Podcast Summary

Podcast: New Books Network
Host: Gregory McNiff
Guest: Antonio Padilla, author of Fantastic Numbers and Where to Find Them: A Cosmic Quest from Zero to Infinity (FSG, 2022)
Episode Date: February 15, 2026

Episode Overview

This episode features a conversation between host Gregory McNiff and theoretical physicist Antonio Padilla about his acclaimed book, Fantastic Numbers and Where to Find Them. The discussion unpacks the interplay between mathematics and physics, using some of the most fascinating, extreme, and mind-bending numbers in science as entry points. Padilla takes listeners on a journey from zero to infinity, exploring the profound mysteries at the interface of math, physics, and philosophy.

Key Discussion Points and Insights

Inspiration and Audience for the Book

• [01:28–03:30]
  • Padilla explains the book began as a result of fundraising lectures inspired by a friend's illness, which were well received and naturally evolved into a book project.
  • Quote:

    "For me, the book is about... that interface between maths and physics. It's how physics can make maths wonderful and maths can make physics wonderful, and the two really go hand in hand. And one without the other is just incomplete, at least in my world."
    — Antonio Padilla [02:29]

Making Relativity Concrete (Usain Bolt Example)

• [04:26–07:58]
  • Padilla uses Usain Bolt as a playful example to demonstrate principles of special relativity, such as time dilation and length contraction, emphasizing the tiny but real effects even at human speeds.
  • Quote:

    "You realize his clock slows down. You realize the track actually shrank from his perspective, so he didn't actually run 100 meters... Maybe we should take his gold medal away or something..."
    — Antonio Padilla [06:35]

  • Relativity's real-world impacts (e.g., GPS satellites) are highlighted.

The Speed of Light & Inertia

• [07:58–09:51]
  • The speed of light as an absolute limit explained: as objects approach light speed, their inertia (resistance to acceleration) becomes infinite, making further acceleration impossible.
  • Quote:

    "Your inertia, your mass, your resistance to motion, actually increases. And actually, at the point that you hit the speed of light, it goes infinite... there's no way you're moving once your masses hit infinity."
    — Antonio Padilla [08:52]

Minkowski, Maxwell, and Elegant Physics

• [09:51–12:16]
  • Discussion on Minkowski's unification of space and time, and how rewriting Maxwell's equations in this framework greatly simplifies their form.
  • Quote:

    "When you write... Maxwell's equations... instead of having this sort of this long, ugly set of equations, what you have is really one beautiful equation... you can write it as two centimeters across, whereas I'm writing Maxwell's equations as they were originally written— I need a whole page."
    — Antonio Padilla [11:31]

Gravity Is Fake?!

• [12:16–14:45]
  • Padilla provocatively asserts gravity is "fake," meaning it isn’t a traditional force but rather an effect of space-time geometry; illustrated via thought experiments like jumping off the Burj Khalifa in a sealed box (a nod to Einstein’s equivalence principle).
  • Quote:

    "If you can get rid of something, then it's not really there. So what do I mean by that?... If you throw yourself off a building... gravity's gone. And gravity is just the shape of space and time in which I find myself."
    — Antonio Padilla [12:40, 14:38]

Entropy and Sadi Carnot: "Entropy Is What Counts"

• [14:45–16:50]
  • The historical contributions of Sadi Carnot and the meaning of entropy are discussed, with Padilla favoring a statistical understanding: entropy is the ways a system can be arranged without changing its macroscopic appearance.
  • Quote:

    "Entropy is counting those microstates."
    — Antonio Padilla [19:03]

  • Example: comparing a messy vs. tidy daughter's bedroom.

Are Doppelgangers Out There? (Googleplex and Finite Arrangements)

• [19:34–24:13]
  • Explores the statistical inevitability of cosmic doppelgangers given a large enough universe, using the concept of a Googleplex— a number vastly bigger than the number of possible human arrangements in a cubic meter.
  • Cosmic inflation theories suggest a sufficiently vast universe could indeed harbor identical copies of us.

Hugeness of Graham’s Number – "Black Hole Head Death"

• [24:13–28:37]
  • Introduction of Graham’s number, an unimaginably large integer arising from a combinatorial proof, and the idea that attempting to mentally store its digits would require so much information your brain would collapse into a black hole.
  • Quote:

    "If you shove so many digits of Graham number into your head... eventually... your head has no choice but to collapse and form a black hole... and you don’t even close the [digits of] Graham’s number by the time you get there."
    — Antonio Padilla [27:45]

The Information Paradox and Black Holes

• [28:37–31:04]
  • Outlines the paradox: information entering a black hole seems irretrievably lost, in contradiction to quantum mechanics’ rules. Hawking radiation doesn't appear to carry that information out.
  • Recent theoretical advances are mentioned, but the resolution remains elusive.

Poincare Recurrence, Tree(3), and Inaccessible Numbers

• [31:04–35:33]
  • Poincare recurrence: in finite systems (like our "cosmic box" universe), after inconceivably long times, states will repeat.
  • But the number of possible steps ("Tree(3)") vastly exceeds even these astronomical recurrence times, meaning certain mathematical events can never happen in our universe.

The Holographic Principle – Dimensions are an Illusion?

• [35:33–39:19]
  • Padilla calls the holographic principle "the most important idea in physics in the past 30 years": the universe’s fundamental information content may live on a lower-dimensional boundary, inspired by black holes.
  • Quote:

    "In some ways our world... is kind of an illusion and that actually we actually live on the boundary of that world in a space which has one dimension less."
    — Antonio Padilla [35:50]

  • The entropy of a black hole scales with its surface area, not its volume.

