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Category: mathematics – Page 2

Joscha Bach is a cognitive scientist focusing on cognitive architectures, consciousness, models of mental representation, emotion, motivation and sociality.

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iTunes: https://podcasts.apple.com/ca/podcast… https://pdora.co/33b9lfP Spotify: https://open.spotify.com/show/4gL14b9… Subreddit r/TheoriesOfEverything: / theoriesofeverything Merch: https://tinyurl.com/TOEmerch 0:00:00 Introduction 0:00:17 Bach’s work ethic / daily routine 0:01:35 What is your definition of truth? 0:04:41 Nature’s substratum is a “quantum graph”? 0:06:25 Mathematics as the descriptor of all language 0:13:52 Why is constructivist mathematics “real”? What’s the definition of “real”? 0:17:06 What does it mean to “exist”? Does “pi” exist? 0:20:14 The mystery of something vs. nothing. Existence is the default. 0:21:11 Bach’s model vs. the multiverse 0:26:51 Is the universe deterministic 0:28:23 What determines the initial conditions, as well as the rules? 0:30:55 What is time? Is time fundamental? 0:34:21 What’s the optimal algorithm for finding truth? 0:40:40 Are the fundamental laws of physics ultimately “simple”? 0:50:17 The relationship between art and the artist’s cost function 0:54:02 Ideas are stories, being directed by intuitions 0:58:00 Society has a minimal role in training your intuitions 0:59:24 Why does art benefit from a repressive government? 1:04:01 A market case for civil rights 1:06:40 Fascism vs communism 1:10:50 Bach’s “control / attention / reflective recall” model 1:13:32 What’s more fundamental… Consciousness or attention? 1:16:02 The Chinese Room Experiment 1:25:22 Is understanding predicated on consciousness? 1:26:22 Integrated Information Theory of consciousness (IIT) 1:30:15 Donald Hoffman’s theory of consciousness 1:32:40 Douglas Hofstadter’s “strange loop” theory of consciousness 1:34:10 Holonomic Brain theory of consciousness 1:34:42 Daniel Dennett’s theory of consciousness 1:36:57 Sensorimotor theory of consciousness (embodied cognition) 1:44:39 What is intelligence? 1:45:08 Intelligence vs. consciousness 1:46:36 Where does Free Will come into play, in Bach’s model? 1:48:46 The opposite of free will can lead to, or feel like, addiction 1:51:48 Changing your identity to effectively live forever 1:59:13 Depersonalization disorder as a result of conceiving of your “self” as illusory 2:02:25 Dealing with a fear of loss of control 2:05:00 What about heart and conscience? 2:07:28 How to test / falsify Bach’s model of consciousness 2:13:46 How has Bach’s model changed in the past few years? 2:14:41 Why Bach doesn’t practice Lucid Dreaming anymore 2:15:33 Dreams and GAN’s (a machine learning framework) 2:18:08 If dreams are for helping us learn, why don’t we consciously remember our dreams 2:19:58 Are dreams “real”? Is all of reality a dream? 2:20:39 How do you practically change your experience to be most positive / helpful? 2:23:56 What’s more important than survival? What’s worth dying for? 2:28:27 Bach’s identity 2:29:44 Is there anything objectively wrong with hating humanity? 2:30:31 Practical Platonism 2:33:00 What “God” is 2:36:24 Gods are as real as you, Bach claims 2:37:44 What “prayer” is, and why it works 2:41:06 Our society has lost its future and thus our culture 2:43:24 What does Bach disagree with Jordan Peterson about? 2:47:16 The millennials are the first generation that’s authoritarian since WW2 2:48:31 Bach’s views on the “social justice” movement 2:51:29 Universal Basic Income as an answer to social inequality, or General Artificial Intelligence? 2:57:39 Nested hierarchy of “I“s (the conflicts within ourselves) 2:59:22 In the USA, innovation is “cheating” (for the most part) 3:02:27 Activists are usually operating on false information 3:03:04 Bach’s Marxist roots and lessons to his former self 3:08:45 BONUS BIT: On societies problems.
Pandora: https://pdora.co/33b9lfP
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Subreddit r/TheoriesOfEverything: / theoriesofeverything.
Merch: https://tinyurl.com/TOEmerch.

0:00:00 Introduction.
0:00:17 Bach’s work ethic / daily routine.
0:01:35 What is your definition of truth?
0:04:41 Nature’s substratum is a \.

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He majored in Mathematical Engineering in 1958 from the University of Tokyo then graduated in 1963 from the Graduate School of the University of Tokyo.

