Breaking Math Podcast Gabriel Hesch and Autumn Phaneuf

Welcome to another engaging episode of the Breaking Math Podcast! Today's episode, titled "What is the Use?," features a fascinating conversation with the renowned mathematician and author, Professor Ian Stewart. As Professor Stewart discusses his latest book "What's the Use? How Mathematics Shapes Everyday Life," we dive deep into the real-world applications of mathematics that often go unnoticed in our daily technologies, like smartphones, and their unpredictable implications in various fields.

We'll explore the history of quaternions, invented by William Rowan Hamilton, which now play a critical role in computer graphics, gaming, and particle physics. Professor Stewart will also shed light on the non-commutative nature of quaternions, mirroring the complexities of spatial rotations, and how these mathematical principles find their correspondence in the natural world.

Furthermore, our discussion will encompass the interconnectivity within mathematics, touching upon how algebra, geometry, and trigonometry converge to paint a broader picture of this unified field. We also discuss the intriguing concept of "Fearful Symmetry" and how symmetrical and asymmetrical patterns govern everything from tiger stripes to sand dunes.

With references to his other works, including "Professor Stewart's Cabinet of Mathematical Curiosities" and "The Science of Discworld," Professor Stewart brings an element of surprise and entertainment to the profound impact of mathematics on our understanding of the world.

So stay tuned as we unlock the mysteries and the omnipresent nature of math in this thought-provoking episode with Professor Ian Stewart!

Summary

Tom Chivers [https://tomchivers.com/] discusses his book 'Everything is Predictable: How Bayesian Statistics Explain Our World' and the applications of Bayesian statistics in various fields. He explains how Bayesian reasoning can be used to make predictions and evaluate the likelihood of hypotheses. Chivers also touches on the intersection of AI and ethics, particularly in relation to AI-generated art. The conversation explores the history of Bayes' theorem and its role in science, law, and medicine. Overall, the discussion highlights the power and implications of Bayesian statistics in understanding and navigating the world. 

The conversation explores the role of AI in prediction and the importance of Bayesian thinking. It discusses the progress of AI in image classification and the challenges it still faces, such as accurately depicting fine details like hands. The conversation also delves into the topic of predictions going wrong, particularly in the context of conspiracy theories. It highlights the Bayesian nature of human beliefs and the influence of prior probabilities on updating beliefs with new evidence. The conversation concludes with a discussion on the relevance of Bayesian statistics in various fields and the need for beliefs to have probabilities and predictions attached to them.

* Takeaways
* Bayesian statistics can be used to make predictions and evaluate the likelihood of hypotheses.
* Bayes' theorem has applications in various fields, including science, law, and medicine.
* The intersection of AI and ethics raises complex questions about AI-generated art and the predictability of human behavior.
* Understanding Bayesian reasoning can enhance decision-making and critical thinking skills. AI has made significant progress in image classification, but still faces challenges in accurately depicting fine details.
* Predictions can go wrong due to the influence of prior beliefs and the interpretation of new evidence.
* Beliefs should have probabilities and predictions attached to them, allowing for updates with new information.
* Bayesian thinking is crucial in various fields, including AI, pharmaceuticals, and decision-making.
* The importance of defining predictions and probabilities when engaging in debates and discussions.

Summary

**Tensor Poster - If you are interested in the Breaking Math Tensor Poster on the mathematics of General Relativity, email us at BreakingMathPodcast@gmail.com

In this episode, Gabriel Hesch and Autumn Phaneuf interview Steve Nadis, [https://www.discovermagazine.com/author/snadis/1] the author of the book 'The Gravity of Math [https://www.hachettebookgroup.com/titles/steve-nadis/the-gravity-of-math/9781541604292/].' They discuss the mathematics of gravity, including the work of Isaac Newton and Albert Einstein, gravitational waves, black holes, and recent developments in the field. Nadis shares his collaboration with Shing-Tung Yau and their journey in writing the book. They also talk about their shared experience at Hampshire College and the importance of independent thinking in education.  In this conversation, Steve Nadis discusses the mathematical foundations of general relativity and the contributions of mathematicians to the theory. He explains how Einstein was introduced to the concept of gravity by Bernhard Riemann and learned about tensor calculus from Gregorio Ricci and Tullio Levi-Civita. Nadis also explores Einstein's discovery of the equivalence principle and his realization that a theory of gravity would require accelerated motion. He describes the development of the equations of general relativity and their significance in understanding the curvature of spacetime. Nadis highlights the ongoing research in general relativity, including the detection of gravitational waves and the exploration of higher dimensions and black holes. He also discusses the contributions of mathematician Emmy Noether to the conservation laws in physics. Finally, Nadis explains Einstein's cosmological constant and its connection to dark energy.



