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Breaking Math Podcast

Breaking Math Podcast

By Breaking Math Podcast

Breaking Math is a podcast that aims to make math accessible to everyone, and make it enjoyable. Every other week, topics such as chaos theory, forbidden formulas, and more will be covered in detail. If you have 45 or so minutes to spare, you're almost guaranteed to learn something new!

SFTM, our umbrella organization, also has another (explicit) podcast called "Nerd Forensics" all about nerd (and other) culture. Check it out wherever you get podcasts!
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87. OpenAI Sora, Physics Informed ML, and Fraud- Oh My!

Breaking Math PodcastFeb 20, 2024

00:00
39:14
87. OpenAI Sora, Physics Informed ML, and Fraud- Oh My!

87. OpenAI Sora, Physics Informed ML, and Fraud- Oh My!

All episodes are available commercial free on patreon at

https://patreon.com/breakingmath

Transcripts will **soon** be posted to our new website at breakingmath.io or breakingmath.wtf. In the meantime, just send us an email at breakingmathpodcast@gmail.com and we’ll send you a transcript.


Open AI’s release of SORA has left many discussing the concept of Physics-informed Machine Learning. Specifically, how much physics of the real world can machine learning ‘learn’ (it is indeed strange to use that term) or demonstrate an understanding of similar to what OpenAi’s SORA has shown thus far.


There are currently fascinating debates and discussions happening on X (Twitter) among subject-matter experts in the field (see here https://x.com/drjimfan/status/1758549500585808071?s=61 and here https://x.com/nandodf/status/1759148460526219383?s=61.


In this multi-part series, we will be discussing how much physics SORA can (has?) learned, understood, and can use in a useful way for human users as well as research into other “Physics-Informed Machine Learning” approaches. We will be relying heavily upon the wonderful work of Dr. Steven Brunton, “@EigenSteve” on social media, who recently released this video on YouTube on an over-view of physics informed machine-learning.


Stay tuned! We will be going over a lot on this very important topic!

Feb 20, 202439:14
71: What's the Matter? An Interview with Chris Cogswell of the Mad Scientist Podcast (Material Science)

71: What's the Matter? An Interview with Chris Cogswell of the Mad Scientist Podcast (Material Science)

Matter is that which takes up space, and has mass. It is what we interact with, and what we are. Imagining a world without matter is to imagine light particles drifting aimlessly in space. Gasses, liquids, solids, and plasmas are all states of matter. Material science studies all of these, and their combinations and intricacies, found in examining foams, gels, meshes, and other materials and metamaterials. Chris Cogswell is a material scientist, and host of The Mad Scientist Podcast, a podcast that takes a critical look at things ranging from technological fads, to pseudoscience, and topics that deserve a critical eye. On the first of a pair of two episodes about material science, we interview Chris about his experience with studying material science, and ask questions about the subject in general.

Links referenced by Chris Cogswell:

- https://www.youtube.com/watch?v=bUvi5eQhPTc is about nanomagnetism and cool demonstration of ferrofluid

- https://www.youtube.com/watch?v=4Dlt63N-Uuk goes over nanomagnetic applications in medicine

- http://yaghi.berkeley.edu/pdfPublications/04MOFs.pdf Great review paper on new class of materials known as MOFs which are going to be very important in coming years

- https://www.youtube.com/watch?v=IkYimZBzguw Crash course engineering on nanomaterials, really good introduction to the field

- https://www.youtube.com/watch?v=t7EYQLOlwDM Oak Ridge national lab paper on using nano materials for carbon dioxide conversion to other carbon molecules

- https://www.youtube.com/watch?v=cxVFopLpIQY Really good paper on carbon capture technology challenges and economics

[Featuring: Sofía Baca, Gabriel Hesch, Meryl Flaherty; Chris Cogswell]

Apr 12, 202201:05:25
70.1: Episode 70.1 of Breaking Math Podcast (Self-Reference)

70.1: Episode 70.1 of Breaking Math Podcast (Self-Reference)

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]

Mar 20, 202246:40
70: This Episode Intentionally Left Blank

70: This Episode Intentionally Left Blank

This episode description intentionally left blank.

