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## John Baez

I'm trying to get mathematicians and physicists to help save the planet.

Occupation: I'm a mathematical physicist. (Centre for Quantum Technologies)

Location: Riverside, California

His ProfilesRankThis is the rank of 'John Baez' out of all Google+ Profiles (individuals).: 2,804 (GenderRankFor the gender 'Men'.: 1,226)

His ProfilesRankThis is the rank of 'John Baez' out of all Google+ Profiles (individuals). in United States: 726 (GenderRankFor the gender 'Men'.: 424)

Followers: 54,379

Following: -

Views: 31,315,688

Cream of the Crop: 11/05/2011

Added to CircleCount.com: 07/21/2011That's the date, where John Baez has been indexed by CircleCount.com.

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### John Baez has been shared in 346 public circles

You can see here the 50 latest shared circles.

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Author | Followers | Date | Users in Circle | Comments | Reshares | +1 | Links | |
---|---|---|---|---|---|---|---|---|

Neil Bailey | 4,132 | If you received the notice you are in this circle, then well done.If you would like to be included in the next Circle Share, you only have to do these simple steps:1 - Include me in your circles (If you haven't already)2 - Share the circle (Publicly) - (cc) me in the comments on the share and I can add you to the next circle immediately. Otherwise I may not notice your activity!3 - Add +1 to the post.4 - Leave a comment if you like.5 - Add the circle or just check it out.Follow your dreams, Share and Be Shared.More you share more you get! :)Thanks!#circles #circleshare #sharedcircle #circlesharing #followers #social #sharedcircles #sharedpubliccircles #circleshared #sharedcircleoftheday #addmetoyourcircles #awesomepeople #circlecount #newfollowers #googleplus #meetingpeoplecircle | 2014-12-15 06:41:38 | 487 | 1 | 2 | 6 | |

exceptional circles | 12,986 | A nice circle for today | 2014-12-13 20:57:47 | 498 | 89 | 105 | 118 | |

Refurio Anachro | 4,796 | Engagers circle October + November. Hi there, you fantastic crowd! Not only have i been feverishly busy of late, and christmas upcoming, on top of that they had strangled my uplink for a week now. So i owe you all a pack of mathy posts, comments daft and curious, and many one-click salutes and appreciations. The people in this circle are friends, all of them curious and critical readers, and many writing original and genuinely interesting stuff. I'm sure everybody here is worthy of consideration to be a friend of yours. Have a look, add us now!Alexander Grothendieck has passed away. There have been some nice obituaries, but maybe not the ones in the press. I should go an collect some, maybe post them with a circle of people who appeared to care...https://plus.google.com/+RefurioAnachro/posts/K4xZTgT2Vf6Apparently, topological sorting can be done using a "normal" sorting algorithm. Do you know more? Or want to? Drop me a note!https://plus.google.com/+RefurioAnachro/posts/EkVfWkgCwik+David Roberts' call for participation, write maths in short words! Maybe just the right occupation for the months where the letters have fallen from the words, to rest beneath sentences in proofwood forest.https://plus.google.com/+RefurioAnachro/posts/UiaXnWuGcDQOn 1+2+3... = -1/12, following up Diagram 20 below. If you found other popular accounts lacking, maybe here's something differently too short for you. Thanks again +Stam Nicolis for prodding, me, who wouldn't see otherwise.https://plus.google.com/+RefurioAnachro/posts/jXAi8a7Gj52A poem by Marion D. Cohen, poet, mathematician.https://plus.google.com/+RefurioAnachro/posts/92PCBKoR7HwDiagram 20: X-Rays of the zeta functionhttps://plus.google.com/+RefurioAnachro/posts/Mux7WctktvoReshared a nice little illustration by +Owen Maresh https://plus.google.com/+RefurioAnachro/posts/DGSdqH5hEDmSeptember engagers circle:https://plus.google.com/+RefurioAnachro/posts/USZFSS95xfn+Spherical Reflections' page, stuff like the above and circle shares.https://plus.google.com/b/117866562756294273963/117866562756294273963/postsYou're in this circle because you reshared, plussed or commented on one of my posts (possibly via +Spherical Reflections), or got into a discussion with me. Thank you!#engage | 2014-12-09 10:38:37 | 90 | 0 | 0 | 0 | |

Rogerio Manica | 29,965 | Engagers #10.I am sharing this circle of recent engagers to celebrate 30,000 followers, which will happen sometime later today. Even tough I was away for many weeks the numbers went only up and I thank circle sharers for keeping me inside their circles. I would also like to thank the people that have engaged with my wife's blog https://havefunwithkids.wordpress.com/ She has finally reached her first 100 followers. It is not an easy task to start a blog at this time. | 2014-12-09 09:02:21 | 308 | 4 | 4 | 14 | |

Sharon Caroline | 3,867 | Hello my friends, good morning/evening for you all!Boost Your visibility On Google+! Add them all!Shared and be shared. :)Thank you for sharing and promoting this. :)#circleshare #sharedcircles #sharingcircles #sharedcircleoftheday | 2014-12-03 10:28:12 | 501 | 0 | 0 | 1 | |

Becky Collins | 19,437 | Diet 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 ? | 2014-12-03 07:12:09 | 426 | 0 | 0 | 0 | |

Rogerio Manica | 29,602 | Engagers #9Most of the people in this circle have engaged with posts from my wife's blog: https://havefunwithkids.wordpress.com/ I have also added engagers of recent photos and people that have included me in their recent shared circles. Engagers 10 will be a brand new circle that I am starting from scratch and will be circulated when I reach 30k followers.Thank you all for the continuous support. | 2014-12-02 11:32:54 | 442 | 23 | 19 | 48 | |

Richard Green | 88,785 | Engagers Showcase Circle, December 1, 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 the posts listed below, in the form of +1s, comments and reshares. I have not posted much in the last couple of months because I have been too busy, and so it has been a long time since the last reshare of the circle.Everyone mentioned below is also included in the circle.Millcreek Canyon Vista (reshared from +Tom Malloy)https://plus.google.com/101584889282878921052/posts/HuXLKw4GBwjAvoiding the unavoidablehttps://plus.google.com/101584889282878921052/posts/TnW3pTWt6d7Hydrangea flowershttps://plus.google.com/101584889282878921052/posts/3LDn2js6pWpMicroscopic Victorian arthttps://plus.google.com/101584889282878921052/posts/ieybEmL7tUCApproximating e using the digits 1–9https://plus.google.com/101584889282878921052/posts/W5E6HyihSuY“Vertebral 03 – Pendant Lampshade” by cordycepthttps://plus.google.com/101584889282878921052/posts/eSo9svRbLapCentred polygonal numbershttps://plus.google.com/101584889282878921052/posts/QowshFUnPZ2Reinventing the wheel: Reuleaux polygonshttps://plus.google.com/101584889282878921052/posts/gDxTM5Ko8hbSunrise at Maroon Lake (reshared from +Jason Hill)https://plus.google.com/101584889282878921052/posts/hvWMqo1HwvVSchmidt arrangementshttps://plus.google.com/101584889282878921052/posts/eM3adto6nsj“Dream Creatures” by Elido Turcohttps://plus.google.com/101584889282878921052/posts/ckjru8sN6AG“The Awakening III—Rebirth” by Luc Railhachttps://plus.google.com/101584889282878921052/posts/KyNg9DD4YnXPoincaré and topologyhttps://plus.google.com/101584889282878921052/posts/bmnd2URRAsfLytham St Annes (reshared from +Paul Haworth)https://plus.google.com/101584889282878921052 | 2014-12-01 22:15:07 | 443 | 146 | 111 | 188 | |

Rajani Vijaya | 0 | My Awesome CircleThis is my circle of the day :)Add people in this circle to increase your follower. Enjoy it!#CircleShare#CircleSharing#Circles#CircleOfTheDay#SharedCircles#Shared#SharedPublicCircles#SharedCircleOfTheDay#Engagers#ShareCircle#SocialMedia#EngagersCircle#Share#Google#SharingCircles#ADD#Friends#SEOtips#Website#Marketing#SEOmarketing#Google#WebDesign#SocialMedia#DigitalMarketing#Business#LocalSEO#OnlineMarketing#Search#SocialMediaMarketing#SEOservices#ContentMarketing#Blogging#SEM#WebDevelopment#SEOStrategy | 2014-11-28 01:58:10 | 480 | 0 | 1 | 2 | |

Ryan Johnson | 19,323 | This circle contains people who are very active on Google+If you received a notification, please reshare to your circlesIf you’d like to be added to the next circle share: • +1 this circle • Share this circle to PUBLIC • Include me in your circles • Comment on this post#circle #Sharedcircles #circleshare #publiccircle #followme #public #sharedpubliccircles #circleoftheday #circleall #circlecircle #circleday #Colombia | 2014-11-27 11:17:05 | 479 | 8 | 4 | 9 | |

Atanas Georgiev Atanasov | 2,751 | SCIENCE AND TECHNOLOGY FRIENDS : Circle V.1.11. Link to my own scientific research topic: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4212005/ To be included in future circle-editions, please ENGAGE: add me to your own circles/+1/re-share/comment on the original circle-post, or on some of the other science-related posts on my wall (this is needed since the number of people that could be circled is limited from Google – and therefore I am forced to keep included just the most active users). Currently featured science-related GOOGLE PLUS post:https://plus.google.com/115938908270684192009/posts/8LU6LVz75jxI would be happy to connect on other networks too:http://about.me/Atanas_At Below I am just pasting some keyords/topics to improve the visibility of the circle and to make it more discoverable: #Science #Research #Technology #NASA #Space #Innovation #Engineering #nutrition #ScienceSunday #Sundayscience #Science #Research #Tech #GameTech #GameTechnology #Microsoft #MicrosoftResearch #innovation #Inflammation #Brain #mindcontrol #photography #tech #socialmedia #googleplus #naturalproduct #artists #foodies #cars | 2014-11-27 06:30:22 | 451 | 4 | 2 | 9 | |

