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SaltyDangerHands t1_jc936do wrote

You have to make a few assumptions to get to "yes". Not only is the universe infinite, but so too is the proliferation of matter, the density and variety, etc. Everywhere has to have had the same amount of "when" too, and who knows how that works or whether the universe exists as a static infinity or a growing one. Our sphere of observation would indicate the former, but we can't really say what fraction of the universe, if it's anything other than infinite, we might see.

But if all of that holds true, then no matter how unlikely this exact configuration of not only matter but also events is to reoccur, it does so an infinite number of times. No matter what the number is, the one in however many trillions of trillions chance of it happening, the opportunity to do so remains "infinity", and that's what the whole expression about monkeys and type-writers means.

It's not really something do we do well with, conceptually. Our brains don't really do "infinity", it was at no point a factor in our evolution and trying to imagine it is probably only something widely attempted over the last two hundred years, we're not equipped to do it. The math makes sense, but the imagination can't follow that road. I mean, unless you're Einstein or Newton or some shit, seems like they did exactly that sort of thing.

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dasBergen t1_jc95kc0 wrote

What about the digits of pi? They do not repeat yet they are infinite.

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SaltyDangerHands t1_jcbdgu8 wrote

Alright, there's a bit to unpack here and I apologize if I explain something that doesn't need to be explained.

The digits of pie all repeat, and in fact, as near as we can tell, do so infinitely.
There are an infinite number of 9's in pie. There are an infinite number of 5's.

What they don't have is a pattern. And that's fine. No one said there had to be pattern. But any sequence of numbers, 123, 6845436, 666, whatever, will not only show up eventually, but if pie is truly infinite, will repeat an infinite number of times. Just not in a pattern.

And no one said it had to be a pattern, in fact, it would be weird if it was. Pie is not a pattern, but somewhere in there, or rather an infinite number of "somewhere's" in there, can be found every sequence of digits, of any length. I can rattle off a ten-thousand place number, it's in there, somewhere. Probably.

I'm not a mathematician, and pie might not follow the true rules of randomness that would otherwise govern something like this, so maybe there aren't a thousand 9's in a row in pie because of the rules of the equation from which it's derived, but there are definitely an infinite number of 9's.

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dasBergen t1_jccfcue wrote

You are saying earth (the variables that brought about earth, etc.) are a piece of the infinite universe, and so can be found in multiple places. I'm arguing that what set the earth in motion was not in fact a separate piece, but is the entire thing. If the moon had slightly more or less mass, the tides would have been different, if Jupiter was not exactly where it is, the meteors that created the moon would have impacted differently, if our neighboring stars had a different make up, the heavy elements necessary for life would not have been prevalent in this part of the galaxy, if our neighboring galaxy was drifting away instead of gravitationally locked with ours the spin of our galaxy would be altered and we may have been in the wrong part of space to gather the elements necessary... Earth is not one of an infinite number of unrelated 5s in an endless string of random digits, earth is a 5 in the 6728th position and any alteration anywhere along the string of digits alters every adjacent digit and propagates through the entire string. So in order to find a second earth, you would need an exact copy of the entire universe, you would need pi to repeat.

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SaltyDangerHands t1_jccjglk wrote

Ok, well, I think you're wrong about a lot of that.

A recreation of just the solar system would do. What Andromeda is doing, or any other galaxies, or hell, most of the milky way, is kind of irrelevant to the Earth. Nothing happening in one of the other spiral arms is making a difference here.

And it has nothing to do with pi. That's... I don't know where you're getting that. Pi is for the geometry of circles.

It's dead simple. The odds of recreating the entire solar system is 1 / an unimaginably huge number. Whatever that unimaginably huge number is, it still fits into infinity an infinite number of times. In an infinite universe, therefor, you get an infinite number of identical solar systems, be they earth's or literally any (every) other solar system.

This isn't my idea or conclusion, either; this is a generally accepted consequence of infinity. In a truly infinite universe, every event, no matter how improbable, HAS TO happen an infinite number of times. They can be separated by great distances of space and time, but they do happen, they never stop happening, they're infinite too.

Getting lost in the symbolism or the examples is, forgive me, kind of pointless. They're only value is in helping illustrate, and any flaws in those metaphors is kind of irrelevant to flaws in the actual nature of infinity. Pi is just that, relative to this conversation, an example, a way to explain how infinity works, it's not at all relevant otherwise.

