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Category: mathematics – Page 85

Stephen Wolfram is at his jovial peak in this technical interview regarding the Wolfram Physics project (theory of everything).
Sponsors: https://brilliant.org/TOE for 20% off. http://algo.com for supply chain AI.

Link to the Wolfram project: https://www.wolframphysics.org/

Patreon: https://patreon.com/curtjaimungal.
Crypto: https://tinyurl.com/cryptoTOE
PayPal: https://tinyurl.com/paypalTOE
Twitter: https://twitter.com/TOEwithCurt.
Discord Invite: https://discord.com/invite/kBcnfNVwqs.
iTunes: https://podcasts.apple.com/ca/podcast/better-left-unsaid-wit…1521758802
Pandora: https://pdora.co/33b9lfP
Spotify: https://open.spotify.com/show/4gL14b92xAErofYQA7bU4e.
Subreddit r/TheoriesOfEverything: https://reddit.com/r/theoriesofeverything.
Merch: https://tinyurl.com/TOEmerch.

TIMESTAMPS:
00:00:00 Introduction.
00:02:26 Behind the scenes.
00:04:00 Wolfram critiques are from people who haven’t read the papers (generally)
00:10:39 The Wolfram Model (Theory of Everything) overview in under 20 minutes.
00:29:35 Causal graph vs. multiway graph.
00:39:42 Global confluence and causal invariance.
00:44:06 Rulial space.
00:49:05 How to build your own Theory of Everything.
00:54:00 Computational reducibility and irreducibility.
00:59:14 Speaking to aliens / communication with other life forms.
01:06:06 Extra-terrestrials could be all around us, and we’d never see it.
01:10:03 Is the universe conscious? What is “intelligence”?
01:13:03 Do photons experience time? (in the Wolfram model)
01:15:07 “Speed of light” in rulial space.
01:16:37 Principle of computational equivalence.
01:21:13 Irreducibility vs undecidability and computational equivalence.
01:23:47 Is infinity “real”?
01:28:08 Discrete vs continuous space.
01:33:40 Testing discrete space with the cosmic background radiation (CMB)
01:34:35 Multiple dimensions of time.
01:36:12 Defining “beauty” in mathematics, as geodesics in proof space.
01:37:29 Particles are “black holes” in branchial space.
01:39:44 New Feynman stories about his abjuring of woo woo.
01:43:52 Holographic principle / AdS CFT correspondence, and particles as black holes.
01:46:38 Wolfram’s view on cryptocurrencies, and how his company trades in crypto [Amjad Hussain]
01:57:38 Einstein field equations in economics.
02:03:04 How to revolutionize a field of study as a beginner.
02:04:50 Bonus section of Curt’s thoughts and questions.

Just wrapped (April 2021) a documentary called Better Left Unsaid http://betterleftunsaidfilm.com on the topic of “when does the left go too far?” Visit that site if you’d like to watch it.

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Year 2012 😗

A Sierpinksi carpet is one of the more famous fractal objects in mathematics. Creating one is an iterative procedure. Start with a square, divide it into nine equal squares and remove the central one. That leaves eight squares around a central square hole. In the next iteration, repeat this process with each of the eight remaining squares and so on (see above). One interesting problem is to find the area of a Sierpinski triangle. Clearly this changes with each iteration. Assuming the original square has area equal to 1, the area after the first iteration is 8/9. After the second iteration, it is (8÷9)^2; after the third it is (8÷9)^3 and so on.

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Kathryn Tunyasuvunakool grew up surrounded by scientific activities carried out at home by her mother—who went to university a few years after Tunyasuvunakool was born. One day a pendulum hung from a ceiling in her family’s home, Tunyasuvunakool’s mother standing next to it, timing the swings for a science assignment. Another day, fossil samples littered the dining table, her mother scrutinizing their patterns for a report. This early exposure to science imbued Tunyasuvunakool with the idea that science was fun and that having a career in science was an attainable goal. “From early on I was desperate to go to university and be a scientist,” she says.

Tunyasuvunakool fulfilled that ambition, studying math as an undergraduate, and computational biology as a graduate student. During her PhD work she helped create a model that captured various elements of the development of a soil-inhabiting roundworm called Caenorhabditis elegans, a popular organism for both biologists and physicists to study. She also developed a love for programming, which, she says, lent itself naturally to a jump into software engineering. Today Tunyasuvunakool is part of the team behind DeepMind’s AlphaFold—a protein-structure-prediction tool. Physics Magazine spoke to her to find out more about this software, which recently won two of its makers a Breakthrough Prize, and about why she’s excited for the potential discoveries it could enable.

All interviews are edited for brevity and clarity.

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Never miss a talk! SUBSCRIBE to the TEDx channel: http://bit.ly/1FAg8hB

Mathematics and sex are deeply intertwined. From using mathematics to reveal patterns in our sex lives, to using sex to prime our brain for certain types of problems, to understanding them both in terms of the evolutionary roots of our brain, Dr Clio Cresswell shares her insight into it all.