Rogerio Manica | 29,448 | Engagers #8Here comes my version 8 circle of engagers. Recently I had posted only a few entries related to our recent trip to the UK which were published in my wife's blog (http://havefunwithkids.wordpress.com/). I have added the people that have engaged with these posts. I have also posted a couple of videos of my kids in their school performance (http://youtu.be/brmuStXIe88) (http://youtu.be/IiL5Jh9Ncnk). | 2014-11-25 04:03:53 | 302 | 16 | 10 | 29 | |

Atanas Georgiev Atanasov | 1,950 | SCIENCE AND TECHNOLOGY + FRIENDS : CIRCLE V.8; maintained by +Atanas Georgiev Atanasov ; You can learn more about my personal scientific research at: http://www.ncbi.nlm.nih.gov/pubmed/25083916 To be added to the circle, please +1/reshare/comment/add me to your circles. I would be happy to connect on other networks too:http://about.me/Atanas_At Below I am just pasting some keyords/topics to improve the visibility of the circle and to make it more discoverable: #Science #Research #Technology #NASA #Space #Innovation #Engineering #NIAC #nutrition #Entrepreneur #Commercial #ScienceSunday #Sundayscience #Science #Research #Tech #GameTech #GameTechnology #Gaming #VideoGaming #Microsoft #MicrosoftResearch #innovation #Inflammation #Brain #mindcontrol #photography #tech #socialmedia #googleplus #naturalproduct | 2014-11-17 05:24:22 | 362 | 5 | 1 | 11 | |

Atanas Georgiev Atanasov | 1,633 | SCIENCE AND TECHNOLOGY + FRIENDS : CIRCLE V.7; maintained by +AtanasGeorgievAtanasov ; You can learn more about my personal scientific research at: http://www.ncbi.nlm.nih.gov/pubmed/25083916 To be added to the circle, please +1/reshare/comment/add me to your circles. I would be happy to connect on other networks too:http://about.me/Atanas_At Below I am just pasting some keyords/topics to improve the visibility of the circle and to make it more discoverable: #Science #Research #Technology #NASA #Space #Innovation #Engineering #NIAC #nutrition #Entrepreneur #Commercial #ScienceSunday #Sundayscience #Science #Research #Tech #GameTech #GameTechnology #Gaming #VideoGaming #Microsoft #MicrosoftResearch #innovation #Inflammation #Brain #mindcontrol #photography #tech #socialmedia #googleplus #naturalproduct #artists #foodies #cars | 2014-11-13 05:47:40 | 346 | 1 | 0 | 1 | |

Atanas Georgiev Atanasov | 1,490 | SCIENCE and TECHNOLOGY + FRIENDS of it : CIRCLE V.6; maintained by +AtanasGeorgievAtanasov ; You can learn more about my personal scientific research here: http://www.ncbi.nlm.nih.gov/pubmed/25083916 To be added to the circle, please +1/reshare/comment/add me to your circles. I would be happy to connect on other networks too:http://about.me/Atanas_At Below I am just pasting some keyords/topics to improve the visibility of the circle and to make it more discoverable: #Science #Research #Technology #NASA #Space #Innovation #Engineering #NIAC #nutrition #Entrepreneur #Commercial #ScienceSunday #Sundayscience #Science #Research #Tech #GameTech #GameTechnology #Gaming #VideoGaming #Microsoft #MicrosoftResearch #innovation #Inflammation #Brain #mindcontrol #photography #tech #socialmedia #googleplus #naturalproduct #artists #foodies | 2014-11-10 06:22:16 | 330 | 0 | 1 | 1 | |

Atanas Georgiev Atanasov | 1,228 | SCIENCE and TECHNOLOGY + FRIENDS of it : CIRCLE V.5; maintained by +AtanasGeorgievAtanasov ; You can learn more about my personal scientific research here: http://www.ncbi.nlm.nih.gov/pubmed/25083916 To be added to the circle, please +1/reshare/comment/add me to your circles. I would be happy to connect on other networks too:http://about.me/Atanas_At Below I am just pasting some keyords/topics to improve the visibility of the circle and to make it more discoverable: #Science #Research #Technology #NASA #Space #Innovation #Engineering #NIAC #nutrition #Entrepreneur #Commercial#ScienceSunday #Sundayscience #Science #Research #Tech#GameTech #GameTechnology #Gaming #VideoGaming +Microsoft#MicrosoftResearch #innovation #Inflammation #Brain#mindcontrol #photography #tech #socialmedia #googleplus#naturalproduct #artists #foodies #cars #sharingiscaring #Liver#sharingmeansthankyou #socialmedia #sports #Smartphones#tablets | 2014-11-06 08:10:34 | 369 | 0 | 5 | 1 | |

Sharon Caroline | 1,629 | Hello my friends, good morning/evening for you all!Boost Your visibility On Google+!Shared and be shared. :)Thank you for sharing and promoting this.#circleshare #sharedcircles #sharingcircles #sharedcircleoftheday | 2014-11-05 08:31:58 | 463 | 0 | 0 | 0 | |

Atanas Georgiev Atanasov | 1,228 | SCIENCE and TECHNOLOGY + FRIENDS of it : Circle V.3, maintained by +AtanasGeorgievAtanasov To be added to the circle, please +1/reshare/comment/add me to your circles. I would be happy to connect on other networks too:http://about.me/Atanas_At You can learn a bit more about my personal scientific research from these links: https://plus.google.com/115938908270684192009/posts/MGt3zvEtTgq http://www.ncbi.nlm.nih.gov/pubmed/25083916 Below I am just pasting some keyords/topics to improve the visibility of the circle and to make it more discoverable: #Science #Research #Technology #NASA #Space #Innovation #Engineering #NIAC #nutrition #Entrepreneur #Commercial #ScienceSunday #Sundayscience #Science #Research #Tech #GameTech #GameTechnology #Gaming #VideoGaming +Microsoft #MicrosoftResearch #innovation #Inflammation #Brain #mindcontrol #photography #tech #socialmedia #googleplus #naturalproduct #artists #foodies | 2014-11-05 07:02:42 | 362 | 1 | 0 | 1 | |

Atanas Georgiev Atanasov | 1,127 | Science and Technology +Friends: Circle 2014 V.2 To be added to the circle, please +1/reshare/comment. I would be happy to connect on other networks too:http://about.me/Atanas_At You can learn a bit more about my personal scientific research from these links: https://plus.google.com/115938908270684192009/posts/MGt3zvEtTgq http://www.ncbi.nlm.nih.gov/pubmed/25083916 Below I am just pasting some keyords/topics to improve the visibility of the circle and to make it more discoverable: #Science #Research #Technology #NASA #Space #Innovation #Engineering #NIAC #nutrition #Entrepreneur #Commercial #ScienceSunday #Sundayscience #Science #Research #Tech #GameTech #GameTechnology #Gaming #VideoGaming +Microsoft #MicrosoftResearch #innovation #Inflammation #Brain #mindcontrol #photography #tech #socialmedia #googleplus #naturalproduct #artists #foodies #cars | 2014-11-04 06:51:44 | 407 | 1 | 0 | 1 | |

Atanas Georgiev Atanasov | 982 | Science and Technology Circle 2014 To be added to the circle, please +1/reshare/comment. I would be happy to connect on other networks too:http://about.me/Atanas_At You can learn a bit more about my personal scientific research from these links: https://plus.google.com/115938908270684192009/posts/MGt3zvEtTgq http://www.ncbi.nlm.nih.gov/pubmed/25083916 Below I am just pasting some keyords/topics to improve the visibility of the circle and to make it more discoverable: #Science #Research #Technology #NASA #Space #Innovation #Engineering #NIAC #nutrition #Entrepreneur #Commercial #ScienceSunday #Sundayscience #Science #Research #Tech #GameTech #GameTechnology #Gaming #VideoGaming #Microsoft #MicrosoftResearch #innovation #Inflammation #Brain #mindcontrol #photography #tech #socialmedia #googleplus #naturalproduct #artists | 2014-11-02 08:37:19 | 453 | 1 | 0 | 1 | |

Becky Collins | 17,500 | Top Active Engager's 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 ? | 2014-10-13 05:05:40 | 478 | 0 | 0 | 2 | |

Refurio Anachro | 4,745 | September engagers circle: This month's buzz has been boosted by curiosity about Hamiltonians - welcome you all and nice to meet you! I found to really like Hamiltonian mechanics, and i'll sure come back to what i meant by describing them as "intriguing like postmodern psychedelic sculpture". Stay tuned, it wouldn't be the same without you!These people are physicists and mathematicians, research scientists, teachers, and enthusiasts. By adding us to your stream you'll find yourself learning about the universe and looking at the beauty of maths.Last month's finds:+Liz Krane found this cool video demonstrating how to mine bitcoins by hand!https://plus.google.com/+RefurioAnachro/posts/ERJpN6vLypGRaytraced spheroidal billiards: A set of high res views, and animated iteration depth. Since then i've been naming some of the features in the comments below, you sure you didn't miss any?https://plus.google.com/+RefurioAnachro/posts/4hDyHdYwmjMThe physical ellipse is the application i had in mind for Hamiltonians. It seems i should be posting about elliptic integrals and their inverses soon.https://plus.google.com/+RefurioAnachro/posts/Q2nDr5phZfQAnother tiger toroid animation. Look in the comments for a link to yet another view, and to meet an expert:https://plus.google.com/+RefurioAnachro/posts/RVCnJ5rH8kCOn Hamiltonians, my first piece about them, a quick introduction. It left me with the desire to dive deeper.https://plus.google.com/+RefurioAnachro/posts/DQZZvMBVPafDiagram 19: "The 59 icosahedra" is a book about the stellations of the icosahedron_...https://plus.google.com/+RefurioAnachro/posts/AHVv1JGLZy8"Dear august engagers", here's previous month's circle:https://plus.google.com/+RefurioAnachro/posts/X6pQCjNR6FiIn that post i claimed to post "impressions of the mandelbrot set" on +Spherical Reflections. Well, i lied, at that time i had just posted a phoenix. It's a different formula! Where are you, Mandelbrot experts?https://plus.google.com/b/115434895453136495635/117866562756294273963/posts/Qmy98YMjuwc+Spherical Reflections' page, stuff like the above and circle shares.https://plus.google.com/b/117866562756294273963/117866562756294273963/postsYou're in this circle because you reshared, plussed or commented on one of my posts (possibly via + | 2014-10-01 09:20:53 | 161 | 0 | 0 | 0 | |

