Breaking Math Podcast (Gabriel Hesch and Autumn Phaneuf)

In this episode of Breaking Math, Autumn and Gabe explore the concept of nothingness and its significance in various fields. They discuss the philosophical, scientific, mathematical, and literary aspects of nothingness, highlighting its role in understanding reality and existence. They mention books like 'Incomplete Nature' by Terence Deacon and 'Zero: The Biography of a Dangerous Idea' by Charles Seife, which delve into the concept of absence and zero. The episode concludes by emphasizing the complexity and versatility of nothingness, inviting listeners to think deeper about its implications.

Keywords: nothingness, philosophy, science, mathematics, literature, reality, existence, absence, zero

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Game theory is all about decision-making and how it is impacted by choice of strategy, and a strategy is a decision that is influenced not only by the choice of the decision-maker, but one or more similar decision makers. This episode will give an idea of the type of problem-solving that is used in game theory. So what is strict dominance? How can it help us solve some games? And why are The Obnoxious Seven wanted by the police?

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It's the last week of our summer break and we have 2 episodes this week for you as a little treat. So check out our show on Friday too for a little bit more fun. We can't wait for our fall lineup because it's packed with surprises. If you have not listened to the last two episodes, then we'd highly recommend going back and listening to those. We're choosing to present this information this way because otherwise we'd waste most of your time re-explaining concepts we've already covered.

Black holes are so bizarre when we measured against the yardstick of the mundanity of our day to day lives that they inspire fear, awe, and controversy. In this last episode of the Abyss series, we will look at some more cutting-edge problems and paradoxes surrounding black holes. So how are black holes and entanglement related? What is the holographic principle? And what is the future of black holes?

Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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There are times in mathematics when we are generalizing the behavior of many different, but similar, entities. One such time that this happens is the use cases of Big O notation, which include describing the long-term behavior of functions, and talking about how accurate numerical calculations are. On this problem episode, we are going to discuss Big O notation and how to use it.

This episode is licensed by Sofia Baca under a Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca]

We communicate every day through languages; not only human languages, but other things that could be classified as languages such as internet protocols, or even the structure of business transactions. The structure of words or sentences, or their metaphorical equivalents, in that language is known as their syntax. There is a way to describe certain syntaxes mathematically through what are known as formal grammars. So how is a grammar defined mathematically? What model of language is often used in math? And what are the fundamental limits of grammar?

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!

Machines, during the lifetime of anyone who is listening to this, have advanced and revolutionized the way that we live our lives. Many listening to this, for example, have lived through the rise of smart phones, 3d printing, massive advancements in lithium ion batteries, the Internet, robotics, and some have even lived through the introduction of cable TV, color television, and computers as an appliance. All advances in machinery, however, since the beginning of time have one thing in common: they make what we want to do easier. One of the great tragedies of being imperfect entities, however, is that we make mistakes. Sometimes those mistakes can lead to war, famine, blood feuds, miscalculation, the punishment of the innocent, and other terrible things. It has, thus, been the goal of many, for a very long time, to come up with a system for not making these mistakes in the first place: a thinking machine, which would help eliminate bias in situations. Such a fantastic machine is looking like it's becoming closer and closer to reality, especially with the advancements in artificial intelligence. But what are the origins of this fantasy? What attempts have people made over time to encapsulate reason? And what is ultimately possible with the automated manipulation of meaning? All of this and more on this episode of Breaking Math. Episode 48: Thinking Machines References: * https://publicdomainreview.org/essay/let-us-calculate-leibniz-llull-and-the-computational-imagination * https://spectrum.ieee.org/tag/history+of+natural+language+processing https://en.wikipedia.org/wiki/Characteristica_universalis https://ourworldindata.org/coronavirus-source-data This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. [Featuring: Sofía Baca, Gabriel Hesch]

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Katharine Hayhoe was the lead author on the 2018 US Climate Assessment report, and has spent her time since then spreading the word about climate change. She was always faced with the difficult task of convincing people who had stakes in things that would be affected by acknowledging the information in her report. In her newest book, “Saving Us: A Climate Scientist’s Case for Hope and Healing in a Divided World”, she discusses the challenges associated with these conversations, at both the micro and macro level. So who is Katherine Heyhoe? How has she learned to get people to acknowledge the reality of climate science? And is she the best, or worst, person to strike up a discussion about how the weather’s been? All of this, and more, on this episode of Breaking Math. Papers Cited: -“99.94 percent of papers agree with the scientific consensus.”

More info: https://journals.sagepub.com/doi/10.1177/0270467617707079

This episode is distributed under a CC BY-NC 4.0 International License. For more information, visit creativecommons.org.

Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker

[Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Katherine Heyhoe, Elliot Smith]

In this episode, Dr. Destine Nock, CEO of Peoples Energy Analytics and a Professor at Carnegie Mellon University, joins Autumn to dive deep into the world of energy equity. They explore how cutting-edge data analytics are revolutionizing the landscape of affordable energy access. As the global demand for sustainable energy solutions continues to grow, the need to ensure fair and inclusive energy distribution becomes more critical than ever. Together, our hosts break down how data-driven insights are being leveraged to develop and implement policies that make energy more accessible to underserved communities, tearing down socioeconomic barriers and paving the way for a more equitable future.

Dr. Nock and Autumn discuss the powerful role that advanced analytics play in everything from analyzing consumption patterns to optimizing renewable energy distribution. They explore real-world case studies, highlight key initiatives, and speak with experts who are at the forefront of these transformative efforts. By the end of this episode, you’ll understand how strategic use of data can drive lasting change and help us build a world where energy is not a privilege but a right accessible to all.

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Follow Dr. Destenie Nock on LinkedIn and on her website. Check out Peoples Energy Analytics as well.

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Mathematics, like any intellectual pursuit, is a constantly-evolving field; and, like any evolving field, there are both new beginnings and sudden unexpected twists, and things take on both new forms and new responsibilities. Today on the show, we're going to cover a few mathematical topics whose nature has changed over the centuries. So what does it mean for math to be extinct? How does this happen? And will it continue forever?

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

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Explore the intriguing intersection of science and spiritualism in the Victorian era. This episode uncovers how prominent scientists like Michael Faraday, William James, and Marie & Pierre Curie engaged with supernatural phenomena and the rise of spiritualism. Discover the scientific efforts to debunk or understand paranormal activities, and how these investigations shaped modern science. Dive into the fascinating legacy of this 19th-century movement and its lasting impact on today's scientific inquiries into the unknown. Perfect for fans of history, science, and the supernatural.

Keywords: Victorian era, spiritualism, science, supernatural, Michael Faraday, William James, Alfred Russell Wallace, Curies, Eleanor Sidgwick, idiomotor effect

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Spheres and circles are simple objects. They are objects that are uniformly curved throughout in some way or another. They can also be defined as objects which have a boundary that is uniformly distant from some point, using some definition of distance. Circles and spheres were integral to the study of mathematics at least from the days of Euclid, being the objects generated by tracing the ends of idealized compasses. However, these objects have many wonderful and often surprising mathematical properties. To this point, a circle's circumference divided by its diameter is the mathematical constant pi, which has been a topic of fascination for mathematicians for as long as circles have been considered.

[Featuring Sofía Baca; Meryl Flaherty]

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The world is a big place with a lot of wonderful things in it. The world also happens to be spherical, which can make getting to those things a challenge if you don't have many landmarks. This is the case when people are navigating by sea. For this reason, map projections, which take a sphere and attempt to flatten it onto a sheet, were born. So what is a map projection? Why are there so many? And why is Gall-Peters the worst? All of this, and more, on this episode of Breaking Math.

