Antonio (Tony) Padilla is a theoretical physicist and cosmologist at the University of Nottingham. He serves as the Associate Director of the Nottingham Centre of Gravity, and in 2016, Tony shared the Buchalter Cosmology Prize for his work on the cosmological constant. Tony is also a star of the Numberphile YouTube channel, where his videos have received millions of views and he is also the author of the book Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity. Patreon: https://www.patreon.com/timothynguyen This episode combines some of the greatest cosmological questions together with mathematical imagination. Tony and I go through the math behind some oft-quoted numbers in cosmology and calculate the age, size, and number of atoms in the universe. We then stretch our brains and consider how likely it would be to find your Doppelganger in a truly large universe, which takes us on a detour through black hole entropy. We end with a discussion of naturalness and the anthropic principle to round out our discussion of fantastic numbers in physics. Part I. Introduction 00:00 : Introduction 01:06 : Math and or versus physics 12:09 : Backstory behind Tony's book 14:12 : Joke about theoreticians and numbers 16:18 : Technical outline Part II. Size, Age, and Quantity in the Universe 21:42 : Size of the observable universe 22:32 : Standard candles 27:39 : Hubble rate 29:02 : Measuring distances and time 37:15 : Einstein and Minkowski 40:52 : Definition of Hubble parameter 42:14 : Friedmann equation 47:11 : Calculating the size of the observable universe 51:24 : Age of the universe 56:14 : Number of atoms in the observable universe 1:01:08 : Critical density 1:03:16: 10^80 atoms of hydrogen 1:03:46 : Universe versus observable universe Part III. Extreme Physics and Doppelgangers 1:07:27 : Long-term fate of the universe 1:08:28 : Black holes and a googol years 1:09:59 : Poincare recurrence 1:13:23 : Doppelgangers in a googolplex meter wide universe 1:16:40 : Finitely many states and black hole entropy 1:25:00 : Black holes have no hair 1:29:30 : Beckenstein, Christodolou, Hawking 1:33:12 : Susskind's thought experiment: Maximum entropy of space 1:42:58 : Estimating the number of doppelgangers 1:54:21 : Poincare recurrence: Tower of four exponents. Part IV: Naturalness and Anthropics 1:54:34 : What is naturalness? Examples. 2:04:09 : Cosmological constant problem: 10^120 discrepancy 2:07:29 : Interlude: Energy shift clarification. Gravity is key. 2:15:34 : Corrections to the cosmological constant 2:18:47 : String theory landscape: 10^500 possibilities 2:20:41 : Anthropic selection 2:25:59 : Is the anthropic principle unscientific? Weinberg and predictions. 2:29:17 : Vacuum sequestration Further reading: Antonio Padilla. Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity Twitter: @iamtimnguyen Webpage: http://www.timothynguyen.org