How long you spent in that shower?
this post was submitted on 03 Jan 2024
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Showerthoughts
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A "Showerthought" is a simple term used to describe the thoughts that pop into your head while you're doing everyday things like taking a shower, driving, or just daydreaming. The best ones are thoughts that many people can relate to and they find something funny or interesting in regular stuff.
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I usually say "There are an infinite number of integers. That does not mean that one of them is a banana".
The mind-bending thing about it is thus: there are an infinite multitude of "you" throughout the multiverse expressing every "you" that could, or even could not, be. However, there are infinitely more realities with no "you" at all. The set of infinities containing an expression of "you" is necessarily smaller than the set of infinities that do not contain an expression of "you" simply owing to the very narrow nature of eventualities required to express "you" into existence. In point of fact, that set if infinitesimal labeled "you" is infinitesimal in comparison to the set labeled "not you", and yet still uncountable in its infinity.
I'm not sure how sound that reasoning is, it's difficult to use intuition to determine whether one infinite set is bigger than another. Infinity is weird.
Say for instance you have two infinite sets: a set of all positive integers (1, 2, 3...) and a set of all positive multiples of 5 (5, 10, 15...). Intuitively you might assume the first set is bigger, after all it has five times as many values, right? But that's not actually the case, both sets are actually exactly the same size. If you take the first set and multiply every value by 5 you have the second set, no need to add or remove any values. Likewise, dividing every value in the second set gives you the first set again. There is no value in one set that can't be directly mapped to a unique value in the other, therefore both sets must be the same size. Pick any random number and it's 5 times as likely to be in the first set than the second, but there are not 5 times as many values in the first set.
With infinitely many universes one particular state being a few times more or less likely doesn't necessarily matter, there can still be as many universes with you as without.
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Don’t worry, in one of those realities, odds are one of the me’s developed a multiversal bomb that destroyed all the realities other than ours.
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This does not make any sense.
If there are an infinite number of fractions between 1 and 2, all you are doing is naming a set of universes with a constricted naming convention, and the set of universes is still infinite, thus contains any possible universe including an infinite number with an exact replica of you, an infinite number with a slightly different version of you, and an infinite number where you do not exist.
Just because constrained infinities of certain kinds of numbers can be nested within other infinities of unconstrained, or less constrained infinities of universes does not mean that somehow this has applications to multiverse theory.
If the given assumption is 'there are an infinite number of alternate universes' then the fact that fractions between 1 and 2 are an infinite set has literally no logical ability to mandate that this would somehow constrain the nature of previously established infinity of universes.
The possibilities of an infinite set of universes would be ultimately constrained by all possible sets of the laws of physics that allow any kind of universe to exist.
We already know that we live in a universe where humans exist, so, again, there will thus be an infinite number of universes with an infinite number of variations of you exist, and and infinite number where you do not exist.
EDIT: Here is maybe another way of looking at this.
There are an infinite number of positive integers.
There are also an infinite number of even integers, as well as odd integers.
The set of all odd integers contains half the number of all integers, though both are still infinite.
The set of all odd integers is constrained by the rule of none of its constituents are cleanly divisible by two.
But the fact that you can arbitrarily chose a rule to constrain one, larger infinite set into a smaller but still infinite set, does not mean that the larger infinite set does not still exist.
For this 'fractional universes' constraint to make any sense, one would have to demonstrate /why/ the constraint would need to apply to a set of all universes, in a way that is actually meaningfully different than /the constraint not being there/.
And that is an astoundingly complex matter of physics, not Set Theory 101.
EDIT 2: My above example from EDIT 1 is not logically valid, so... I played myself on that one, and worse it seems to have confused the whole discussion, so, apologies for that.
Check out leftzero's link for a more accurate analogy that I /should/ have used.
I still believe my original main point still stands though: The fact that there are an infinite number of fractions between 1 and 2 in no way means anything whatsoever about possible multiverses.
Possible and Impossible universes are defined by the laws of physics.
To override my comment elsewhere in this thread:
A universe without gravity could conceptually exist, but stars would not form, so we would probably not have any of the atomic elements produced by novae and super novae. Also, no galaxies, no black holes, no planets, no life as we know it, as it seems life requires a planet.
A universe without the Strong Nuclear Force would just be 'quark soup'.
A universe without the Weak Nuclear Force on the other hand has been demonstrated by at least one, perhaps now multiple papers to actually possibly be relatively similar to ours in some ways... very big picture kind of ways.
A universe without ElectroMagnetism ... at bare minimum would have vastly different Chemistry than ours. Organic Chemistry seems largely impossible, so no life as we know it, other than possibly some primitive extremophiles.
But these are just thought experiments.
My main point was the whole 'infinite fractions existing between 1 and 2 has no ramifications on multiverses that could exist' thing, and I again apologize for an incorrect and misleading example.
The set of all integers is not larger than the set of all odd integers.
The set of all real numbers, on the other hand, is.
https://en.m.wikipedia.org/wiki/Cardinality_of_the_continuum
Ah, you are correct, my example was flawed.
Thats what /I/ get for not having brushed up on Set Theory 101 in a decade.
Derp.
