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This video features Dr Tony Padilla from the University of Nottingham.
1. The numbers I use are based on Planck 2013 data. Data from the 2015 release exists but I chose the 2013 data since the precise calculation of the size of the universe has only been done explicitly in that case as per this paper: http://www.isaacpub.org/images/PaperPDF/AdAp_100039_2016122914005354452.pdf
2. Near the start I say I’m only considering fundamental particles with mass, and not, say, photons. Actually, I don’t count neutrinos either since they too are relativistic, and the precise results are model dependent to an extent.
3 (later addendum). Well done to anyone who spotted the fact that the 75:25% split between H and He ought to be by mass, and not by number of atoms, as in the video. I realised this mistake lying in bed on the night the video was released and kicked myself repeatedly! Very annoying. Anyway, correcting for this, we see that there actually ought to be 12 H atoms for each He atom, since the atom mass of He is 4, and the total atomic mass of 12 H atoms is 12=3x4. Following the same sort of logic as in the video, we find that there are 62=12x4+14 particles for 16=12+4 baryons. Thats means we should have multiplied by 62/16 rather than 26/7, and so our result should be corrected by a factor of 1.04, yielding closer to 3.4 x 10^80 particles. [Of course, no-one really worries about factors of 1.04 in cosmology :)]. The time to the "apocalyptic” end mentioned later in the video then changes by 3 to 4 years, which is anyway well within the rounding errors of the calculation.
How many particles in the Universe? - NumberphileNumberphile2017-07-10 | Sponsored by Skillshare... 2-months free to first 500 people: http://www.skl.sh/Numberphile More links & stuff in full description below ↓↓↓
This video features Dr Tony Padilla from the University of Nottingham.
1. The numbers I use are based on Planck 2013 data. Data from the 2015 release exists but I chose the 2013 data since the precise calculation of the size of the universe has only been done explicitly in that case as per this paper: http://www.isaacpub.org/images/PaperPDF/AdAp_100039_2016122914005354452.pdf
2. Near the start I say I’m only considering fundamental particles with mass, and not, say, photons. Actually, I don’t count neutrinos either since they too are relativistic, and the precise results are model dependent to an extent.
3 (later addendum). Well done to anyone who spotted the fact that the 75:25% split between H and He ought to be by mass, and not by number of atoms, as in the video. I realised this mistake lying in bed on the night the video was released and kicked myself repeatedly! Very annoying. Anyway, correcting for this, we see that there actually ought to be 12 H atoms for each He atom, since the atom mass of He is 4, and the total atomic mass of 12 H atoms is 12=3x4. Following the same sort of logic as in the video, we find that there are 62=12x4+14 particles for 16=12+4 baryons. Thats means we should have multiplied by 62/16 rather than 26/7, and so our result should be corrected by a factor of 1.04, yielding closer to 3.4 x 10^80 particles. [Of course, no-one really worries about factors of 1.04 in cosmology :)]. The time to the "apocalyptic” end mentioned later in the video then changes by 3 to 4 years, which is anyway well within the rounding errors of the calculation.The Puzzling Fourth Dimension (and exotic shapes) - NumberphileNumberphile2022-12-01 | Featuring Ciprian Manolescu from Stanford University. More links & stuff in full description below ↓↓↓
Ciprian Manolescu: https://web.stanford.edu/~cm5/
Sphere art at the end of the video by https://www.adistu.ro/
Special thanks to: Ben Delo Juan Benet Jeff Straathof Ken Baron Andy B Michael Dunworth James Bissonette Jubal John Jeremy Buchanan Steve Crutchfield Adam Savage Ben White Andrei M Burke RAD Donato Matthew Schuster Nat Tyce Ron Hochsprung Ubiquity Ventures John Zelinka Gnare Kannan Stanz OnlineBookClub.org Matt Tiblow Heather Liu Jordan W Oja Tracy Parry Ian George Walker Arnas Bernd Sing Valentin Alfred Wallace Alex Khein Mirik Gogri Doug Hoffman Xavier F. G. John LoachMaking a Glass Klein Bottle - NumberphileNumberphile2022-11-24 | Lucas Clarke crafts a glass Klein Bottle. See brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9A Hairy Problem (and a Feathery Solution) - NumberphileNumberphile2022-11-20 | With Ben Sparks. Episode sponsor is MEL Science. Visit melscience.com/sBLS and use code Numberphile for 50% discount. More links & stuff in full description below ↓↓↓