Theme was written by Elliot Smith.

This episode is distributed under a Creative Commons 4.0 Attribution-ShareAlike-NonCommercial International License. For more information, visit CreativeCommons.org.

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In this conversation, Gabriel and Autumn interview Jeff Perry, a career coach and author of the book 'The Intentional Engineer'. They discuss the importance of being intentional in one's career, understanding one's passions and skills, and building a strong professional network. Jeff shares his journey from being an engineer to becoming an engineer coach and offers advice on how to navigate career transitions. They also explore the concept of 'genius zones' and how to identify and leverage one's unique strengths and talents. In this conversation, Jeff discusses the concept of the zone of incompetence, competence, excellence, and genius. They share personal anecdotes and examples to illustrate these zones and emphasize the importance of self-awareness and collaboration. They also touch on the role of mindset in driving behavior and results, particularly in the context of engineering and tech careers. Jeff offers coaching and resources for individuals looking to make intentional career shifts or upgrades.

Keywords: career, intentionality, engineering, skills, passions, network, genius zones, strengths, talents, zone of incompetence, zone of competence, zone of excellence, zone of genius, self-awareness, collaboration, mindset, engineering, tech careers, intentional career shifts

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Follow Jeff Perry on LinkedIn or learn more at jeff-perry.com. You can also find his book The Intentional Engineer, on Amazon.

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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!

Mathematics is full of all sorts of objects that can be difficult to comprehend. For example, if we take a slip of paper and glue it to itself, we can get a ring. If we turn it a half turn before gluing it to itself, we get what's called a Möbius strip, which has only one side twice the length of the paper. If we glue the edges of the Möbius strip to each other, and make a tube, you'll run into trouble in three dimensions, because the object that this would make is called a Klein flask, and can only exist in four dimensions. So what is a fiber? What can fiber bundles teach us about higher dimensional objects?

All of this, and more, on this episode of Breaking Math.

[Featuring: Sofía Baca, Meryl Flaherty]

Happy Summer! Check out part one of our three part series on black holes from 2018. Enjoy!

The idea of something that is inescapable, at first glance, seems to violate our sense of freedom. This sense of freedom, for many, seems so intrinsic to our way of seeing the universe that it seems as though such an idea would only beget horror in the human mind. And black holes, being objects from which not even light can escape, for many do beget that same existential horror. But these objects are not exotic: they form regularly in our universe, and their role in the intricate web of existence that is our universe is as valid as the laws that result in our own humanity. So what are black holes? How can they have information? And how does this relate to the edge of the universe?


Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Look at all you phonies out there.

You poseurs.

All of you sheep. Counting 'til infinity. Counting sheep.

*pff*

What if I told you there were more there? Like, ... more than you can count?

But what would a sheeple like you know about more than infinity that you can count?

heh. *pff*

So, like, what does it mean to count til infinity? What does it mean to count more? And, like, where do dimensions fall in all of this?

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(Correction: at 12:00, the paradox is actually due to Galileo Galilei)

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org

Music used in the The Great Courses ad was Portal by Evan Shaeffer

[Featuring: Sofía Baca, Gabriel Hesch]

Hello listeners. You don't know me, but I know you. I want to play a game. In your ears are two earbuds. Connected to the earbuds are a podcast playing an episode about game theory. Hosting that podcast are two knuckleheads. And you're locked into this episode. The key is at the end of the episode. What is game theory? Why did we parody the Saw franchise? And what twisted lessons will you learn?

-See our New Youtube Show "Turing Rabbit Holes Podcast" at youtube.com/TuringRabbitHolesPodcast.   Also available on all podcast players.  

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This episode description intentionally left blank!   As in completely on purpose.   Fun Fact!  The creators of the Breaking Math Podcast, Sofia and Gabriel always thought it was funny that many books that we've read - even going back to our childhood - had a page in it with the sentence printed, "This Page Intentionally Left Blank."   Like-  okay; what does this 'intentionally left blank page' add to the reading experience?  Does anyone know?  Oh look here!  There is a wikipedia page on it. Huh.  Now I know.  Now we know.   And knowing is half the battle!  

 Sofia would frequently leave post-it notes on Gabe's laptop saying, "This Post-it note intentionally left blank."  Because . . . . why?   Sofia would often leave a twitter or facebook post that declared "This post intentionally left blank."   

And now - we release an entire podcast episode that is intentionally left blank.  Are we trolls?  NO!  We prefer to think of ourselves as artists in the style of Banksy making a statement! 

Michael Brooks is a science writer who specializes in making difficult concepts easier to grasp. In his latest book, Brooks goes through several mathematical concepts and discusses their motivation, history, and discovery. So how do stories make it easier to learn? What are some of the challenges associated with conveying difficult concepts to the general public? And who, historically, has been a mathematician? All of this and more on this episode of Breaking Math.  Songs were Breaking Math Intro and Outro by Elliot Smith of Albuquerque.  This episode is published under a Creative Commons 4.0 Attribute-ShareAlike-NonCommercial license. For more information, visit CreativeCommons.org  [Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Michael Brooks]

t

In this exciting episode of Breaking Math, we explore the groundbreaking discovery of the largest prime number ever found—M136279841, a Mersenne prime with over 41 million digits! Join us as we dive deep into the story behind this astonishing mathematical achievement, led by Luke Durant, a volunteer from the Great Internet Mersenne Prime Search (GIMPS) project.

Discover how Mersenne primes work, why they’re so important to the world of mathematics, and how cutting-edge technology like GPUs has revolutionized the search for these massive numbers. We also discuss the critical role that prime numbers play in cryptography and online security, making this discovery relevant far beyond just the realm of theoretical mathematics.

Learn about the global collaborative effort that made this record-breaking discovery possible, and find out how you can join the hunt for the next giant prime! Whether you're a math enthusiast, a tech geek, or just curious about the wonders of numbers, this episode is packed with insights that will inspire you to think about prime numbers in a whole new way.

Key Takeaways:

• The discovery of M136279841, a prime number with 41,024,320 digits.
• The role of Luke Durant and the GIMPS project in pushing the boundaries of prime number research.
• How GPUs are transforming the way we discover massive primes.
• The importance of prime numbers in modern cryptography and technology.
• The connection between Mersenne primes and perfect numbers.

Links Mentioned:

• Join the GIMPS project and search for the next prime: www.mersenne.org/download
• Learn more about Mersenne primes: Mersenne Prime History
  

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If you are there, and I am here, we can measure the distance between us. If we are standing in a room, we can calculate the area of where we're standing; and, if we want, the volume. These are all examples of measures; which, essentially, tell us how much 'stuff' we have. So what is a measure? How are distance, area, and volume related? And how big is the Sierpinski triangle? All of this and more on this episode of Breaking Math.

Ways to support the show:

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The theme for this episode was written by Elliot Smith.

Episode used in the ad was Buffering by Quiet Music for Tiny Robots.

[Featuring: Sofía Baca; Meryl Flaherty]

How many piano tuners are there in New York City? How much cheese is there in Delaware? And how can you find out? All of this and more on this problem-episode of Breaking Math.

This episode distributed under a Creative Commons Attribution-ShareAlike-Noncommercial 4.0 International License. For more information, visit creativecommons.org

Featuring theme song and outro by Elliot Smith of Albuquerque.