His Master of Engineering in 1960 was entitled Topological and Information-Theoretical Foundation of Diakoptics and Codiakoptics. His Doctor of Engineering in 1963 was entitled Diakoptics of Information Spaces.

Shun’ichi Amari received several awards and is a visiting professor of various universities.

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This is the Fourier Transform. You can thank it for providing the music you stream every day, squeezing down the images you see on the Internet into tiny little JPG files, and even powering your noise-canceling headphones. Here’s how it works.

The equation owes its power to the way that it lets mathematicians quickly understand the frequency content of any kind of signal. It’s quite a feat. But don’t just take my word for it—in 1867, the physicist Lord Kelvin expressed his undying love for this fine piece of mathematics, too. He wrote, “Fourier’s theorem is not only one of the most beautiful results of modern analysis, but it may be said to furnish an indispensable instrument in the treatment of nearly every recondite question in modern physics.” And so it remains.

Math Will Tear Us Apart

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Somehow, we all know how a warp drive works. You’re in your spaceship and you need to get to another star. So you press a button or flip a switch or pull a lever and your ship just goes fast. Like really fast. Faster than the speed of light. Fast enough that you can get to your next destination by the end of the next commercial break.

Warp drives are staples of science fiction. And in 1994, they became a part of science fact. That’s when Mexican physicist Miguel Alcubierre, who was inspired by Star Trek, decided to see if it was possible to build a warp drive. Not like actually build one with wrenches and pipes, but to see if it was even possible to be allowed to build a warp drive given our current knowledge of physics.

Physics is just a mathematical exploration of the natural universe, and the natural universe appears to play by certain rules. Certain actions are allowed, and other actions are not allowed. And the actions that are allowed have to proceed in a certain orderly fashion. Physics tries to capture all of those rules and express them in mathematical form. So Alcubierre wondered: does our knowledge of how nature works permit a warp drive or not?

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Researchers will soon be able to study biological changes at scales and speeds not previously possible to significantly expand knowledge in areas such as disease progression and drug delivery.

Physicists at The University of Queensland have used “tweezers made from light” to measure activity within microscopic systems over timeframes as short as milliseconds. Professor Halina Rubinsztein-Dunlop from UQ’s School of Mathematics and Physics said the method could help biologists understand what was happening within single living cells.

“For example, they will be able to look at how a cell is dividing, how it responds to outside stimuli, or even how affect cell properties,” Professor Rubinsztein-Dunlop said.

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Here Harkos et al. review the role of continuous models and discrete models in predicting and understanding therapy delivery and efficacy in solid tumours. They propose ways to integrate mechanistic and AI-based models to further improve patient outcomes.

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I’m back, baby. I’ve been away traveling for podcasts and am excited to bring you new ones with Michael Levin, William Hahn, Robin Hanson, and Emily Riehl, coming up shortly. They’re already recorded. I’ve been recovering from a terrible flu but pushed through it to bring you today’s episode with Urs Schreiber. This one is quite mind-blowing. It’s quite hairy mathematics, something called higher category theory, and how using this math (which examines the structure of structure) allows one manner of finding \.

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Reinforcement learning (RL) has become central to advancing Large Language Models (LLMs), empowering them with improved reasoning capabilities necessary for complex tasks. However, the research community faces considerable challenges in reproducing state-of-the-art RL techniques due to incomplete disclosure of key training details by major industry players. This opacity has limited the progress of broader scientific efforts and collaborative research.

Researchers from ByteDance, Tsinghua University, and the University of Hong Kong recently introduced DAPO (Dynamic Sampling Policy Optimization), an open-source large-scale reinforcement learning system designed for enhancing the reasoning abilities of Large Language Models. The DAPO system seeks to bridge the gap in reproducibility by openly sharing all algorithmic details, training procedures, and datasets. Built upon the verl framework, DAPO includes training codes and a thoroughly prepared dataset called DAPO-Math-17K, specifically designed for mathematical reasoning tasks.

DAPO’s technical foundation includes four core innovations aimed at resolving key challenges in reinforcement learning. The first, “Clip-Higher,” addresses the issue of entropy collapse, a situation where models prematurely settle into limited exploration patterns. By carefully managing the clipping ratio in policy updates, this technique encourages greater diversity in model outputs. “Dynamic Sampling” counters inefficiencies in training by dynamically filtering samples based on their usefulness, thus ensuring a more consistent gradient signal. The “Token-level Policy Gradient Loss” offers a refined loss calculation method, emphasizing token-level rather than sample-level adjustments to better accommodate varying lengths of reasoning sequences. Lastly, “Overlong Reward Shaping” introduces a controlled penalty for excessively long responses, gently guiding models toward concise and efficient reasoning.

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