Kenneth Nicholson | 3,806 | Active users on Google+. Circle Share. If you received a notification, please reshare to your circles If you’d like to be added to the next circle share: • +1 this circle • Share this circle to PUBLIC • Include me in your circles • Comment on this post*More you share more you get! :)Thanks!*#awesomecircle #circleme #sharedpoint #sharewithyou #ShareYourCircle #epicengagers #davidromaphotography #addcircle #addpeople #affiliate #awesome #awesomecircles #awesomepeople #besocial #bestengagers #bestsharedcircle #circle #circlefriday #circlemonday | 2014-09-25 13:06:13 | 485 | 45 | 51 | 79 | |

Becky Collins | 16,609 | Science 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 ? | 2014-09-16 05:24:00 | 459 | 1 | 0 | 2 | |

Richard Green | 81,215 | Engagers 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 Sittner | 2014-09-14 15:25:57 | 463 | 224 | 129 | 234 | |

Cableicous | 2,882 | Thanks for all teh cablezThanks muchly to all those who have contributed their #Cableicous imagery for this 14th circle of 99 people who have contributed their cableicous grandeur - your continued support of my cable fetish is much enjoyed.And a new circle of 99 begins...#photography #cables #cableicous #circleshare #2014 #cableriacirculus | 2014-09-10 10:47:19 | 99 | 12 | 4 | 42 | |

Becky Collins | 15,950 | Dance 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 05:00:43 | 471 | 30 | 9 | 35 | |

EDZUL FREDY KRISNAWAN | 0 | Meet the People who WILL...Take This Circle To The TopLet 'er Rip! You guys and gals are SUPERSTARS!!!Want to be added to the #hyperadd?1) Add me to your circles.2) Share, +1, and Comment This Share3) Reshare anything that interests you on my stream (profile) from today or the rest of this week.#circlesharing #sharedcircles #circles #circlemaster | 2014-08-29 11:28:10 | 485 | 11 | 4 | 13 | |

Wendy Thanh Hồng | 43 | GOOGLE FRIENDS! - RESHARE if you want to be included *'"*:•:••:*:•-:¦:* *SHARE AND BE SHARED* *:¦:-•:*:••-:•:''''* This is a super Circle and in it I put together a group of really interesting and active people on Google Plus to add in your circles.I'm talking about the top Google + users that share unique and original contents.Follow this advice and grow your G+ community with people that share amazing content that will surprise you:boost visibility on Google+ - Share the circle!If you want to be added to the next Circle you have to do these simple steps:1 - Include me in your circles 3 - Share the circle (Publicly) 4 - Add +1 to the post 5 - Follow your dreams and smile to life.More you share More you get! :)I will thankful if you plus and share this circle!#circles #shared #share #add #friends #circle #share #sharecircle #circleshare | 2014-08-25 05:58:23 | 486 | 11 | 3 | 15 | |

Kieu Trinh | 0 | GOOGLE FRIENDS! - RESHARE if you want to be included *'"*:•:••:*:•-:¦:* *SHARE AND BE SHARED* *:¦:-•:*:••-:•:''''* This is a super Circle and in it I put together a group of really interesting and active people on Google Plus to add in your circles.I'm talking about the top Google + users that share unique and original contents.Follow this advice and grow your G+ community with people that share amazing content that will surprise you:boost visibility on Google+ - Share the circle!If you want to be added to the next Circle you have to do these simple steps:1 - Include me in your circles 3 - Share the circle (Publicly) 4 - Add +1 to the post 5 - Follow your dreams and smile to life.More you share More you get! :)I will thankful if you plus and share this circle!#circles #shared #share #add #friends #circle #share #sharecircle #circleshare | 2014-08-25 05:34:03 | 486 | 13 | 6 | 18 | |

Cableicous | 2,902 | Thanks for all teh cablezThanks muchly to all those who have contributed their #Cableicous imagery for another grand week of beautaliciousness.And a new week begins...#photography #cables #cableicous #circleshare #2014 #cableriacirculus | 2014-08-09 22:10:58 | 40 | 6 | 1 | 19 | |

Richard Green | 77,832 | Engagers Showcase Circle, August 7, 2014If I sent you a notification, it means that you are included in my Engagers Showcase Circle. “Showcase” means that you are invited to leave a comment (on the original post) with a link to one of your own posts, which ideally should be one of your best recent posts.This circle consists of people who have engaged with one of my recent posts in the form of +1s, comments and reshares.Everyone mentioned below is also included in the circle.Our cat, Chesterhttps://plus.google.com/101584889282878921052/posts/ToxRHsMHytsFibonacci numbers and corridors of width 4https://plus.google.com/101584889282878921052/posts/gCTyaSV4ugzWalk in the rainhttps://plus.google.com/101584889282878921052/posts/gVPzuv7aKHALenticular cloud (reshared from +Sean R. Heavey)https://plus.google.com/101584889282878921052/posts/giTgt4PUd1GGlass Paperweight by Paul Stankardhttps://plus.google.com/101584889282878921052/posts/fLfKWxFj3f2“Mathematistan” by Martin Kuppehttps://plus.google.com/101584889282878921052/posts/AcUBb8Y9uBjCat's back on the menu, boys!https://plus.google.com/101584889282878921052/posts/aP3cZEnaqquWaterfall (reshared from +Keith Boone)https://plus.google.com/101584889282878921052/posts/S2pmsTTyiZzOak tree at “The Pig”https://plus.google.com/101584889282878921052/posts/cv8pi2ffX1NThe Bargate, Southamptonhttps://plus.google.com/101584889282878921052/posts/LsYSEpUS1bLCosmos flowerhttps://plus.google.com/101584889282878921052/posts/KqvLW32KyXfThe Ashton Memorialhttps://plus.google.com/101584889282878921052/posts/aK1E3XqWWSSThrough the castle windowhttps://plus.google.com/101584889282878921052/posts/MT7uBM2SUt7Friedman numbershttps://plus.google.com/101584889282878921052/posts/32tzjfB8NnMThe Norfolk Knifehttps://plus.google.com/101584889282878921052/posts/DHf4jfSkUKKThe lake at Wyresdale Parkhttps://plus.google.com/101584889282878921052/posts/3xFACaympiNCastle of the Clouds | 2014-08-07 21:46:51 | 451 | 213 | 121 | 238 | |

Nick Warner | 645 | Check out these awesome Crowdfunders | 2014-08-07 16:05:31 | 470 | 0 | 0 | 1 | |

Refurio Anachro | 4,492 | This july engagers circle comes packed with curiosity, brought to life by questions and answers, and people sharing their enthusiasm. Take your chance, get acquainted to this party of very nice people and deep thinkers, add it now!+John Baez had asked for an inside view of a mirror ellipsoid i was happy to provide. The result's actually a spheroid because it has a symmetry axis. Since then, i did quite some staring at ellipsoids, see below... https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/5zcrptKx3C3This reshare of +Xah Lee's "math is programing" rant got me into ugly. Gracefully handling distractions would be nice to have more of. If you must know, i heard one can retrieve deleted comments using the search...https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/TZpAUuQfzSn“Mathematistan” by Martin Kuppe offers innocuous glances aside from the popular maths mainstream. Thanks +Richard Green for sharing and noting similarities to the all time favorite "Hitchikers guide to the galaxy"!https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/UnXikyENJo1A raytraced perspective down a mirror cylinder showing quite a lot about billiard trajectories on a bunch of elliptic tables. Learn what Birkhoff, Poincare, and Poncelet had to do with it...https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/Vmrx7GMRe2iReshare of 6d toroid animations, thanks +Owen Maresh and +Cornus Ammonis for sharing!https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/gSma1ksKFeiThis ellipsoid glossary and coordinate system came with puzzles! Special thanks to +Bruce Elliott for taking part in the fun. Apparently i didn't add a clean solution putting everything together at the end... More to come, stay tuned!https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/L6C4Kob2bNeLast june's engagers circlehtt | 2014-08-03 23:22:23 | 113 | 14 | 3 | 10 | |

Marius Kiupelis | 279 | If you received this notification you are in this circle♚♚ If you want to be shared in this circle ♚♚♚♚♚♚♚ Then just keep sharing! ♚♚♚♚♚ | 2014-08-03 19:05:53 | 201 | 0 | 3 | 6 | |

Lynda Chervil | 890 | Add this circle of excellent engagers, thinkers, innovators, and future tech leaders. My ++Solar Power++ Circle will provide you with the latest and greatest from the world of tech innovations, especially in the renewable energy sector. Simply add this circle and then share it!If you'd like to be added to this circle, please comment below, share and add the circle. Only those who qualify with content and expertise will be added. Thanks! #Tesla #nikolatesla #elonmusk #solarenergy #innovation #technology #solarpower #hydroelectric #science #STEM #research #education #futuretech #futuretechnology | 2014-07-31 14:24:32 | 343 | 1 | 2 | 5 | |