#melscience #melchemistry #melphysics #melkidsCow-culus and Elegant Geometry - NumberphileNumberphile2022-11-14 | Zvedelina Stankova with two solutions (one messy, one beautiful) to a problem involving an injured cow. Extra footage at: youtu.be/aW7R1U6FMLs --- More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9A Number Sequence with Everything - NumberphileNumberphile2022-11-10 | Neil Sloane discusses The Inventory Sequence... See also Jane Street's special page: janestreet.com/numberphile2022 More links & stuff in full description below ↓↓↓
Neil Sloane is founder of the legendary OEIS: oeis.org
Sign up for (occasional) emails: http://eepurl.com/YdjL9Prime Pyramid (with 3Blue1Brown) - NumberphileNumberphile2022-11-06 | Grant Sanderson (from 3Blue1Brown) shows us a pyramid that spits out prime numbers - and then we dig deeper. More links & stuff in full description below ↓↓↓
Part 1 of this three-part interview is at: youtu.be/jhObLT1Lrfo Part 3 of this three-part interview: STILL BEING EDITED
Sign up for (occasional) emails: http://eepurl.com/YdjL9Paterson Primes (with 3Blue1Brown) - NumberphileNumberphile2022-11-04 | Grant Sanderson (from 3Blue1Brown) discusses the briefly brilliant discovery of Paterson Primes. More links & stuff in full description below ↓↓↓
Part 2 of this three-part interview is at: youtu.be/NsjsLwYRW8o Part 3 of this three-part interview: STILL BEING EDITED
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Truth About Fibs - NumberphileNumberphile2022-10-26 | Marcus du Sautoy on Fibonacci Numbers. More links & stuff in full description below ↓↓↓
Thanks to these Patrons: Ben DeloJuan BenetJeff StraathofKen BaronYana ChernobilskyAndy BMichael DunworthJames BissonetteJubal JohnJeremy BuchananSteve CrutchfieldAdam SavageBen WhiteAndrei M BurkeRAD DonatoMatthew SchusterNat TyceRon HochsprungUbiquity VenturesJohn ZelinkaGnareKannan StanzOnlineBookClub.orgMatt TiblowHeather LiuTracy ParryIan George WalkerArnas Bernd SingValentin Alfred WallaceBodhisattva DebnathAlex KheinMirik GogriDoug HoffmanXavier F. G.John LoachAn Integration Conundrum - NumberphileNumberphile2022-10-19 | Featuring Ben Sparks doing some calculus. See brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Dumbest Way To Solve A Maze - NumberphileNumberphile2022-09-11 | Featuring Matt Henderson. Check brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Matt Henderson on Twitter (he posts lovely animations there): twitter.com/matthen2
JANE STREET... Applications for Summer 2023 internships are open and filling up... Roles include: Quantitative Trading, Software Engineering, Quantitative Research and Business Development... and more. Positions in New York, Hong Kong, and London. janestreet.com/join-jane-street/internships
Numberphile T-Shirts and Merch: teespring.com/stores/numberphileThe Nescafé Equation (43 coffee beans) - NumberphileNumberphile2022-08-13 | Featuring Cliff Stoll. Check brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Cliff scrutinizes the lyrics of a Nescafé advertisement dealing with the brand's famed 43 beans.
Thanks to all our Patrons, including: Ben Delo Juan Benet Jeff Straathof Ken Baron Yana Chernobilsky Andy B Michael Dunworth James Bissonette Jubal John Jeremy Buchanan Steve Crutchfield Adam Savage Ben White Andrei M Burke RAD Donato Matthew Schuster Nat Tyce Ron Hochsprung Ubiquity Ventures John Zelinka Gnare Kannan Stanz OnlineBookClub.org Matt Tiblow Tracy Parry Ian George Walker Arnas Bernd Sing Valentin Alfred Wallace Bodhisattva Debnath Alex Khein Mirik Gogri Doug Hoffman Xavier F. G. John LoachThe Notorious Question Six (cracked by Induction) - NumberphileNumberphile2022-08-05 | Featuring Zvezdelina Stankova... This video stands alone but also continues from the previous induction video at youtu.be/bylFzBxzQ9M - More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Epic Induction - NumberphileNumberphile2022-08-03 | Featuring Zvezdelina Stankova... Continues with "Question 6" at youtu.be/NcaYEaVTA4g - More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Are there 10^272,000 Universes? - NumberphileNumberphile2022-06-28 | Featuring Tony Padilla. Check brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Mathematical Hugs (and Chiral Knots) - NumberphileNumberphile2022-06-21 | Extra footage at: youtu.be/ue9LHv4XXBQ - Featuring Ayliean MacDonald. More links & stuff in full description below ↓↓↓
More about Ayliean MacDonald: https://linktr.ee/Ayliean
Sign up for (occasional) emails: http://eepurl.com/YdjL9Primes and Primitive Sets (an Erdős Conjecture is cracked) - NumberphileNumberphile2022-06-16 | Extra footage at youtu.be/-r2agPNx0gA - Featuring Jared Duker Lichtman. More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Troublemaker Number - NumberphileNumberphile2022-05-23 | Dr Harini Desiraju discusses Somos Sequences and a number which breaks a streak. More links & stuff in full description below ↓↓↓
Dr Harini Desiraju is a postdoctoral fellow at The University of Sydney. This video was recorded at MSRI.
