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Infinity is fun :) It reminds me of that (totally wrong) quote in The Hitchhikers Guide To The Galaxy that the population of the universe is mathematically zer

Infinity is fun :) 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.”

inventingwithmo 9y ago
I realise I'm arguing against a work of comedy, but: > But not all of them are populated; therefore only a finite number are. There are infinities of different sizes
- b3lvedere 9y ago
  Of course. Of course. You are totally right. https://www.youtube.com/watch?v=23I5GS4JiDg https://www.youtube.com/watch?v=23I5GS4JiDg
- SideburnsOfDoom 9y ago
  My understanding is that the infinity of "all integers greater than zero" and of "all integers greater than zero and divisible by 2" are in fact infinities of the _same_ size. 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.
  - zimpenfish 9y ago
    As best I understand it, all those reduce to aleph-zero because they're countably infinite and can be mapped to the natural numbers. But aleph-one exists and is provably bigger than aleph-zero despite both being infinite. https://en.wikipedia.org/wiki/Aleph_number https://en.wikipedia.org/wiki/Aleph_number http://www.alephzero.co.uk/what.htm http://www.alephzero.co.uk/what.htm
vog 9y ago
I know this is not meant to be taken seriously, but some claims don't even make sense from a purely mathematical point of view. > 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.
- maze-le 9y ago
  > Right now there is more evidence for the universe to be finite rather than 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.
  - CuriousSkeptic 9y ago
    But if there can be no data about it. Does it even make sense to talk about it as existing? 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.
ajuc 9y ago
I know it's wrong on purpose, but still... > 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.
- falsprofet 9y ago
  Wouldn't you get aleph_1 divisions, if, by methods left as exercise to the reader, making a cut for each real number? For example, how many angles are there in a circle? But the real kicker is, that taking the 2D surface of a ball, certainly the area is finite even if there are no bounds at all.
  - falsprofet 9y ago
    Addendum: The set of cuts would then include all points of the 2D-surface. So in principle, as the number of cuts approaches real infinity (pun intended; if you might call it that) the area left between the cuts approaches zero. That's certainly not infinite. But this cannot be done with only circle and straight edge - thus in no system of only two dimensions, pretty much by analogy - yikes - I mean the apparent isomorphism between Cartesian and polarized coordinate-systems is the only one I know in 2D. 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.

inventingwithmo 9y ago

I realise I'm arguing against a work of comedy, but: > But not all of them are populated; therefore only a finite number are. There are infinities of different sizes

b3lvedere 9y ago
Of course. Of course. You are totally right. https://www.youtube.com/watch?v=23I5GS4JiDg https://www.youtube.com/watch?v=23I5GS4JiDg
SideburnsOfDoom 9y ago
My understanding is that the infinity of "all integers greater than zero" and of "all integers greater than zero and divisible by 2" are in fact infinities of the _same_ size. 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.
- zimpenfish 9y ago
  As best I understand it, all those reduce to aleph-zero because they're countably infinite and can be mapped to the natural numbers. But aleph-one exists and is provably bigger than aleph-zero despite both being infinite. https://en.wikipedia.org/wiki/Aleph_number https://en.wikipedia.org/wiki/Aleph_number http://www.alephzero.co.uk/what.htm http://www.alephzero.co.uk/what.htm

vog 9y ago

I know this is not meant to be taken seriously, but some claims don't even make sense from a purely mathematical point of view. > 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.

maze-le 9y ago
> Right now there is more evidence for the universe to be finite rather than 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.
- CuriousSkeptic 9y ago
  But if there can be no data about it. Does it even make sense to talk about it as existing? 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.

ajuc 9y ago

I know it's wrong on purpose, but still... > 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.

falsprofet 9y ago
Wouldn't you get aleph_1 divisions, if, by methods left as exercise to the reader, making a cut for each real number? For example, how many angles are there in a circle? But the real kicker is, that taking the 2D surface of a ball, certainly the area is finite even if there are no bounds at all.
- falsprofet 9y ago
  Addendum: The set of cuts would then include all points of the 2D-surface. So in principle, as the number of cuts approaches real infinity (pun intended; if you might call it that) the area left between the cuts approaches zero. That's certainly not infinite. But this cannot be done with only circle and straight edge - thus in no system of only two dimensions, pretty much by analogy - yikes - I mean the apparent isomorphism between Cartesian and polarized coordinate-systems is the only one I know in 2D. 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.