https://youtube.com/@TheMansionsofScience Science has its cathedrals, built by a few architects and many workers. The House of Science has Many Mansions. Talk to me here: felex@themansionsofscience.com TV & Film Podsync generator (support us at https://github.com/yangtfu/podsync) en-us Tue, 27 Oct 2026 12:18:17 +0000 Mon, 16 May 2022 13:02:51 +0000 https://yt3.ggpht.com/-YC1mdC2oWHwiR1WhVAY3aH5JOn4b7yEZcX5nKdkt2XUzSGJH4FL3Q8j4ChsMak7eaupluAO=s800-c-k-c0x00ffffff-no-rj https://youtube.com/@TheMansionsofScience @TheMansionsofScience The Mansions of Science yes no 8S4Vg1jpCgI https://youtube.com/watch?v=8S4Vg1jpCgI Timestamps 12:09 Why modify the Newtonian gravitational potential 12:24 RMS vs MHL 16:08 Algebraic variety 16:50, 1:31:42 Monads and category theory 21:27 A new explanation for dark energy 27:37, 54:00, 1:02:40 Newtonian big bang 30:03, 1:01:26 The universe’s goal is not maximum entropy 30:49, 34:52, 44:08 The universe is not in a box. The arguments are wrong 31:38, 34:36 Is there even a heat death of the universe 35:30 Shantaram 35:59 Is ultimate complexity even understandable to humans 38:39 Types of complexity: Kolmogorov, effective complexity, fractal complexity and thermodynamic depth 41:16 Zermelo (of ZFC fame) 41:30 If you are in space, there IS NO up or down. There is no time either 47:06 Gravitational arrow of time. Best explanation of arrow of time 50:00 Radical ideas 56:15 Hawking and Penrose’s outrageous boxes 1:01:10 Exchanging a hard question for another hard question 1:11:09 Wheeler-DeWitt equation 1:11:24 No wavefunctions 1:23:48 Art and science 1:25:45 Higher dimensional descriptors (relational descriptors) 1:31:54 Topos theory 1:32:36 Goldilocks 1:33:18 Set theory 1:34:23 Fields and wavefunctions are too much 1:36:56 Relationality vs relativity 1:37:49 Carlo Rovelli’s relational quantum mechanics 1:39:17 There are no photons or bosons 1:44:21 No gauge theory either 1:44:43 Intrinsic derivative 1:51:04 Does the universe have 0 energy 1:52:01 Von Neumann helps Claude Shannon win arguments 1:52:44 The new concept of entaxy and its relation to entropy 1:54:46 Everyone should read Leibniz 1:55:08 Physicists are wrong about the 2nd law of thermodynamics 1:58:38 The gravitational constant has no meaning 2:00:36 Adding general relativity 2:03:29 Riemannian geometry is too much 2:04:04 World function 2:07:17 No measurement devices are accurate 2:09:10 There is no quantum gravity 2:11:11 Which book to read first 2:15:07 Favorite quote 2:16:31 Part 2 teaser: Boltzmann brains and consciousness Julian Barbour is a theoretical physicist and emeritus visiting professor of physics at the University of Oxford. He is well known for proposing that time does not actually exist. For decades, he has worked outside an academic environment. He financially supported himself for many years by translating Russian. Professor Barbour is author of the following books: The Discovery of Dynamics, The End of Time and The Janus Point. In this episode, we go over: - Topos theory, set theory and Zermelo's beef with Boltzmann - Algebraic varieties and monads in category theory - Why physicists are wrong about the 2nd law of thermodynamics - The real goal of the universe is complexity and variation, not entropy - Hawking and Penrose's outrageous arguments - Why we don't need wavefunctions, photons, bosons or gauge fields - Why there is no quantum gravity - Von Neumann's hilarious advice to Claude Shannon - The intrinsic derivative - Combining art and science Professor Barbour’s links: Website: http://www.platonia.com/ Papers: https://inspirehep.net/authors/1058373 Books: http://www.platonia.com/books.html Financial times AI article: https://drive.google.com/file/d/16PN7NYMqDSWf_KpQc9cqZkIxVWPpr7ih Maria Lourenco's art and science pictures: https://drive.google.com/drive/folders/1yeZEzviCcDkQlVLcepok49U8-Kxh3pb6 (Can you tell which one Professor Barbour thought was the most striking?) There are 9 masses for m2: 2, 5, 20, 80, 160, 420, 900, 1200 and 2000. The 2000 case has no hydrogen atoms (I looked). Mon, 19 Oct 2026 20:56:44 +0000 @TheMansionsofScience The universe doesn't care about maximizing entropy | Julian Barbour 2:16:50 no 1 lhE4DZWFQ1U https://youtube.com/watch?v=lhE4DZWFQ1U Timestamps 00:00 The five fundamental arithmetic operations: Addition, subtraction, multiplication, division and modular forms 06:50 Geometric intuition for modular forms 11:54 String theory coincidence 1 14:10 The Riemann zeta function should really be named the Euler zeta function 18:38 Peter Scholze's style 30:48 Sphere packing upper bounds 33:56 Class field theory 43:40 Unimodular lattices are everywhere 45:40 Lorentzian lattices and string theory 50:23 String theory coincidence 2 51:22 Deep holes in the Leech lattice are ABSOLUTELY bizarre 58:40 String theory coincidence 3 1:06:10 The E8 group is its own dual group 1:09:37 Contrahomology 1:14:35 Tension between Witt and Emmy Noether 1:23:25 The Leech lattice controls everything. 