Infinite Debates

[Do not look here]

Okay, simple example. Although it's math simple, so might be tad... weird. Let me take older quote:

Okay, as Mage wrote, relationships between sets. Sets A and B got equal amount of elements, if there's a relationship between them that for EACH element of set A assigns EXACTLY ONE element from set B. Simple example: you've got set of two apples, yellow and red, and set of two children, boy and girl. Relation assigns red apples to girls and yellow to boys, SHAZAM, you can clearly see sets are equal in elements.

Here I've made the terrible mistake. It's obvious that there should be not only EXACTLY one element of set B assigned, as it only shows that set B has more elements than A. It must be exactly one element and no elements of set B may be out of relation

Now, take real intervals, for example [0;1] and [0;2], and Lebesgue's measure of them. Their measures - in this case length of interval - are, in order, 1 and 2.

Now take the natural numbers, there's no way you could "number" all those from [0;1] interval. You can number 0 as 1st, 1 as 2nd, now it gets tricky. You take 1/2 as 3rd, then 1/4 as 4th and 3/4 as 5th... and so on, and so on. The problem is, you can't find two real numbers that are one after another.
Take 0 and 0,000...****loadsofzeroes...0001. There's, for example, 0,000...****loadofzeroes...00005 between them. So you can divide them over and over again, never finishing, not even in infinity. That's the second, "bigger" type of infinity, the uncountable one.

You take now those intervals and set easy relation between them - for each x from [0;1] you take exactly 2x. That way for each element of first interval you assign exactly one element of second set and there's none left, so they are equal in amount of elements.

Still their measures differ.

 

[Splintert]

One thing that this 1:1 chance and infinite parallel worlds blah did make me think of (might be completely unrelated, but shall write it down anyways):

If there's an exact 50/50 chance of something happening in each universe, then half the Earths would get wiped down and destroyed this nanosecond by a huge meteorite, no? And the chances of them getting destroyed the next nanosecond would again be 50/50 (and so on and so on), which would leave relatively few Earths to pass around

Especially if Earth surviving throughout the whole span of time is 50/50 as well...

The infinity business would still leave it a bit questionable, seeing that since there being infinite options, even the amount of undestroyed Earths would be infinite. Same with the destroyed ones. One would think that ∞/∞ would be 50/50 (or 50:50 or 1:1 or however one would want to put it). But considering that infinity is NOT a number, you can't really go around treating it as one. Goin' with the 50/50 chance of getting destroyed every nanosecond, you wouldn't have very high chances of finding a universe with it intact in a few thousand years. Especially not a 50% chance.

What I'm getting at is pretty much a rewording of what Mage has been going at (at least as far as I've understood it), even if there's only two options of something happening (destroyed/not), it doesn't necessarily leave a strict 50% chance on everything.

I think I understand what you're both trying to say, but I'm trying to say that a lot of these universes fall under the set in which neither "desirable" or "undesirable" is the case.

If we take a single universe X, at time Y = 0 (the beginning of existence?), and begin spawning parallel universes off of it, for every single possible thing that happens its either a "yes it happened" or "no it didn't", upon which X will split into 2 more universes and time Y increments by some arbitrary value.

Leading up to Y = the release date of SimCity, and we have a split choice "LOD clipping good" and "LOD clipping bad". All of the universes that never reached the decision of "LOD clipping" are irrelevant to the ratio. The only universes that count are the ones that had the choice to make. It would be an extremely "small" subset of the set of all universes, even though its infinitely deep. Since the only ones that are counted in the ratio are the ones that were able to make the decision, and there are only two possible choices, half of the universes absolutely must be "desirable" and the other half "undesirable" unless there's a way to delete universes from existence.

If you instead take into consideration every single universe in the total complete set of universes, of course it won't be 1:1 because a "majority" of the infinite universes at time [release date of SimCity] + Y never had the chance to make the decision.

 

[Do not look here]

And you're still wrong. Even if we put aside the fact that parallel universes aren't created by yes-no decisions, but yes-no-anything between.

You HAVE to consider what happened before the decision.
You've said my example with three gates was wrong, but it wasn't. It was just taking in consideration what happened before. The problem is still 0-1, win-lose. The background of the problem is there are three gates.

What you are saying here, can be translated to this example like that: "Because one can win or loose, there's half the possibilities one won and half one lose. The fact there are three gates is irrelevant".

It's a problem made by sci-fi books explaining that parallel universes are like this scene is completely the same, except that I'm wearing red sneakers instead of leather shoes.
But that's not true, because that way they're not taking in account starting values. If every choice up to this point led to this situation, with me being myself, then why should I wear red sneakers? I don't like red and I don't even wear sneakers. But I like leather shoes. So as the infinity of trials go - that's the parallel universe one can say, whole probability space actually happening - in most of them I will wear leather shoes. Most, no 1:1 ratio, maybe slight variation of other boots.
You can say "but there might be universe where you like wearing red sneakers".
Yeah, so? If the guy standing there likes wearing red sneakers, then he's no longer me and it's no longer the same situation and those starting values never led to me choosing whether I will wear red sneakers or leather shoes. That's not the universe we're considering.

 

[Splintert]

We can't determine this from the perspective of our universe, the concept of "you" is nonexistent. You're looking in from the outside.

The only thing that matters is the non-sentient idea of "LOD clipping", whether it exists, and if its a good or bad thing. All variables are irrelevant except the one in question. Why should we have to take into consideration completely independent variables when we know every possible permutation of those variables exists?

 

[Do not look here]

Okay, I'm ending my participation here.

There's full of variables, like, for example, sheer existence of modern, sentient civilization that are not only NOT independent from the LOD clipping problem but will also largely influence the choice. You cannot take one point without considering that UNIVERSES that got so far had to go through other choices so far.

Saying that choice in LOD clipping problem is TOTALLY independent from preferences of civilization which makes the choice is plain stupid.
Because most of the civilizations which WOULD choose one of the ways, may be long nonexistent at the point when they could make the choice.

 

[Dryvus]

This looks like a thread worth avoiding.

Mage made it boring with all his "you can't do that"ing. He's like Dr. Crusher.

 

[Mage246]

Okay, I'm ending my participation here.

A wise decision. He seems a bit too thick for this.

 

[Splintert]

For the most part you're just saying "no you can't do that" and providing examples of unrelated cases.

If you can set up a situation that follows all of the necessary parameters, then we can discuss on the same terms.

 

[Dusk Voyager]

Re: mere choices vs. expected values/probabilities.

I agree with DnLH in this thread, but a move based on which one above is right still has no definite answer in some cases.