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?

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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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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?

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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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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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?

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?