> it is impossible to import things into something that has infinite volume because by definition there is no outside to import things from.
If you cut a 2d plane with a line, then both halves are infinite, yet both have "outside". You can repeat this and get infinite (aleph 0) number of divisions, each still as infinite as the initial plane.
Same way you can cut infinite 4d universe into countably many infinite 4d universes.
> not all of them are populated; therefore only a finite number are
By same logic: not all integer numbers are even, therefore only a finite number of numbers are even.
Certainly, cutting is the arch example of proportional rationing, so the word alone implies rational numbers. Then, cutting is the act of removing a set of points from one set. So, the same construction over the real line but circled only a quarter around a midpoint is effectively removing two quandrants, half of the circle. So then you could say you have two infinite sets, but exactly because they don't touch (interact with) each other.
> Area: The area of the Universe is infinite.
Right now there is more evidence for the universe to be finite rather than infinite.
But apart from that: Just because it has no borders doesn't mean it is infinite. This is a classic failure in understanding infinity. For example, the area of the surface of a torus is finite, yet when living on a torus surface you won't find any borders. Same for higher dimensions.
> Imports: None. This is a by product of infinity; it is impossible to import things into something that has infinite volume because by definition there is no outside to import things from.
This has nothing to do with infinity. This is solely due to the definition of a universe.
A finite universe doesn't import anything as well, and this is no contradiction whatsoever.
Also, an inifinitely large "part" can still import and export, despite being infinite. For example, take an infinite universe and split it into two halfs. Those "parts" import and export, despite being infinite.
There is the observable universe and there are good reasons to believe that there is "some universe" beyond the observable universe. The observable universe is finite, the reason for that is the geometry of spacetime and the consequences of it (cosmological horizon/particle horizon). But I would not make absolute statements about what lies beyond the horizon(s), since there is (and can be) no data that would justify a statement about the infinity of space or the falsification of it.
IIUC everything in the observable universe is sufficiently far away from anything else that any causal relationship with anything is either from before inflation or within the universe we can observe.
And given how the existence of matter seems to be rather connected to time, it self a by product of interaction, it seems to follow that there is, relatively speaking, nothing beyond the horizon.
>> IIUC everything in the observable universe is sufficiently far away from anything else that any causal relationship with anything
I don't think that is correct. Suppose you have a particle that is very very near the horizon. This particle has its own observable universe and we are at the edge of its horizon. Now, this particle can have casual contact with the other parts of the universe (the parts beyond). But by the time the interaction takes place, it has already slipped out of our horizon. So from the perspective of the particle casual contact is possible. But from our perspective: Not even a chance to detect this interaction.
To be honest, that question never made any sense to me, because this whole discussion is merely about refining a semantic detail of the common word "existing". It says nothing about the particle itself, but just about our language.
For me, a far more interesting question is: Is it relevant? (for science?)
And the answer is: As long as it doesn't interact in any way with us, it is certainly not relevant whatsoever.
> A finite universe doesn't import anything as well, and this is no contradiction whatsoever.
It's not far-fetched that a satirical sci-fi series could have multiple universes with travel between them.
The Hitchiker's Guide actually both does and doesn't if you look at the "Whole Sort of General Mish Mash" joke. Though the WSOGMM joke is pretty explicit that it's one infinite mish-mash with infinite perspectives and universes are just an illusion.
> Also, an inifinitely large "part" can still import and export, despite being infinite. For example, take an infinite universe and split it into two halfs. Those "parts" import and export, despite being infinite.
He actually covers this in the quote on WSOGMM.
> The reason they are not universes is that any given universe is not actually a thing as such, but is just a way of looking at what is generally known as the WSOGMM, or Whole Sort of General Mish Mash. The Whole Sort of General Mish Mash doesn't actually exist either, but it is just the sum total of all the different ways there would be of looking at it if it did.
> The reason they are not parallel is the same reason that the sea is not parallel. It doesn't mean anything. You can slice the Whole Sort of General Mish Mash any way you like and you will generally come up with something that someone will call home. Please feel free to blither now.
You can split the universe anyway you like, it doesn't make 2 universes, just a divide in the universe. Your 2 divides are exporting/importing but the universe as a sum is not.
Of course, we're just arguing over a joke in a fictional universe now. But if you're going to do that you should get the fictional physics right :P
This part of the Hitchhikers' Guide might not have aged well, but because it contributed to that effect.
> But not all of them are populated; therefore only a finite number are.
There are infinities of different sizes
The same would apply for "divisible by 100" or "divisible by 1 million". This would apply to the fraction of worlds that are populated, whatever fraction of them are.
https://en.wikipedia.org/wiki/Aleph_number http://www.alephzero.co.uk/what.htm
It reminds me of that (totally wrong) quote in The Hitchhikers Guide To The Galaxy that the population of the universe is mathematically zero.
The Universe is a very big thing that contains a great number of planets and a great number of beings. It is Everything. What we live in. All around us. The lot. Not nothing. It is quite difficult to actually define what the Universe means, but fortunately the Guide doesn't worry about that and just gives us some useful information to live in it.
Area: The area of the Universe is infinite.
Imports: None. This is a by product of infinity; it is impossible to import things into something that has infinite volume because by definition there is no outside to import things from.
Exports: None, for similar reasons as imports.
Population: None. Although you might see people from time to time, they are most likely products of your imagination. Simple mathematics tells us that the population of the Universe must be zero. Why? Well given that the volume of the universe is infinite there must be an infinite number of worlds. But not all of them are populated; therefore only a finite number are. Any finite number divided by infinity is zero, therefore the average population of the Universe is zero, and so the total population must be zero.
Art: None. Because the function of art is to hold a mirror up to nature there can be no art because the Universe is infinite which means there simply isn't a mirror big enough.
Sex: None. Although in fact there is quite a lot, given the zero population of the Universe there can in fact be no beings to have sex, and therefore no sex happens in the Universe.”