Peter Edenist | 31,015 | 2014 Super Sci-FI Circle : No, the Sky is not Falling!!! Also the Gravity is not sucking you in... please +1 this post to support it or you may have to take a trip in Snowpiercer, no need to thank me. Please reshare if you think this is a worthwhile circle. If you have been notified, you are in the circle!All the people in this circle are linked to our community (see link further down). As usual, please tag and recommend anyone who you think should be in this circle. Live long and prosper!Sci-FI Community here: http://goo.gl/s1NVd Science Fiction Pics: http://goo.gl/sOSPK5Mighty Shiny Browncoats : http://goo.gl/9osg1tDoctor Who : http://goo.gl/z3uWX3Ultimate Star Wars : http://goo.gl/Wu8bv6Ultimate Star Trek : http://goo.gl/JJPql9Science on G+ community here: http://goo.gl/46uFH #sciencefiction #sf #scifi | 2014-07-24 12:58:07 | 462 | 118 | 60 | 145 | |

Becky Collins | 13,434 | Mobile Operator Circle:Circle of very #social #engagerspeople and companiesTo be included in my shares (#sharedcircle), be so kind to:1 - Do +1 t the post2 - Comment the post and specify your "category" (job or interest) Ex: Fashion, SEO, Companies, Social Media Marketing, Sailing, Photography, Bloggers/Writers, Web graphics and design, Italy, Artists, Sport, Finance/Economy ...3 - include the circle among your circles4 - share the circle (include yourself)Improve your popularity, be social be cool !Keep yourself updated, enjoy the Shared Circles Hellenic Alliance, you can share your shared circles inside the upcoming Community:https://plus.google.com/communities/112552559573595396104 #socialmedia #media #circles #circleshare #circlesharing #circlecircle #beckyscircle #sharedcircles #sharedpubliccircles #sharedcircleoftheday +Becky Collins ? | 2014-07-24 05:16:12 | 476 | 3 | 1 | 12 | |

Able Lawrence | 100,166 | 100K Engagers Celebration Circle Thank you all those who have followed me and engaged with my posts and taking me to the milestone of 100,000 followers. Goolge+ has been an exhilarating journey of 3 years and I would like to thank all those who have followed me and engaged on my posts whether they were on Science or Birds or Technology. The circle has been created using * +Circloscope * which is the work of +Ehsan Ahmadi Gharacheh All of you are free to share your favorite posts in the comments and also reshare this circle. If you are included in the circle, you will get a notification. | 2014-07-17 17:22:18 | 340 | 49 | 17 | 87 | |

Doug Hyatt | 5,196 | THIS 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 15:49:10 | 477 | 15 | 14 | 21 | |

Richard Green | 74,896 | Engagers 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 05:31:36 | 476 | 209 | 123 | 224 | |

Refurio Anachro | 4,312 | June engagers circle: Say hello to almost 200 nice people who joined in to participate in math topics. If you're intelligent, curious, like well written posts and engaged discussion - these people will not dissappoint. Go on and add them now!Last month's posts:Spin story continues (part 3): Angular velocity and tilings in spin space. While i locked myself in a cycle, struggling to follow, +wendy krieger blew the bubble and lifted the party up to dimension 4! I couldn't resist but to guest post this gem. Next time i'll find a picture first, promised!:https://plus.google.com/115434895453136495635/posts/6F9sxQxiqEaClifford Algebra (part 1): Into Clifford algebra. Because with those one can easily describe spin in any dimension.https://plus.google.com/115434895453136495635/posts/1CtiDXou6RqUnicode math cheat sheet: ⁵√7+x² – ℵ₀ – ℝⁿ – x̅ ≟ x*⊕x⁎ – αβ ≺ ∇ϕhttps://plus.google.com/115434895453136495635/posts/GNoCEmBxSWSClifford Algebra (part 2): Multiplication in geometric algebra.https://plus.google.com/115434895453136495635/posts/NKqs5BwsCqqCardioid gears, a reshare of +Rob Kook's very unexpected video find:https://plus.google.com/115434895453136495635/posts/UMBXJihPgcaCan we get anything faster than light that way? While arguing below +John Baez' cool post i suddenly started hearing vikings...https://plus.google.com/115434895453136495635/posts/jjYu4KhHaCTClifford Algebra (part 3): Cayley graphs and a strange clock. My first attempt to quickly put my thoughts down for you to see. I guess i'll have to practice a bit to make it more appealing on shorter glance, so more people can benefit.https://plus.google.com/115434895453136495635/posts/bkHQAZLzpt8Last may's engagers circle:https://plus.google.com/115434895453136495635/posts/hGPebLWRcU2You're in this circle because you reshared, plussed or commented on one of my posts (possibly via +Spherical Reflections), or got into a discussion with me. Thank you!#engagers #engagerscircle #engagersshowcasecircle #circleshare #circlesharing #circl | 2014-07-02 13:23:15 | 194 | 6 | 5 | 9 | |

Peter Edenist | 30,747 | TESLA Super Science Circle 2014 - June Edition!!!! : A quality circle curated carefully and tended since 2011. Who is in this circle? people who are either involved in science, love science or are active on the Science on G+ community. Community link is here http://goo.gl/46uFH and the Page is +Science on G+!Have you wondered where one can meet with like-minded people who love science and like to read about the real stuff? This is the ultimate SUL on science.... add and share to keep it alive.--------------------------------------------------------------------------------------------------Want to nominate someone? Please do so in comments. If you want to recommend something let us know. People who are notified are part of the circle.#science #tesla #scienceongplus #scienceeveryday | 2014-06-19 13:39:49 | 342 | 75 | 56 | 93 | |

David Wees | 4,496 | This is a circle of 346 math educators. If you are interested in following the work of innovative mathematics educators, this circle is for you.If you are a mathematics educator, and I have not included you in this circle, let me know. | 2014-06-11 16:24:03 | 346 | 0 | 1 | 0 | |

Dina Tika | 0 | Here 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 05:53:52 | 479 | 0 | 0 | 1 | |

Refurio Anachro | 4,141 | May engagers circle: Meet the people who made the fabulous cheer of this week's spin party. Many curious people, all of them worth to add!Diagram 18: rotations and spinorshttps://plus.google.com/b/115434895453136495635/115434895453136495635/posts/dpPMfoH6zc5This is actually part two, but got posted earlier (see below). You just made my first +100, thank you! Stay tuned for more on spinning and spinors.https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/TLkA6tCNwEeIf you want to know what an earlier stage of Diagram 18 looked like, see here. I posted 2/3rd of the final post with a question marking my progess. Also note the discussion below, thanks to everybody who helped me out!https://plus.google.com/b/115434895453136495635/115434895453136495635/posts/THePbpcPnqDYou're in this circle because you reshared, plussed or commented on one of my posts (possibly via +Spherical Reflections), or got into a discussion with me. Thank you!Last april's engagers circlehttps://plus.google.com/b/115434895453136495635/115434895453136495635/posts/RFMY2aYscJJ#engagers #engagerscircle #engagersshowcasecircle #circleshare #circlesharing #circle #circleoftheday #addcircle #findcircles #publicsharedcircles #addpeople #plussers #awesomepeople #sciencecircle #commenterscircle #mathematicians #friends | 2014-06-02 11:57:02 | 158 | 4 | 4 | 7 | |

John Nuntiatio | 37,493 | 30k+ Circle - A circle worth adding and followingThe people from this circle have more than 30,000 followers. | 2014-06-02 08:54:46 | 140 | 4 | 9 | 6 | |

Becky Collins | 10,282 | Mobile Circle :Circle of very #social #engagerspeople and companiesTo be included in my shares (#sharedcircle), be so kind to:1 - Do +1 t the post2 - Comment the post and specify your "category" (job or interest) Ex: Fashion, SEO, Companies, Social Media Marketing, Sailing, Photography, Bloggers/Writers, Web graphics and design, Italy, Artists, Sport, Finance/Economy ...3 - include the circle among your circles4 - share the circle (include yourself)Improve your popularity, be social be cool !Keep yourself updated, enjoy the Shared Circles Hellenic Alliance, you can share your shared circles inside the upcoming Community:https://plus.google.com/communities/112552559573595396104 #socialmedia #media #circles #circleshare #circlesharing #circlecircle #beckyscircle #sharedcircles #sharedpubliccircles #sharedcircleoftheday +Becky Collins ? | 2014-05-28 05:03:17 | 477 | 7 | 2 | 19 | |

Jasmina Brozović | 53,426 | Notification CircleThis is a circle of people I don't wanna miss any new posts from!Great Circle idea by +Zvonimir FrasRead more :https://plus.google.com/u/0/+ZvonimirFras/posts/VsZjS7H7vJf#circles #circlethis #circleyoushare #sharedcircles #addcircle #sharedpubliccircles #circleshare #publicsharedcircles #circleoftheweek #circlesharing #publiccircle #sharedcircle #circleshare #circle #motivateme | 2014-05-20 16:26:14 | 179 | 27 | 10 | 31 | |

Daniel Zawadzki | 7,897 | This #circle is #great, #amazing, #wonderful,Boost your visibility on Google+ - Share the circle!#1 - Click add people and create your circle#2 - share the circle (include yourself)#3 - add +1 to the post#circle #circleshare #circlesharing #circleoftheday #circleoftheweek #share #sharedcircles #sharedpubliccircles #sharedcircleoftheday #engagers #engagerscircle #engagerspeople | 2014-05-19 20:33:55 | 470 | 94 | 46 | 122 |

### Activity

#### Average numbers for the latest posts (max. 50 posts, posted within the last 4 weeks)

comments per post

reshares per post

+1's per post

characters per posting

Top posts in the last 50 posts

### Most comments: 171

2014-11-03 18:18:00 (171 comments, 17 reshares, 151 +1s)

**Suspiciously cute**

Last week many of my old posts started getting +1ed by beautiful women.

One theory is that at finally, at the age of 53 and happily married, I've become an irresistible babe magnet. Maybe it's my skill at explaining advanced concepts in math and science. Maybe it's my devilish good looks.

It's time to look for another theory.

Obviously, the other theory is that these are entities posing as beautiful women. I wasn't born yesterday! This type of thing has been happening for a long time on G+.

