Yesterday's post concluded:

To form accurate beliefs about something, you really do have to observe it. It's a very physical, very real process: any rational mind does "work" in the thermodynamic sense, not just the sense of mental effort... So unless you can tell me which specific step in your argument violates the laws of physics by giving you true knowledge of the unseen, don't expect me to believe that a big, elaborate clever argument can do it either.

One of the chief morals of the mathematical analogy between thermodynamics and cognition is that the constraints of probability are inescapable; probability may be a "subjective state of belief", but the laws of probability are harder than steel.

People learn under the traditional school regimen that the teacher tells you certain things, and you must believe them and recite them back; but if a mere student suggests a belief, you do not have to obey it. They map the domain of belief onto the domain of authority, and think that a certain belief is like an order that must be obeyed, but a probabilistic belief is like a mere suggestion.

They look at a lottery ticket, and say, "But you can't prove I won't win, right?" Meaning: "You may have calculated a low probability of winning, but since it is a probability, it's just a suggestion, and I am allowed to believe what I want."

Here's a little experiment: Smash an egg on the floor. The rule that says that the egg won't spontaneously reform and leap back into your hand is merely probabilistic. A suggestion, if you will. The laws of thermodynamics are probabilistic, so they can't really be laws, the way that "Thou shalt not murder" is a law... right?

So why not just ignore the suggestion? Then the egg will unscramble itself... right?

It may help to think of it this way - if you still have some lingering intuition that uncertain beliefs are not authoritative:

In reality, there may be a very small chance that the egg spontaneously reforms. But you cannot expect it to reform. You must expect it to smash. Your mandatory belief is that the egg's probability of spontaneous reformation is ~0. Probabilities are not certainties, but the laws of probability are theorems.

If you doubt this, try dropping an egg on the floor a few decillion times, ign...

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