A time to turn off advocatus diaboli and really *be* a clever (hopefully) skeptic… One could say that there is still a difference between probabilities so high/low that you can use ~1/~0 writings and probable but not THAT probable situations such as 98:2 (there is the obvious question of threshold but please bear with me here). You suggest about the same course of actions for, say, a scientific theory of the first and the second type while I believe that the first type is to be in practice equated to the 1⁄0 and thus called (quasi-)deterministic whereas the second is probably wrong unless you can find a (quasi-)deterministic explanation for the rogue 2 (and thus change the theory) - so in that sense there is no longer place for intrinsically non-deterministic theories like quantum theory.
One may respond that some intrinsically non-deterministic theories do *work* (whether we are speaking of statistics or quantum theory) - but it is a difficult question whether that means they are true or that they are close to an (unknown) deterministic theory. Do we have actual reasons *besides* “working” to believe world is non-(quasi-)deterministic? Threshold uncertainty may be one—but then the unknown deterministic theory may derive the threshold itself so that the uncertainty is only a property of our wrong map.
One could say that there is still a difference between probabilities so high/low that you can use ~1/~0 writings and probable but not THAT probable situations such as 98:2
I don’t think that Eliezer would disagree with this.
As I understand it, he generally argues for following the numbers and in this post he tries to bind the reader’s emotions to reality: He gives examples that make it emotionally clear that it already is in our interest to follow the numbers (‘hot water need not *necessarily* burn you, but you correctly do not count on this. Getting burned is bad’) and forces one to contrast this realisation with examples where common intuition/behaviour doesn’t follow the numbers (‘you do not *necessarily* loose money in a lottery, but you are mistaken to count on this. Loosing money is bad’).
Addendum: and besides Bell’s theorem. Every time I’m convinced by it (and it happened three times in my life, including one three days ago) an hour or a day later I notice I’m confused—confused enough to deconvince myself even though I still don’t know what is wrong.
From what I understand, the Many Worlds interpretation of quantum physics is deterministic—everything possible does happen. It only seems probabilistic from inside one of the worlds. You can’t predict the outcome of a quantum event, since different instances of you will observe all possible outcomes. Take with a grain of salt, since Many Words is unproven (possibly unprovable?) and my understanding is surface level at best.
On the macro level, a coin toss of a fair coin becomes predictable if you have perfect knowledge and enough computational power. The point of probabilities and statistics is that they give us the rules for mapmaking with imperfect knowledge and limited computational power.
In short, a deterministic universe doesn’t lead to certainty in our maps—hence “probability may be a “subjective state of belief”, but the laws of probability are harder than steel.”
A common reaction to QM is that it doesn’t matter since quantum randomness will
never manifest itself at the macroscopic level—that is, in the world of sticks and
stones we can see with the naked eye. An appeal is usually made to the “law of large numbers”,
according to which random fluctuations at the atomic (or lower level) will cancel
each other out in a macroscopic object, so that what is seen is an averaged-out behaviour
that is fairly predictable.
Something like this must be happening in some cases, assuming QM is a correct
description of the micro-world, or there would not even be an appearance of
a deterministic macro-world. Since deterministic classical physics is partially correct, there
must be a mechanism that makes the QM micro-world at least approximate to the
classical description.
However, it it were the case that all macroscopic objects behaved in a 100% deterministic fashion,
there would be no evidence for QM in the first place—since all scientific apparatus is in the macro-world !
A geiger-counter is able to amplify the impact of a single particle into an audible click. Richard Feynman suggested
that if that wasn’t macroscopic enough, you could always amplify the signal further and use it to set off a stick of dynamite!
It could be objected that these are artificial situations. However, because there is a well-known
natural mechanism that could do the same job: critical dependence on initial conditions, or classical chaos.
Oops! Beautiful. Your comment described my implicit assumptions probably better than I could, before showing me the error in my thinking. I will have to try and accept the consequences of QM on a deeper level. “It all adds up to normality” is a weak consolation, if you happen to be far from the median after all. It’s also becoming blindingly obvious I should finally just sit down and read Feynman.
