I have a new math chalk talk up: The Game of Infinity Questions.
This is back to establishing the “reasonableness” of Kolmogorov’s Axiom of continuity (in his actual formulation of his axiomatization of probability).
Remember, his argument is “it is a bit off to have strong opinions on infinite processes, as we will never live to see one.” So he argues, “let’s pick axioms that make infinite processes look a lot like finite ones, as you will never know the difference.” This can fail. Not all things that are true
in the finite case can hold in the infinite case, we get contridictions if we so try. So what one picks as the “obvious properties to keep” completely changes what properties we are ascribing to infinite sets and infinite processes. So the games is: show try to show the alternative to what you want looks awful.
In the game of infinity questions, we try to eliminate probability distritutions where limits are not respected.
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Categories: Mathematics Tutorials
jmount
Data Scientist and trainer at Win Vector LLC. One of the authors of Practical Data Science with R.