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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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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. --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

#BLACKOUTDAY2020 George Perry Floyd was murdered by police on May 25, 2020. Learn more on twitter or your favorite search engine by searching #BLACKOUTDAY2020 --- Support this podcast: https://anchor.fm/breakingmathpodcast/support

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 --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

Join Gabriel and Sofía as they delve into some introductory calculus concepts. [Featuring: Sofía Baca, Gabriel Hesch] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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 · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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] --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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 --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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. This episode is distributed under a CC BY-SA 4.0 license (https://creativecommons.org/licenses/by-sa/4.0/) --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

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) --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

We've been doing this show for a while, and we thought it'd be fun to put out our first forty intros, especially since we passed 500,000 listens very recently. License: CC BY-SA 4.0 (creativecommons.org for more info) --- Support this podcast: https://anchor.fm/breakingmathpodcast/support

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.   License is Creative Commons Attribution-ShareAlike 4.0 (See https://creativecommons.org/licenses/by-sa/4.0/) --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support

A calendar is a system of dividing up time into manageable chunks so that we can reference how long ago something happened, agree on times to do things in the future, and generally just have a sense of reckoning time. This can be as simple as recognizing the seasons of the year, as arcane as the Roman Republican calendar, or as accurate as atomic clocks. So what are the origins of calendars? What is intercalation? And when is Easter? --- This episode is sponsored by · Anchor: The easiest way to make a podcast. https://anchor.fm/app Support this podcast: https://anchor.fm/breakingmathpodcast/support