[Featuring: Sofía Baca, Meryl Flaherty]

Numbering was originally done with tally marks: the number of tally marks indicated the number of items being counted, and they were grouped together by fives. A little later, people wrote numbers down by chunking the number in a similar way into larger numbers: there were symbols for ten, ten times that, and so forth, for example, in ancient Egypt; and we are all familiar with the Is, Vs, Xs, Ls, Cs, and Ds, at least, of Roman numerals. However, over time, several peoples, including the Inuit, Indians, Sumerians, and Mayans, had figured out how to chunk numbers indefinitely, and make numbers to count seemingly uncountable quantities using the mind, and write them down in a few easily mastered motions. These are known as place-value systems, and the study of bases has its root in them: talking about bases helps us talk about what is happening when we use these magical symbols.

Tom Chivers 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.

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Join Gabriel and Sofía as they delve into some introductory calculus concepts.

[Featuring: Sofía Baca, Gabriel Hesch]

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In this episode Autumn and Anil Ananthaswamy discuss the inspiration behind his book “Why Machines Learn” and the importance of understanding the math behind machine learning. He explains that the book aims to convey the beauty and essential concepts of machine learning through storytelling, history, sociology, and mathematics. Anil emphasizes the need for society to become gatekeepers of AI by understanding the mathematical basis of machine learning. He also explores the history of machine learning, including the development of neural networks, support vector machines, and kernel methods. Anil highlights the significance of the backpropagation algorithm and the universal approximation theorem in the resurgence of neural networks.

Keywords: machine learning, math, inspiration, storytelling, history, sociology, gatekeepers, neural networks, support vector machines, kernel methods, backpropagation algorithm, universal approximation theorem, AI, ML, physics, mathematics, science

You can find Anil Ananthaswamy on Twitter @anilananth and his new book “Why Machines Learn”

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Voting systems are, in modern times, essential to the way that large-scale decisions are made. The concept of voicing an opinion to be, hopefully, considered fairly is as ancient and well-established as the human concept of society in general. But, as time goes on, the recent massive influx of voting systems in the last 150 years have shown us that there are as many ways to vote as there are flaws in the way that the vote is tallied. So what problems exist with voting? Are there any intrinsic weaknesses in group decision-making systems? And what can we learn by examining these systems? All of this, and more, on this episode of Breaking Math.

Licensed under Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org.

Surprise! It's a Friday episode for you! Yes, yes it is a rerun, but we wanted to share it anyways.  We can't wait for our fall lineup because it's packed with surprises. See you back on Tuesday. 

Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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Join Sofia and Gabriel on this problem episode where we explore "base 3-to-2" — a base system we explored on the last podcast — and how it relates to "base 3/2" from last episode.

[Featuring: Sofía Baca; Gabriel Hesch]

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, the author of the book 'The Gravity of Math.' 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

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Join Sofía Baca with her guest Millicent Oriana from the newly launched Nerd Forensics podcast as they discuss some apparent paradoxes in probability and Russian roulette.

Intro is "Breaking Math Theme" by Elliot Smith. Ads feature "Ding Dong" by Simon Panrucker

[Featuring: Sofía Baca; Millicent Oriana]

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Children who are being taught mathematics often balk at the idea of negative numbers, thinking them to be fictional entities, and often only learn later that they are useful for expressing opposite extremes of things, such as considering a debt an amount of money with a negative sum. Similarly, students of mathematics often are puzzled by the idea of complex numbers, saying that it makes no sense to be able to take the square root of something negative, and only realizing later that these can have the meaning of two-dimensional direction and magnitude, or that they are essential to our modern understanding of electrical engineering. Our discussion today will be much more abstract than that. Much like in our discussion in episode five, "Language of the Universe", we will be discussing how math and physics draw inspiration from one another; we're going to talk about what different fields (such as the real, complex, and quaternion fields) seem to predict about our universe. So how are real numbers related to classical mechanics? What does this mean complex numbers and quaternions are related to? And what possible physicses exist?

Update:  Dr. Alex Alaniz and the Breaking Math Podcast have teamed up to create a new youtube show called the "Turing Rabbit Holes Podcast."  We discuss science, math, and society with spectacular visuals.    Available at youtube.com/TuringRabbitHolesPodcast and on all other podcast platforms.  

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License is Creative Commons Attribution-ShareAlike 4.0 (See https://creativecommons.org/licenses/by-sa/4.0/)

Seldom do we think about self-reference, but it is a huge part of the world we live in. Every time that we say 'myself', for instance, we are engaging in self-reference. Long ago, the Liar Paradox and the Golden Ratio were among the first formal examples of self-reference. Freedom to refer to the self has given us fruitful results in mathematics and technology. Recursion, for example, is used in algorithms such as PageRank, which is one of the primary algorithms in Google's search engine. Elements of self-reference can also be found in foundational shifts in the way we understand mathematics, and has propelled our understanding of mathematics forward. Forming modern set theory was only possible due to a paradox called Russel's paradox, for example. Even humor uses self-reference. Realizing this, can we find harmony in self-reference? Even in a podcast intro, are there elements of self-reference? Nobody knows, but I'd check if I were you. Catch all of this, and more, on this episode of Breaking Math. Episode 70.1: Episode Seventy Point One of Breaking Math Podcast

[Featuring: Sofía Baca, Gabriel Hesch; Millicent Oriana]

Learn more about radiative forcing, the environment, and how global temperature changes with atmospheric absorption with this Problem Episode about you walking your (perhaps fictional?) dog around a park.  This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

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This episode is sponsored by 

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In this episode of Breaking Math, we explore the unexpected link between sheep herding and fluid dynamics!  Did you know that the way sheep move in a herd is governed by the same mathematical principles as water flowing in a river? By following simple rules of alignment, cohesion, and separation, sheep create a coordinated, fluid-like movement that scientists can model to predict behavior.

Join us as we break down how these principles apply not only to animal herds but also to real-world applications like robotics, autonomous vehicles, and crowd management. Whether you're a math lover, curious about animal behavior, or fascinated by the science behind traffic flow, this episode reveals the incredible power of mathematics in nature. Don’t forget to subscribe for more insights into the surprising connections between math and the world around us!

Timestamps:
00:00 - Introduction to Sheep Herding and Fluid Dynamics
02:15 - What is Fluid Dynamics?
06:30 - How Sheep Behave Like Particles in a Fluid
10:45 - Mathematical Models of Herding Behavior
16:20 - Real-world Applications: From Farming to Robotics
20:55 - Conclusion & Key Takeaways

Tags: #BreakingMath #FluidDynamics #AnimalBehavior #MathInNature #SheepHerding #Robotics #ScienceExplained #EmergentBehavior

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Math is a gravely serious topic which has been traditionally been done by stodgy people behind closed doors, and it cannot ever be taken lightly. Those who have fun with mathematics mock science, medicine, and the foundation of engineering. That is why on today's podcast, we're going to have absolutely no fun with mathematics. There will not be a single point at which you consider yourself charmed, there will not be a single thing you will want to tell anyone for the sake of enjoyment, and there will be no tolerance for your specific brand of foolishness, and that means you too, Kevin.

In mathematics, nature is a constant driving inspiration; mathematicians are part of nature, so this is natural. A huge part of nature is the idea of things like networks. These are represented by mathematical objects called 'graphs'. Graphs allow us to describe a huge variety of things, such as: the food chain, lineage, plumbing networks, electrical grids, and even friendships. So where did this concept come from? What tools can we use to analyze graphs? And how can you use graph theory to minimize highway tolls? All of this and more on this episode of Breaking Math.

