Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity

by Antonio Padilla

Overview

A fun, dazzling exploration of the strange numbers that illuminate the ultimate nature of reality.

For particularly brilliant theoretical physicists like James Clerk Maxwell, Paul Dirac, or Albert Einstein, the search for mathematical truths led to strange new understandings of the ultimate nature of reality. But what are these truths? What are the mysterious numbers that explain the universe?

In Fantastic Numbers and Where to Find Them, the leading theoretical physicist and YouTube star Antonio Padilla takes us on an irreverent cosmic tour of nine of the most extraordinary numbers in physics, offering a startling picture of how the universe works. These strange numbers include Graham’s number, which is so large that if you thought about it in the wrong way, your head would collapse into a singularity; TREE(3), whose finite nature can never be definitively proved, because to do so would take so much time that the universe would experience a Poincaré Recurrence—resetting to precisely the state it currently holds, down to the arrangement of individual atoms; and 10^{-120}, measuring the desperately unlikely balance of energy needed to allow the universe to exist for more than just a moment, to extend beyond the size of a single atom—in other words, the mystery of our unexpected universe.

Leading us down the rabbit hole to a deeper understanding of reality, Padilla explains how these unusual numbers are the key to understanding such mind-boggling phenomena as black holes, relativity, and the problem of the cosmological constant—that the two best and most rigorously tested ways of understanding the universe contradict one another. Fantastic Numbers and Where to Find Them is a combination of popular and cutting-edge science—and a lively, entertaining, and even funny exploration of the most fundamental truths about the universe.

Product Details

ISBN-13:	9780374600563
Publisher:	Farrar, Straus and Giroux
Publication date:	07/26/2022
Pages:	352
Sales rank:	430,049
Product dimensions:	5.90(w) x 8.80(h) x 1.20(d)

About the Author

Antonio Padilla is a leading theoretical physicist and cosmologist at the University of Nottingham. In 2016, he and his team shared the Buchalter Cosmology Prize for their work on the cosmological constant. He is also a star of the Numberphile YouTube network, where his most popular videos include a discussion of Ramanujan’s sum of all positive integers, which has been viewed more than seven million times.

Table of Contents

A Chapter That's Not a Number 1

Big Numbers

1.000000000000000858 9

A Bolt of relativity 9

The Challenger Deep 22

A glimpse into the abyss 33

A Googol 39

The tales of Gerard Grant 39

The entropic captor 42

A Googolplex 57

The quantum sorcerer 57

Where is your doppelgänger? 80

Graham's Number 88

Black hole head death 88

Too much information 99

Think of a number 110

Tree(3) 117

The Game of Trees 117

The cosmic reset 129

The holographic truth 135

Little Numbers

Zero 149

A beautiful number 149

A history of nothing 155

Zero is symmetry 173

Finding zero 177

0.0000000000000001 185

The unexpected Higgs boson 185

Particle particulars 192

The inevitable Higgs boson 198

Technically, it's not natural 219

The Scarlet Pimpernel 224

10^-120 230

An embarrassing number 230

Albert Einstein's most difficult relationship 237

The golden ticket 249

The ghost of Sir Isaac Newton 254

Infinity

Infinity 261

The infinite gods 261

The aleph and the omega 270

Close encounters of the infinite kind 289

The Theory of Everything 301

Notes 313

Acknowledgements 319

Index 323

Editorial Reviews

★ 05/30/2022

Numbers explain the universe in the electrifying debut from Padilla, a theoretical physicist and YouTuber on the math channel Numberphile. Using metaphors, analogies, and carefully constructed commentary, Padilla tackles such subjects as general and special relativity, black holes, the elusive Higgs boson particle, quantum mechanics, and string theory. He includes mini-biographies of physics’ key players, including “savant of symmetry” Emmy Noether, “quantum pioneer” Wolfgang Pauli, and “rock-star physicist” Richard Feynman. Naturally, there are numbers galore: googols (a one followed by 100 zeros), used to explain the “vastness of infinity”; googolplexes, “a one followed by zeroes ‘until you get tired,’ ” per its creator; and the enormous Tree(3), based on a game that mathematicians believe can end, though it could “easily last beyond the lifetime of a human, a planet or even a galaxy.” Padilla caps his survey with an intriguing discussion of infinity in which he looks at the possibility that some infinities can be bigger than others. He’s a stellar guide, shifting from playful to serious with ease, and his love for his subject is infectious and his knowledge vast in a way that is fitting for the material. This one deserves wide readership. (July)