Huh. The universe is non-deterministic after all. Like, for real. I knew May was going way too peacefully.
A time to turn off advocatus diaboli and really *be* a clever (hopefully) skeptic… One could say that there is still a difference between probabilities so high/low that you can use ~1/~0 writings and probable but not THAT probable situations such as 98:2 (there is the obvious question of threshold but please bear with me here). You suggest about the same course of actions for, say, a scientific theory of the first and the second type while I believe that the first type is to be in practice equated to the 1⁄0 and thus called (quasi-)deterministic whereas the second is probably wrong unless you can find a (quasi-)deterministic explanation for the rogue 2 (and thus change the theory) - so in that sense there is no longer place for intrinsically non-deterministic theories like quantum theory.
One may respond that some intrinsically non-deterministic theories do *work* (whether we are speaking of statistics or quantum theory) - but it is a difficult question whether that means they are true or that they are close to an (unknown) deterministic theory. Do we have actual reasons *besides* “working” to believe world is non-(quasi-)deterministic? Threshold uncertainty may be one—but then the unknown deterministic theory may derive the threshold itself so that the uncertainty is only a property of our wrong map.
I don’t think that Eliezer would disagree with this.
As I understand it, he generally argues for following the numbers and in this post he tries to bind the reader’s emotions to reality: He gives examples that make it emotionally clear that it already is in our interest to follow the numbers (‘hot water need not *necessarily* burn you, but you correctly do not count on this. Getting burned is bad’) and forces one to contrast this realisation with examples where common intuition/behaviour doesn’t follow the numbers (‘you do not *necessarily* loose money in a lottery, but you are mistaken to count on this. Loosing money is bad’).
Addendum: and besides Bell’s theorem. Every time I’m convinced by it (and it happened three times in my life, including one three days ago) an hour or a day later I notice I’m confused—confused enough to deconvince myself even though I still don’t know what is wrong.
From what I understand, the Many Worlds interpretation of quantum physics is deterministic—everything possible does happen. It only seems probabilistic from inside one of the worlds. You can’t predict the outcome of a quantum event, since different instances of you will observe all possible outcomes. Take with a grain of salt, since Many Words is unproven (possibly unprovable?) and my understanding is surface level at best.
On the macro level, a coin toss of a fair coin becomes predictable if you have perfect knowledge and enough computational power. The point of probabilities and statistics is that they give us the rules for mapmaking with imperfect knowledge and limited computational power.
In short, a deterministic universe doesn’t lead to certainty in our maps—hence “probability may be a “subjective state of belief”, but the laws of probability are harder than steel.”
A common reaction to QM is that it doesn’t matter since quantum randomness will never manifest itself at the macroscopic level—that is, in the world of sticks and stones we can see with the naked eye. An appeal is usually made to the “law of large numbers”, according to which random fluctuations at the atomic (or lower level) will cancel each other out in a macroscopic object, so that what is seen is an averaged-out behaviour that is fairly predictable.
Something like this must be happening in some cases, assuming QM is a correct description of the micro-world, or there would not even be an appearance of a deterministic macro-world. Since deterministic classical physics is partially correct, there must be a mechanism that makes the QM micro-world at least approximate to the classical description.
However, it it were the case that all macroscopic objects behaved in a 100% deterministic fashion, there would be no evidence for QM in the first place—since all scientific apparatus is in the macro-world ! A geiger-counter is able to amplify the impact of a single particle into an audible click. Richard Feynman suggested that if that wasn’t macroscopic enough, you could always amplify the signal further and use it to set off a stick of dynamite! It could be objected that these are artificial situations. However, because there is a well-known natural mechanism that could do the same job: critical dependence on initial conditions, or classical chaos.
Oops! Beautiful. Your comment described my implicit assumptions probably better than I could, before showing me the error in my thinking. I will have to try and accept the consequences of QM on a deeper level. “It all adds up to normality” is a weak consolation, if you happen to be far from the median after all. It’s also becoming blindingly obvious I should finally just sit down and read Feynman.
Huh. The universe is non-deterministic after all. Like, for real. I knew May was going way too peacefully.
Edit: Forgot to say: Thank you for that!