Episode distributed under an Creative Commons Attribution-ShareAlike-NonCommercial 4.0 International License. For more information, visit CreativeCommons.org

[Featuring: Sofía Baca, Meryl Flaherty]

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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:  

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Forecasting is a constantly evolving science, and has been applied to complex systems; everything from the weather, to determining what customers might like to buy, and even what governments might rise and fall. John Fuisz is someone who works with this science, and has experience improving the accuracy of forecasting. So how can forecasting be analyzed? What type of events are predictable? And why might Russia think a Missouri senator's race hinges upon North Korea? All of this and more on this episode of Breaking Math.

The theme for this episode was written by Elliot Smith.

[Featuring: Sofía Baca, Gabriel Hesch; John Fuisz]

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 and YouTube 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.

30% Off ZenCastr Discount

Use My Special Link to save e 30%  Off Your First Month of Any ZenCastr Paid Plan

In this conversation, Gabe and Autumn celebrate the 101st episode of Breaking Math and discuss the evolution of the podcast. They highlight the importance of creativity in teaching mathematics and share their plans to expand Breaking Math into Breaking Math Media. They also discuss the history of physics and the big questions that inform the podcast. The hosts express their desire to collaborate with listeners and explore practical applications of math in different fields. They also mention books like 'A Quantum Story' and 'Incomplete Nature' that delve into the mysteries of quantum mechanics and consciousness. The hosts highlight the unique and creative nature of their podcast, inviting listeners to join them in the Math Lounge, a metaphorical nightclub where math and creativity intersect.

Keywords: Breaking Math, podcast, creativity, mathematics, Breaking Math Media, physics, history, quantum mechanics, book discussion, double-slit experiment, quantum mechanics, interdisciplinary discussions, machine learning, neuroscience, gamification of math, collaboration, practical applications, consciousness, Math Lounge

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Join Sofía and Gabriel as they discuss an old but great proof of the irrationality of the square root of two.

[Featuring: Sofía Baca, Gabriel Hesch]

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Merchandise

Ad contained music track "Buffering" from Quiet Music for Tiny Robots.

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit creativecommons.org.

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 and Twitter

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Have suggestions or want to come on the show? Fill out the form here. 

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.

Happy Summer! We have another week of our summer break after this episode from 2018. We will be back shortly with more content and surprises!

Black holes are objects that seem exotic to us because they have properties that boggle our comparatively mild-mannered minds. These are objects that light cannot escape from, yet glow with the energy they have captured until they evaporate out all of their mass. They thus have temperature, but Einstein's general theory of relativity predicts a paradoxically smooth form. And perhaps most mind-boggling of all, it seems at first glance that they have the ability to erase information. So what is black hole thermodynamics? How does it interact with the fabric of space? And what are virtual particles?

Keywords: Black holes, gravity, universe, physics, ai, machine learning, education, statistics, engineering, humanity

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In this episode Autumn and Dr. Jonathan Schwabish discuss the importance of strategic thinking in data visualization and the key elements of good data. He emphasizes the need to understand the data and how it was collected, as well as the importance of starting bar charts at zero. He also highlights common mistakes in data visualization, such as distorting or lying with visuals, and the potential impact of data visualization on policy decisions. Looking to the future, he discusses the role of AI in data visualization, the integration of AI into visualization tools, and the potential of augmented reality and virtual reality in data visualization. Jon Schwabish discusses the different data visualization tools he uses, including Excel, R, Tableau, Datawrapper, and Flourish. He emphasizes the importance of choosing the right tool for the specific use case and audience. He also highlights the need for policymakers and individuals to be trained in interpreting and using data visualizations effectively. Schwabish discusses the ethical considerations in data visualization, such as using inclusive language and considering accessibility.

Keywords: data visualization, strategic thinking, good data, common mistakes, impact on policy decisions, AI, augmented reality, virtual reality, data visualization tools, Excel, R, Tableau, Datawrapper, Flourish, policymakers, data interpretation, ethical considerations, inclusive language, accessibility

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Follow Jon Schwabish  on Twitter  and on YouTube. Also go give PolicyViz Podcast a follow

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This is a rerun of one of our favorite episodes! We hope that you enjoy it if you haven't listened to it yet. We'll be back next week with new content! Thank you so much for listening to Breaking Math!

Math is a gravely serious topic which has been traditionally been done by stodgy people behind closed doors, and it cannot ever be taken lightly. Those who have fun with mathematics mock science, medicine, and the foundation of engineering. That is why on today's podcast, we're going to have absolutely no fun with mathematics. There will not be a single point at which you consider yourself charmed, there will not be a single thing you will want to tell anyone for the sake of enjoyment, and there will be no tolerance for your specific brand of foolishness, and that means you too, Kevin.

Theme by Elliot Smith.

Neuroscience is a topic that, in many ways, is in its infancy. The tools that are being used in this field are constantly being honed and reevaluated as our understanding of the brain and mind increase. And it's no surprise: the brain is responsible for the way we interact with the world, and the idea that ideas hone one another is not new to anyone who possesses a mind. But how can the tools that we use to study the brain and the mind be linked? How do the mind and the brain encode one another? And what does Bayes have to do with this? All of this and more on this episode of Breaking Math.

[Featuring: Sofía Baca, Gabriel Hesch; Peter Zeidman]

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This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

One tells a lie, the other the truth! Have fun with Sofía and Meryl as they investigate knight, knave, and spy problems!

Intro is "Breaking Math Theme" by Elliot Smith. Music in the ads were Plug Me In by Steve Combs and "Ding Dong" by Simon Panrucker. You can access their work at freemusicarchive.org.

[Featuring: Sofia Baca; Meryl Flaherty]

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. (Find out more about the Ray Kitty Creation Workshop by clicking here).  

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 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 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?  by authors Dr. Kelly and Zach Weinersmith.  Zach Weinersmith is the artist and creator of the famous cartoon strip Saturday Morning Breaking Cereal!  
  
  We've got a lot of great episodes coming up!  Stay tuned.  

Mathematical Patterns in Plants: Fibonacci, Golden Ratio & Nature's Hidden Math with Christophe Gole & Nancy Pick
In this episode of Breaking Math, host Autumn interviews authors Christophe Gole and Nancy Pick about the captivating world of mathematical patterns in plants, inspired by their book Do Plants Know Math?. Explore the intersection of mathematics and biology as they discuss the Fibonacci sequence, the golden ratio, and spiral formations that reveal nature's mathematical beauty. Learn about the optimization of plant structures, the role of women in mathematics, and get recommendations for further reading. Topics include phyllotaxis, fractals, and their connections to AI, physics, and topology.

Keywords: mathematics, biology, plant math, Fibonacci, phylotaxis, spirals, golden ratio, fractals, nature, science, women in math,topology, ai, physics, math, plants, gardening

Become a patron of Breaking Math for as little as a buck a month

You can connect with Christophe Gole and Nancy Pick on LinkedIn, and find their Book “Do Plants Know Math?” on Amazon.

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Time is something that everyone has an idea of, but is hard to describe. Roughly, the arrow of time is the same as the arrow of causality. However, what happens when that is not the case? It is so often the case in our experience that this possibility brings not only scientific and mathematic, but ontological difficulties. So what is retrocausality? What are closed timelike curves? And how does this all relate to entanglement?

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

In this episode of Breaking Math, hosts Autumn and Gabriel take a deep dive into the paper “Towards Equilibrium Molecular Conformation Generation with GFlowNets” by Volokova et al., published in the Digital Discovery Journal by the Royal Society of Chemistry. They explore the cutting-edge intersection of molecular conformations and machine learning, comparing traditional methods like molecular dynamics and cheminformatics with the innovative approach of Generative Flow Networks (GFlowNets) for molecular conformation generation.