But here's the interesting part. Each old post is getting +1ed just once - each by a different entity. Each of these entities does not merely post ads for some company, the way a typical fake does. They post about a variety of things - but with a lot of photos of themselves riding horses, dressed upin Hall... more »

### Most reshares: 137

2014-11-22 17:43:26 (52 comments, 137 reshares, 260 +1s)

**The virus has landed**

This is a virus called a **T4 bacteriophage**. It has landed on a bacterium. Now it's getting ready to lower its tail, puncture the bacterium's cell wall, and inject its DNA.

When this happens:

1. It immediately stops the bacterium's own genes from being expressed.

2. In 5 minutes, its DNA starts synthesizing enzymes needed to make new copies of the virus.

3. In 10 minutes, its DNA starts replicating.

4. In 12 minutes, new copies of the virus start being formed.

5. In 30 minutes, the bacterium bursts, releasing 100 to 150 new copies of the virus!

This deadly machine is only 0.2 micrometers tall. Its DNA - the instruction book that makes everything work - is contained in the head, which is shaped like an icosahedron. The DNA is 169,000 base pairs long, and itcodes for... more »

### Most plusones: 303

2014-10-09 20:07:55 (145 comments, 58 reshares, 303 +1s)

**Hollow Earth**

There have been lots of theories saying the Earth is hollow, but I know only one that could be true.

Edmond Halley, the guy who discovered the famous comet, had a theory where Earth consists of a hollow shell about 800 kilometers thick, two smaller shells nested inside, and a ball in the middle - all separated by atmospheres and rotating at different speeds! It sounds nutty, but Halley was trying to explain the Earth's rather complicated magnetic fields: each of his shells was magnetic.

People sometimes accuse Leonhard Euler, the famous mathematician and physicists, of believing the Earth was hollow. But that's not true. In fact, all Euler did was propose a famous thought experiment:**Puzzle:** If you could drill a hole all the way through the Earth, and drop a stone in, what would happen?

With the passage of time,sci... more »

Latest 50 posts

2014-12-18 16:38:45 (24 comments, 13 reshares, 113 +1s)

**Sky scraper**

+Yonas Kidane wanted to see how big the Empire State Building would look if it were sitting on the asteroid 67P/Churyumov–Gerasimenko. So, he figured it out and made this image, based on a photo taken by the Rosetta space probe. The hard part was getting the shadow right.

His original post is here:

https://plus.google.com/u/0/117534618780996601977/posts/5rgkKpL6BqZ

This office building has a great view... but the commute is terrible.

2014-12-17 16:47:20 (28 comments, 15 reshares, 62 +1s)

**The California Drought**

Down here in Southern California, we've had three good rains since the summer. Up north, they've gotten even more! In the first storm, ending December 3rd, San Francisco got more rain than they did all last year! They got 9.4 centimeters of rain in four days, compared to just 8.6 in 2013.

But we'd need a lot more rain to break the drought. It will take about 11 trillion gallons of water - 42 cubic kilometers! - to fully recover from the drought. That's what researchers at NASA say, based on satellite data including measurements of the Earth's gravitational field, which depends on how much groundwater there is.

They say that since 2011, the Sacramento and San Joaquin river basins have decreased in volume by four trillion gallons of water each year - 15 cubic kilometers. About two-thirds of the loss is dueto deplet... more »

2014-12-16 18:37:18 (23 comments, 23 reshares, 100 +1s)

Soon the famous mathematical physicist Barry Simon will be publishing a "comprehensive course in analysis" - 3000 pages of material, in 5 volumes:

Real Analysis

Basic Complex Analysis

Advanced Complex Analysis

Harmonic Analysis

Operator Theory

You can see a table of contents here.

If you know Reed and Simon's series Methods of Modern Mathematical Physics you'll know why I'm excited. The style of those books is simultaneously elegant yet friendly. They put in just enough detail to make the proofs easy to follow... but include lots of side-remarks that explain the point of what's going on, and the history of the subject.

When I was a junior at Princeton I had to choose an advisor for my senior thesis. I wanted to work on logic and quantum mechanics. So I asked Simon Kochen if he would be my advisor. He'sa log... more »

2014-12-15 18:14:08 (41 comments, 16 reshares, 86 +1s)

**Delightful demicubes**

If you take every other corner of a cube, you get the corners of a **demicube**.

In 3 dimensions a demicube is just a regular tetrahedron! So you get two tetrahedra in a cube, as shown here. Together they form a **stellated octahedron**. In other words, you can also get this shape by taking a regular octahedron and sticking a tetrahedron on each of its faces - getting a kind of 3-dimensional star! It makes a great Christmas tree ornament.

What's a demicube in 4 dimensions? A 4-dimensional cube has 2^4 = 16 corners, so the demicube has 8. The cool part, special to 4 dimensions, is that all these corners point at right angles to each other, as viewed from the center of the cube!

If the corners of the 4-dimensional cube are

(±1, ±1, ±1, ±1)

then we can get a demicube by takingthose with an e... more »

2014-12-15 05:38:22 (16 comments, 1 reshares, 31 +1s)

**Late night music**

Richie Hawtin's 1998 album Artifakts starts with three linked tunes, all hypnotic - but this, the third, is the real star. **Richie Hawtin is making largely beautiful music, and sometimes he's making it eat into your brain, too.** - Musical Express

There are three big events in this piece:

1) the start, when an icy-cold, three note melody wafts into view like a wistful signal from a long-dead alien civilization;

2) the moment one minute later when some slinky, crisp percussion enters;

3) the moment around 2:30 when the more lively Roland TB-303 synthesizer line appears.

The 303 is a famous instrument. It was made for only 18 months in the 1980s, but later it became popular in acid house music, because you can get it to play a repeating pattern and then turn knobs to adjust the sound in a veryf... more »

2014-12-13 16:03:14 (71 comments, 33 reshares, 123 +1s)

**Context matters!**

The two disks are exactly the same in every way. Only their surroundings differ.

This is a metaphor for many things in life. What's the best example where the context of an event changed your perception of it?

For more great visual effects by the psychologist Akiyoshi Kitaoka, go here:

http://www.ritsumei.ac.jp/~akitaoka/index-e.html#allpages

2014-12-12 18:16:50 (53 comments, 47 reshares, 143 +1s)

See the small squares divided into 2 black squares and 2 white ones? These are confusing your poor eyes.

2014-12-11 18:54:31 (67 comments, 30 reshares, 109 +1s)

**The Salt Pit****On Dec. 31, 2003, I took a bus from Germany to Macedonia. When we arrived, my nightmare began. Macedonian agents confiscated my passport and detained me for 23 days. I was not allowed to contact anyone, including my wife.****At the end of that time, I was forced to record a video saying I had been treated well. Then I was handcuffed, blindfolded and taken to a building where I was severely beaten. My clothes were sliced from my body with a knife or scissors, and my underwear was forcibly removed. I was thrown to the floor, my hands pulled behind me, a boot placed on my back. I was humiliated.****Eventually my blindfold was removed, and I saw men dressed in black, wearing black ski masks. I did not know their nationality. I was put in a diaper, a belt with chains to my wrists and ankles, earmuffs, eye pads, a blindfold and a hood. I was thrown... more »**

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2014-12-10 13:06:42 (17 comments, 3 reshares, 80 +1s)

My talk on climate networks is coming up in one hour! There are 2100 people at this conference - six hotels are completely sold out - and I'm giving the only talk from 9 to 10 am, in a HUGE room, so everyone can attend.

The pressure is on! Luckily, while I'm shy and quiet in ordinary life, a big audience transforms me into a showman - I like being the center of attention. I only learned this after teaching for several years. At first I hated teaching - standing in front of a crowd of bored teenagers talking about calculus. Then I realized this was my big chance to entertain people, get them interested in the things I love, and - let's be frank - show off.

Then came the internet, and I realized I could entertain the world from the privacy of my own home. But there's nothing like a crowd of hundreds to make me excited. One man's stage fright is another'sadrena... more »

2014-12-07 16:02:22 (34 comments, 40 reshares, 141 +1s)

**We're all in the gutter, but some of us are looking at the stars**

This is the ceiling of the tomb of the famous Persian poet **Hafez**, who was born in the city of Shiraz in 1315, and died there in 1390. The current version of the tomb dates back only to 1935 and was designed by the French architect and archaeologist André Godard. But the design is beautiful!

There's a lot of fun stuff to see if you zoom in, but let's think about the star.**Puzzle 1:** How many points do the stars here have?**Puzzle 2:** How many different kinds of stars are there with this many points?

For example, there's just one kind of 5-pointed star, but two kinds of 7-pointed star. There's a 7-pointed star with blunt points where you draw a line from each dot to the dot 2 after it, and one with sharp points where you draw a line fromeach... more »

2014-12-05 22:27:34 (39 comments, 19 reshares, 118 +1s)

**The beauty of the 24th dimension**

My main hobby these days is working with Greg Egan on lattices. Roughly, these are repeating patterns of points, like the centers of atoms in a crystal. But you can study lattices in different dimensions - and a lot of fun happens in 24 dimensions!

If you look for the densest ways to pack spheres in different dimensions, you'll be led to some interesting lattices. In 3 dimensions, the usual way of stacking oranges gives the **D3 lattice**: when you center your spheres at points of this lattice, each sphere touches 12 others. This is known to be the densest packing of spheres in 3 dimensions.

In 4 dimensions the densest known sphere packing comes from the **D4 lattice**, where each sphere touches 24 others.

These **D lattices** are easy to build: you draw a higher-dimensional checkerboard withalte... more »

2014-12-01 16:54:34 (11 comments, 4 reshares, 47 +1s)

**Climate networks****Complex network theory** is the study of large networks. Can we use this to get new insights about the Earth's climate? That's what I'm talking about next week at a conference called the Neural Information Processing Seminar.

This map was made by a team of scientists using complex network theory. They claim that the center of the Pacific Ocean - the **El Niño basin** - plays a crucial role in the Earth's climate.

