje, że znalazłem już dwa błędy we wzorach i oznaczeniach i kilka przeoczeń redaktorskich w tekście. O ile mogę odpuścić to co w tekście, zwłaszcza, że wystąpiły niekrytycznych fragmentach, o tyle do tych "matematycznych" stosunek mam bardziej skomplikowany. Otóż młoda osoba, lub niekoniecznie młoda ale sięgająca po jeden z tekstów by poszerzyć swoje horyzonty może być poważnie skonfundowana i, w przypadku gdy dodatkowo jest niepewna swoichzdolności zrozumienia uznać po prostu, że ni... more »

Czytam sobie z przyjemnością "Matematykę przy kominku" Michała Szurka. Zbiór esejów i "małych form" na tematy około matematyczne. Część znana mi z dawnych lektur różnych pism w rodzaju "Młodego Technika" dawno temu, ale wg. słów autora opracowana na nowo. Lektura miła, sympatyczna, kulturalna - a przez to "dawno temu" trochę sentymentalna.
Trochę mnie wszak denerwuje, że znalazłem już dwa błędy we wzorach i oznaczeniach i kilka przeoczeń redaktorskich w tekście. O ile mogę odpuścić to co w tekście, zwłaszcza, że wystąpiły niekrytycznych fragmentach, o tyle do tych "matematycznych" stosunek mam bardziej skomplikowany. Otóż młoda osoba, lub niekoniecznie młoda ale sięgająca po jeden z tekstów by poszerzyć swoje horyzonty może być poważnie skonfundowana i, w przypadku gdy dodatkowo jest niepewna swoich zdolności zrozumienia uznać po prostu, że nie rozumie dlaczego tak, bo nie ma "talentu do matematyki". W tekście popularyzującym (ale wciąż matematycznym) błąd (zwykle przecież w takim tekście jakiś głupi, typograficzny czy jakaś zamiana liter np.) to poważny grzech. W tym przypadku bardziej redaktora merytorycznego niż autora.
W ogólności, w świecie literatury matematycznej dla zawodowców, nie jest to jakaś straszna sprawa. Wytrawny i wierzący w swoje siły czytelnik zwykle zauważy, że coś jest nie tak i albo od razu skoryguje w umyśle, albo "odłoży sobie na stosie", że coś jest nie tak, pójdzie dalej i zwykle wszystko się wkrótce wyjaśnia. No chyba, że to luka wymagająca większej pracy by ją wypełnić, albo prawdziwy Błąd.
W każdym razie książkę Michała Szurka szczerze polecam, mimo tych kilku grzechów redaktorskich. Świetna lektura dla lubiących myśleć i lubiących czytać lubiących myśleć i pisać.___

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2014-08-14 18:36:17 (0 comments, 0 reshares, 10 +1s)Open 

“Maurits, stop picking at it. You'll only make it worse.” by David Swart

Maurits was the first name of the Dutch artist M.C. Escher (1898–1972), and this 2006 picture by David Swart is based on Escher's pictures Rind and Bond of Union.

The tiling shown in the picture is a Penrose tiling. It is possible to tile the entire plane with tiles like these, in such a way that the tiling has fivefold rotational symmetry, but no translational symmetry. Penrose tilings are named after the mathematical physicist Roger Penrose. Penrose and his father, Lionel Penrose, devised the physically impossible Penrose stairs, which feature in Escher's picture Ascending and Descending.

David Swart's Flickr page (https://www.flickr.com/photos/dmswart) contains many other excellent Escherified photographs. If you look at thecomme... more »

“Maurits, stop picking at it. You'll only make it worse.” by David Swart

Maurits was the first name of the Dutch artist M.C. Escher (1898–1972), and this 2006 picture by David Swart is based on Escher's pictures Rind and Bond of Union.

The tiling shown in the picture is a Penrose tiling. It is possible to tile the entire plane with tiles like these, in such a way that the tiling has fivefold rotational symmetry, but no translational symmetry. Penrose tilings are named after the mathematical physicist Roger Penrose. Penrose and his father, Lionel Penrose, devised the physically impossible Penrose stairs, which feature in Escher's picture Ascending and Descending.

