Sunday, March 15, 2015

Discussing technical material ≠ arguing opinions

A problem of discussing [minimally] technical material with educated non-technical people is that they don't understand the difference between arguing opinions and discussing technical material.

This problem becomes much greater when the material is probability and when the example is something that the non-technical persons have been using for a while to assert their mastery of quantitative thinking.

Take, for example, the boy-girl problem: "one of two children is a boy, how likely is it that the other is also a boy?"

The right answer is one-half, though figuring that out requires some minimal understanding of probability, namely the difference between states and events and the mechanics of using prior and conditional probability to compute a posterior probability.

That computation is not the point.

The point is that even after this explanation, even in-person, some people think that they can argue for $1/3$. And that verb, "argue," is the problem.

Given a mathematical derivation yielding a result you don't like, the first step in a discussion of the result has to be pointing out the error in the derivation. My video does that for the $1/3$: the error is assigning "prior" probabilities after observing an event, in particular an informative event. (It's at the end of the computation because I need to introduce the basics of probability thinking first.)

But the people arguing for $1/3$ after that video never think they have to find the error; they either want both solutions to be valid (and don't understand why that's a problem, which is much more worrisome than not knowing how to think about probability) or appeal to some form of authority, like "I saw the $1/3$ on SciShow and they have millions of views" (which is an even bigger problem and one that is widespread, probably a consequence of how science is being popularized).

For a successful technological society, reality must take precedence over self-esteem, for nature cannot be fooled, paraphrasing a much smarter person (last sentence of report).