Take temperature data at a grid of points on the Earth. Subtract out the seasonal variations in temperature. Then, for each pair of points, work out the **mutual information** between the temperature at one point and the other point. In other words: how many bits of information these two pieces of data have in common!

Next, connect two points with an edge if their mutual informationis much h... more »

2014-11-29 16:44:51 (25 comments, 62 reshares, 237 +1s)

**Mr. Tower's spherical steam engine**

In the 1800s there was an intense exploration of different designs for steam engines. One of the most unusual is this spherical steam engine designed by a fellow named Beauchamp Tower. It got a lot of publicity around 1885. It was actually used for generating electricity to light carriages on the locomotives of the Great Eastern Railway in Britain! It was also used on some ships.

But it needed a lot of steam for the power it produced - perhaps due to leaks - so it never really caught on.

I got this picture, made by Bill Todd, from Douglas Self's wonderfu online museum of old technologies. He writes:**The operation of the engine is not easy to comprehend, but goes something like this: The "cylinder" is spherical, and contains two quarter-spheres, with a thin circular disc between them.The two ... more »**

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**2014-11-28 18:00:53 (18 comments, 8 reshares, 75 +1s)

**Boron - not boring**

This is **boron carbide**, an extremely hard ceramic material used in macho gear like tank armor, bulletproof vests, and engine sabotage powder.

(Engine sabotage powder? Yes, you can pour this into the oil supply, and it will make a car engine grind itself to death.)

If diamond has a hardness of 10, this comes in at 9.497. But its crystal structure is even cooler than diamond!

A group of 12 boron atoms likes to form an icosahedron. You can see 8 of these icosahedra here - the green things. These form the corners of a rhombohedron - a kind of squashed cube. These repeat over and over, forming a **rhombohedral lattice**.

But that's not all! The icosahedra are connected by struts! These struts have carbon atoms at their ends and a boron in the middle. Only one strut is shown in detail here. The carbon at... more »

2014-11-27 16:47:13 (65 comments, 27 reshares, 187 +1s)

**The universal Turing machine**

I'm looking forward to The Imitation Game, a movie about Alan Turing. But right now I'm reading the book that inspired it: Alan Turing: the Enigma, by Andrew Hodges.

In 1936, Turing conceived of a universal computing device - a machine that could compute anything that's computable. He used this idea to prove that some questions could not be systematically answered by any computing device.

But by 1945, thanks to his job cracking German codes, he became more interested in actually building such a machine:**There will positively be no internal alterations made even if we wish suddenly to switch from calculating the energy levels of a xenon atom to the enumeration of the groups of order 720.**

Or as he put it in 1948:**We do not need to have an infinity of different machines doingdif... more »**

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**2014-11-25 17:25:21 (35 comments, 31 reshares, 168 +1s)

**Diamonds are forever**

Diamonds are one of hardest known substances. They're made of carbon, with each atom connected to 4 others in a pattern called the **diamond cubic**.

The same pattern appears in crystals of silicon, germanium, and tin. These are other elements in the same column of the periodic table. They all like to hook up with 4 neighbors.

The diamond cubic is elegant but a bit tricky. Look at it carefully here! We start by putting an atom at each corner of a cube. Then we put an atom in the middle of each face of the cube. So far, this is called a **face-centered cubic**.

But then: the tricky part! We put 4 more atoms inside the cube. Each of these has 4 nearest neighbors, which form the corners of a tetrahedron.

What are the coordinates of these points? It's good to start with a 4×4×4 cube. Itscorners are:

2014-11-24 17:56:05 (17 comments, 11 reshares, 90 +1s)

**Don't go there**

The Taklamakan Desert in western China is one of the toughest, most forbidding deserts in the world: icy cold in winter, hot in summer, bone-dry with plenty of sand storms all year round. Its name means "those who go there do not return". Now there's a highway across it! But before you plan a road trip, talk to the locals.

Annoyingly, I can't remember the coordinates of this Google map!**Puzzle:** where exactly is this place?

It's somewhere on the Tarim Desert Highway. But this highway has several parts. The longest part, the **Lunmin Highway**, links the city of Luntai on the northern edge of the desert with Minfeng on the southern edge. This road is 550 kilometers long - with about 450 kilometers in uninhabited areas covered by shifting sand dunes. It's the longest desert highway in theworld!

2014-11-22 17:43:26 (52 comments, 137 reshares, 260 +1s)

**The virus has landed**

This is a virus called a **T4 bacteriophage**. It has landed on a bacterium. Now it's getting ready to lower its tail, puncture the bacterium's cell wall, and inject its DNA.

When this happens:

1. It immediately stops the bacterium's own genes from being expressed.

2. In 5 minutes, its DNA starts synthesizing enzymes needed to make new copies of the virus.

3. In 10 minutes, its DNA starts replicating.

4. In 12 minutes, new copies of the virus start being formed.

5. In 30 minutes, the bacterium bursts, releasing 100 to 150 new copies of the virus!

This deadly machine is only 0.2 micrometers tall. Its DNA - the instruction book that makes everything work - is contained in the head, which is shaped like an icosahedron. The DNA is 169,000 base pairs long, and itcodes for... more »

2014-11-21 16:07:28 (26 comments, 6 reshares, 69 +1s)

**Heptagons - worst of all?**

This picture by Toby Hudson shows the densest known packing of the regular heptagon. Of all convex shapes, the regular heptagon is believed to have the lowest maximal packing density.

Let's see how the competition stacks up!

You can pack equal-sized circles with a density of at most

0.9068996…

For regular octagons, the best you can do is

0.9061636…

If you smooth the corners of these octagons in a certain way, the best you can do is

0.902414…

This smoothed octagon is conjectured to be the worst shape for dense packing that's both convex and centrally symmetric. **Convex** means that if you draw a line segment between two points in your shape, the whole line segment is in the shape. **Centrally symmetric** means that if you reflect the shape vertically andthen h... more »

2014-11-20 17:14:00 (47 comments, 39 reshares, 127 +1s)

**A secret code**

This is the **Golay code**. Each row in this picture shows a string of 24 bits. There are 12 rows. If you look at any two rows, you'll see they differ in at least 8 places.

Here's how to get the Golay code. Take a 12 x 12 square of bits with all 0's except for 1's down the diagonal - you can see that at left here. Take another 12 x 12 square of bits that tells you when two faces of a dodecahedron share an edge: 0 if they do, 1 if they don't. Stick these squares together and you get the Golay code!

Some guys around here keep asking if the math I talk about is good for anything. In this case it is!

The Voyager 1 and 2 spacecraft needed to transmit hundreds of color pictures of Jupiter and Saturn in their 1979, 1980, and 1981 fly-bys. They had very little bandwidth, so they needed a good error-correctingcode. Th... more »

2014-11-19 15:42:15 (62 comments, 19 reshares, 84 +1s)

**Severe inequality**

In 2005, white US households were about 10 times more wealthy than black ones, as measured by median net worth. By 2011, they were 14 times as wealthy!

From 2005 to 2011, the Great Recession knocked American white households' median net worth down by 21%. But for blacks, it dropped by 42%.

The numbers are from the US Census:

https://www.census.gov/people/wealth/data/disttables.html

2014-11-18 15:57:33 (24 comments, 9 reshares, 81 +1s)

**Lockheed Martin tries nuclear fusion**

I'm skeptical about this, but it would be a big deal if it works. The company Lockheed Martin is famous for building airplanes. But they have a research group that's working on nuclear fusion, and they're making very bold claims:**A reactor small enough to fit on a truck could provide enough power for a small city of up to 100,000 people. Building on more than 60 years of fusion research, the Lockheed Martin Skunk Works approach to compact fusion is a high beta concept. This concept uses a high fraction of the magnetic field pressure, or all of its potential, so we can make our devices 10 times smaller than previous concepts. That means we can replace a device that must be housed in a large building with one that can fit on the back of a truck.**

They've been publicizing their work on fusion since 2013. But... more »

2014-11-17 17:27:56 (48 comments, 38 reshares, 132 +1s)

**A new improved 2nd law of thermodynamics**

The 2nd law of thermodynamics says entropy increases. This is a powerful and useful idea, because you can compute the entropy of different things, like different mixtures of chemicals, and use this idea to see which things can or cannot turn into which other things. But is the 2nd law always true? And if so, why?

People have studied this for over a century. It's clear by now that the 2nd law is only true under certain conditions... which happen to include the conditions we usually see around us. That's no coincidence. These are the situations that allow for life as we know it!

But the laws of physics allow for situations where entropy is very high and occasionally decreases for a short time, then comes back up... and also situations where entropy starts out high and decreases.

In the secondcase, we... more »

2014-11-16 20:06:09 (44 comments, 26 reshares, 135 +1s)

**Annie Oakley**

Europeans have trouble understanding the USA's love affair with guns. Me too. But here is one of our folk heroes: **Annie Oakley**.

Born in 1860 in a log cabin in Ohio, at the age of 10 she was 'bound out' to a nearby family to help care for son, on the false promise of fifty cents a week and an education. Being 'bound out' was pretty common for poor children: at best it was like becoming an apprentice, at worst it was pretty much like slavery. Annie always called this family "the wolves" - and at the age of 12 she ran away back to her mother.

She'd started hunting at the age of 8 to help support her brothers and sisters, and she got good at shooting. Really good.

A travelling show called Baughman & Butler came to town. Butler was a marksman. He placed a $100 bet that he could beat anylocal ... more »

2014-11-14 16:55:46 (140 comments, 41 reshares, 149 +1s)

**In Alabama, 1/3 of black men cannot vote**

Why not? Because if you go to prison in that state, you may never be allowed to vote after that. Since black men are imprisoned at an extremely high rate, many can't vote.

There are 11 states in the US with laws like this. Others deny the vote for shorter periods of time - for example, while you're in prison or are on parole. Here are some of the consequences:

31% of black men in Florida can't vote.

