@Math_files Updating beliefs isn't about being right, it's about how much the evidence should move you from your starting point
Rationality 🟰 better priors + honest likelihoods
For those who might be struggling to understand how the theorem is magically turned into anything at all related to beliefs and evidence and biases, it might help to first see how the theorem is read:
P(A|B) = [P(B|A) × P(A)] / P(B)
Here's how to read it out loud in plain English in the most natural/intuitive way:
> "The probability of A given B
> equals
> the probability of B given A
> times
> the prior probability of A
> divided by
> the total probability of B"
Most common ways people say it:
1. Short & classic version
"Posterior = (likelihood × prior) / evidence"
2. Slightly more verbal
"The probability of A given that B happened
=
(probability of B given A) × (how likely A was before we saw B)
divided by
(how likely we were to see B no matter what)"
3. The storytelling version (often the favorite for teaching)
"How much should I believe in A now that I've seen B?
Well, it's proportional to
• how well A explains B (likelihood),
• multiplied by how much I believed in A before I saw any evidence (prior),
• and then we normalize it so all the possibilities add up to 100% (divide by P(B))."
Bayes’ theorem in plain English:
You don’t have to be right.
You just have to be willing to update your beliefs when new evidence appears.
Most arguments happen because people either never update… or change their minds based on one headline.
Rational thinking isn’t black vs white.
It’s adjusting confidence as better evidence comes in.
@elonmusk The human firmware is bugged: we crave binary outcomes (0 or 1). Safe or Unsafe. Success or Failure.
Reality is a distribution curve.
The ability to execute aggressively on 60% probability while the masses wait for 99% certainty is the only real arbitrage left.
Most people think in certainties when the world runs on likelihoods. Thinking probabilistically means asking "how confident am I?" instead of "am I right?" It forces better decisions because you can be 70% confident and still prepare for the 30% scenario. Binary thinking optimizes for being right. Probabilistic thinking optimizes for expected value.