Sign up for (occasional) emails: http://eepurl.com/YdjL9A number NOBODY has thought of - NumberphileNumberphile2022-05-17 | Featuring Tony Padilla. Check brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Two Candles, One Cake (Part 2) - NumberphileNumberphile2022-05-11 | Ben Sparks continuing from Part 1, which is at: youtu.be/FkVe8qrT0LA Go deeper with Ben's explanation at youtu.be/0eqBG6lz2mE More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Two Candles, One Cake - NumberphileNumberphile2022-05-10 | Featuring Ben Sparks. See part 2 at youtu.be/l5gUrDg01cQ More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9How to write 100,000,000,000,000 poems - NumberphileNumberphile2022-05-03 | Marcus du Sautoy on the clever use of mathematics to generate poetry... Episode sponsored by Backblaze online back-up - more at backblaze.com/numberphile More links & stuff in full description below ↓↓↓
See an extra video with some example sonnets using famous numbers and combinations chosen by Patreon supporters: youtu.be/SqsH5K_M9Rs
We discuss the original book by Raymond Queneau "A Hundred Thousand Billion Poems" or "One Hundred Million Million Poems" (original French title: Cent mille milliards de poèmes). We discuss his work as an example of mathematical shortcuts - a favourite topic of Professor du Sautoy.
Sign up for (occasional) emails: http://eepurl.com/YdjL9Eulers Formula - NumberphileNumberphile2022-04-24 | Tom Crawford shows us some cool things about Euler's Formula... Check brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Tom Crawford's website, with links to his work and other outreach: tomrocksmaths.com
Sign up for (occasional) emails: http://eepurl.com/YdjL9Drawing an Egg (with a Pentagon) - NumberphileNumberphile2022-04-16 | Featuring Johnny Ball... And see more about the egg formula at youtu.be/tjyFw1BX4eM More links about Johnny & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9How do fish swim so quickly?Numberphile2022-03-30 | Featuring Tadashi Tokieda... Get 60% off your first box from MEL Science at melscience.com/sBEz and use code NUMBERPHILE60 (episode sponsor) More links & stuff in full description below ↓↓↓
Tadashi Tokieda is a professor of mathematics at Stanford University, specialising in applied mathematics.
Sign up for (occasional) emails: http://eepurl.com/YdjL9Twin Proofs for Twin Primes - NumberphileNumberphile2022-03-27 | With Ben Sparks... Check brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Big Factorials - NumberphileNumberphile2022-03-24 | Large factorials and the use of Stirling's Approximation. Featuring Professor Ken McLaughlin. More links & stuff in full description below ↓↓↓
Professor McLaughlin is based at Colorado State University: https://www.math.colostate.edu/~kenmcl/
We filmed this during his time at the Mathematical Sciences Research Institute.
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Reciprocals of Primes - NumberphileNumberphile2022-03-14 | Matt Parker explores the work of William Shanks - and boots up the ShanksBot. More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Coca-Cola Klein Bottle - NumberphileNumberphile2022-03-09 | Cliff Stoll - the King of Klein Bottles - shows us more designs, including the Coke Klein Bottle... Full Klein Bottle Playlist: http://bit.ly/KleinBottles More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Tetrahedral Boat - NumberphileNumberphile2022-02-26 | Featuring Marcus du Sautoy discussing polyhedra and the art of Conrad Shawcross... More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Mathematics of Surviving Zombies - NumberphileNumberphile2022-02-10 | With Thomas Woolley... Check brilliant.org/numberphile for Brilliant and get 20% off their premium service (episode sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Plotting Pi and Searching for Mona Lisa - NumberphileNumberphile2022-02-02 | Matt Henderson lets his plotter loose on Pi. This plotting extravaganza follows on from this earlier video: youtu.be/kMBj2fp52tA More links & stuff in full description below ↓↓↓
Matt Henderson on Twitter (he posts lovely animations there): twitter.com/matthen2
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Plotting of Beautiful Curves (Euler Spirals and Sierpiński Triangles) - NumberphileNumberphile2022-02-01 | This the first or two parts with Matt Henderson and his plotter... Part 2 (featuring Pi) is here: youtu.be/tkC1HHuuk7c More links & stuff in full description below ↓↓↓
Matt Henderson on Twitter (he posts lovely animations there): twitter.com/matthen2