The point is that people tend to claim the opposite, that an infinite amount of universes means everything and anything is happening in some universe somewhere. Which can't be true, as a universe where someone creates some device that destroys all universes does not exist (as proven by our own existence).
Therefore it follows that there must be some constraints, though what those constraints actually are is obviously a very difficult problem.
The "infinite fractions between 1 and 2 which are not 3" is an example that shows that infinite =/= everything.
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You made me realize that we always think of infinity as an immensely large number, but it can be an immensely small number (0.0(infinite)1).
We imagine the vastness of space and forget that people are studying what makes up quarks.
So thanks for making me realize infinity stretches in both the inifinitely large and the infinitely small. Wasn’t expecting to get a ride on the total perspective vortex from showerthoughts today.
I feel like you've completely missed the point. I feel like OP is implying that just because there are infinite universes, it doesn't mean you're the leader of the world in any of them. Not all things are possible, even with an infinite number of universes.
As you said, existence is constrained by laws of physics of this universe and by potentially different laws/constraints in other universes that we can’t possibly know. Because we lack the ability to observe the infinite expanse of universes as a whole, we can’t know what the constraints are (if any) so we can only understand them as infinite possibilities without constraints, but this doesn’t mean that there are not constraints that we’re just incapable of observing, and I feel like this was OPs point with this post. We don’t know what we don’t know.
This doesn't make sense. OP just provided an example of "infinite universes" that even tho they are infinite, they do not contain all possibilities. Because we can't see all universes at the same time, we cannot know if they have any constraints at all. For instance, all universes might only have me being born in some odd day for some weird reason for all we know.
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OP discovers countable infinity
That's not at all what they're saying. They're saying that 3 is not between 1 and 2. They could have also have said there's a continuum of real numbers between 1 and 2 but none of them are 3.
Maybe the real 3 was the friends we made along the way?
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if there are an infinite amount of multiverses, logically, there must be many in which you do not exist.
Not necessarily. You could be the one constant throughout them all for whatever reason and it wouldn't put any damper on there being an infinite number of universes. That's the whole point of OPs example; infinity can still be bound by limits.
That’s the whole point of OPs example; infinity can still be bound by limits.
such as there being no constants? can that not be a limit?
We can't really know what's possible I suppose, it's more that there's sort of different "levels" of infinity where one level can contain another within itself, but both are still infinite just the same. When people imagine infinity they picture everything, but it doesn't need to be.
Hilbert's hotel is a good example that illustrates how infinities are weird.
And at least one where this post wasn't made.
quantum humor. cute.
Those are the lucky universes.
But what makes the infinite versions of you bound to a range of 1-2 rather than infinity itself?
If “>2 and <1” in this scenario are dimensions where you don’t exist, wouldn’t the range of 1-2 cover every possibility of who you could be?
No, that's the point. The numbers between one and two are infinite; there's no "infinity itself". You can have infinite possibilities without having "every" possibility. There are infinitely many things that could be excluded from infinite universes, and there'd still be infinite universes just the same.
For something to be a possible universe vs an impossible universe, we would be talking about possible laws of physics that do and do not allow for a universe to exist.
That would be the constraints to an infinite set of possible universes.
The fact that there exist an infinity of fractions between one and two is irrelevant and has no bearing on this at all.
There are absolutely not an infinite number of things that could be excluded from the set of infinite possible universes.
Gravity, for example.
Last I checked, it was posited that a universe could possibly exist without the Weak Nuclear Force, but I have never heard of a possible universe that could exist without the Strong Nuclear Force or Electromagnetism.
The fact that there exist an infinity of fractions between one and two is irrelevant and has no bearing on this at all.
It's an analogy to help people grasp that infinities are weird. Just like there are infinite numbers between 1 and 2, there are also infinite numbers that aren't between 1 and 2. Just because there's infinite universes doesn't mean one of them must have unicorns, in the same way that the infinite set between 1 and 2 doesn't contain 3. A common misconception people have is that infinite universes must mean there's one just like the Marvel universe, or that you win the lottery in one, but we can easily have infinity without including those things.
All of the universes could have our exact same laws of physics and that wouldn't prevent there from there being infinitely many. They could all have the same guy named Gary. The point is, you could have infinite universes just tweaking one variable infinitely many ways, and there are infinite variables....
You're assuming that physics would be the same in every other universe. Physics works the way it does in our universe largely because of constants, but we don't know why many of these constants exist and we probably never will. The idea of a god creating out universe seems like an obvious explanation, but more likely it's survivor bias. Specifically, the idea that since we happen to live in a universe where everything is just right and so we look at that as a miracle and probably planned. In reality, it's more likely that there are actually an infinite number of universes with different physics where life is impossible, but that means that even if less than 1% of all of those infinite universes is able to support life, there are still so, so many universes in which it was. Many of them being nearly identical to our own, and many of them being so strange and alien that we probably couldn't even wrap our heads around the strangeness even if we had an eternity to study them.
basically, imagine an infinite amount of universes which are identical to this one. now say every second one has one thing changed about it. theres still infinite universes, but only 2 possibilities.
And if infinite possibilities exist then there must be a universe in which all other universe are a carbon copy of that one and not at the same time. It can be expanded well past the absurd.
There are different kinds of infinity.
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