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It's simply not possible to prove the universe is infinite, unless of course you have infinite time on your schedule.

by 1970-01-01 3y ago

postalrat 3y ago
What can you prove is infinite without defining it as infinite?
- AnimalMuppet 3y ago
  The rational numbers.
  - tshaddox 3y ago
    I was gonna say prime numbers.
    - quickthrower2 3y ago
      Good one. You could argue they are defined as infinite though because the proof that there are infinitely many is not hard. If there are finite, multiply them all and add one. This number is prime. QED
      - lovecg 3y ago
        On that topic, this is a very common misconception about how that proof works. Multiplying all the primes and adding one does not have to be a prime (just try 2 x 3 x … x 13 + 1) - the point is it’s not divisible by any of the supposedly finite number of primes, so it must have some other prime divisor.
        quickthrower2 3y ago
        Thanks I worded it wrong! You are correct.
        im3w1l 3y ago
        Your original proof is correct. Yes the number may not actually be prime, but given the assumption that you have finitely many primes it follows that the number you have constructed is prime, since it has no divisors. 2 x 3 x … x 13 + 1 isn't prime but that's because that's just a subset of the primes, not all of them. And the argument relies on using all of them.
        lovecg 3y ago
        This is a confusing way to present this argument. We can’t say, by assumption we used up all the primes, so the new number must be a new prime - this doesn’t make sense. And you might as well say the new number has some new prime divisors (could be the number itself, could be new primes smaller than the number), which is at least slightly more correct. The actual proof is by contradiction, and goes something like this: 1) Let’s assume there’s a finite number of primes 2) Multiply them all and add one 3) Since we assumed 1), the result in 2) must have a divisor that’s one of those finite number of primes 4) But that’s not the case since we always get a remainder of one 3) and 4) is a contradiction, therefore 1 is false. At no point it follows that the number in 2) is a prime. The misconception also often causes people to assume that any first N primes + 1 is a prime itself, which is not correct. Someone will use this to make an insecure cryptographic system eventually :) Just kidding, but you see my point how it’s not just a technical detail.
        tshaddox 3y ago
        > We can’t say, by assumption we used up all the primes, so the new number must be a new prime - this doesn’t make sense. I'm not sure what you mean. Are you simply pointing out that it's a contradiction? Because, indeed, it is a contradiction, and that's the point. It's a proof by contradiction! The contradiction you state in step 4 is precisely equivalent to the contradiction "the new number must be a new prime." Stating "N has non-zero remainder when divided by each prime less than N" is equivalent to stating "N is prime." However this is not equivalent to the statement "any first N primary + 1 is prime" which is indeed a misconception.
  - postalrat 3y ago
    Are defined as infinite.
    - Groxx 3y ago
      I define this sophistry as capable of wasting infinite time. We can accurately predict many things with these definitions of infinity. They are useful, unlike... whatever this is.
    - AnimalMuppet 3y ago
      No, the natural numbers are defined as infinite. The rationals are proven to be infinite (with the assumption that the naturals are).
    - eru 3y ago
      There are many alternative definitions of the rational numbers. I am sure you can come up with one that includes infinity in their clauses. But there are other definitions where that is a logical conclusion instead.
  - Stratoscope 3y ago
    There are infinitely many rational numbers, but there are even more irrational numbers. https://www.cantorsparadise.com/this-may-seem-more-irrational-than-rational-317fe1a9cbd https://www.cantorsparadise.com/this-may-seem-more-irrationa... https://archive.ph/m7qjz https://archive.ph/m7qjz
- 1970-01-01 3y ago
  A black hole's density at the singularity is my guess. I don't believe that's been proven however.
  - quickthrower2 3y ago
    So just grab a zero and stick it in a denominator!
- User23 3y ago
  You can’t logically prove anything about anything unless it follows from the premises. Do you mean to suggest that all consequences of the premises are in some way part of the definition of said premises? That’s not irrational, but I don’t think it’s particularly illuminating either.
  - postalrat 3y ago
    Suggesting that proving the universe is infinite isn't any different than proving anything else is infinite. And you shouldn't be surprised it's impossible.
    - User23 3y ago
      We can’t actually prove much at all about the universe beyond that it exists (cogito ergo sum). Basically everything else is talking about some model and not the actual universe. The map still isn’t the territory no matter how much we might wish it were.
- throwaway290 3y ago
  Time it takes to reach the end of a closed loop.
- eru 3y ago
  The prime numbers, for example.
eikenberry 3y ago
Luckily science works by disproving things.
- kuchenbecker 3y ago
  And Special Relativity was the simple observation the constant speed of light was incompatible with euclidean geometry.
thatguysaguy 3y ago
You're right, but: I think we could imagine finding something like "if the universe is infinite we can describe it with this simple set of laws, otherwise we need to use this much more complex set of laws." That would at least be suggestive.
Nevermark 3y ago
If we found an elegant theory that managed to unify, explain and fit all experimental knowledge of the observable universe, … But it broke down with singularities, violated symmetries, required special arbitrary numbers, didn’t conserve information, etc, … Unless the universe was infinite, … Then with great respect for Occam’s Razor, we could dispense with those unnecessary complications, and safely assume the universe was infinite, … Until we saw the back of our heads! Occams’s Razor is the scientific principle that lets you accept a seemingly perfect theory without forever watching (for) your back. O_o It’s the final back stop.
kibwen 3y ago
Even with infinite time on your hands you'd never even be able to reach the edge of the currently-observable universe, because the rate of the expansion of the universe is increasing, and objects are already receding from us too quickly, even for a traveler moving at the speed of light.
- jhoechtl 3y ago
  So it is effectively unbounded.
deleted 3y ago
[deleted]
ordu 3y ago
I think it is a statement when philosophy draws its tongue and starts making faces. Technically you cannot prove anything about the universe, because you need some presumptions to start any proof. Like you need to believe your senses for example. Nevertheless we are confident in a lot of things in the universe, because we have some means to distinguish true statements about the universe from false ones. These methods go beyond rules of pure logic and they use a lot of presumtions (oftentimes in an implicit manner), and I'm not sure there are anything true these methods cannot prove. I mean I cannot prove or disprove such a statement. (I always wondered about "I think, therefore I am": how can we talk about "I" before we proved that "I" exists? Maybe it was not Descartes who thought "his" thoughts? Maybe they were induced by aliens? So you need to accept very complex presumptions just to be able to start thinking.) Some downvoted comment above suggested Occam's razor: if we have 2 theories of the universe and the one assuming the universe to be infinite is simplier, then we should believe the universe is infinite. Maybe it doesn't seem as a proof, but if the theory explains all known phenomena, then we have no reason to doubt it. Like with our senses: they work in practice therefore we accept them as a source of truth. I can get to a point from a different direction. If we assume the universe to be infinite, and come with a falsifiable prediction from this assumption, and test it, then it could convince us that universe is infinite. No one can think of such a prediction today, but it doesn't mean that no one will think of one tomorrow.