Mar 19, 202244:56
Season 4 Announcement (and a Rerun of Forbidden Formulas)

Season 4 Announcement (and a Rerun of Forbidden Formulas)

Hello, listeners! This is Sofia with an announcement.

Season 4 is about to start, and we have some great episodes planned. The last few weeks have been busy for us in our personal lives, and we apologize for our spotty release schedule lately. We're excited to bring you more of the content you've grown to love.

Today, we're going to have a rerun of our first episode on. This episode is a little rough at points, but we're choosing to rerun it because it captures the spirit of the podcast so elegantly. So, without further ado, here is Breaking Math episode 1: Forbidden Formulas.

[Featuring: Sofía Baca, Gabriel Hesch; Amy Lynn]

Feb 20, 202201:00:08
Rerun of P1: Peano Addition

Rerun of P1: Peano Addition

On this problem episode, join Sofía and guest Diane Baca to learn about what an early attempt to formalize the natural numbers has to say about whether or not m+n equals n+m.

[Featuring: Sofía Baca; Diane Baca]

Jan 27, 202234:12
69: An Interview with Michael Brooks, Author of "The Art of More: How Mathematics Created Civilization"

69: An Interview with Michael Brooks, Author of "The Art of More: How Mathematics Created Civilization"

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]

Jan 23, 202201:03:38
P12: O My God (Big O Notation)

P12: O My God (Big O Notation)

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]

Jan 04, 202223:52
68: LOL!!! SO RANDOM (Random Variables)

68: LOL!!! SO RANDOM (Random Variables)

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.

Interact with the hosts:
@SciPodSofia
@TechPodGabe

Or the guest:
@KampPodMillie

Patreon here: patreon.com/breakingmathpodcast

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]

Dec 23, 202135:51
67: Wrath of Math (Mathematics Used Unwisely)

67: Wrath of Math (Mathematics Used Unwisely)

Mathematics is a subject that has been used for great things over time: it has helped people grow food, design shelter, and in every part of life. It should be, then, no surprise that sometimes mathematics is used for evil; that is to say, there are times where mathematics is used to either implement or justify regressive things like greed, racism, classism, and even genocide. So when has math been used for destructive purposes? What makes us mis-apply mathematics? And why can oversimplification lead to devastation? All of this, and more, on this episode of Breaking Math.

Theme song is Breaking Math Theme by Elliot Smith of Albuquerque.

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

Dec 09, 202122:05
P11: Feeling Lucky? (Probability and Intuition)

P11: Feeling Lucky? (Probability and Intuition)

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]

Nov 30, 202132:56
66: Hayhoe, Let's Go! (An Interview With Climate Scientist Katharine Hayhoe)

66: Hayhoe, Let's Go! (An Interview With Climate Scientist Katharine Hayhoe)

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]

Nov 21, 202101:13:08
P10: Chivalry is Dead (Knights and Knaves #1)

P10: Chivalry is Dead (Knights and Knaves #1)

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]

Nov 14, 202122:15
65: An Interview with Author Ian Stewart (Book About Everyday Math)
Oct 24, 202148:19
64: What Projection Is This? (Map Projections)

64: What Projection Is This? (Map Projections)

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.

Sep 29, 202147:53
RR36: The Most Boring Episode Ever (Rerun: Math Games)
Sep 19, 202148:43
63: Broken Voting Systems (Voting Systems and Paradoxes)

63: Broken Voting Systems (Voting Systems and Paradoxes)

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.

Sep 05, 202133:03
62: The Atom Bomb of Information Operations (An Interview with John Fuisz of Veriphix)

62: The Atom Bomb of Information Operations (An Interview with John Fuisz of Veriphix)

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]

Aug 22, 202144:46
RR38: The Great Stratagem Heist (Game Theory: Iterated Elimination of Dominated Strategies)

RR38: The Great Stratagem Heist (Game Theory: Iterated Elimination of Dominated Strategies)

This is a rerun of one of our favorite episodes while we change our studio around.