Dr Clio Cresswell is a Senior Lecturer in Mathematics at The University of Sydney researching the evolution of mathematical thought and the role of mathematics in society. Born in England, she spent part of her childhood on a Greek island, and was then schooled in the south of France where she studied Visual Art. At eighteen she simultaneously discovered the joys of Australia and mathematics, following on to win the University Medal and complete a PhD in mathematics at The University of New South Wales. Communicating mathematics is her field and passion. Clio has appeared on panel shows commenting, debating and interviewing; authored book reviews and opinion pieces; joined breakfast radio teams and current affair programs; always there highlighting the mathematical element to our lives. She is author of Mathematics and Sex.

TEDxSydney is an independently organised event licensed from TED by longtime TEDster, Remo Giuffré (REMO General Store) and organised by his General Thinking network of fellow thinkers and other long time collaborators.

TEDxSydney has become the leading platform and pipeline for the propagation of Australian ideas, creativity, innovation and culture to the rest of the world.

In the spirit of ideas worth spreading, TEDx is a program of local, self-organized events that bring people together to share a TED-like experience. At a TEDx event, TEDTalks video and live speakers combine to spark deep discussion and connection in a small group. These local, self-organized events are branded TEDx, where x = independently organized TED event. The TED Conference provides general guidance for the TEDx program, but individual TEDx events are self-organized.* (*Subject to certain rules and regulations)

Continue reading “Mathematics and sex | Clio Cresswell | TEDxSydney” | >

Sound waves, like an invisible pair of tweezers, can be used to levitate small objects in the air. Although DIY acoustic levitation kits are readily available online, the technology has important applications in both research and industry, including the manipulation of delicate materials like biological cells.

Researchers at the University of Technology Sydney (UTS) and the University of New South Wales (UNSW) have recently demonstrated that in order to precisely control a particle using ultrasonic waves, it is necessary to take into account both the shape of the particle and how this affects the acoustic field. Their findings were recently published in the journal Physical Review Letters.

Sound levitation happens when sound waves interact and form a standing wave with nodes that can ‘trap’ a particle. Gorkov’s core theory of acoustophoresis, the current mathematical foundation for acoustic levitation, makes the assumption that the particle being trapped is a sphere.

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The information security landscape is rapidly changing in response to quantum computing technology, which is capable of cracking modern encryption techniques in minutes, but a promising US government encryption algorithm for the post-quantum world was just cracked in less than an hour thanks to a decades-old math theorem.

In July 2022, the US National Institute of Standards and Technology (NIST) chose a set of encryption algorithms that it hoped would stand up to the encryption-cracking power of quantum computers and tasked researchers with probing them for vulnerabilities, offering a $50,000 prize for anyone who was able to break the encryption.

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There is a deep root of mathematics within biology. How this came to be, you’ll have to watch the video to find out.

Created by Prompt Suathim (2nd year undergrad, Integrated Science, UBC)

Books referenced:

Music:
City Life – Artificial. Music (No Copyright Music)
Link: https://www.youtube.com/watch?v=caT3jZ0q6Z0&list=PLhZpTkc-Gz…ex=1&t=29s.
Pure Water by Meydän.
Link: https://youtu.be/BU85yzb0nMU
Forever Sunrise — by Jonny Easton.
Link: https://youtu.be/9Xndx7nhGAs

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Continuous-time neural networks are one subset of machine learning systems capable of taking on representation learning for spatiotemporal decision-making tasks. Continuous differential equations are frequently used to depict these models (DEs). Numerical DE solvers, however, limit their expressive potential when used on computers. The scaling and understanding of many natural physical processes, like the dynamics of neural systems, have been severely hampered by this restriction.

Inspired by the brains of microscopic creatures, MIT researchers have developed “liquid” neural networks, a fluid, robust ML model that can learn and adapt to changing situations. These methods can be used in safety-critical tasks such as driving and flying.

However, as the number of neurons and synapses in the model grows, the underlying mathematics becomes more difficult to solve, and the processing cost of the model rises.

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Gnawing on his left index finger with his chipped old British teeth, temporal veins bulging and brow pensively squinched beneath the day-before-yesterday’s hair, the mathematician John Horton Conway unapologetically whiles away his hours tinkering and thinkering — which is to say he’s ruminating, although he will insist he’s doing nothing, being lazy, playing games.

Based at Princeton University, though he found fame at Cambridge (as a student and professor from 1957 to 1987), Conway, 77, claims never to have worked a day in his life. Instead, he purports to have frittered away reams and reams of time playing. Yet he is Princeton’s John von Neumann Professor in Applied and Computational Mathematics (now emeritus). He’s a fellow of the Royal Society. And he is roundly praised as a genius. “The word ‘genius’ gets misused an awful lot,” said Persi Diaconis, a mathematician at Stanford University. “John Conway is a genius. And the thing about John is he’ll think about anything.… He has a real sense of whimsy. You can’t put him in a mathematical box.”

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