Probability, Statistics and Truth Part 1

Richard Von Mises (19 April 1883–14 July 1953) was a mathematician from Austria that moved to the United States during the second world war, participated in Austria’s aeronautical program during world war one and was a founder of modern probability.

He wrote a few books about probability in the 1930s that have laid a great foundation for current probability. This blog post in particular is about Richard’s book: Probability, Statistics and Truth.

One of the most interesting things about this book is the lack of mathematical notation. Almost every paper published to an academic journal or publication has tremendous amounts of notation. LaTeX is the markup used everywhere. This book reads much more like a think piece and is much more easy to approach. It reads as an interesting lecture that I wish I could have taken in school.

Another interesting thing I noticed is the comparison of words used in the book to modern statistical terminology. In his book Richard refers to what is now a “population” as the collective. This is interesting because it shows how the words have changed and how this field isn’t set in stone. Sometimes reading on mathematical topics it seems as if everything is written in stone and has a finality to it. Maybe because all modern papers tend to use the same terminology. It’s fascinating to see the growth of the field.

My biggest take away from this book so far is that in multiple parts of the book Richard mentions that probability really only works for large repeatable things and doesn’t work for one significant event.

Richard starts this off on page 10 being very straight forward that probability cannot apply to anything that does not repeat itself with a great number of uniform elements.

And again later on in the text Von Mises talks more about the limitations of probability and how it only applies to the collective and not to the probability of winning a battle because it’s a standalone instance and essentially not converging on the “law of large numbers”. This is on page 15:

Once more on page 18:

If you haven’t got the point he totally realizes that probability only works when there’s a large population in this case a “collective”. There is no probability without a collective.

This steps into the next concept introduced by Von Mises which is called the “impossibility of a gambling system” concept. He outlines that if you take a random subsequence of a dice roll or a coin flip you cannot build a system in which you can alter your selection to have desirable outcomes. E.g. A simple system of betting on heads every 3rd, 7th, or 21st toss, etc., does not change the odds of winning in the long run

This is by far one of the best math books I have ever read likely because of the prose and the nature of how Von Mises wants the readers to understand his topic and not just look on in awe at his mathematical notation.

I’m going to continue reading this book and have a part 2 or 3 and draw some of my own conclusions from the topics introduced above and dig further into the details Richard Von Mises shows us.

Originally published on:

https://thecompute.substack.com/

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