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?

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

[Featuring: Sofía Baca; Diane Baca]

May 23, 202132:02
61: Look at this Graph! (Graph Theory)

61: Look at this Graph! (Graph Theory)

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]

Apr 25, 202129:20
P9: Give or Take (Back-of-the-Envelope Estimates / Fermi Problems)

P9: Give or Take (Back-of-the-Envelope Estimates / Fermi Problems)

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]

Apr 19, 202130:49
60: HAMILTON! [But Not the Musical] (Quaternions)

60: HAMILTON! [But Not the Musical] (Quaternions)

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]

Apr 03, 202128:35
59: A Good Source of Fibers (Fiber Bundles)

59: A Good Source of Fibers (Fiber Bundles)

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]

Mar 21, 202146:37
58: Bringing Curvy Back (Gaussian Curvature)
Mar 03, 202143:58
P8: Tangent Tango (Morikawa's Recently Solved Problem)
Feb 25, 202122:08
P7: Root for Squares (Irrationality of the Square Root of Two)

P7: Root for Squares (Irrationality of the Square Root of Two)

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]

Ways to support the show:

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brilliant.org/breakingmath Sign up at brilliant.org, where breaking math listeners get a 20% off of a year's subscription of Brilliant Premium!

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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.

Feb 07, 202116:16
57: You Said How Much?! (Measure Theory)

57: You Said How Much?! (Measure Theory)

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:

-Visit our Sponsors:   theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking here and signing up!   
brilliant.org/breakingmath Sign up at brilliant.org, where breaking math listeners get a 20% off of a year subscription of Brilliant Premium!

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

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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]

Feb 01, 202132:17
P6: How Many Angles in a Circle? (Curvature; Euclidean Geometry)

P6: How Many Angles in a Circle? (Curvature; Euclidean Geometry)

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:

-Visit our Sponsors:   theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking the link and signing up!          

 brilliant.org/breakingmath Sign up at brilliant.org, where breaking math listeners get a 20% off of a year subscription of Brilliant Premium!

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

Merchandise
Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast

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]

Jan 28, 202130:48
56: More Sheep than You Can Count (Transfinite Cardinal Numbers)

56: More Sheep than You Can Count (Transfinite Cardinal Numbers)

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?

Ways to support the show:

-Visit our Sponsors:   theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking the link and signing up!             

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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]

Jan 24, 202136:31
55: Order in the Court (Transfinite Ordinal Numbers)
Jan 14, 202133:46
54: Oodles (Large Numbers)
Dec 21, 202027:23
53: Big Brain Time (An Interview with Peter Zeidman from the UCL Institute of Neurology)
Dec 11, 202044:21
52: Round (Circles and Spheres)
Dec 05, 202031:08
P5: All Your Base Are Belong to Us (Fractional Base Proof)

P5: All Your Base Are Belong to Us (Fractional Base Proof)

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]

Nov 26, 202013:13
51: Episode "-2,0,1" (Bases; Exotic Bases)
Nov 15, 202034:30
50: Episode "101" (Bases)

50: Episode "101" (Bases)

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.

Aug 31, 202044:05
#BLACKOUTDAY2020

#BLACKOUTDAY2020

#BLACKOUTDAY2020

George Perry Floyd was murdered by police on May 25, 2020.