David Swart's Flickr page (https://www.flickr.com/photos/dmswart) contains many other excellent Escherified photographs. If you look at the comments section for this picture, you will find a brief explanation of how he created this effect.

Relevant links

Rind by M.C. Escher: http://www.mcescher.com/gallery/most-popular/rind/

Bond of Union by M.C. Escher: http://www.mcescher.com/gallery/recognition-success/bond-of-union/

Ascending and Descending by M.C. Escher: http://en.wikipedia.org/wiki/Ascending_and_Descending

Penrose tilings: http://en.wikipedia.org/wiki/Penrose_tiling

Here's a post by me with more details on the mathematics of Penrose tilings: https://plus.google.com/101584889282878921052/posts/7PZPSLaFkAx

#art #artist #escher #mathematics___

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2014-08-13 11:16:37 (4 comments, 0 reshares, 24 +1s)Open 

To nasi!

A bad day for some tech support person...___To nasi!

2014-08-13 09:40:34 (1 comments, 0 reshares, 1 +1s)Open 

An elementary example of adjoint functors. I like it :-)

http://arxiv.org/abs/1408.2596

Title: Continuity is an adjoint functor
Author: Edward S. Letzter

Abstract: For topological spaces X and Y, a (not necessarily continuous) function f:X --> Y naturally induces a functor from the category of closed subsets of X (with morphisms given by inclusions) to the category of closed subsets of Y. The function f also naturally induces a functor from the category of closed subsets of Y to the category of closed subsets of X. Our aim in this expository note is to show that the function f is continuous if and only if the first of the above two functors is a left adjoint to the second. We thereby obtain elementary examples of adjoint pairs (apparently) not part of the standard introductory treatments of this subject.

#arXiv  

An elementary example of adjoint functors. I like it :-)

http://arxiv.org/abs/1408.2596

Title: Continuity is an adjoint functor
Author: Edward S. Letzter

Abstract: For topological spaces X and Y, a (not necessarily continuous) function f:X --> Y naturally induces a functor from the category of closed subsets of X (with morphisms given by inclusions) to the category of closed subsets of Y. The function f also naturally induces a functor from the category of closed subsets of Y to the category of closed subsets of X. Our aim in this expository note is to show that the function f is continuous if and only if the first of the above two functors is a left adjoint to the second. We thereby obtain elementary examples of adjoint pairs (apparently) not part of the standard introductory treatments of this subject.

#arXiv  ___

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2014-08-13 07:13:31 (0 comments, 0 reshares, 5 +1s)Open 

___

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2014-08-06 18:00:46 (1 comments, 0 reshares, 9 +1s)Open 

Did You Know: The History of Numerals: Indian Numerals

Did You Know: The History of Numerals: Indian Numerals___

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2014-07-31 20:10:59 (7 comments, 2 reshares, 29 +1s)Open 

If we only had an easy way to put IP layer on It....

___If we only had an easy way to put IP layer on It....

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2014-07-26 22:09:35 (1 comments, 1 reshares, 1 +1s)Open 

Z cyklu: co robić po matematyce.

Z cyklu: co robić po matematyce.___

2014-07-24 15:02:10 (4 comments, 0 reshares, 15 +1s)Open 

Od kiedym wrócił z urlopu w sobotę, nie było chyba dnia, by mnie w komunikacji miejskiej nie kontrolowano. Tacy się kanarinios i ich mocodawcy chytrzy na pieniądze, turystów chyba, porobili. Do dziś mi nie przeszkadzało, ale dziś grałem na telefonie i mnie ich napad z nienacka życie kosztował.

Od kiedym wrócił z urlopu w sobotę, nie było chyba dnia, by mnie w komunikacji miejskiej nie kontrolowano. Tacy się kanarinios i ich mocodawcy chytrzy na pieniądze, turystów chyba, porobili. Do dziś mi nie przeszkadzało, ale dziś grałem na telefonie i mnie ich napad z nienacka życie kosztował.___

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2014-07-21 07:44:03 (0 comments, 0 reshares, 2 +1s)Open 

Na końcu artykułu duuużo matematyki, czyli narzędzia przekrętu.

Na końcu artykułu duuużo matematyki, czyli narzędzia przekrętu.___

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