Some see the world of thought divided into two types of ideas: evolutionary and revolutionary ideas. However, the truth can be more nuanced than that; evolutionary ideas can spur revolutions, and revolutionary ideas may be necessary to create incremental advancements. General relativity is an idea that was evolutionary mathematically, revolutionary physically, and necessary for our modern understanding of the cosmos. Devised in its full form first by Einstein, and later proven correct by experiment, general relativity gives us a framework for understanding not only the relationship between mass and energy and space and time, but topology and destiny. So why is relativity such an important concept? How do special and general relativity differ? And what is meant by the equation G=8πT?



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21: Einstein's Biggest Idea (General Relativity)

Hosted by Gabriel Hesch and Autumn Phaneuf, who have advanced degrees in EE and industrial engineering/operations research respectively, come together to discuss mathematics as a pure field al in its own as well as how it describes the language of science, engineering, and even creativity. &nbsp;

Breaking Math brings you the absolute best in interdisciplinary science discussions - &nbsp;bringing together experts in varying fields including artificial intelligence, neuroscience, evolutionary biology, physics, chemistry and materials-science, and more - &nbsp;to discuss where humanity is headed. website: &nbsp;breakingmath.io&nbsp; linktree: &nbsp;linktree.com/breakingmathmedia email: &nbsp;breakingmathpodcast@gmail.com

Science

Mathematics

In this conversation, Autumn Phaneuf interviews Zach Weinersmith, a cartoonist and writer, about the feasibility and implications of space settlement. They discuss the challenges and misconceptions surrounding space colonization, including the idea that it will make us rich, mitigate war, and make us wiser. They explore the potential of the moon and Mars as settlement options, as well as the concept of rotating space stations. They also touch on the physiological effects of space travel and the need for further research in areas such as reproduction and ecosystem design. The conversation explores the challenges and implications of human settlement in space. It discusses the lack of data on the long-term effects of space travel on the human body, particularly for women. The conversation also delves into the need for a closed-loop ecosystem for sustainable space settlement and the legal framework surrounding space exploration and resource extraction. The main takeaways include the importance of addressing reproductive and medical challenges, the need for a better legal regime, and the debunking of misconceptions about space settlement.

Follow Zach Weinersmith on his website [https://www.smbc-comics.com/] and Twitter [https://x.com/ZachWeiner]

Subscribe to Breaking Math wherever you get your podcasts.

Become a patron of Breaking Math [https://www.patreon.com/breakingmath] for as little as a buck a month

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Folllow Gabe on Twitter [https://x.com/TechPodGabe].

Have suggestions or want to come on the show? Fill out the form here [https://forms.gle/1kLJ3ZUmqTrBkPBXA]. 

email: breakingmathpodcast@gmail.com

A City on Mars, Keywords space settlement, feasibility, challenges, misconceptions, moon, Mars, rotating space stations, reproduction, ecosystem design, space settlement, human reproduction, closed-loop ecosystem, space law, resource extraction, logistics, math.

97:  (Part 2) Can We Survive on Mars? Hot Tips with Zach Weinersmith

In this conversation, Autumn Phaneuf and Zach Weinersmith discusses his new book, A City on Mars, which takes a humorous look at the challenges of building a Martian society. He explores the misconceptions and myths surrounding space settlement and the feasibility of colonizing Mars. He argues that space is unlikely to make anyone rich and that the idea that space will mitigate war is unsupported. He also discusses the potential benefits and limitations of settling on the Moon and Mars, as well as the technical challenges involved.

Follow Zach Weinersmith on his website [https://www.smbc-comics.com/] and Twitter [https://x.com/ZachWeiner]

Subscribe to Breaking Math wherever you get your podcasts.

Become a patron of Breaking Math [https://www.patreon.com/breakingmath] for as little as a buck a month

Follow Breaking Math on Twitter [https://www.patreon.com/breakingmath], Instagram [https://www.instagram.com/breakingmathmedia/], LinkedIn [https://www.linkedin.com/company/breaking-math/], Website [https://breakingmath.io/]

Follow Autumn on Twitter [https://x.com/1autumn_leaf] and Instagram [https://www.instagram.com/1autumnleaf/]

Folllow Gabe on Twitter [https://x.com/TechPodGabe].

email: breakingmathpodcast@gmail.com

A City on Mars, space settlement, Mars colonization, misconceptions, myths, feasibility, space myths, space economics, war, Moon settlement, technical challenges, logistics, math.

96: Can We Survive on Mars? Hot Tips with Zach Weinersmith

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!

What's the Use?  Interview 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.

95:  Bayes' Theorem  Explains It All:  An Interview with Tom Chivers

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

21: Einstein's Biggest Idea (General Relativity)

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