Chapters

00:00 Introduction and Book Overview

08:09 Collaboration and Writing Process

25:48 Interest in Black Holes and Recent Developments

35:30 The Mathematical Foundations of General Relativity

44:55 The Curvature of Spacetime and the Equations of General Relativity

56:06 Recent Discoveries in General Relativity

01:06:46 Emmy Noether's Contributions to Conservation Laws

01:13:48 Einstein's Cosmological Constant and Dark Energy

Summary:  The episode discusses the 10,000 year dilemma, which is a thought experiment on how to deal with nuclear waste in the future.  Today's episode is hosted by guest host David Gibson, who is the founder of the Ray Kitty Creation Workshop [https://www.youtube.com/@RayKitty]. (Find out more about the Ray Kitty Creation Workshop by clicking here [https://mrdave.raykitty.com/]).  

Gabriel and Autumn are out this week, but will be returning in short order with 3 separate interviews with authors of some fantastic popular science and math books including:


* The Gravity of Math:  How Geometry Rules the Universe [https://www.hachettebookgroup.com/titles/steve-nadis/the-gravity-of-math/9781541604292/] by Dr. Shing-Tung Yau and Steve Nadis.    This book is all about the history of our understanding of gravity from the theories of Isaac Newton to Albert Einstein and beyond, including gravitational waves, black holes, as well as some of the current uncertainties regarding a precise definition of mass.  On sale now!  
* EVERYTHING IS PREDICTABLE: How Bayesian Statistics Explain Our World [https://www.netgalley.com/widget/516523/redeem/23dc460e436c2d0582e559b4d84ee909cf774accba78999f2291a8f97813bae0] by Tom Chivers.  Published by Simon and Schuster.   This book explains the importance of Baye's Theorem in helping us to understand why  highly accurate screening tests can lead to false positives, a phenomenon we saw during the Covid-19 pandemic; How a failure to account for Bayes' Theorem has put innocent people in jail; How military strategists using the theorem can predict where an enemy will strike next, and how Baye's Theorem is helping us to understang machine learning processes - a critical skillset to have in the 21st century.
Available 05/07/2024
* A CITY ON MARS: Can we settle space, should we settle space, and have we really thought this through? [https://www.penguinrandomhouse.com/books/639449/a-city-on-mars-by-kelly-and-zach-weinersmith/]  by authors Dr. Kelly and Zach Weinersmith.  Zach Weinersmith is the artist and creator of the famous cartoon strip Saturday Morning Breaking Cereal [https://www.smbc-comics.com/]!  

We've got a lot of great episodes coming up!  Stay tuned.  

An interview with Prof. Marcus du Sautoy about his book Around the Wold in Eighty Games . . . .a Mathematician Unlocks the Secrets of the World's Greatest Games.  

Topics covered in Today's Episode: 

1. Introduction to Professor Marcus du Sautoy and the Role of Games

- Impact of games on culture, strategy, and learning

- The educational importance of games throughout history

2. Differences in gaming cultures across regions like India and China

3. Creative Aspects of Mathematics

4. The surprising historical elements and banned games by Buddha

5. Historical and geographical narratives of games rather than rules

6. Game Theory and Education

7.  Unknowable questions like thermodynamics and universe's infinity

8. Professor du Sautoy's Former Books and Collections

9.  A preview of his previous books and their themes

10. Gaming Cultures and NFTs in Blockchain

11. Gamification in Education

12. The Role of AI in Gaming

13. Testing machine learning in mastering games like Go

14. Alphago's surprising move and its impact on Go strategies

15 . The future of AI in developing video game characters, plots, and environments

16. Conclusion and Giveaway Announcement

*Free Book Giveaway of Around The World in 88 Games . . .  by Professor Marcus Du Sautory!  Follow us on our socials for details:  

Follow us on X:  @BreakingMathPod [https://twitter.com/breakingmathpod]

Follow us on Instagram:  @Breaking Math Media [https://www.instagram.com/breakingmathmedia/]

Email us:  BreakingMathPodacst@gmail.com 

Summary

Brain Organelles, A.I. and Defining Intelligence in  Nature- 

In this episode, we continue our fascinating interview with GT, a science content creator on TikTok [https://www.tiktok.com/@bearbaitofficial] and YouTube [https://www.youtube.com/@bearbaitofficial] known for their captivating - and sometimes disturbing science content.

GT can be found on the handle '@bearBaitOfficial' on most social media channels.  

In this episode, we resume our discussion on Brain Organelles -  which are grown from human stem cells - how they are being used to learn about disease, how they may be integrated in A.I.  as well as eithical concerns with them.

We also ponder what constitutes intelligence in nature, and even touch on the potential risks of AI behaving nefariously.

You won't want to miss this thought-provoking and engaging discussion.

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