It's simply not possible to prove the universe is infinite, unless of course you have infinite time on your schedule.

postalrat 3y ago

What can you prove is infinite without defining it as infinite?

AnimalMuppet 3y ago
The rational numbers.
- tshaddox 3y ago
  I was gonna say prime numbers.
  - quickthrower2 3y ago
    Good one. You could argue they are defined as infinite though because the proof that there are infinitely many is not hard. If there are finite, multiply them all and add one. This number is prime. QED
    - lovecg 3y ago
      On that topic, this is a very common misconception about how that proof works. Multiplying all the primes and adding one does not have to be a prime (just try 2 x 3 x … x 13 + 1) - the point is it’s not divisible by any of the supposedly finite number of primes, so it must have some other prime divisor.
      - quickthrower2 3y ago
        Thanks I worded it wrong! You are correct.
        im3w1l 3y ago
        Your original proof is correct. Yes the number may not actually be prime, but given the assumption that you have finitely many primes it follows that the number you have constructed is prime, since it has no divisors. 2 x 3 x … x 13 + 1 isn't prime but that's because that's just a subset of the primes, not all of them. And the argument relies on using all of them.
        lovecg 3y ago
        This is a confusing way to present this argument. We can’t say, by assumption we used up all the primes, so the new number must be a new prime - this doesn’t make sense. And you might as well say the new number has some new prime divisors (could be the number itself, could be new primes smaller than the number), which is at least slightly more correct. The actual proof is by contradiction, and goes something like this: 1) Let’s assume there’s a finite number of primes 2) Multiply them all and add one 3) Since we assumed 1), the result in 2) must have a divisor that’s one of those finite number of primes 4) But that’s not the case since we always get a remainder of one 3) and 4) is a contradiction, therefore 1 is false. At no point it follows that the number in 2) is a prime. The misconception also often causes people to assume that any first N primes + 1 is a prime itself, which is not correct. Someone will use this to make an insecure cryptographic system eventually :) Just kidding, but you see my point how it’s not just a technical detail.
        tshaddox 3y ago
        > We can’t say, by assumption we used up all the primes, so the new number must be a new prime - this doesn’t make sense. I'm not sure what you mean. Are you simply pointing out that it's a contradiction? Because, indeed, it is a contradiction, and that's the point. It's a proof by contradiction! The contradiction you state in step 4 is precisely equivalent to the contradiction "the new number must be a new prime." Stating "N has non-zero remainder when divided by each prime less than N" is equivalent to stating "N is prime." However this is not equivalent to the statement "any first N primary + 1 is prime" which is indeed a misconception.
- postalrat 3y ago
  Are defined as infinite.
  - Groxx 3y ago
    I define this sophistry as capable of wasting infinite time. We can accurately predict many things with these definitions of infinity. They are useful, unlike... whatever this is.
  - AnimalMuppet 3y ago
    No, the natural numbers are defined as infinite. The rationals are proven to be infinite (with the assumption that the naturals are).
  - eru 3y ago
    There are many alternative definitions of the rational numbers. I am sure you can come up with one that includes infinity in their clauses. But there are other definitions where that is a logical conclusion instead.
- Stratoscope 3y ago
  There are infinitely many rational numbers, but there are even more irrational numbers. https://www.cantorsparadise.com/this-may-seem-more-irrational-than-rational-317fe1a9cbd https://www.cantorsparadise.com/this-may-seem-more-irrationa... https://archive.ph/m7qjz https://archive.ph/m7qjz
1970-01-01 3y ago
A black hole's density at the singularity is my guess. I don't believe that's been proven however.
- quickthrower2 3y ago
  So just grab a zero and stick it in a denominator!
User23 3y ago
You can’t logically prove anything about anything unless it follows from the premises. Do you mean to suggest that all consequences of the premises are in some way part of the definition of said premises? That’s not irrational, but I don’t think it’s particularly illuminating either.
- postalrat 3y ago
  Suggesting that proving the universe is infinite isn't any different than proving anything else is infinite. And you shouldn't be surprised it's impossible.
  - User23 3y ago
    We can’t actually prove much at all about the universe beyond that it exists (cogito ergo sum). Basically everything else is talking about some model and not the actual universe. The map still isn’t the territory no matter how much we might wish it were.
throwaway290 3y ago
Time it takes to reach the end of a closed loop.
eru 3y ago
The prime numbers, for example.