80,000,000,000,000,000 lattices in 32 dimensions 1:29:37 The first Monster construction was a tour de force 1:37:07 The pain of non-associative algebras 1:41:42 The best way to learn representation theory 1:40:50 Representation theory is utterly unrecognizable 1:46:10 Algebra is the devil, you need to give up your soul 1:51:10 4D Quantum field theory might not even be possible 1:53:32 Why he works on unpopular problems 1:57:47 Virasoro algebra from string theory 1:59:56 Generalized Kac-Moody algebras (Borcherds algebras) 2:04:19 Automorphic forms are even more magical 2:05:48 Moduli stacks 2:11:42 String theory coincidence 4 2:16:00 Amazing memory and recall 2:20:24 Lev Landau (the physicist) and how additive number theory is stupid 2:25:00 Doomsday algorithm 2:25:50 How to teach math the right way 2:27:50 Ramanujan's style 2:28:14 Peter Scholze's style again 2:30:00 The Langlands dual group 2:32:59 Polynomials act like numbers 2:36:30 Functors were defined BEFORE category theory 2:38:54 Does “the book” exist? (Erdos) 2:40:09 Math is archaeology 2:42:37 Einstein hated teaching. Does Professor Borcherds like teaching on YouTube? 2:42:10 Life inside neutron stars 2:43:30 Grothendieck primes 2:44:10 Jacobian conjecture counterexample 2:45:18 Ramanujan didn’t even need our tools. He was just so good 2:46:46 How often he thinks about Godel’s incompleteness theorem 2:48:30 Favorite Terry Pratchett novel 2:50:33 Currently working on Richard Borcherds is a British mathematician who made seminal contributions to lattices, modular forms, group theory, representation theory and infinite-dimensional algebras. He is well known for his proof of the monstrous moonshine conjecture using ideas from string theory, for which he was awarded the Fields Medal in 1998. He is currently Professor of Mathematics at UC Berkeley. In this episode we go over: - How modular forms show up everywhere - The countless coincidences in string theory - The power of the Leech lattice to control all lower dimensions - Unimodular lattices and Lorentzian lattices - How to construct the Langlands dual group - Peter Scholze, Grothendieck and Ramanujan's styles - Category theory and contrahomology - Vertex algebras, infinite-dimensional algebras and Kac-Moody algebras - Elliptic curves - Automorphic forms and hyperbolic reflection groups - Analytic number theory vs algebraic number theory - The first construction of the Monster group - "The Book" of most beautiful proofs - How to teach math - Math as archaeology - His current work - Neutron stars, Terry Pratchett and more Professor Borcherds' YouTube Channel: https://www.youtube.com/@richarde.borcherds7998/videos Sat, 26 Sep 2026 05:37:21 +0000 @TheMansionsofScience The most magical subject in math (modular forms) | Fields Medalist Richard Borcherds 2:52:21 no 2 _3TslhCBQ1E https://youtube.com/watch?v=_3TslhCBQ1E Timestamps 0:00 Toposes are not scary 1:28 What Urs is working on right now 11:05 Fields that the higher gauge model works for and doesn’t work for 12:45 Using toposes since spacetime is not “absolute” and general relativity is background independent 20:25 The accuracies and inaccuracies of QED, QFT and QCD 28:24 How to extract information from a topos (finally!) 37:16 Carlo Rovelli’s relational quantum mechanics 39:33 The first uses of toposes in physics (William Lawvere) 44:24 How toposes treat black holes, singularities and the collapse of the wavefunction 51:12 How topos logic differs from Boolean logic 57:45 How toposes treat many-body (condensed matter) systems 1:00:25 The best explanation of fractional charges (quasiparticles) 1:03:07 2 electrons and 7 fluxes = 2 electrons with 3 fluxes and 1 flux acting like 1/3 of an electron! 