Sunday, January 15, 2023

Logical Isomorphism Example: Probability and Calculus

I sometimes talk about logical isomorphism but keep forgetting to provide good examples.

Claim: probability as chance is a limit approximation, like Newtonian physics is an approximation of physics where c = ∞ and ħ = 0. 

The logic that proves probability isn't real is isomorphic to the epsilon-delta definition of a limit. (Bit of fun meaningless recursion there.)

Anything which proves probability is inherently a real thing will also nuke the definition of a limit. Every piece of evidence that the epsilon-delta definition works also supports probabililty-as-approximation. (Certainly makes my job a lot easier, what with all the work having already been done.)

Studying epistemology to obtain certainty* is largely about learning and spotting these isomorphisms. Logic stops being about object propositions and becomes about logical relationships. (Spot the masculine/feminine lunar/solar isomorphism.) Displacing any particular object merely replaces it with dark matter that has to be there due to the relationship web surrounding it, leading to robust understanding and robust models.

*(predictions with probability within epsilon of 100%)

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