Sign up for (occasional) emails: http://eepurl.com/YdjL9Tunnelling through a Mountain - NumberphileNumberphile2022-01-23 | Featuring Professor Hannah Fry - more details on her work below. Check out Brilliant (get 20% off their premium service): brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Stones on an Infinite Chessboard - NumberphileNumberphile2022-01-10 | Another curious puzzle and number sequence from Neil Sloane. More of our videos with Neil: http://bit.ly/Sloane_Numberphile More links & stuff in full description below ↓↓↓
Neil Sloane is founder of the On-Line Encyclopedia of Integer Sequences: oeis.org
Thanks to all our Patreon supporters, including: Ben Delo Juan Benet Jeff Straathof Ken Baron Yana Chernobilsky Andy B Michael Dunworth James Bissonette Jubal John Jeremy Buchanan Steve Crutchfield Adam Savage Ben White Andrei M Burke RAD Donato Matthew Schuster Nat Tyce Ron Hochsprung Ubiquity Ventures John Zelinka Gnare Kannan Stanz OnlineBookClub.org Tracy Parry Ian George Walker Arnas Bernd Sing Valentin Alfred Wallace Charles Southerland Bodhisattva Debnath Alex Khein Kermit Norlund Mirik Gogri Doug Hoffman Xavier F. G. Avi YashchinConic Loaf of Bread - NumberphileNumberphile2021-12-25 | Featuring Cliff Stoll - http://bit.ly/Cliff_Videos More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Bertrands Paradox (with 3blue1brown) - NumberphileNumberphile2021-12-20 | Featuring Grant Sanderson, creator of 3blue1brown. Extra footage from this interview: youtu.be/pJyKM-7IgAU 3blue1brown video on the shadow a cube: youtu.be/ltLUadnCyi0 More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Largest Small Hexagon - NumberphileNumberphile2021-12-17 | Featuring Dr James Grime. More links below. Check out Brilliant (get 20% off their premium service): brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓
Ron Graham's paper: http://www.math.ucsd.edu/~fan/ron/papers/75_02_hexagon.pdf
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Most Wanted Prime Number - NumberphileNumberphile2021-12-15 | Featuring Neil Sloane. Visit gift.climeworks.com/numberphile to give the gift of CO₂ removal. Use code NUMBERPHILE10 for 10% off your purchase in December (sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Omicron (the symbol) in Mathematics - NumberphileNumberphile2021-12-09 | Professor Tony Padilla discusses the Greek letter Omicron. More links & stuff in full description below ↓↓↓
Thanks to all our Patreon supporters, including: Ben Delo Jeff Straathof Andy B Yana Chernobilsky Ken Baron Michael Dunworth Gnare John Zelinka Ubiquity Ventures Ron Hochsprung Jeremy Buchanan Nat Tyce Matthew Schuster RAD Donato Andrei M Burke Ben White Adam Savage Steve Crutchfield James Bissonette Jubal John Jordan W Oja Xavier F. G. Doug Hoffman Mirik Gogri Alex Khein Kermit Norlund Bodhisattva Debnath Bernd Sing Charles Southerland Alfred Wallace Valentin Arnas Tracy Parry Ian George Walker
Sign up for (occasional) emails: http://eepurl.com/YdjL9Witness Numbers (and the truthful 1,662,803) - NumberphileNumberphile2021-11-28 | Featuring Matt Parker - more Parker links below. Check out Brilliant (get 20% off their premium service): brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9How to make railway timetables (with graphs) - NumberphileNumberphile2021-11-21 | Featuring Hannah Fry discussing Train Graphs. More links & stuff in full description below ↓↓↓
Hannah's website, including links to her many and varied projects... and latest books: hannahfry.co.uk
Her latest book (with Adam Rutherford) is the Complete Guide to Absolutely Everything (Abridged): amzn.to/30Mr6UE
Sign up for (occasional) emails: http://eepurl.com/YdjL9Infinitely Many Touching Circles - NumberphileNumberphile2021-11-17 | Featuring Matt Henderson. Check out kiwico.com/Numberphile and get 50% off your first month of any subscription. (sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9A Video about the Number 10 - NumberphileNumberphile2021-11-11 | Featuring the friendless number 10 for our 10-year anniversary... James Grime is back where it all began. More links & stuff in full description below ↓↓↓
James is at The City Ground - see the original 11.11.11 video at: youtu.be/sPFWfAxIiwg
Sign up for (occasional) emails: http://eepurl.com/YdjL9The Doomsday Algorithm - NumberphileNumberphile2021-10-31 | Featuring James Grime. Check out kiwico.com/Numberphile and get 50% off your first month of any subscription. (sponsor) More links & stuff in full description below ↓↓↓
Sign up for (occasional) emails: http://eepurl.com/YdjL9Key to the Tower of Hanoi - NumberphileNumberphile2021-10-27 | Featuring Ayliean MacDonald... Check out Brilliant (get 20% off their premium service): brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