Join Ads Marketplace to earn through podcast sponsorships.
Manage your ads with dynamic ad insertion capability.
Monetize with Apple Podcasts Subscriptions via Podbean.
Earn rewards and recurring income from Fan Club membership.
Get the answers and support you need.
Resources and guides to launch, grow, and monetize podcast.
Stay updated with the latest podcasting tips and trends.
Check out our newest and recently released features!
Podcast interviews, best practices, and helpful tips.
The step-by-step guide to start your own podcast.
Create the best live podcast and engage your audience.
Tips on making the decision to monetize your podcast.
The best ways to get more eyes and ears on your podcast.
Everything you need to know about podcast advertising.
The ultimate guide to recording a podcast on your phone.
Steps to set up and use group recording in the Podbean app.
Join Ads Marketplace to earn through podcast sponsorships.
Manage your ads with dynamic ad insertion capability.
Monetize with Apple Podcasts Subscriptions via Podbean.
Earn rewards and recurring income from Fan Club membership.
Get the answers and support you need.
Resources and guides to launch, grow, and monetize podcast.
Stay updated with the latest podcasting tips and trends.
Check out our newest and recently released features!
Podcast interviews, best practices, and helpful tips.
The step-by-step guide to start your own podcast.
Create the best live podcast and engage your audience.
Tips on making the decision to monetize your podcast.
The best ways to get more eyes and ears on your podcast.
Everything you need to know about podcast advertising.
The ultimate guide to recording a podcast on your phone.
Steps to set up and use group recording in the Podbean app.
16| Gábor Domokos — The Gömböc, a shape at the limit of possibility
The Gomboc is a curious shape. So curious many mathematicians thought it could not exist. And even to the untrained eye, it looks alien: neither the product of human or natural processes.
This week Gábor Domokos relates his decade-long quest to prove the existence of a (convex, homogenous) shape with only two balance points.
The Gömböc is not just a mathematical curio, its discovery led to a theory of how "things fall apart", of the processes of abrasion that — whether on Earth, mars, or deep space — ineluctably reduce the number of balance points of objects.
The Gomboc is the shape all pebbles want to be, but can never reach.
Show notes at multiverses.xyz
(00:00) Intro
(2:40) Start of conversation — what is a Gomboc?
(4:30) The Gomboc is the “ultimate shape” it has only two balance points
(5:30) The four vertex theorem: why a 2D shape must have 4 balance points
(6:30) (almost) nobody thought a Gomboc existed
(8:30) Vladimir Ilych Arnold’s conjecture
(9:00) Hamburg 1995, the beginning of a quest
(10:30) “Mathematics is a part of physics where experiments are cheap”
(11:50) A hungry scholar sits next to a mathematical superstar
(13:00) Ten years of searching
(15:00) Domokos and Varkonyi's gift for Arnold
(15:30) Arnold’s response: “good, but now do something serious”
(16:50) We cannot easily speak about shapes.
(18:00) A system for naming shapes
(21:00) “The evolution of shapes is imprinted in these numbers”
(21:50) Pebbles evolve towards the Gomboc, but never get there
(24:50) How to find the balance points of shapes by hand
(30:00) Physical intuition and empirical exploration can inform mathematics
(30:30) A beach holiday (and a marital bifurcation point)
(34:00) “No this was not fun, it was a markov process”
(36:40) Working with NASA to understand the age of martian pebbles
(38:20) An asteroid, or a spaceship?
(43:00) The mechanisms of abrasion
(45:50) The isoperimetric ratio — does not evolve monotonically …
(47:50) … But the drift to less balance points is monotonic
(49:00) The process of abrasion is a process of simplifying
(50:00) We can name the shape of Oumuamua because it is so simple
(51:00) Relationship between Gomboc and (one way of thinking about) entropy
(55:00) Abrasion and the heat equation — curvature is “like” heat and gets smoothed out
(58:00) The soap bar model — why pointy bits become smooth
(1:00:00) Richard Hamilton, the Poincaré conjecture and pebbles
(1:04:00) The connection between the Ricci flow and pebble evolution
(1:09:00) Turning the lights on in a darkened labyrinth
(1:12:00) The importance of geometric objects in physics (string theory)
(1:13:30) Another way of naming natural shapes: the average number of faces and vertices
(1:15:00) “Earth is made of cubes” — it turns out Plato was right
(1:16:30) Could Plato’s claim have been empirically inspired?
(1:17:50) “Everything happens between 20 and 6”
(1:18:30) The Cube and the Gomboc are the bookends of natural shapes
(1:19:30) The Obelisk in 2001 — an unnatural, but almost natural shape
(1:22:00) Poincaré on dreaming: genius taps the subconscious
Create your
podcast in
minutes
It is Free