Publishers Weekly

"A fast-paced and dramatic telling of the history of mathematics that is ultimately concerned with convincing us why we should care . . . Conceptualizing the real-world application of abstract mathematics is every professor's dream for their students, and Padilla makes it a reality." —Amy Brady, Scientific American

"[An] electrifying debut . . . [Padilla is] a stellar guide, shifting from playful to serious with ease, and his love for his subject is infectious and his knowledge vast in a way that is fitting for the material. This one deserves wide readership." —Publishers Weekly (starred review)

"A fascinating book that guides us through the labyrinth of numbers and what they mean . . . [A] lively history . . . Padilla has a knack for effectively deconstructing difficult concepts . . . Like James Gleick’s Chaos and Stephen Hawking’s A Brief History of Time, [Fantastic Numbers and Where to Find Them] is a remarkable piece of work . . . Astonishing in its sweep and depth, this book offers a unique way of looking at the universe." —Kirkus Reviews

"It was said of the famous Indian mathematician Ramanujan that he knew every number as his personal friend. If you'd like to get to know some of the most charismatic of these characters then Antonio Padilla has written a beautiful Who's Who of the world of numbers and their role in the make-up of our universe." —Marcus du Sautoy, author of Thinking Better

"This is an extraordinary book. Tony Padilla has been able to weave a remarkable set of mathematical facts into a mesmerising story that kept me gripped throughout. He has an intensity and passion that I haven't seen for a long time in popular science." —Pedro G. Ferreira, author of The Perfect Theory

“This delightful book purports to be about numbers, but is really a window onto the astonishing scope and scale of the universe in which we live. You will be amazed at the mind-bending ideas science has proposed in order to grasp reality, and be impressed that our minds are able to bend that far.” —Sean Carroll, author of Something Deeply Hidden: Quantum Worlds and the Emergence of Spacetime

From the Publisher

01/01/2022

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Library Journal

2022-05-10
A fascinating book that guides us through the labyrinth of numbers and what they mean.

Theoretical physicist Padilla, whose research focuses on the intersection of advanced mathematics, physics, and cosmology, sees the world as a collection of particles, waves, and forces described by a spectrum of numbers ranging from the vanishingly small to the unbelievably large. Dividing the book into “big numbers” and “little numbers,” the author traces the history of each of his fields of study, providing sketches of the people who made the key breakthroughs. This is lively history, from the Newtonian world of movement and collisions to the mysteries of quantum mechanics, with Einstein and a host of others making appearances. Finding numbers large enough to make sense of the universe has been a constant problem. Graham’s number, usually written as a mixture of numerals and esoteric symbols, was the standard for a while; Padilla describes it as a “black hole head death,” too big for the human brain to handle as anything but an abstraction. Graham’s number was eventually surpassed by TREE(3), the product of a self-replicating series. At the other end of the numerical scale, Padilla stares into the abyss of supertiny particles and components of atoms, confronting the randomness of the way they stick together, or don’t. “It worries me to think that everything I know should never have existed: me, my family, my closest friends,” he writes. “This book should never have existed and yet, somehow, you’re reading it, right now, in a moment that might never have arrived.” Padilla has a knack for effectively deconstructing difficult concepts, using explanations that include Usain Bolt, Lego, and Squid Game. Though parts of the book are extremely challenging, like James Gleick’s Chaos and Stephen Hawking’s A Brief History of Time, it is a remarkable piece of work that is well worth the effort.

Astonishing in its sweep and depth, this book offers a unique way of looking at the universe.

Kirkus Reviews