The episode covers empirical results that showcase the effectiveness of GFlowNets in computational chemistry, their scalability, and the role of energy estimators in advancing fields like drug discovery. Tune in to learn how machine learning is transforming the way we understand molecular structures and driving breakthroughs in chemistry and pharmaceuticals.

Keywords: molecular conformations, machine learning, GFlowNets, computational chemistry, drug discovery, molecular dynamics, cheminformatics, energy estimators, empirical results, scalability, math, mathematics, physics, AI

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You can find the paper  “Towards equilibrium molecular conformation generation with GFlowNets” by Volokova et al in Digital Discovery Journal by the Royal Society of Chemistry.

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In this episode, Gabriel and Autumn interview mathematician, comedian, and author Matt Parker about his latest book, "Love Triangle." They discuss the unique page numbering system in the book, which is based on the sine function, and how it adds an extra layer of discovery for readers. They also explore the use of triangles and quads in 3D modeling, the concept of Perlin noise, and the perception of randomness. The conversation touches on the intersection of mathematics and creativity, as well as the practical applications of mathematical concepts in various fields. The conversation explores various topics related to mathematics, including the analysis of the Mona Lisa, the use of math in playing pool, the discovery of new shapes, and the application of math in various fields. The speakers discuss the motivation behind exploring these topics and the interplay between math and art. They also provide advice for science and math content creators on YouTube.

Keywords: mathematics, book, Love Triangle, page numbering, sine function, triangles, quads, 3D modeling, Perlin noise, randomness, creativity, practical applications, mathematics, Mona Lisa, parallax, pool, shapes, Fourier analysis, YouTube, physics, AI, machine learning

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Follow Matt Parker on Twitter  and on YouTube at @StandUpMaths and find his book "Love Triangle" on Amazon

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In this episode of Breaking Math, Autumn and Andrew Novick delve into the intricate world of timekeeping, exploring the significance of precise time measurement in modern technology. They discuss the evolution from traditional atomic clocks to cutting-edge optical clocks, the critical role of time in various industries, and the implications of time on fundamental physics, including Einstein's theories. The conversation also touches on the quirky concept of leap seconds and the future advancements in timekeeping technology, emphasizing the relative nature of time and its perception.

You can learn more about Time at time.gov and NIST at nist.gov.

All opinions are of the individual scientist and do not reflect the opinions of  NIST or the federal Government.

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Ben Orlin has been a guest on the show before. He got famous with a blog called 'Math With Bad Drawings", which is what it says on the tin: he teaches mathematics using his humble drawing skills. His last book was a smorgasbord of different mathematical topics, but he recently came out with a new book 'Change is the Only Constant: the Wisdom of Calculus in a Madcap World', which focuses more on calculus itself.

This episode is distributed under a CC BY-SA license. For more info, visit creativecommons.org

In this captivating episode of Breaking Math, hosts Gabriel and Autumn dive deep into chaos theory—a fascinating branch of mathematics that explores the behavior of complex systems highly sensitive to initial conditions. They break down the butterfly effect, revealing how tiny variations can lead to major consequences and discuss the inherent unpredictability in weather forecasting and the financial markets. The episode also uncovers chaos theory’s influence on human physiology, such as heart rate variability, and the mathematical beauty of fractals. Additionally, the hosts explore philosophical viewpoints, emphasizing how accepting life’s uncertainties can foster adaptability and resilience.

Key Takeaways:

Chaos Theory: Small actions can trigger significant outcomes, impacting everything from nature to human-made systems.

Butterfly Effect: Demonstrates how tiny differences in initial conditions can lead to vastly different outcomes.

Weather Forecasting: An excellent real-world illustration of chaos theory, showing how unpredictable weather can be.

Financial Markets: A reminder of the chaotic, complex forces that drive economic shifts and unpredictability.

Human Physiology: Chaos theory sheds light on natural processes, like the variability of heart rhythms.

Fractals: These intricate patterns showcase self-similarity and are visually striking examples of chaos in nature.

Philosophical Implications: Embracing chaos and uncertainty equips us to be more adaptable and creative.

Life's Unpredictability: A reflection of chaotic systems, reminding us to value flexibility.   Interconnectedness: Understanding chaos theory enhances our appreciation of how interwoven our world truly is.

Keywords: Chaos Theory, Butterfly Effect, Weather Forecasting, Economics, Fractals, Unpredictability, Complex Systems, Human Physiology, Philosophical Implications, Adaptability.

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Statistics is a field that is considered boring by a lot of people, including a huge amount of mathematicians. This may be because the history of statistics starts in a sort of humdrum way: collecting information on the population for use by the state. However, it has blossomed into a beautiful field with its fundamental roots in measure theory, and with some very interesting properties. So what is statistics? What is Bayes' theorem? And what are the differences between the frequentist and Bayesian approaches to a problem?

Distributed under a Creative Commons Attribution-ShareAlike 4.0 International License (creativecommons.org)

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In this minisode, Autumn explores the basics in the world of journal rankings and metrics. She discusses the importance of journal rankings and how they are determined, focusing on metrics like impact factor, mathematical citation quotient (MCQ), and publication power approach (PPA). She explains how these metrics provide insights into a journal's influence and performance, but also emphasizes the need for a comprehensive evaluation of research beyond just metrics.

Keywords: journal rankings, journal metrics, impact factor, mathematical citation quotient, publication power approach, research evaluation, math, physics, ai, machine learning, education, publishing, academic journals

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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 and Twitter

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

Sofía and Gabriel discuss the question of "how many angles are there in a circle", and visit theorems from Euclid, as well as differential calculus.

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

Ways to support the show:

Patreon-Become a monthly supporter at patreon.com/breakingmath

The theme for this episode was written by Elliot Smith.

Music in the ad was Tiny Robot Armies by Quiet Music for Tiny Robots.

[Featuring: Sofía Baca, Gabriel Hesch]

Summary

This episode of Breaking Math explores the fundamental concept of measurement, its importance in daily life, and the necessity for standardized units. The discussion highlights the role of the International System of Units (SI) and the National Institute of Standards and Technology (NIST) in maintaining measurement accuracy. It also touches on historical measurement failures and the evolution of measurement definitions, emphasizing the future of measurement in technology and science.

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Math & Cartography: Dr. Paula Rowinska on Map Projections, Gerrymandering & Real-World Math
In this episode of Breaking Math, host Autumn interviews Dr. Paula Rowinska about her unique journey from earning a PhD in mathematics to writing about math and cartography. They discuss the fascinating connection between map-making and mathematics, debunking misconceptions about map projections and exploring key topics like the coastline paradox, gerrymandering, and the traveling salesman problem. Learn how these mathematical concepts play a crucial role in areas like crime analysis, geopolitics, and more. Perfect for enthusiasts of math, cartography, and real-world problem-solving.

The conversation also celebrates the contributions of underrepresented women in mathematics and underscores the importance of math in everyday life. Tune in to discover how mathematics shapes our understanding of the world through cartography, topology, and even AI.

Keywords: mathematics, cartography, map projections, coastline paradox, gerrymandering, women in math, traveling salesman problem, crime analysis, topology, metric map, ai, physics, math

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Follow Dr. Paula Rowinska at paulinarowinska.com and @PaulaRowinska on Twitter. You can also find her book Mapmatics on Amazon.

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Climate change is an issue that has become frighteningly more relevant in recent years, and because of special interests, the field has become muddied with climate change deniers who use dishonest tactics to try to get their message across. The website SkepticalScience.com is one line of defense against these messengers, and it was created and maintained by a research assistant professor at the Center for Climate Change Communication at George Mason University, and both authored and co-authored two books about climate science with an emphasis on climate change. He also lead-authored a 2013 award-winning paper on the scientific consensus on climate change, and in 2015, he developed an open online course on climate change denial with the Global Change Institute at the University of Queensland. This person is John Cook.

