I want to note that just because the probability is 0 for X happening does not in general mean that X can never happen.

A good example of this is that you can decide with probability 1 whether a program halts, but that doesn’t let me turn it into a decision procedure on a Turing Machine that will analyze arbitrary/every Turing Machine and decide whether they halt or not, for well known reasons.

(Oracles and hypercomputation in general can, but that’s not the topic for today here.)

In general, one of the most common confusions on LW is assuming that probability 0 equals the event can never happen, and probability 1 meaning the event must happen.

This is a response to this part of the post.

And while 0 is the mode of this distribution, it’s still just a single point of width 0 on a continuum, meaning the probability of any given effect size being exactly 0, represented by the area of the red line in the picture, is almost 0.

You’re right of course—in the quoted part I link to the wikipedia article for “almost surely” (as the analogous opposite case of “almost 0″), so yes indeed it can happen that the effect is actually 0, but this is so extremely rare on a continuum of numbers that it doesn’t make much sense to highlight that particular hypothesis.

I want to note that just because the probability is 0 for X happening does not in general mean that X can never happen.

A good example of this is that you can decide with probability 1 whether a program halts, but that doesn’t let me turn it into a decision procedure on a Turing Machine that will analyze arbitrary/every Turing Machine and decide whether they halt or not, for well known reasons.

(Oracles and hypercomputation in general can, but that’s not the topic for today here.)

In general, one of the most common confusions on LW is assuming that probability 0 equals the event can never happen, and probability 1 meaning the event must happen.

This is a response to this part of the post.

You’re right of course—in the quoted part I link to the wikipedia article for “almost surely” (as the analogous opposite case of “almost 0″), so yes indeed it can happen that the effect is actually 0, but this is so extremely rare on a continuum of numbers that it doesn’t make much sense to highlight that particular hypothesis.