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Sophie Maclean Counting Polyominoes and Janet Axelrud Making New Math

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It's really hard to know you've done these counting problems right, as I recall. There's a useful thing called called the Orbit-Stabilizer Theorem of a group action , but it's still easy to make a mistake. I guess that in these we're only talking about polyominoes made of squares, not ones made of equilateral triangles or hexagons, so it's not that complicated. Subscribe to Numberphile . Daniel Tubbenhauer has done a series of lectures on the Analytic Theory of Monoidal Categories, which is something he made up himself, I think. It's about the curious fact that some of these asymptotic formulae are far easier to prove than you might expect, based on how hard the underlying counting problems are. This is lecture one, which is actually the only part I even vaguely understand! The other four parts are in this playlist . Part II where he talks about sums and products and dimensions, ... I got lost about half-way through this one: Subscribe to Visual Math . Math...

Jenn Grant - The Bells Are Ringing

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From Jennytown, in Gaza. Featuring  the children's choir of Halifax, NS and Southern G * z a   All proceeds of the sale and stream of this song go to The English Learning Tent A school for the children in Southern G * z a Please buy and share here! https://jenngrant.bandcamp.com/track/bells-are-ringing Subscribe to Jenn Grant . Avshalom Elitzur on Kurt Jaimungal's Theories of Everything Podcast. It's a very interesting interview but I'm barely an hour into it. 43:07 John Cramer's transactional interpretation of Quantum Mechanics: The transactional interpretation of quantum mechanics, Rev. Mod. Phys. 58, 647 (July, 1986) is based on Wheeler and Feynman's work on absorber theory in electrodynamics: The basic element of this interpretation is the transaction describing a quantum event as an exchange of advanced and retarded waves, as implied by the work of Wheeler and Feynman, Dirac, and others. The transactional interpretation is explicitly nonlocal and thereb...

Math-Life Balance - Algebraic K-Theory

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The first time someone got a Fields Medal for a definition! See Daniel Quillen . I watched some of these and always found myself floundering after about a minute or so, ... I should have watched this one first. There is an amazing gallery of graphs of algebraic surfaces here: https://www.imaginary.org/gallery/herwig-hauser-classic The surfaces are just the 3D coordinates of a set of points (x,y,z) which satisfy some equation. For example the set {(x,y,z)∈ℝ^3 : x^2+y^2+z^2=1} is the surface of a sphere which includes irrational points such as (1/√3,1/√3,1/√3). These shapes are called algebraic varieties : "Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers." So the subject of Algebraic Geometry seems to hinge on the idea of closed fields (such as the rationals or the reals) when they are considered as the domains of functions which represent systems of polynomial equations and questio...

Janet Akselrud and The Museum of Ideas - Creating the Dictionary of the Future

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Her word is great! "Sparkle-talking-freedom" It sounds like a Native American concept to me. See Laura in Lake Placid and Vermont! See the comments and video description on YouTube . The Dictionary of the Future is at https://www.themuseumofideas.com/about-5 . Subscribe to Architect of Ideas .

Laura in Lake Placid and Vermont!

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See  Hiking With Goldilocks in Michigan and Laura Driving from Michigan to New York . From the National Park Service page Adirondacks: Native Americans Paleo-Indian (15,000 to 7000 B.C.) sites have been found around the region dating to 9000 B.C. These peoples lived near the shore of the Champlain Sea, which covered the Adirondack Mountains. The first Archaic (8000 to 1000 B.C.) people in New York came from the St. Lawrence River Valley to the area around Lake Champlain and into the Hudson River Valley. Other related groups settled at Oneida Lake via the Oswego River system. These Archaic people, referred to as the Laurentian culture, were semi-nomadic hunters and gathers. They used spear-throwers and bone harpoons for hunting. Tools crafted from Lake Superior copper, obtained via trade, were also utilized. The Laurentian culture was gradually replaced by other traditions. Between 2200 and 1500 B.C., the Sylvan Lake and River cultures appeared in eastern New York. Succeeding the...

Numberphile Video about Langton's Ant and Sabine Hossenfelder on Wolfram's Theory of Everything

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I remember there was once some heated discussion on the Foundations of Mathematics list concerning a prize Steven Wolfram had awarded to Alex Smith for proving that a particular one-dimensional cellular automaton was Turing complete. The discussion was centered on the question of whether an infinite starting pattern was allowable, because that is what is needed to be able to simulate a Turing machine's infinite tape on any cellular automata. But I only just now heard that in 2000 A. Gajardo, A. Moreira and E. Goles of the Universty of Chile's Department for Mathematical Engineering had shown that Langton's Ant can do the same thing. See their paper Complexity of Langton’s ant Langton's Ant is a rule that applies to just one point at a time on an infinite two-dimensional grid. Subscribe to Numberphile and Numberphile2 . Sabine on Wolfram's Theory of Everything ... and some possible experimental observations ... Here's her earlier video: Subscribe to Sabine...

Laura Driving from Michigan to New York

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Mostly at night! See Hiking With Goldilocks in Michigan . She saw the Northern Lights on October 7, see Happy Birthday John Lennon . She has some really beautiful trips on her blog: https://lauratheexplorablog.com/ Subscribe to Goldilocks .

Sabine Hossenfelder, Gabriele Carcassi and Dan Bullard on Quantum Horse Shit

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There's an hilarious discussion on her Patreon page , if I may say so myself! 😀 Subscribe to Sabine Hossenfelder . Here's Gabriele Carcassi  flogging a dead horse: See Projective Hilbert Space , Hopf fibration and Bloch sphere . See also Janet Axelrud and Roger Penrose on Singularities and Gabriele Carcassi on Quantum States and  Curt Jaimungal Talking With Roger Penrose . And on infinite dimensional quantum spaces: See Julian Barbour - Complexity as Time . Julian recommends the book Quantum Theory at the Crossroads: Reconsidering the 1927 Solvay Conference . See also the 500+ page paper of the same title https://arxiv.org/abs/quant-ph/0609184 : We reconsider the crucial 1927 Solvay conference in the context of current research in the foundations of quantum theory. Contrary to folklore, the interpretation question was not settled at this conference and no consensus was reached; instead, a range of sharply conflicting views were presented and extensively discussed. Today...

Hiking With Goldilocks in Michigan

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Oh wow, this is the best. It feels like you're actually there with her. I hope Hannah doesn't get jealous, ... Actually this was six weeks ago. When I see those abandoned places, because that 's what most of the United States feels like to a foreigner, I can't help thinking about the people who lived there before and how they felt looking at all of this unspoilt and incredibly beautiful land. South Dakota, Minnesota and Wisconsin: yeah!   Subscribe to Goldilocks . The Ojibwe--Anishinaabe were into Geometry and Mathematics as well as birch trees. Subscribe to Jaguar Bird . CBC Documentary about Birch trees: Subscribe to CBC Docs .

Angela's Richard Feynman Video

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Oh wow. This is an amazing story. I made it up to 1:56:48, only another fifty or so minutes to go, ... later! Subscribe to Angela Collier . and see her Patreon: https://www.patreon.com/acollierastro .