Nov

15

 

Ignorance is preferable to error and he is less remote from the truth who believes nothing than he who believes what is wrong. — Thomas Jefferson (Notes On Virginia)

During my ongoing Bayesian spelunking, I have run across the idea of “complete ignorance” and “stated truth”.

Reading probability theory shows background to things we know.

  1. The differences between people who both claim to know nothing about a situation must be tested anyhow.
  2. The similarities in answers between people do not differentiate the volume of perspective.

Complete Ignorance:

One might think that such a thing is an important part of Probability Theory, alot like zero-ness.

But it seems nailing down what you do not know results in discovering things one does know. Discovering if a problem is location or scale or rotationally invariant provides an idea of what one does not know: that is, the problem itself encodes what you do not know.

And that complete ignorance may only be relative to the problem and not the observer (being dumb does not count in this exercise).

A full blown modeling of “complete ignorance” would create a starting point for building knowledge, but that is off in another realm of thinking.

Stated Truth:

As an experiment, one can play with meta-distributions of probabilities: Ap

P(A | Ap, X) = p

Ap means regardless of anything else you might have been told, the probability of A IS p

The net effect of this “rule” is: for new information to update the meta-distribution Ap, the probability of P(New | Ap) must have some slope effect to either narrow the distribution or provide some focus to the uniform.

The integrals are fun to play with, the regular case of arguing with someone who has an Ap distribution in his head we all know, his receptiveness to new ideas is mathematically predetermined, if the new information creates unwanted redefinition, there is no need to reprocess the meta-distribution. Dogma about Ap is different than knowing why Ap is relevant.


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