The Rest Is Science – "This Toothpick Contains Everything Ever Said"

Hosted by Professor Hannah Fry and Michael Stevens (Vsauce)
Release Date: April 6, 2026

Episode Overview

In this mind-bending episode, Hannah Fry and Michael Stevens dive deep into the concept of infinity, exploring its strangeness, mathematical rigor, and the dizzying philosophical questions it raises about reality, the universe, and even our own existence. The conversation weaves playful analogies with rigorous logic, tackling everything from encoding all human knowledge onto a toothpick, to the question of whether the universe is infinite or simply very, very big (and maybe shaped like a donut). The duo also considers the implications of infinity in mathematics and cosmology, and whether we might all just be living in a simulation after all.

Key Discussion Points

1. The Toothpick Analogy: Every Possible Statement Encoded (00:35 – 03:29)

• Encoding Knowledge on a Toothpick:
  Michael introduces a physical toothpick and demonstrates in theory how—assuming “infinite precision”—you could encode every possible statement or piece of information on it. A code is used where each letter is numbered (A=01, B=02, ..., Z=26) and marked as a decimal along the length of the toothpick.
  • Michael: “Everything that could ever be said is on this toothpick.” (01:12)
  • The idea is: with infinite precision, infinitely long decimal codes could contain everything—“the entire Encyclopedia Britannica on a single notch on this one toothpick.” (03:00)
• Infinity at Any Scale:
  This segues into a discussion of how infinity isn’t just about the very large but also the very small—layer upon layer of possible knowledge or arrangements, all potentially encoded in an arbitrarily tiny space.

2. The Hierarchy of Infinities: Alephs, Beths, and Beyond (05:15 – 19:44)

• Cardinalities and the Names of Infinity:
  Hannah and Michael review basic types of infinity:
  • Aleph-null (ℵ₀): “the smallest size of infinity, how many counting numbers there are.” (05:42)
  • Beth numbers: A different hierarchy—“the number of real numbers there are” (Beth 1), then power sets leading to larger and larger infinities.
  • Michael: “If I have three things... I can fill a basket... Basically, there’s two to the third power number of ways to do that. And as it turns out, two to the power of Aleph null is Beth 1.” (11:08)
• Well-Ordering vs. Power Sets:
  Two different ways to generate larger infinities:
  • Well-ordering things (like lining up infinite marathon finishers—Omega, Omega+1, Omega+2…).
  • Taking all possible combinations (power sets) of prior infinities.
• The Boss Infinity – Aleph Omega:
  There’s an “ultimate boss” infinity, Aleph Omega, which is the first Aleph larger than all Beths below it, and then inaccessible cardinals—“the jump from Aleph null, the smallest infinity, to an inaccessible cardinal is like the jump from zero to infinity.” (19:04)
  • Hannah: “If you get to that, you’ve hacked into the mainframe at that stage.” (18:57)
• Theoretical vs. Practical:
  Even if these sound like playful inventions, “hard, credible, rigorous mathematical proofs demonstrate, irrefutably, beyond any doubt that one of these numbers is larger than the other.” (16:15)

3. Do Infinities Exist in Reality? (20:05 – 25:59)

• Applied vs. Pure Mathematics:
  Discussion of the difference: applied mathematicians test math on real phenomena, while pure mathematicians “search for keys without ever caring about what locks they fit into.” (21:18)
  • Fry: “A lot of the time, these wild ideas... end up sometimes 150, 200 years later to be absolutely foundational to what we need to understand the world.”
• Unreasonable Effectiveness:
  Why do pure math discoveries end up describing the universe so well? “Hundreds of years later, someone finds that lock in the real world and they go, holy crud, math got there before we did.” (22:22)
• Is Any Physical Thing Infinite?
  Returning to Aristotle, who “thought you could have an infinite process but not something that contains infinity.” (24:50)
  • If infinity exists for real, maybe it’s in the cosmos—is the universe infinite?

4. The Shape and Size of the Universe: Bubbles, Donuts, and Flatness (25:03 – 33:43)

• Cosmic Visibility and the Ant on a Rubber Band (25:44):
  • The universe is expanding, not from a point like shrapnel, but “space itself” is stretching.
  • Are we in a bubble with boundaries, or a space like the Pac-Man donut where “you can go forever but are nonetheless bounded”?
  • Fry: “Pac Man lives on a donut. Okay, so, so it could be that the universe is actually infinite in the sense that you can carry on going and going and going… but nonetheless it is contained within a finite surface.” (29:17)
• Have We Seen the Backs of Our Own Heads? (30:00):
  • If the universe loops, distant objects could repeat—but “we haven’t found any evidence that the universe wraps back on itself.” (30:18)
• Current Consensus: Flat and Possibly Infinite:
  • Space appears flat, not curved like a sphere or a donut, suggesting it might “just go on forever.” (31:46)