The Deep Significance of Zero and Symmetry

• [41:38–43:42]
  • Reflecting on why zeros arise in physics (e.g., perfectly balanced "ins and outs") often leads scientists to search for underlying symmetries, guiding new theoretical breakthroughs.

The Higgs Boson and Spontaneous Symmetry Breaking

• [43:42–46:16]
  • The Higgs mechanism is described as a "profound idea" giving mass to matter through the breaking of symmetry. Without this, protons, electrons— and thus everything— couldn't exist.
  • The observed Higgs mass is “like finding a snowman in the fires of hell,” an unexplained balance of tremendous quantum corrections.

Supersymmetry (“Beauty Beyond All Beauty”)—But Not Yet Seen

• [48:38–49:54]
  • Supersymmetry is mathematically beautiful, resolves certain theoretical problems, but remains undetected at the Large Hadron Collider.
  • Quote:

    "We can do the mathematics... and then we're naturally very much led to supersymmetry... Only there is a snag— no one has ever seen such beauty."
    — Antonio Padilla [48:57]

The Cosmological Constant and Dark Energy’s Confounding Smallness

• [49:54–52:21]
  • Quantum mechanics predicts empty space (the cosmological constant) should have immense energy, but observations show it’s minuscule. This "worst prediction in theoretical physics" remains a mystery.

Cantor and Infinity—Genius and Madness

• [52:21–54:21]
  • The mathematician Georg Cantor classified infinities, "counting beyond infinity"— but his groundbreaking logic led to intellectual isolation and mental deterioration in his later life.

String Theory, Quantum Gravity, and the "Theory of Everything"

• [54:21–58:18]
  • String theory is described as the best current candidate for unifying quantum mechanics and gravity, owing to its mathematical origins and ability to yield (in principle) gravity and other features of our universe. But it remains unfinished and experimentally elusive.
  • Quote:

    "String theory has a kind of mathematical uniqueness and a mathematical elegance that none of the others I would say do... But it's not perfect and we do need a revolution in our understanding."
    — Antonio Padilla [57:40]

K2 and K3: Peaks of Earth and Math

• [58:18–60:58]
  • Comparison between the dangerous “savage mountain” K2 and the mathematical challenge of K3 surfaces, critical in string theory’s formulation of extra dimensions.

Is Mathematics Universal or Merely a Tool?

• [60:58–63:09]
  • In closing, Padilla ponders the philosophical question: is math an invented human language, or is the cosmos inherently mathematical?
  • Quote:

    "We have this tool, this amazing tool which is mathematics, which we as humans have invented. And this tool seems to do this incredible job of describing the physical world... But you can ask the question, is everything in our universe able to be described by this amazing tool? ...I don't think the answer to that is answered, actually."
    — Antonio Padilla [61:32]

Notable Quotes & Memorable Moments

• On why he wrote the book:

  "For me, the book is about... that interface between maths and physics. It's how physics can make maths wonderful and maths can make physics wonderful..." [02:29]

• On relativity and Usain Bolt:

  "You realize his clock slows down. You realize the track actually shrank from his perspective, so he didn’t actually run 100 meters." [06:35]

• On gravity:

  "If you can get rid of something, then it's not really there... Gravity is just the shape of space and time in which I find myself." [12:40, 14:38]

• On Graham's number:

  "If you shove so many digits of Graham number into your head... your head has no choice but to collapse and form a black hole..." [27:45]

• On the cosmological constant:

  "It's probably the worst prediction in theoretical physics. Huge on one side, tiny actual value that you see." [51:23]

• On string theory:

  "String theory has a kind of mathematical uniqueness and a mathematical elegance that none of the others I would say do. It can be connected to the low energy world in a way that the others can't." [57:40]

• On mathematics and reality:

  "We have this tool, this amazing tool which is mathematics... And this tool seems to do this incredible job... But... is everything in our universe able to be described by this amazing tool?... I don't think the answer to that is answered, actually." [61:32]

Suggested Listening Guide

• Book’s Origin and Audience – [01:28–03:30]
• Relativity, Usain Bolt, and Limits of Speed – [04:26–09:51]
• Minkowski and Elegant Equations – [09:51–12:16]
• Is Gravity Fake? – [12:16–14:45]
• Entropy, Carnot, and Information – [14:45–19:34]
• Googleplex, Doppelgangers, and the Size of the Universe – [19:34–24:13]
• Mind-blowing Large Numbers: Graham’s Number – [24:13–28:37]
• Black Holes, Information Paradox, and Holography – [28:37–39:19]
• The Magic of Zero and Its Symmetries – [41:38–43:42]
• Higgs, Supersymmetry, and Unsolved Mysteries – [43:42–49:54]
• The Cosmological Constant Catastrophe – [49:54–52:21]
• Infinity and Cantor’s Legacy – [52:21–54:21]
• String Theory and the Quest for a Theory of Everything – [54:21–58:18]
• Mountains and Mathematical Surfaces: K2 and K3 – [58:18–60:58]
• Universal Language: Math and the Universe – [60:58–63:09]

This engaging episode will thrill anyone curious about physics, mathematics, and the mysterious scale of reality— from the tiniest quantum effects to the endless reach of infinity. Padilla’s infectious enthusiasm, clear analogies, and delight in the mathematical beauty of the cosmos make profound topics both accessible and exciting.