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Category: mathematics – Page 3

Perhaps I could best describe my experience of doing mathematics in terms of entering a dark mansion. One goes into the first room, and it’s dark, completely dark. One stumbles around bumping into the furniture, and gradually, you learn where each piece of furniture is, and finally, after six months or so, you find the light switch. You turn it on, and suddenly, it’s all illuminated. You can see exactly where you were.

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A new study published in Proceedings of the National Academy of Sciences has turned traditional thinking on its head by highlighting the role of human interactions during the shift from hunting and gathering to farming—one of the biggest changes in human history—rather than earlier ideas that focused on environmental factors.

The transition from a foraging lifestyle, which humanity had followed for hundreds of thousands of years, to a settled farming one about 12,000 years ago has been widely discussed in popular books like “Sapiens: A Brief History of Humankind” by Yuval Noah Harari.

Researchers from the University of Bath, the Max Planck Institute for Evolutionary Anthropology in Germany, the University of Cambridge, UCL, and others have developed a new mathematical model that challenges the traditional view that this major transition was driven by external factors, such as climate warming, increased rainfall, or the development of fertile river valleys.

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Summary: ChatGPT4 has demonstrated superiority in various student exams, revealing its potential to support academic learning and improve educational outcomes, particularly in test preparation. With its accessibility and affordability compared to traditional tutoring services, AI tutoring can help address the increasing demand for academic support, especially as universities begin to reinstate standardized testing requirements.

In 2023, OpenAI shook the foundation of the education system by releasing ChatGPT4. The previous model of ChatGPT had already disrupted classrooms K–12 and beyond by offering a free academic tool capable of writing essays and answering exam questions. Teachers struggled with the idea that widely accessible artificial intelligence (AI) technology could meet the demands of most traditional classroom work and academic skills. GPT3.5 was far from perfect, though, and lacked creativity, nuance, and reliability. However, reports showed that GPT4 could score better than 90 percent of participants on the bar exam, LSAT, SAT reading and writing and math, and several Advanced Placement (AP) exams. This showed a significant improvement from GPT3.5, which struggled to score as well as 50 percent of participants.

This marked a major shift in the role of AI, from it being an easy way out of busy work to a tool that could improve your chances of getting into college. The US Department of Education published a report noting several areas where AI could support teacher instruction and student learning. Among the top examples was intelligent tutoring systems. Early models of these systems showed that an AI tutor could not only recognize when a student was right or wrong in a mathematical problem but also identify the steps a student took and guide them through an explanation of the process.

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The DeepSeek-V3-0324, named after its predecessor and the launch date, has “enhanced reasoning capabilities, optimised front-end web development and upgraded Chinese writing proficiency”, according to a notice on the company’s website.

The new version and DeepSeek V3 are both foundation models trained on vast data sets that can be applied in different use cases, including that of a chatbot. DeepSeek R1, the reasoning model, is based on DeepSeek V3.

The updated foundation model has made improvements in several benchmarks, especially the American Invitational Mathematics Examination (AIME), where it scored 59.4 compared with 39.6 for its predecessor, while achieving an increase of 10 points on LiveCodeBench to achieve 49.2, DeepSeek data showed.

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Pedestrian crossings generally showcase the best in pedestrian behavior, with people naturally forming orderly lanes as they cross the road, smoothly passing those coming from the opposite direction without any bumps or scrapes. Sometimes, however, the flow gets chaotic, with individuals weaving through the crowd on their own haphazard paths to the other side.

Now, an international team of mathematicians, co-led by Professor Tim Rogers at the University of Bath in the UK and Dr. Karol Bacik at MIT in the US has made an important breakthrough in their understanding of what causes human flows to disintegrate into tangles. This discovery has the potential to help planners design road crossings and other pedestrian spaces that minimize chaos and enhance safety and efficiency.

In a paper appearing in the journal Proceedings of the National Academy of Sciences, the team pinned down the precise point at which crowds of pedestrians crossing a road collapse from order to disorder.

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In the ebb and flow of crowded crosswalks, a surprising pattern emerges: people can naturally form neat lanes of movement. But what flips the switch from graceful organization to chaotic weaving?

An international team of researchers has pinpointed a specific tipping point: when pedestrians deviate more than 13 degrees from their path, order collapses. Backed by math, experiments, and real-world testing, this discovery could revolutionize how cities manage foot traffic.

From flow to frenzy: what disrupts pedestrian order?

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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
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 \.

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