Learn more on twitter or your favorite search engine by searching #BLACKOUTDAY2020

Jun 03, 202008:45
49: Thinking Machines II (Techniques in Artificial Intelligence)

49: Thinking Machines II (Techniques in Artificial Intelligence)

Machines have been used to simplify labor since time immemorial, and simplify thought in the last few hundred years. We are at a point now where we have the electronic computer to aid us in our endeavor, which allows us to build hypothetical thinking machines by simply writing their blueprints — namely, the code that represents their function — in a general way that can be easily reproduced by others. This has given rise to an astonishing array of techniques used to process data, and in recent years, much focus has been given to methods that are used to answer questions where the question or answer is not always black and white. So what is machine learning? What problems can it be used to solve? And what strategies are used in developing novel approaches to machine learning problems? This episode is distributed under a CC BY-SA 4.0 license. For more information, visit CreativeCommons.org. For more Breaking Math info, visit BreakingMathPodcast.app [Featuring: Sofía Baca, Gabriel Hesch] References: https://spectrum.ieee.org/tag/history+of+natural+language+processing

Ways to support the show:

-Visit our Sponsors:       theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking the link and signing up!         brilliant.org/breakingmath Sign up at brilliant.org, where breaking math listeners get a 20% off of a year's subscription of Brilliant Premium!

Patreon Become a monthly supporter at patreon.com/breakingmath

Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast

May 26, 202056:03
48: Thinking Machines (Philosophical Basis of Artificial Intelligence)

48: Thinking Machines (Philosophical Basis of Artificial Intelligence)

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]

Ways to support the show:

-Visit our Sponsors:       theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking the link and signing up!         brilliant.org/breakingmath Sign up at brilliant.org, where breaking math listeners get a 20% off of a year's subscription of Brilliant Premium!

Patreon Become a monthly supporter at patreon.com/breakingmath

Merchandise Purchase a Math Poster on Tensor Calculus at our facebook store at facebook.com/breakingmathpodcast

May 18, 202058:06
P4: Go with the Flow (Conceptual Calculus: Related Rates of Change)

P4: Go with the Flow (Conceptual Calculus: Related Rates of Change)

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

[Featuring: Sofía Baca, Gabriel Hesch]

Ways to support the show:

-Visit our Sponsors:       theGreatCoursesPlus.com/breakingmath Get a free month of the Great Courses Plus while supporting this show by clicking the link and signing up!         brilliant.org/breakingmath Sign up at brilliant.org, where breaking math listeners get a 20% off of a year's subscription of Brilliant Premium!

Patreon Become a monthly supporter at patreon.com/breakingmath

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Mar 10, 202036:58
47: Blast to the Past (Retrocausality)

47: Blast to the Past (Retrocausality)

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]

Feb 29, 202030:33
RR30: The Abyss (Part One; Black Holes; Rerun)

RR30: The Abyss (Part One; Black Holes; Rerun)

Sofia is still recovering from eye surgery, so this will be a rerun. We'll probably be back next week.

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?

[Featuring: Sofía Baca, Gabriel Hesch]

Feb 18, 202053:36
P3: Radiativeforcenado (Radiative Forcing)

P3: Radiativeforcenado (Radiative Forcing)

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]

Feb 03, 202040:44
46: Earth Irradiated (the Greenhouse Effect)

46: Earth Irradiated (the Greenhouse Effect)

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]

Jan 20, 202042:28
45: Climate Denialism and Cranky Uncles (Interview with John Cook of Skeptical Science)

45: Climate Denialism and Cranky Uncles (Interview with John Cook of Skeptical Science)

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]

Dec 10, 201926:27
44: Vestigial Math (Math That Is Not Used like It Used to Be)

44: Vestigial Math (Math That Is Not Used like It Used to Be)

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]

Nov 03, 201937:25
P2: Walk the Dog (Calculus: Chain Rule)

P2: Walk the Dog (Calculus: Chain Rule)

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]

Oct 30, 201920:20
43: Interview II with Author Ben Orlin (Change is the Only Constant: the Wisdom of Calculus in a Madcap World)

43: Interview II with Author Ben Orlin (Change is the Only Constant: the Wisdom of Calculus in a Madcap World)

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

Oct 23, 201944:03
P1: Peano Addition
Sep 29, 201935:32
42: Maybe? (Probability and Statistics)
Aug 15, 201933:26