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dasBergen t1_jcd5k4m wrote

Yes, our disagreement is that "an exact replica of earth" is possible without the exact universe we have.

I do not dispute that in an infinite universe anything that can happen has happened.

I just don't think that an exact replica is one of the things that can happen.

Let me put it this way, when does exact earth stop being exact? Light from 14 billion years ago is reaching the earth just now to inform our astronomers about the early universe, if that history is not a part of your 'copy' of earth, then your earth's astronomer is different than the ones here, your earth is different. So our observable universe is necessary to copy earth. But to copy our observable universe, everything that universe can observe is necessary, and so on.

You say Andromeda is irrelevant, but our history is filled with usages of Andromeda to inform ourselves what our galaxy may look like, the pull from our galaxy on Andromeda informs us of the mass of our galaxy, Andromeda contains several important stars we use as standard candles... So yes, I think life happened, humans probably happened, a moon, a 8/9 planet solar system happened, but not an exact replica.

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SaltyDangerHands t1_jcdi70w wrote

I feel like you fundamentally misunderstand my point, which I should remind you isn't even my point but instead a generally accepted property of infinity. It's literally "an infinite number of monkeys on an infinite number of typewriters", this is the exact sort of thing that saying is about.

Nothing you've said is downright impossible, so straight up mathematically, as in "we can prove this with math" and not "this is a difference of equally credible opinions", that makes it eventual. Do the stars and shapes in the sky need to match? That's less probable, only, not impossible, so it STILL happens an infinite number of times. There are an infinite number of exactly-like-earth copies staring at an infinite number of identical-to-ours-skies because that's ONLY fantastically unlikely, not impossible, and given an infinite number of opportunities to happen, it will, according to the math, according to presently considered "proven" properties of infinity, happen an infinite number of times.

I am trying to be super clear here, we do not disagree, you are simply wrong. You can believe or not believe whatever you want, go nuts, but according to math, the people who study math, and the fundamental rules of probability (which is just math), this is how a genuinely infinite universe would work. None of this is opinion. These are the facts about infinity.

I'm not trying to be rude or dismissive or condescending here, but you're not arguing with me, you're arguing with the institution of "math", this is not what I say, this is what we find when we actually sit down to calculate how infinity works. I'm sorry, genuinely, but you're just wrong here.

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dasBergen t1_jce48ya wrote

I enjoy the debate, and fully admit I may be wrong. An infinite number of monkeys will create Shakespeare, but cannot produce a list of all typewritten lists that do not contain themselves as it is simply a paradox, not an improbability.

This is why I compare to pi. You can find an infinite number of 1s, infinite number of 14159s an infinite number of a million digits of pi, but it does not repeat. So if you say an exact earth is 15 digits long then yes you will find an infinite number of those digits (and every other combination of 15 digits). But you will not find anywhere that pi starts at 14159 runs any distance and then repeats 14159 and on exactly. How does this relate to the copy of earth? Earth has influenced and been influenced by everything within 14 billion light years, so 14 digits of pi let's say, you can certainly find an infinite number of those, but at the edge of that 14 billion years those influenced objects have been influencing things for 14 billion years as well. (I'll grant that we're probably getting into less than plank lengths so I'll admit I'm wrong here, but hear me out anyway) the continuous expansion of the sphere of influence encompasses the entire infinite universe in this way. So in order to create an exact copy, with the same history, same future, same influence you need a copy of the whole universe, the entire length of pi... And pi does not repeat, though it is infinite.

Anything less than an entire universe copy will eventually diverge from our earth (perhaps after the heat death of the universe and be really really really hard to notice but would be different none the less)

If you are talking about a multiverse, infinite big bangs, then clearly yes this happening once is proof it is possible, and would happen infinite more times.

If the size of your copy is infinite you need a new infinite universe to put it in.

The other point I'd like to raise is that not everything is random, so something like the same earth but I'm left handed may not be a possibility. The genetics of my parents may not be capable of creating left handed children, and the mutations that would create left handedness probably require several other changes to the world, plus the experiences I would have being left handed my entire life would shape me into a different person with different thoughts.

So the exact way the earth was assembled is a cause and effect relationship, without one you don't get the other. If you don't care what history the atoms of earth had before assembly then you can find infinite earths, but I argue that is not an exact copy.

Thank you for your thoughtful and respectful responses.

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