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch; John Cook]

--- 

This episode is sponsored by 

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Since time immemorial, blacksmiths have known that the hotter metal gets, the more it glows: it starts out red, then gets yellower, and then eventually white. In 1900, Max Planck discovered the relationship between an ideal object's radiation of light and its temperature. A hundred and twenty years later, we're using the consequences of this discovery for many things, including (indirectly) LED TVs, but perhaps one of the most dangerously neglected (or at least ignored) applications of this theory is in climate science. So what is the greenhouse effect? How does blackbody radiation help us design factories? And what are the problems with this model?

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

--- 

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The world is often uncertain, but it has only been in the last half millennium that we've found ways to interact mathematically with that concept. From its roots in death statistics, insurance, and gambling to modern Bayesian networks and machine learning, we've seen immense productivity in this field. Every way of looking at probability has something in common: the use of random variables. Random variables let us talk about events with uncertain outcomes in a concrete way. So what are random variables? How are they defined? And how do they interact? All of this, and more, on this episode of Breaking Math.

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Featuring music by Elliot Smith. For info about music used in ads, which are inserted dynamically, contact us at breakingmathpodcast@gmail.com

[Featuring: Sofía Baca, Gabriel Hesch; Millicent Oriana]

In introductory geometry classes, many of the objects dealt with can be considered 'elementary' in nature; things like tetrahedrons, spheres, cylinders, planes, triangles, lines, and other such concepts are common in these classes. However, we often have the need to describe more complex objects. These objects can often be quite organic, or even abstract in shape, and include things like spirals, flowery shapes, and other curved surfaces. These are often described better by differential geometry as opposed to the more elementary classical geometry. One helpful metric in describing these objects is how they are curved around a certain point. So how is curvature defined mathematically? What is the difference between negative and positive curvature? And what can Gauss' Theorema Egregium teach us about eating pizza?

This episode distributed under a Creative Commons Attribution ShareAlike 4.0 International License. For more information, go to creativecommons.org

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[Featuring: Sofía Baca, Meryl Flaherty]

A numerical base is a system of representing numbers using a sequence of symbols. However, like any mathematical concept, it can be extended and re-imagined in many different forms. A term used occasionally in mathematics is the term 'exotic', which just means 'different than usual in an odd or quirky way'. In this episode we are covering exotic bases. We will start with something very familiar (viz., decimal points) as a continuation of our previous episode, and then progress to the more odd, such as non-integer and complex bases. So how can the base systems we covered last time be extended to represent fractional numbers? How can fractional numbers be used as a base for integers? And what is pi plus e times i in base i + 1?

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca; Merryl Flaherty]

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There are a lot of things in the universe, but no matter how you break them down, you will still have far fewer particles than even some of the smaller of what we're calling the 'very large numbers'. Many people have a fascination with these numbers, and perhaps it is because their sheer scale can boggle the mind. So what numbers can be called 'large'? When are they useful? And what is the Ackermann function? All of this and more on this episode of Breaking Math

[Featuring: Sofía Baca; Diane Baca]

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Learn more about calculus, derivatives, and the chain rule with this Problem Episode about you walking your (perhaps fictional?) dog around a park.

This episode is distributed under a CC BY-SA license. For more information, visit CreativeCommons.org.

[Featuring: Sofía Baca, Gabriel Hesch]

--- 

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AI & Consciousness: Philosophical Debates, Ethical Implications & the Future of Conscious Machines
In this episode of Breaking Math, hosts Autumn and Gabriel explore the intricate relationship between artificial intelligence (AI) and consciousness. Delve into historical perspectives, philosophical debates, and the ethical questions surrounding the creation of conscious machines. Key topics include the evolution of AI, challenges in defining and testing consciousness, and the potential rights of AI beings. We also examine the Turing Test, the debate between strong AI vs. weak AI, and concepts like personhood and integrated information theory. Perfect for anyone interested in AI ethics, the nature of consciousness, and the responsibilities of advanced AI technology.

Keywords: AI, consciousness, Turing test, strong AI, weak AI, ethics, philosophy, personhood, integrated information theory, neural networks

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Math & Language: Creativity, Quantification, and Making Math Accessible with Ben Orlin
In this episode of Breaking Math, hosts sit down with Ben Orlin, author of Math for English Majors and Math with Bad Drawings, to explore the intersection of math and language. Discover the unique skill sets required for mathematics and creativity, how math education can be made more accessible, and the role of quantification in empowering individuals across various fields, including literature and the arts. The conversation highlights the historical contributions of women in math, including the impact of Einstein’s wife on his work. Ben also shares insights into his writing process and the challenges of making math relatable to a broad audience. Learn how mathematical thinking can enhance one's appreciation for literature and the world.

Keywords: math, language, skill sets, math education, accessibility, quantification, power of math, women in math, Einstein's wife, math, literature, book, writing, perspective, abstraction, relationships

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i^2 = j^2 = k^2 = ijk = -1. This deceptively simple formula, discovered by Irish mathematician William Rowan Hamilton in 1843, led to a revolution in the way 19th century mathematicians and scientists thought about vectors and rotation. This formula, which extends the complex numbers, allows us to talk about certain three-dimensional problems with more ease. So what are quaternions? Where are they still used? And what is inscribed on Broom Bridge? All of this and more on this episode of Breaking Math.

This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org.

The theme for this episode was written by Elliot Smith.

[Featuring: Sofía Baca, Meryl Flaherty]

In this episode of Breaking Math, hosts Gabriel Hesch and Autumn Phaneuf dive into the cutting-edge world of Generative Flow Networks (GFlowNets) and their role in artificial intelligence and material science. The discussion centers on how GFlowNets are revolutionizing the discovery of new materials for carbon capture, offering a powerful alternative to traditional AI models. Learn about the mechanics of GFlowNets, their advantages, and the groundbreaking results in developing materials with enhanced CO2 absorption capabilities. The episode also explores the future potential of GFlowNets in AI-driven material discovery and beyond, emphasizing their transformative impact on carbon capture technology and sustainable innovation.

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You can find the paper “Discovery of novel reticular materials for carbon dioxide capture using GFlowNets” by Cipcigan et al in Digital Discovery Journal by the Royal Society of Chemistry.

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This discussion Autumn and Gabe delves into Ismar Volic's personal background and inspiration for writing the book, “Making Democracy Count” as well as the practical and theoretical aspects of voting systems. Additionally, the conversation explores the application of voting systems to everyday decision-making and the use of topological data analysis in understanding societal polarization. The conversation covers a wide range of topics, including data visualization, gerrymandering, electoral systems, and the intersection of mathematics and democracy. Volic, shares insights on the practical implications of implementing mathematical improvements in electoral systems and the legal and constitutional hurdles that may arise. He also discusses the importance of educating oneself about the quantitative underpinnings of democracy and the need for interdisciplinary discussions that bridge mathematics and politics.

