Making Probability Mathematical | Infinite Series

Find out the players probability of winning based on their current score (Link referenced at 2:24):

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Previous Episode

Written and Hosted by Kelsey Houston-Edwards
Produced by Rusty Ward
Graphics by Ray Lux
Assistant Editing and Sound Design by Mike Petrow

Resources and Special thanks:

Kolmogorov - Foundations of the Theory of Probability
Ian Hacking - The Emergence of Probability

Throughout much of human history, people consciously and intentionally produced randomness. They frequently used dice - or dice-shaped animal bones and other random objects - to gamble, for entertainment, predict the future and communicate with deities. Despite all this engagement with controlled random processes, people didn’t really think of probability in mathematical terms prior to 1600. All of the ingredients were there -- people had rigorous theories of geometry and algebra, and the ability to rig a game of dice would have certainly provided an incentive to study probability -- but, there’s very little evidence that they thought about randomness in mathematical terms.

Challenge Winner:

Zutaca

Comments answered by Kelsey:

Ja-Shwa Cardell

[flymypg]

THANK YOU for discussing probability WITHOUT mentioning statistics!

Probability and statistics are often lumped together as if they formed one big word. Addressing each separately is necessary before we can realize the immense power inherent in using them together.

[minewarz]

*Me thinking*
Yes, summer vacations, no school for weeks!

Now let's watch a video about mathmatics...

[ComputerNerd]

speaking of measure theory I went to the barber yesterday.

he asked me what kind of haircut I wanted and I replied "give me the cantor set"

I am now bald

[BabelRedeemed]

I love explanations of how thinking tools we're invented. The dice-leading-to-probability story is gem for intellectual history, and a great example of a philosophical technology.

[Melomathics]

Your take on Gödel's incompleteness theorems would be interesting.

[heliguerrero]

Yes! Probability is my favourite field of math!
What I love about it is the implications of some of its results are amazing! Specially when applied to other fields of math, other sciences and even real life.
For example, Central Limit Theorem and the Law of Big Numbers. Things that happen at random can have clear patterns with rational thinking and, why not, a bit intuition.
(Though I guess all of my comment can be applied to Mathematics in general)

[iamstickfigure]

Poor Pascal. He must have been unaware of other religions around the world. Lol.

[NunoTiagoMartins]

Regarding ideas for future episodes, how about diving into Bachelier’s work on Mathematical Finance, Black-Scholes, etc? I know it’s heavy stuff but you guys manage to come up with such easy ways to explain really complex topics I’d be interested to see your take on that :) Thanks For the amazing work!

[AlejandroBravo]

The solution in the description is really curious, cause the probability for each one to win does not depend on how many points they need to get (I mean, it doesen't matter if they need to get 10 or 1000) as long as the points each of them need is the same; the probability each one has to win just depend on how many more points they need to win
(It would be the same if they were 8 to 7 and they need to get 10, than if they were 98 to 97 and the goal was 100)

[bestnocture]

The thing I love about probability is that you can use it anywhere you aren't certain of the outcomes, you can determine what is most possible and what is not, also, I think this is why we use probabilistic models to describe the quantum world.

[hellodarknessmyoldfriend]

can u please make a video dealing with partial differential equations, I'm taking that course in a week so it might be nice if I could see an introduction by this incredible channel.

[ondrejkubu]

You should make a video on Bayes' Theorem. It is crucial for the understanding of the scientific method.

[rkpetry]

Probable, also means probe-able, testable, deterministic (which is generally taken as an antonym when meant totally), e.g. Can you probe a jar for cookies, depends on whether your hand fits its mouth, whether there are cookies in the jars, etc. This is mathematics: that statements are logical, and, arithmetical, and the consistency is left as homework...

[robharwood]

Since this video was about probability, and you mentioned that we want to make decisions rationally, I suggest doing a deeper exploration into this topic in a future video, and especially address Bayes' Theorem and Bayesian Reasoning.

In particular, the host, Kelsey, may enjoy reading E.T. Jaynes' book "Probability Theory: The Logic of Science", which develops a framework for Bayesian reasoning from the ground up. I'm currently watching a video lecture series 'reading course' of Jaynes' book, which helps lower the slope of the learning curve of the book. Search YouTube for 'Aubrey Clayton' or 'Probability Theory: The Logic of Science' to check it out. BTW: Jaynes, following R.T. Cox, develops the laws of probability *without* axioms, instead relying on an informal list of 'desiderata' which he formalizes in a general way, showing that Probability Theory is the *only* valid mathematical way to reason about 'plausibility'. This is an interesting alternative to Kolmogorov, and does not rely on Measure Theory.

[Petch]

Thank for all the good you do.

I would like to learn more about
1. linear algebra (matrix calculations, algorithms, egen values, egen vector and so on)
2. fft or discrete fft (way and how it works, how to preserve amplitudes and so on)
3. approximating curves with sums of sin functions (how to kompres images using sums of sin)

I know these are topics for engeners and I use some of them every day. But I only know them good enough to used dem. I want to have a better understanding of them. And I believe these are topics many people would benefit from know.

Have a nice day.

[simpleprogrammer]

Gerolamo Cardano who lived in the first half of the 16th century and known as the first to publish methods that solved reduced cubics also expressed probability by ratio

[CacchiusMan]

For now my favourite part of probability theory is the existence of limit theorems, for series of indipendent or dependent variables. it's really curious to see how in the long run even random behaviors tend somehow to something stable. Plus stochastic process on their own are interesting for resolving PDE sometimes, as far as i know.

[mikeguitar]

I think the sort of numbers that engineers and physicists use, with a "margin of error", and "significant digits", imply a 1-dimensional interval, at least on the marginal part.

The way that mathematicians use transcendental numbers, like "Real" decimals, seems analogous to the physics of wave-particle duality. A photon travels as a (higher dimensional) wave but interacts as a particle (at a 0-D point). Similarly a transcendental decimal transcends 0-dimensions and like a wave it can potentially intercept a range of points. Sure it may collapse to a single point, but this is a bit like the wave function collapsing. It's very interesting the way both of these examples cross dimensions, so to speak. It definitely serves a particular purpose in this way.

[Bdoserror]

Did anyone else notice that the dice @6:10 are flawed? Opposite sides are supposed to add to 7 (1-6, 2-5, 3-4) but they have 5 and 6 opposite each other.

[xXVtalXx]

What is the probability that Kelsey is wearing that wedding ring to diminish the probability of random internet math nerds proposing?