5. Philosophical Consequences of an Infinite Universe (33:06 – 37:02)

• The Pigeonhole Principle and Cosmic Doppelgängers:
  • If the universe is infinite, then—even given a finite number of arrangements of matter—every possible arrangement must occur somewhere, including duplicates of our entire solar system, and copies of ourselves.
    • Michael: “There’s another me there and another you there. And we’re doing this podcast… except my shirt’s blue.” (33:43)
• Uncomfortable Outcomes:
  • Both infinite and finite-bubbled universes have “equally uncomfortable” implications, from infinite duplicates to universes with radically different laws of physics. (37:02)

6. On the Smallest Scales: Discrete Universe and Planck Length (38:05 – 41:14)

• Can Space Be Infinitely Divided?
  • The Planck Length (10^-35 meters) is the scale at which “our equations break,” but we don’t know if that’s fundamental or a limitation of current physics.
  • Michael: “The closer you get, the more and more detail you see. Because I don’t see how the Pythagorean theorem could hold true if things became discrete at a certain level.” (39:37)
• If the Universe Is Discrete, Circles Don’t Exist:
  • At the smallest scale, if space is pixelated, “perfect spheres cease to exist.” (40:24)
    • Fry: “Either circles and infinity exist for real, or neither of them do.” (40:47)

7. Are We Living in a Simulation? (41:43 – 45:35)

• Simulation Theory:
  Computer scientists are comfortable with discrete space—it’s how computers work. If we found indivisible spatial units, “we might have found some good evidence that we live in a simulation.” (42:10)
  • The idea is: in games, reality only renders what you see—maybe the universe is the same.
• Quantum Mechanics Tie-In:
  The “collapse of the wave function” could make sense as a simulation trick: only render reality when observed. (44:09)
  • Michael: “Saying that we live in a simulation is kind of a good bet… overall it’s more likely that I would find myself in a simulation than in a real universe.” (44:35)
  • Ultimately, both prefer to believe in a real, unsimulated universe—though “there is some suspicious stuff going on.” (45:23)

8. Looking Ahead and Final Thoughts (45:43 – 47:26)

• Answers about the universe’s size are beyond reach for now, but new breakthroughs in particle physics may come during our lifetimes.
• Fry: “Either infinity doesn’t exist, it’s all a figment of our imaginations… or there are some really uncomfortable things that are the conclusions that we must draw.” (46:30)
• Michael’s poetic summary: “We founded infinity like we invented it, but someday we will find that it was always there.” (46:50)
• Celebrating mathematician Georg Cantor, the pioneer of infinite sets. (47:06)

Notable Quotes & Memorable Moments

• “Everything that could ever be said is on this toothpick.” – Michael, 01:12
• “The jump from Aleph null, the smallest infinity, to an inaccessible cardinal is like the jump from zero to infinity.” – Michael, 19:04
• “Pure mathematicians are the ones who are searching for keys without ever caring about what locks they fit into.” – Hannah, 21:18
• “Hundreds of years later, someone finds that lock in the real world and they go, holy crud, Math got there before we did.” – Michael, 22:22
• “Pac Man lives on a donut.” – Hannah, 29:17
• “There’s another me there and another you there, and we’re doing this podcast exactly the way it is, except my shirt’s blue…” – Michael, 33:43
• “Either circles and infinity exist for real, or neither of them do.” – Hannah, 40:47
• “We founded infinity like we invented it, but someday we will find that it was always there.” – Michael, 46:50

Essential Timestamps

• Physical metaphor for infinity and toothpick encoding: 01:12 – 03:29
• Defining different sizes of infinity (Alephs and Beths): 05:42 – 11:43
• Infinity in races and ordering—Omega and Aleph 1: 13:53 – 15:43
• Philosophical/practical use of higher infinities and Cantor’s leap: 16:43 – 19:44
• Flat vs. curved universe; donut analogy: 28:27 – 31:46
• Pigeonhole principle and cosmic doubles: 33:06 – 34:45
• Simulation hypothesis tie-in: 41:43 – 44:35

Tone and Style

Lively, playful, and mind-expanding. The hosts oscillate between accessible analogies (toothpicks, Pac-Man, card shuffling), mathematical rigor, and wide-eyed philosophical curiosity. There’s frequent friendly banter and encouragement for listeners to relish these “strange weirdnesses,” whether for winning number-naming competitions with kids or for pondering the limits of reality itself.

Conclusion

If you want to think deeper about the nature of reality, the mathematics that describes it, and whether every fact, conversation, or even you yourself might exist somewhere else in the universe—or on a toothpick—this episode is a playground for the mind and soul. And as the hosts suggest, maybe infinity is something we dreamed up…but perhaps it was there all along, waiting for us to notice.