The Big Problem — the root cause of so many mistakes and fights and wasted resources — is the natural human tendency to imagine that beliefs are true or false. This is (almost always) wrong:
| Belief is a Knob Not a Switch! |
Outside of definitions and math (and even within much math) there are degrees of certainty, odds and likelihoods, ranges of numbers rather than specific answers, errors distributed across a zone, a universe of multiple possibilities.
When new information comes in — evidence — it's vital to update beliefs rather than throw them away. "Turn the Knob", more or less, based on the balance between the weight of prior knowledge and the strength of new data. That's Bayes Theorem, in a qualitative nutshell.
Don't be too sure!
(cf. Statistics - A Bayesian Perspective (2010-08-13), Introduction to Bayesian Statistics (2010-11-20), Fallibilism (2013-05-14), Adventure of the Bayesian Clocks - Part One (2013-12-04), Adventure of the Bayesian Clocks - Part Two (2014-01-05), ...) - ^z - 2017-07-03