Keywords: math podcast, creativity, mascot, background, Matlab, ranked choice voting, elections, author's background, inspiration, voting systems, topological data analysis, societal polarization, mathematics, democracy, data visualization, gerrymandering, electoral systems, interdisciplinary discussions, practical implications, legal hurdles, constitutional considerations

You can find Ismar Volic on Twitter and LinkedIn @ismarvolic. Please go check out the Institute for Mathematics and Democracy and Volic’s new book “Making Democracy Count”

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As a child, did you ever have a conversation that went as follows:

"When I grow up, I want to have a million cats"

"Well I'm gonna have a billion billion cats"

"Oh yeah? I'm gonna have infinity cats"

"Then I'm gonna have infinity plus one cats"

"That's nothing. I'm gonna have infinity infinity cats"

"I'm gonna have infinity infinity infinity infinity *gasp* infinity so many infinities that there are infinity infinities plus one cats"

What if I told you that you were dabbling in the transfinite ordinal numbers? So what are ordinal numbers? What does "transfinite" mean? And what does it mean to have a number one larger than another infinite number?

[Featuring: Sofía Baca; Diane Baca]

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This episode is released under a Creative Commons attribution sharealike 4.0 international license. For more information, go to CreativeCommoms.org

This episode features the song "Buffering" by "Quiet Music for Tiny Robots"

Join Sofía and Gabriel as they talk about Morikawa's recently solved problem, first proposed in 1821 and not solved until last year!

Also, if you haven't yet, check out our sponsor The Great Courses at thegreatcoursesplus.com/breakingmath for a free month! Learn basically anything there.

The paper featured in this episode can be found at https://arxiv.org/abs/2008.00922

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For more information, visit CreativeCommons.org!

[Featuring: Sofía Baca, Gabriel Hesch]

In this episode of Breaking Math, we dive deep into the transformative power of large language models (LLMs) like GPT-4 in the fields of chemistry and materials science, based on the article "14 examples of how LLMs can transform materials science and chemistry: a reflection on a large language model hackathon" by Jablonka et al. from the Digital Discovery Journal. Discover how AI is revolutionizing scientific research with predictive modeling, lab automation, natural language interfaces, and data extraction from research papers. We explore how these models are streamlining workflows, accelerating discovery, and even reshaping education with personalized AI tutors.

Tune in to learn about real-world examples from a hackathon where scientists used LLMs to tackle some of the most pressing challenges in materials science and chemistry—and what this means for the future of scientific innovation.

Keywords: GPT-4, large language models, AI in chemistry, AI in materials science, predictive modeling, lab automation, AI in education, natural language processing, LLM hackathon, scientific research, molecular properties, Digital Discovery Journal, Jablonka

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Robert Black is an author who has written a six-book series about seven influential mathematicians, their lives, and their work. We interview him and his books, and take a peek into the lives of these influential mathematicians.

Addendum: Hey Breaking Math fans, I just wanted to let y'all know that the second material science podcast is delayed.

[Featuring: Sofía Baca; Robert Black]

Physical objects are everywhere, and they're all made out of molecules, and atoms. However, the arrangement and refinement of these atoms can be the difference between a computer and sand, or between a tree and paper. For a species as reliant on tool use, the ability to conceieve of, design, create, and produce these materials is an ongoing concern. Since we've been around as humans, and even before, we have been material scientists in some regard, searching for new materials to make things out of, including the tools we use to make things. So what is the difference between iron and steel? How do we think up new things to make things out of? And what are time crystals? All of this and more on this episode of Breaking Math.

This episode is released under a Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. More information here: https://creativecommons.org/licenses/by-nc/4.0/

[Featuring: Sofía Baca, Gabriel Hesch; Taylor Sparks]

The world around us is a four-dimensional world; there are three spatial dimensions, and one temporal dimension. Many of these objects emit an almost unfathomable number of photons. As we developed as creatures on this planet, we gathered the ability to sense the world around us; and given the amount of information represented as photons, it is no surprise that we developed an organ for sensing photons. But because of the amount of photons that are involved, and our relatively limited computational resources, it is necessary to develop shortcuts if we want to simulate an environment in silico. So what is raytracing? How is that different from what happens in games? And what does Ptolemy have to do with 3D graphics? All of this and more on this episode of Breaking Math.

An interview with Dr. Sabine Hossenfelder about her second book Existential Physics. Sabine is host of the famous youtube show Science with Sabine. 

Join Sofia Baca and her guests Millicent Oriana from Nerd Forensics and Arianna Lunarosa as they discuss energy.

The sound that you're listening to, the device that you're listening on, and the cells in both the ear you're using to listen and the brain that understands these words have at least one thing in common: they represent the consumption or transference of energy. The same goes for your eyes if you're reading a transcript of this. The waves in the ears are pressure waves, while eyes receive information in the form of radiant energy, but they both are still called "energy". But what is energy? Energy is a scalar quantity measured in dimensions of force times distance, and the role that energy plays depends on the dynamics of the system. So what is the difference between potential and kinetic energy? How can understanding energy simplify problems? And how do we design a roller coaster in frictionless physics land?[Featuring: Sofia Baca; Millicent Oriana, Arianna Lunarosa]

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. Full text here: https://creativecommons.org/licenses/by-sa/4.0/

Christopher Roblesz is a math educator who, until the pandemic, worked as a teacher. It was his experiences during the pandemic, and his unwavering passion for preparing disadvantaged youth for STEM careers, that eventually led him to developing mathnmore, a company focused on providing an enriched educational experience for sstudents who are preparing for these careers.More on energy and entropy next time!All of this and more on this interview episode of Breaking Math!

[Featuring: Sofia Baca; Christopher Roblesz]

As you listen to this episode, you'll be exerting mental effort, as well as maybe exerting effort doing other things. The energy allowing your neurons to continually charge and discharge, as well as exert mechanical energy in your muscles and chemical energy in places like your liver and kidneys, came from the food you ate. Specifically, it came from food you chewed, and then digested with acid and with the help of symbiotic bacteria. And even if that food you're eating is meat, you can trace its energy back to the sun and the formation of the earth. Much of this was established in the previous episode, but this time we're going to explore a fundamental property of all systems in which heat can be defined. All of these structures had a certain order to them; the cow that might have made your hamburger had all the same parts that you do: stomach, lips, teeth, and brain. The plants, such as the tomatoes and wheat, were also complex structures, complete with signaling mechanisms. As you chewed that food, you mixed it, and later, as the food digested, it became more and more disordered; that is to say, it became more and more "shuffled", so to speak, and at a certain point, it became so shuffled that you'd need all the original information to reconstruct it: reversing the flow of entropy would mean converting vomit back into the original food; you'd need all the pieces. The electrical energy bonding molecules were thus broken apart and made available to you. And, if you're cleaning your room while listening to this, you are creating order only at the cost of destroying order elsewhere, since you are using energy from the food you ate. Even in industrial agriculture where from 350 megajoules of human and machine energy, often 140 gigajoules of corn can be derived per acre, a ratio of more than 400:1, the order that the seeds seem to produce from nowhere is constructed from the energy of the chaotic explosion from a nearby star. So why are the concepts of heat, energy, and disorder so closely linked? Is there a general law of disorder? And why does the second law mean you can't freeze eggs in a hot pan? All of this and more on this episode of Breaking Math.

Distributed under a CC BY-SA 4.0 License (https://creativecommons.org/licenses/by-sa/4.0/)

[Featuring: Sofia Baca; Millicent Oriana, Jacob Urban]

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Join Sofia Baca and Nerd Forensics co-host Jacob Urban as they discuss all things counting!

Counting is the first arithmetic concept we learn, and we typically learn to do so during early childhood. Counting is the basis of arithmetic. Before people could manipulate numbers, numbers had to exist. Counting was first done on the body, before it was done on apparatuses outside the body such as clay tablets and hard drives. However, counting has become an invaluable tool in mathematics itself, as became apparent when counting started to be examined analytically. How did counting begin? What is the study of combinatorics? And what can be counted? All of this and more, on this episode of Breaking Math.