31% of black men in Alabama can't vote.

29% of black men in Mississippi can't vote.

28% of black men in Wyoming can't vote.

26% of black men in Iowa can't vote.

25% of black men in Virginia can't vote.

24% of black men in New Mexico can't vote.

24% of black men in Washington can't vote.

21% ofblack... more »

2014-11-14 16:25:49 (7 comments, 11 reshares, 65 +1s)

One of humanity's deepest thinkers died yesterday. RIP Alexander Grothendieck.

In a mathematical conversation, someone suggested to Grothendieck that they should consider a particular prime number. “You mean an actual number?” Grothendieck asked. The other person replied, yes, an actual prime number. Grothendieck suggested, “All right, take 57.”

That's from this article by Allyn Jackson about the man, his maths, and life:

http://www.ams.org/notices/200410/fea-grothendieck-part2.pdf

Here's the news of the death (French):

http://www.liberation.fr/sciences/2014/11/13/alexandre-grothendieck-ou-la-mort-d-un-genie-qui-voulait-se-faire-oublier_1142614

2014-11-13 16:38:39 (42 comments, 5 reshares, 54 +1s)

**Tiger on the loose - near Paris!**

A tiger has been seen in the town of Montévrain just outside Paris! The weird part: nobody knows how it got there.

The wife of a supermarket owner in Montévrain was the first to see the tiger from the supermarket parking lot at 8:30 am local time today. She called her husband to say she thought she had seen a lynx, and took a photograph, which the couple then showed to municipal authorities. Local and national police together with firefighters, immediately launched a search with helicopters. Their goal was to capture it without hurting it, with a dart gun.

A young tiger was spotted two hours later, with the latest reports saying that it's hiding in some bushes behind some tennis courts. "We urge you to be careful and not to walk within the perimeter, which has been secured since this morning," Montévrainautho... more »

2014-11-11 16:11:54 (19 comments, 26 reshares, 118 +1s)

**Arabesque**

+Craig Kaplan has been taking ideas from Islamic wall tilings and adapting them to spheres. It's a great way to bring new life to an glorious old tradition.

See that star with 10 points and 5 nearest neighbors? That's 5-fold symmetry. You can't get perfect 5-fold symmetry in a tiling of the plane. The best you can do is fake it in various ways - and by 1200 AD the great tile masters of Afghanistan, Iran, Morocco and Turkey had figured out most of these ways.

Patterns with decagons and pentagons that fool the eye into thinking there's 5-fold symmetry! Quasiperiodic tilings - later rediscovered by Penrose - that never quite repeat but have 5-fold symmetry on average. Their discoveries were remarkable.

But when you tile a sphere, the dodecahedron comes to your aid: it has 5-fold symmetry, and things the old tileexperts ... more »

2014-11-10 22:11:22 (20 comments, 37 reshares, 98 +1s)

**France prefers to pay twice for its researchers' work**

Instead of giving everyone access to the work of its scientists - work it has financed - France prefers to pay 172 million euros to a Dutch publisher.

That's a headline in the newspaper Rue89. In their latest round of negotiaitons, after threatening to quit taking Elsevier journals, the French Ministry of Research caved in and agreed on a secret contract with this publisher. But now Rue89 has published a copy of this contract! Here it is in French:

http://rue89.nouvelobs.com/sites/news/files/assets/document/2014/11/marche_elsevier.pdf

Here it is in English:

http://tinyurl.com/qjps3mv

The whole article is below, or here in English:

http://tinyurl.com/qfxtwz2

These English translations are pretty crude, made by Google Translate. The Frenchmath... more »

2014-11-08 17:59:44 (46 comments, 36 reshares, 206 +1s)

**Cosmological billiards and spacetime crystals**

In 1970, Belinksii, Khalatnikov and Lifschitz discovered that when you run time backwards toward the Big Bang, a homogeneous universe behaves like a billiard ball. As you run time back, the universe shrinks, but also its shape changes. Its shape moves around in some region of allowed shapes... and it 'bounces' off the 'walls' of this region!

These guys considered the simplest case: a universe with 3 dimensions of space and 1 dimension of time, containing gravity but nothing else. In this case the region of allowed shapes is a triangle in the hyperbolic plane. I showed it to you last time.

So, running time backwards in this kind of universe is mathematically very much like watching a frictionless billiard ball bounce around on a strangely curved triangular pool table.

But you can playthe s... more »

2014-11-08 04:08:44 (16 comments, 12 reshares, 63 +1s)

**Man was winged hopefully. He had in him to go further than this short flight, now ending. He proposed even that he should become the Flower of All Things, and that he should learn to be the All-Knowing, the All-Admiring. Instead, he is to be destroyed. He is only a fledgling caught in a bush-fire. He is very small, very simple, very little capable of insight. His knowledge of the great orb of things is but a fledgling's knowledge. His admiration is a nestling's admiration for the things kindly to his own small nature. He delights only in food and the food-announcing call. The music of the spheres passes over him, through him, and is not heard.****Yet it has used him. And now it uses his destruction. Great, and terrible, and very beautiful is the Whole; and for man the best is that the Whole should use him.****But does it really use him? Is the beauty of the Whole... more »**

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**2014-11-06 16:31:17 (45 comments, 31 reshares, 119 +1s)

**Cosmological billiards**

What happened before the Big Bang? That's what I call a boring question.

It might not make sense. But don't believe anyone who confidently asserts that it doesn't make sense. It might make sense. We have no idea! We just don't know enough about physics to make much progress on this question right now! Maybe later.

What happened right after the Big Bang? That's much more interesting, because we don't know the complete answer, but we know a lot of stuff, and we have at least a chance of making progress.

Here's something easy you can do: take a solution of Einstein's equation for gravity, run it back in time, and see what it says about the shape of the universe as you get closer and closer to the Big Bang.

You might not think this is easy if you haven't taken a course onthis stuf... more »

2014-11-03 18:18:00 (171 comments, 17 reshares, 151 +1s)

**Suspiciously cute**

Last week many of my old posts started getting +1ed by beautiful women.

One theory is that at finally, at the age of 53 and happily married, I've become an irresistible babe magnet. Maybe it's my skill at explaining advanced concepts in math and science. Maybe it's my devilish good looks.

It's time to look for another theory.

Obviously, the other theory is that these are entities posing as beautiful women. I wasn't born yesterday! This type of thing has been happening for a long time on G+.

But here's the interesting part. Each old post is getting +1ed just once - each by a different entity. Each of these entities does not merely post ads for some company, the way a typical fake does. They post about a variety of things - but with a lot of photos of themselves riding horses, dressed upin Hall... more »

2014-11-03 16:13:05 (70 comments, 41 reshares, 101 +1s)

**The action-perception loop**

A lot is happening when you walk down the street! You're constantly processing new information from your senses and stored information from the past and using this to decide on your motions, which then affects your position and the environment around you. It's a feedback loop: if you lean a bit too far to the left your muscles will automatically push you back to the right. You don't need to consciously think about it very much. It's called the **action-perception loop**.

Natural selection has pushed organisms to be very good at this loop. Try catching a cockroach and you'll see what I mean!

Among other things, we need to balance the cost of storing information about the past against the payoff of achieving our desired goals in the future.

If information processing were free, we couldremember e... more »

2014-10-30 14:27:47 (28 comments, 2 reshares, 68 +1s)

**Shy bird**

This puffin looks afraid to come out of its burrow. It's probably perfectly happy. But the lines around its eye make it look like a cartoon of nervousness.**Atlantic Puffins** spend most of their time at sea - they're good at swimming, using their wings to ‘fly’ underwater as they search for fish to eat. They come to land each spring to breed in colonies on north Atlantic seacoasts and rocky islands. They live in burrows - I just learned this yesterday! Each pair lays one egg, with the male and female sharing incubation duties for about 40 days. After the chick hatches both parents feed it fish for approximately 45 days. After that the young **puffling** is ready to leave the nest.

You can see life in a puffin burrow here:

http://explore.org/live-cams/player/puffin-burrow-cam

I got my info from thatwebsite. ... more »

2014-10-29 18:11:18 (63 comments, 90 reshares, 226 +1s)

I'm listening to a talk on the origin of life at a workshop on **Biological and Bio-Inspired Information Theory**. The speaker said something like this... and I was amazed, again, at how wonderful living organisms are.

You can see videos of the talks here:

http://www.birs.ca/videos/2014

I gave a talk on "Biodiversity, entropy and thermodynamics":

http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410291038-Baez.mp4

but what really blew my mind was Naftali Tishby's talk on "Sensing and acting under information constraints - a principled approach to biology and intelligence":

http://www.birs.ca/events/2014/5-day-workshops/14w5170/videos/watch/201410281032-Tishby.mp4

It wasn't easy for me to follow - you should already know rate-distortion theory and the Bellman equation, and I... more »

2014-10-28 20:31:04 (32 comments, 35 reshares, 132 +1s)

**The mitochondrial genetic code**

Your cells contain **mitochondria**, little factories that help convert food into useful chemical energy, using oxygen. These guys were once bacteria in their own right! About 1.5 billion years ago they joined forces with cells that couldn't handle oxygen. Now you need them and they need you.

But they still have their own DNA, separate from the rest of the DNA in your cells. Mitochondria are passed down only from mother to child, via the egg cell. So, your **mitochondrial DNA** gives information about you, your mother, your grandmother, and so on.

Why does mitochondrial DNA come only from the mother? For starters, an egg cell contains 100,000 to 1,000,000 molecules of mitochondrial DNA, while a sperm has only 100 to 1000. On top of that, most mitochondria in a sperm cell stay in the tail, and sometimes thetail is ... more »

2014-10-26 14:51:07 (11 comments, 102 reshares, 242 +1s)

**Looping Lorentzian lattice**

A rapidly moving observer will see time (the vertical axis) and space (the horizontal axis) in a different way than you do at rest. As their speed increases the warping increases.

