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> Mathematicians Will Never Stop Proving the Prime Number Theorem Entropy in the universe is finite (as far as we know). At some point mathematicians will not

by jupp0r 6y ago

> Mathematicians Will Never Stop Proving the Prime Number Theorem Entropy in the universe is finite (as far as we know). At some point mathematicians will not be able to continue trying to prove the prime number theorem. qed.

gmfawcett 6y ago
For extra rigour (!), replace "as far as we know" with one of the classic weaselly proof introductions: "Clearly, ..." , "It can easily be shown that...", "It is left as an exercise to the reader to show..."
- jupp0r 6y ago
  Thanks for the peer review! It can be easily shown that entropy in the universe is finite. Thus, at some point mathematicians will not be able to continue trying to prove the prime number theorem. qed.
  - Koshkin 6y ago
    "Exercise. Complete the proof by filling in all the missing details."
  - brutt 6y ago
    > It can be easily shown that entropy in the universe is finite. Finite Universe can get stuck in a "dead" state. Giving infinite time, it will definitely will do so. The only solution for this problem is to have infinite Universe. Infinite Universe will never stop. (non native speaker)
    - gmfawcett 6y ago
      This reminds me of the "Boltzmann universe" theory! "Proof by appeal to authority: see Boltzmann." :) https://en.wikipedia.org/wiki/Boltzmann_brain#Boltzmann_universe https://en.wikipedia.org/wiki/Boltzmann_brain#Boltzmann_univ...
pdonis 6y ago
> Entropy in the universe is finite (as far as we know). It is? The universe, as far as we know, is spatially infinite.
- jupp0r 6y ago
  True, but the second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. So I think the discussion at this point will revolve around whether a spacially infinite universe can be seen as an isolated system. My original point was merely to use humor to caution against the use of "never", which breeds statements that are never true.
  - pdonis 6y ago
    > the second law of thermodynamics states that the total entropy of an isolated system can never decrease over time If you use this definition, then... > I think the discussion at this point will revolve around whether a spacially infinite universe can be seen as an isolated system. ...it can't. "Isolated system" in the above definition of the second law means, basically, "a system that you can enclose in a box and measure its properties from outside". You can't do that with a spatially infinite universe. Actually, you can't even do it with a spatially finite universe, because even such a universe has no boundary and no "outside". So if you want to apply the second law to the universe at all, you need to use some other definition that can be applied to the whole universe.
  - breuleux 6y ago
    Then one might also caution against the use of "never" in stating the second law of thermodynamics. It is a statistical law: the probability that entropy decreases in an isolated system is not zero, it is just extremely small. If you wait for long enough, it is bound to happen.

by jupp0r 6y ago

gmfawcett 6y ago

For extra rigour (!), replace "as far as we know" with one of the classic weaselly proof introductions: "Clearly, ..." , "It can easily be shown that...", "It is left as an exercise to the reader to show..."

jupp0r 6y ago
Thanks for the peer review! It can be easily shown that entropy in the universe is finite. Thus, at some point mathematicians will not be able to continue trying to prove the prime number theorem. qed.
- Koshkin 6y ago
  "Exercise. Complete the proof by filling in all the missing details."
- brutt 6y ago
  > It can be easily shown that entropy in the universe is finite. Finite Universe can get stuck in a "dead" state. Giving infinite time, it will definitely will do so. The only solution for this problem is to have infinite Universe. Infinite Universe will never stop. (non native speaker)
  - gmfawcett 6y ago
    This reminds me of the "Boltzmann universe" theory! "Proof by appeal to authority: see Boltzmann." :) https://en.wikipedia.org/wiki/Boltzmann_brain#Boltzmann_universe https://en.wikipedia.org/wiki/Boltzmann_brain#Boltzmann_univ...

pdonis 6y ago

> Entropy in the universe is finite (as far as we know). It is? The universe, as far as we know, is spatially infinite.

jupp0r 6y ago
True, but the second law of thermodynamics states that the total entropy of an isolated system can never decrease over time. So I think the discussion at this point will revolve around whether a spacially infinite universe can be seen as an isolated system. My original point was merely to use humor to caution against the use of "never", which breeds statements that are never true.
- pdonis 6y ago
  > the second law of thermodynamics states that the total entropy of an isolated system can never decrease over time If you use this definition, then... > I think the discussion at this point will revolve around whether a spacially infinite universe can be seen as an isolated system. ...it can't. "Isolated system" in the above definition of the second law means, basically, "a system that you can enclose in a box and measure its properties from outside". You can't do that with a spatially infinite universe. Actually, you can't even do it with a spatially finite universe, because even such a universe has no boundary and no "outside". So if you want to apply the second law to the universe at all, you need to use some other definition that can be applied to the whole universe.
- breuleux 6y ago
  Then one might also caution against the use of "never" in stating the second law of thermodynamics. It is a statistical law: the probability that entropy decreases in an isolated system is not zero, it is just extremely small. If you wait for long enough, it is bound to happen.