eikenberry 3y ago

Luckily science works by disproving things.

kuchenbecker 3y ago
And Special Relativity was the simple observation the constant speed of light was incompatible with euclidean geometry.

thatguysaguy 3y ago

You're right, but: I think we could imagine finding something like "if the universe is infinite we can describe it with this simple set of laws, otherwise we need to use this much more complex set of laws." That would at least be suggestive.

Nevermark 3y ago

If we found an elegant theory that managed to unify, explain and fit all experimental knowledge of the observable universe, … But it broke down with singularities, violated symmetries, required special arbitrary numbers, didn’t conserve information, etc, … Unless the universe was infinite, … Then with great respect for Occam’s Razor, we could dispense with those unnecessary complications, and safely assume the universe was infinite, … Until we saw the back of our heads! Occams’s Razor is the scientific principle that lets you accept a seemingly perfect theory without forever watching (for) your back. O_o It’s the final back stop.

kibwen 3y ago

Even with infinite time on your hands you'd never even be able to reach the edge of the currently-observable universe, because the rate of the expansion of the universe is increasing, and objects are already receding from us too quickly, even for a traveler moving at the speed of light.

jhoechtl 3y ago
So it is effectively unbounded.

deleted 3y ago

[deleted]

ordu 3y ago

I think it is a statement when philosophy draws its tongue and starts making faces. Technically you cannot prove anything about the universe, because you need some presumptions to start any proof. Like you need to believe your senses for example. Nevertheless we are confident in a lot of things in the universe, because we have some means to distinguish true statements about the universe from false ones. These methods go beyond rules of pure logic and they use a lot of presumtions (oftentimes in an implicit manner), and I'm not sure there are anything true these methods cannot prove. I mean I cannot prove or disprove such a statement. (I always wondered about "I think, therefore I am": how can we talk about "I" before we proved that "I" exists? Maybe it was not Descartes who thought "his" thoughts? Maybe they were induced by aliens? So you need to accept very complex presumptions just to be able to start thinking.) Some downvoted comment above suggested Occam's razor: if we have 2 theories of the universe and the one assuming the universe to be infinite is simplier, then we should believe the universe is infinite. Maybe it doesn't seem as a proof, but if the theory explains all known phenomena, then we have no reason to doubt it. Like with our senses: they work in practice therefore we accept them as a source of truth. I can get to a point from a different direction. If we assume the universe to be infinite, and come with a falsifiable prediction from this assumption, and test it, then it could convince us that universe is infinite. No one can think of such a prediction today, but it doesn't mean that no one will think of one tomorrow.