[perl4ever]

"There is always an infinite range of possible states of nature"

Well, I think that is definitely and unambiguously false. The universe is not infinite, nor infinitely divisible, as far as we know, and the number of future states of any particular person (or humanity) are even smaller than those of the universe. Limits in time mean limits in space, and limits in space mean limits in particles and possibilities.

I'm not sure I can make a case that it matters, but if it doesn't matter, why say infinite?

[jbay808]

I guess this is a tangent. First of all my point really doesn't hinge on the infinity; it can be finite (but really big) but regardless, whenever you apply minmax you must first crop your decision space to a probability threshold, or else you'll make nonsensical decisions based on what gives the best outcome if the sun should happen to explode.

But secondly, I think (although I'd happily concede if convinced otherwise) that the space of possible scenarios really is infinite, even if the observable universe is not. The space I'm talking about is not the actual state space of the universe, which in some interpretations of physics might be finite or even unitary. It spans the space of hypothetical universes that are all consistent with your information with nonzero probability, which I think is probably infinite, but again, if it's not infinite that's a technicality. If you include the states that have with zero probability (because why not? GGP was advocating that the probability is irrelevant to minmax decisions) then the space is definitely infinite, because even physically impossible states of nature will impact our decision making.

[brownbat]

Another way to conceptualize the "cropping" is to get rid of all future states where planning would have been meaningless anyway.

We are momentary Boltzmann brains? We'll assume not, because if so, nothing really matters.

Trivial difference, but that avoids potentially difficult threshold problems and cousins of the St. Petersburg paradox or even Pascal's mugger, at the risk of being slightly more hand wavy.

Arguably an aesthetic distinction at this point, I generally think your description and approach are right.

[6gvONxR4sf7o]

>Well, I think that is definitely and unambiguously false. The universe is not infinite, nor infinitely divisible, as far as we know...

This seems wrong. We don't know whether the universe is infinitely divisible.

See this for a nice discussion: https://physics.stackexchange.com/questions/33273/is-spaceti...

[perl4ever]

I think it's sophistry to pretend we haven't any more idea of that since pre-Democritus. Thousands of years of science has shown that infinities are always a problem in our heads, with our theories. Does that prove they don't exist? No more than it's proven that the sun will come up tomorrow, I guess.

[jbay808]

Just to be clear why this whole conversation thread is a TypeError, let's say I assign a probability of 99.9% to the hypothesis that the state space of the universe is finite, and 0.1% to the state space of the universe being infinite...

... In that case, how big is my hypothesis space about possible states of the universe?

[sooheon]

If you had a blog of thoughts along these lines I’d subscribe.

[jbay808]

Not as of yet but hopefully soon! Thanks for the encouragement =)

[perl4ever]

What if you assign a probability of 0.1% to the possibility of 2 + 2 = 5?

[jbay808]

Then you might have this experience: https://www.lesswrong.com/posts/6FmqiAgS8h4EJm86s/how-to-con...

[krastanov]

There are plenty of examples of inifinities that are not problematic. Infinitely small wavelengths make our current understanding of physics break down, indeed. Or maybe infinitely divisible solids that lead to paradoxes like Banach-Tarski's. On the other hand, infinitely dimensional configuration spaces or continuous parameterization (e.g. coordinates, field strengths, phases) are trivial unoffensive parts of classical and quantum mechanics.

[earthboundkid]

So you agree with Aristotle that there are only potential infinities, no actual infinities?

Do you agree with Aquinas’ corollary, that absent an actual infinity, there must be some First Cause, which we call God?

[dragonwriter]

> Do you agree with Aquinas’ corollary, that absent an actual infinity, there must be some First Cause, which we call God?

Note that even if you agree with Aristotle’s position, which is essentially an arbitrary assumption, and the corollary that there must then be a first cause, there's nothing except the boat of being stepped in a particular religious tradition to suggest that the first cause should have any of the other traits of any particular concept of God. It works just as well to take the earliest known thing on the sequence of causes and say “this cause is uncaused”.

[tsimionescu]

In modern times, we actually call it Big Bang.

[earthboundkid]

Aquinas' argument is that there can't be an actual infinity, so even though it appears that everything has a prior cause, it must be that there is something which is self-causing. "The Big Bang" qua event clearly didn't cause itself (events only cause events that are later in time), so the typical way to cash this out is "the Big Bang" qua set-of-physical-laws is self-causing.

This leads to a new problems (why this set of laws vs. some other), unless you posit that the laws are somehow perfect or necessary (which is essentially Deism), but the laws of our universe seem to be contingent (lots of unexplained physical constants).

You can make a metaphysically plausible case of a Big Bang-Big Crunch cycle that goes on forever, but then you're back to believing in an actual infinity.

[dragonwriter]

> This leads to a new problems (why this set of laws vs. some other), unless you posit that the laws are somehow perfect or necessary

Those problems are only problems with the aesthetic preference that the universe be perfect or necessary. Once you accept that the universe can be without adhering to any such aesthetic preference, they cease to be problems.