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License (full text: https://creativecommons.org/licenses/by-sa/4.0/)

[Featuring: Sofia Baca; Jacob Urban]

The history of mathematics, in many ways, begins with counting. Things that needed, initially, to be counted were, and often still are, just that; things. We can say we have twelve tomatoes, or five friends, or that eleven days have passed. As society got more complex, tools that had been used since time immemorial, such as string and scales, became essential tools for counting not only concrete things, like sheep and bison, but more abstract things, such as distance and weight based on agreed-upon multiples of physical artifacts that were copied. This development could not have taken place without the idea of a unit: a standard of measuring something that defines what it means to have one of something. These units can be treated not only as counting numbers, but can be manipulated using fractions, and divided into arbitrarily small divisions. They can even be multiplied and divided together to form new units. So where does the idea of a unit come from? What's the difference between a unit, a dimension, and a physical variable? And how does the idea of physical dimension allow us to simplify complex problems? All of this and more on this episode of Breaking Math.

Distributed under a CC BY-SA 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/

[Featuring: Sofía Baca; Millicent Oriana, Jacob Urban]

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Join Sofía Baca and her guests, the host and co-host of the Nerd Forensics podcast, Millicent Oriana and Jacob Urban, as they explore what it means to be able to solve one problem in multiple ways.

This episode is distributed under a Creative Commons Attribution-ShareAlike 4.0 International License. For full text, visit: https://creativecommons.org/licenses/by-sa/4.0/

[Featuring: Sofía Baca; Millicent Oriana, Jacob Urban[

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Transcripts of this episode are avialable upon request.  Email us at BreakingMathPodcast@gmail.com. 

In this episode Gabriel Hesch interviews Taylor Sparks, a professor of material science and engineering, about his recent paper on the use of generative modeling a.i. for material disovery.  The paper is published in the journal Digital Discovery and is titled 'Generative Adversarial Networks and Diffusion MOdels in Material Discovery. They discuss the purpose of the call, the process of generative modeling, creating a representation for materials, using image-based generative models, and a comparison with Google's approach. They also touch on the concept of conditional generation of materials, the importance of open-source resources and collaboration, and the exciting developments in materials and AI. The conversation concludes with a discussion on future collaboration opportunities.

Takeaways

• Generative modeling is an exciting approach in materials science that allows for the prediction and creation of new materials.
• Creating a representation for materials, such as using the crystallographic information file, enables the application of image-based generative models.
• Google's approach to generative modeling received attention but also criticism for its lack of novelty and unconditioned generation of materials.
• Open-source resources and collaboration are crucial in advancing materials informatics and machine learning in the field of materials science.

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  How is Machine Learning being used to further original scientific discoveries?  

In this episode (part 1 of 2), I interview Brit Cruise, creator of the YouTube channel 'Art of the Problem.' On his channel, he recently released the video "ChatGPT: 30 Year History | How AI learned to talk." We discuss examples of intelligence in nature and what is required in order for a brain to evolve at the most basic level. We use these concepts to discuss what artificial intelligence - such as Chat GPT - both is and is not.

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Help Support The Podcast by clicking on the links below:

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Part 2/2 of the interview with Brit Cruise, creator of the YouTube channel "Art of the Problem," about interesting mathematics,, electrical and computer engineering problems. 

In Part 1, we explored what 'intelligence' may be defined as by looking for examples of brains and proto-brains found in nature (including mold, bacteria, fungus, insects, fish, reptiles, and mammals). 

In Part 2, we discuss aritifical neural nets and how they are both similar different from human brains, as well as the ever decreasing gap between the two. 

Brit's YoutTube Channel can be found here: Art of the Problem - Brit Cruise

Transcript will be made available soon! Stay tuned. You may receive a transcript by emailing us at breakingmathpodcast@gmail.com.

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We are joined today by content creator Levi McClain to discuss the mathematics behind music theory, neuroscience, and human experiences such as fear as they relate to audio processing. 

For a copy of the episode transcript, email us at BreakingMathPodcast@gmail.com.  

For more in depth discussions on these topics and more, check out Levi's channels at: 

Patreon.com/LeviMcClain

youtube.com/@LeviMcClain

Tiktok.com/@levimcclain

Instagram.com/levimcclainmusic

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Transcripts are available upon request. Email us at BreakingMathPodcast@gmail.com

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Summary

Levi McClean discusses various topics related to music, sound, and artificial intelligence. He explores what makes a sound scary, the intersection of art and technology, sonifying data, microtonal tuning, and the impact of using 31 notes per octave. Levi also talks about creating instruments for microtonal music and using unconventional techniques to make music. The conversation concludes with a discussion on understanding consonance and dissonance and the challenges of programming artificial intelligence to perceive sound like humans do.

Takeaways:

• The perception of scary sounds can be analyzed from different perspectives, including composition techniques, acoustic properties, neuroscience, and psychology.
• Approaching art and music with a technical mind can lead to unique and innovative creations.
• Sonifying data allows for the exploration of different ways to express information through sound.
• Microtonal tuning expands the possibilities of harmony and offers new avenues for musical expression.
• Creating instruments and using unconventional techniques can push the boundaries of traditional music-making.
• Understanding consonance and dissonance is a complex topic that varies across cultures and musical traditions.
• Programming artificial intelligence to understand consonance and dissonance requires a deeper understanding of human perception and cultural context.

Chapters

00:00 What Makes a Sound Scary

03:00 Approaching Art and Music with a Technical Mind

05:19 Sonifying Data and Turning it into Sound

08:39 Exploring Music with Microtonal Tuning

15:44 The Impact of Using 31 Notes per Octave

17:37 Why 31 Notes Instead of Any Other Arbitrary Number

19:53 Creating Instruments for Microtonal Music

21:25 Using Unconventional Techniques to Make Music

23:06 Closing Remarks and Questions

24:03 Understanding Consonance and Dissonance

25:25 Programming Artificial Intelligence to Understand Consonance and Dissonance

OpenAI's Sora, a text-to-video model, has the ability to generate realistic and imaginative scenes based on text prompts. This conversation explores the capabilities, limitations, and safety concerns of Sora. It showcases various examples of videos generated by Sora, including pirate ships battling in a cup of coffee, woolly mammoths in a snowy meadow, and golden retriever puppies playing in the snow. The conversation also discusses the technical details of Sora, such as its use of diffusion and transformer models. Additionally, it highlights the potential risks of AI fraud and impersonation. The episode concludes with a look at the future of physics-informed modeling and a call to action for listeners to engage with Breaking Math content.

Takeaways

• OpenAI's Sora is a groundbreaking text-to-video model that can generate realistic and imaginative scenes based on text prompts.
• Sora has the potential to revolutionize various industries, including entertainment, advertising, and education.
• While Sora's capabilities are impressive, there are limitations and safety concerns, such as the potential for misuse and the need for robust verification methods.
• The conversation highlights the importance of understanding the ethical implications of AI and the need for ongoing research and development in the field.

Chapters

00:00 Introduction to OpenAI's Sora

04:22 Overview of Sora's Capabilities

07:08 Exploring Prompts and Generated Videos

12:20 Technical Details of Sora

16:33 Limitations and Safety Concerns

23:10 Examples of Glitches in Generated Videos

26:04 Impressive Videos Generated by Sora

29:09 AI Fraud and Impersonation

35:41 Future of Physics-Informed Modeling

36:25 Conclusion and Call to Action

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Contact us at breakingmathpodcast@gmail.com

Summary

#OpenAiSora #