1:07:14 Why Urs is looking for IR-completion (long range, low energy) as opposed to the famous UV-completion (high energy) 1:13:00 How to make quantum computers not collapse (topological protection) 1:14:04 How to engineer quantum computing materials 1:17:53 How to use classifying spaces 1:24:10 How quantum computing experimentalists will use classifying spaces 1:30:53 What specific information a classifying space gives a quantum computer engineer 1:36:45 Abelian anyons don’t work. Making universal quantum computing gates with non-abelian anyons 1:39:45 Quantum computing programming languages and linear homotopy type theory 1:45:10 Why did homotopy theory marry type theory 1:51:04 Moving to infinity toposes 1:52:47 Why exactly is homotopy needed in type theory 2:09:40 Type transport 2:15:52 nlab and the writing process 2:18:40 What gets lost in translation with Hegel 2:28:45 Dualities in topos theory vs physics 2:31:16 The difference between math and physics 2:35:33 We need more math. String theory is not mathematical enough, contrary to popular press 2:39:24 Do we need a theory of everything? 2:50:48 Book recommendations 2:51:22 Where can people find Urs Full transcript: https://ncatlab.org/schreiber/show/MoS+2026 Urs Schreiber is Senior Research Scientist at the Mathematics Division of Science of New York University in Abu Dhabi. He is a theoretical physicist who applies tools from algebraic topology, homotopy theory and topos theory to understand quantum phenomena. His current research includes quantum computing programming languages and questions left unanswered by quantum field theory. In this episode we go over: - Why toposes are not scary. They are actually simple. Just unfamiliar - How to extract information from (probe) a topos - The history of toposes in physics - The questions left unanswered by quantum field theory - What toposes have to say about the collapse of the wave function - Using toposes to find possible quantum computing materials - The different type of logic needed for quantum computers - The different type of programming language needed for quantum computers - The influence of Hegel on his work Urs' links: nlab profile: https://ncatlab.org/nlab/show/Urs+Schreiber NYU profile: https://nyuad.nyu.edu/en/research/faculty-labs-and-projects/cqts/urs-schreiber.html Google Scholar: https://scholar.google.com/citations?user=bDfHFDcAAAAJ&hl=en YouTube: https://www.youtube.com/@UCNgcO7xJwTqahpZCICSo8Ug Twitter/X: https://x.com/UrsSchreiber Sat, 12 Sep 2026 23:36:46 +0000 @TheMansionsofScience Toposes are NOT scary | Urs Schreiber 2:52:25 no 3 iu4-TIWqFN4 https://youtube.com/watch?v=iu4-TIWqFN4 Start with a finite field F_q (meaning there are a finite number of elements, actually exactly q elements). Meaning, any element K of F_q, when raised to the q power, becomes itself again. K^q = K. Make sure q is equal to a prime raised to the some n power, so q = p^n. To repeat, K = K^q when you do arithmetic in this field. The Frobenius map FM takes in an element and raises it to the q power. Now, no matter what element R of F_q we input to FM, we get output R^q. That’s useless. We already know that R = R^q. So the input equals the output! BUT! If you take the algebraic closure of F_q, say F_qc, then in general a random element Y of F_qc, when plugged in to FM, will produced Y^q such that Y DOES NOT EQUAL Y^q! In fact, FM is an element of the Galois group G(F_qc/F_q) and repeated applications of FM generates the entire Galois group. Sat, 20 Jun 2026 15:59:00 +0000 @TheMansionsofScience Frobenius Map Generates the Entire Galois Group 4:55 no 4 hV8DK2emA_A https://youtube.com/watch?v=hV8DK2emA_A Suppose you start with a bunch of uncorrelated qubits. This is called the “trivial product state”, state P. Now, you have a desired end state, state Q. There are 4 cases. You can either use a finite depth quantum circuit (FDQC) to change P to Q. Or, you can’t. You can also choose to use matrices (a quantum gate can represent a matrix) that commute with the symmetry group matrices of Q (called “enforcing symmetry”). Case 1: Using FDQC (constraint) and enforcing symmetry (constraint), you can still change P to Q. We call Q “trivial”. Case 2: Using FDQC and enforcing symmetry CANNOT change P to Q. BUT, when you stop using FDQC (you start using any depth), you CAN change to P to Q. We say that Q is a “Symmetry Protected Topological Phase”. P needs to undergo a phase transition to get to Q. Case 3: Using FDQC but do not enforce symmetry, you can change P to Q. We again call Q “trivial”. The “topology wasn’t intrinsic”. It was held together by the symmetry constraint. Case 4: Only by NOT using FDQC and NOT using symmetry, you can change P to Q. Q is “intrinsically topological.” “Real” topology. Sat, 20 Jun 2026 07:00:02 +0000 @TheMansionsofScience Finite Depth Quantum Circuits and Symmetry Protected Topological Phases 10:01 no 5