Each black dot is a point in spacetime. As viewed by faster and faster observers, it moves along a hyperbola. But after a while, the whole lattice of black dots gets back to the same pattern it started with!

The warpings of spacetime shown here are called **Lorentz transformations**. Greg Egan made this movie to illustrate how we can do a Lorentz transformation to a lattice in spacetime and get back the same lattice. This is the one of the symmetries that you get in what I was calling a 'spacetime crystal' - technically, a lattice coming from a hyperbolic Dynkin diagram.

For many beautiful pictures related to looping Lorentzianlattic... more »

2014-10-24 16:33:55 (56 comments, 12 reshares, 88 +1s)

**Toward a post-carbon world**

Big news! European leaders have signed a deal obliging the EU to cut greenhouse gases by at least **40% by 2030**, relative to the 1990 level of emissions. They'd already agreed to cut them 20% by 2020, and they're close to meeting that goal already.

The president of the EU Council said:

"It was not easy, not at all, but we managed to reach a fair decision. It sets Europe on an ambitious yet cost effective climate and energy path. Climate change is one of the biggest challenges of mankind. Ultimately this is about survival."

This is great. And there's some self-interest here, too. The EU plans to make money in the long term by getting ahead of other countries on implementing technologies that reduce carbon emissions. If they lead by example, it increases the chance that others will follow.

more »

2014-10-23 16:08:43 (60 comments, 55 reshares, 145 +1s)

**Spacetime crystals**

You know about crystals in space. What's a crystal in spacetime? It's a repetitive pattern that has a lot of symmetries including reflections, translations, rotations and Lorentz transformations. Rotations mix up directions in space. **Lorentz transformations** mix up space and time directions.

We can study spacetime crystals mathematically - and the nicest ones are described by gadgets called **hyperbolic Dynkin diagrams**, which play a fascinating role in string theory.

How do these diagrams work?

Each dot stands for a reflection symmetry of our spacetime crystal. Dots not connected by an edge are reflections along axes that are at right angles to each other. Dots connected by various differently labelled edges are reflections at various other angles to each other. To get a spacetime crystal, the diagramneeds to... more »

2014-10-20 05:38:33 (8 comments, 4 reshares, 78 +1s)

In case you started thinking the whole world is just that tiny part of it that makes sense...**Lotus Flower**

I will shape myself into your pocket

Invisible, do what you want, do what you want

I will shrink and I will disappear

I will slip into the groove and cut me up, and cut me up

There's an empty space inside my heart

Where the weeds take root

And now I'll set you free

I'll set you free

There's an empty space inside my heart

Where the weeds take root

Tonight I'll set you free

I'll set you free

Slowly we unfurl

As lotus flowers

'Cause all I want is the moon upon a stick

Just to see what if

Just to see what is

I can't kick your habit

Just to feed your fast ballooning head

Listen to your heart

We will shrink and be quiet as mice... more »

2014-10-18 15:55:11 (19 comments, 29 reshares, 88 +1s)

**Inspirograph**

http://nathanfriend.com/inspirograph/

If you ever had a spirograph, or even better if you never had one: now there's a good one on your web browser!

It's easy to use. You just move one gear around the other using your mouse (or finger). I still prefer the actual spirograph: working with actual physical tools is a much more immersive experience than twiddling a computer. People are getting starved for contact with interesting matter. But not everyone has access to a spirograph!

It's written using TypeScript - a typed superset of JavaScript that compiles to plain JavaScript:

http://www.typescriptlang.org/

#geometry

2014-10-17 16:06:27 (123 comments, 111 reshares, 204 +1s)

**The moving sofa problem**

You've probably tried to move a sofa around a bend in a hallway. It's annoying. But it leads to some fun math puzzles. Let's keep things simple and work in 2 dimensions. Then the **moving sofa problem** asks:

What is the shape of largest area that can be maneuvered through an L-shaped hallway of width 1?

This movie shows one attempt to solve this problem. It's called the **Hammersley sofa**, since it was discovered by John Hammersley. It has an area of

π/2 + 2/pπ = 2.20741609916...

But it's not the best known solution! In 1992, Joseph Gerver found a shape of area 2.2195 that works.

On the other hand, Hammersley showed that any solution has area at most

2 sqrt(2) = 2.82842712475...

So, the **moving sofa problem** remains unsolved. Anothereasily stat... more »

2014-10-16 19:59:25 (14 comments, 21 reshares, 99 +1s)

**The densest way to pack octagons**

This image made by +Graeme McRae shows the densest way to pack equal-sized regular octagons in the plane. The cool part: the density is slightly less than the best you can do for circles!

You can pack equal-sized circles with a density of at most

90.68996%

or so. For equal-sized regular octagons, the best you can do is

90.61636%

That's just about 0.07% worse, but it's enough to prove that a circle isn't the **pessimal plane packer** - that is, the shape whose densest packing is the lowest of all.

And one reason that is interesting is that Stanislaw Ulam conjectured that in 3 dimensions, the sphere is the pessimal packer! That conjecture is still open.

For more about this story, visit my blog Visual Insight:

h... more »

2014-10-13 16:21:49 (18 comments, 35 reshares, 80 +1s)

**Network Theory**

The world needs some new kinds of math, which deal with networks. So, check out this video! I start with a quick overview of network theory, and then begin building a category where the morphisms are electrical circuits - a warmup for more complicated kinds of networks. You can also read lecture notes:

• Network theory (part 30), http://johncarlosbaez.wordpress.com/2014/10/03/network-theory-part-30/

With luck, this video will be the first of a series. I’m giving a seminar on network theory at U.C. Riverside this fall. I’ll start by sketching the results in this new paper:

• John Baez and Brendan Fong, A compositional framework for passive linear networks, http://math.ucr.edu/home/baez/circuits.pdf

A couple of weeks ago I talked about having a Hangout on Air, but I didn't get my act together in time to set one upwith a ca... more »

2014-10-10 22:35:04 (7 comments, 35 reshares, 146 +1s)

**Hyperbubbles**

This great image by +Paul Nylander is based on a tiling of the hyperbolic plane. You can tile it with regular heptagons, three meeting at each corner. It's called the **{7,3} tiling** - and I've shown you several versions already! But in this one, each heptagon is artistically drawn as a bubble, thanks to a suggestion by Robert Bagula.

I think I learned about this picture from +Steve Esterly - he liked how bubbles of foam on a cup of coffee get smaller near the edges, sort of like how things get scrunched up near the edges of the hyperbolic plane when we squash it down to the Poincare disk.

You can see more of Paul Nylander's hyperbolic art here:

http://bugman123.com/Hyperbolic/index.html

If you aren't friends with the {7,3} tiling yet, get to know it here:

... more »

2014-10-09 20:07:55 (145 comments, 58 reshares, 303 +1s)

**Hollow Earth**

There have been lots of theories saying the Earth is hollow, but I know only one that could be true.

Edmond Halley, the guy who discovered the famous comet, had a theory where Earth consists of a hollow shell about 800 kilometers thick, two smaller shells nested inside, and a ball in the middle - all separated by atmospheres and rotating at different speeds! It sounds nutty, but Halley was trying to explain the Earth's rather complicated magnetic fields: each of his shells was magnetic.

People sometimes accuse Leonhard Euler, the famous mathematician and physicists, of believing the Earth was hollow. But that's not true. In fact, all Euler did was propose a famous thought experiment:**Puzzle:** If you could drill a hole all the way through the Earth, and drop a stone in, what would happen?

With the passage of time,sci... more »

2014-10-05 16:36:09 (38 comments, 56 reshares, 190 +1s)

**The mystery of neutrinos**

Neutrinos come in 3 kinds, but the 3 kinds with definite masses are not the same as the 3 kinds with definite flavors. They're related by a 3×3 matrix.

Every particle is also a wave, and a particle at rest is a standing wave: it wiggles without going anywhere, like a vibrating piano string. The mass, or **rest mass**, of a particle is simply the frequency at which this standing wave vibrates.

But sometimes a particle at rest can wiggle in several different ways with different frequencies. A neutrino can wiggle in 3 ways, and these are called its **mass eigenstates**. They have boring names: 1, 2 and 3.

The **flavor** of a neutrino says how it interacts with other particles via the weak force. The flavors have cool names: e (electron), μ (muon), and τ (tau particle).

But a neutrino with adefinite f... more »

2014-10-03 18:31:31 (63 comments, 29 reshares, 88 +1s)

**3-adic integers**

Math is full of wonderful number systems. Here are the **3-adic integers**. A 3-adic integer is like an integer written in base 3, except that its digits can go on forever to the left. So, something like this:

.......1012010212

The usual positive integers sit inside the 3-adic integers. For example, the number 21 (in base 3) gives the 3-adic integer

.......0000000021

But there are lots of other 3-adic integers: the ones that go on forever.

We can add and multiply these in the usual way, carrying the digits as usual. It just takes longer. For example:

...........1012010212

+ ...........0120210101

------------------------------------

...........1202221020

The picture here, created by Christopher Cutler, uses a clever trick to draw 3-adicintegers as point... more »

2014-10-02 15:40:38 (35 comments, 19 reshares, 98 +1s)

**Infinity-gons**

Here's a picture of the hyperbolic plane tiled with **apeirogons** - polygons with infinitely many sides!

Regular polygons with infinitely many sides are one of those things that make hyperbolic geometry more fun than ordinary Euclidean geometry.

"Apeiro-" is a Greek prefix meaning "infinite" or "unlimited". You know the word "perimeter", meaning boundary or limit? Well, "apeiro-" means having no limit. Greek mathematicians were pretty nervous about the infinite, because they thought its unlimitedness made it inherently vague, even chaotic.

The apeirogons are white, and there are 3 meeting at each corner.

In blue we see the **dual** tiling: there's one blue vertex in the middle of each white polygon, and one blue edge crossing each white edge, and oneblue po... more »

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