4 ms·

Fun fact: just 103 more bits and it would be enough to address every point in the observable universe distinguishible by Planck length [1]. Not my thought orig

Fun fact: just 103 more bits and it would be enough to address every point in the observable universe distinguishible by Planck length [1]. Not my thought originally, I heard it from somewhere else but can't find it. Possibly from Foone Turing. [1] https://www.wolframalpha.com/input?i=log2%28+volume+of+universe+%2F+planck+length%5E3+%29 https://www.wolframalpha.com/input?i=log2%28+volume+of+unive...

benj111 3y ago
Tbf though, I'm sure the number of cat pics floating about the internet dwarfs this number, so it depends on the data I suppose. Plus rather simple things like pi could create rather a long message.
- gumby 3y ago
  I suppose pi has a cheat code: if you made the largest possible circle in the universe you only need enough digits to distinguish points on its circumference that are a Planck distance apart. Then you can either ignore any digits beyond that or even simply make them up, as there would be no way to measure the difference.
spacebanana7 3y ago
I wonder whether there’s an upper bound on the largest number that can be expressed in the observable universe. All digital representations rely on discrete states in hardware, and there’s a finite number of those in the observable universe, so there should a finite maximum number for computers.
- chaxor 3y ago
  Related to https://en.m.wikipedia.org/wiki/Berry_paradox https://en.m.wikipedia.org/wiki/Berry_paradox Just as a quick example of why it's a bit absurd - I name that number you just defined $zeta$. Now I make $zeta'$ = zeta^zeta. Or whatever manipulation you like. Adding constraints is addressed in the link.
  - marcosdumay 3y ago
    And zeta' can not be expressed by any state of the visible Universe. The GP question was not about encoding, and thus is not subject to compression. The largest number we can measure of anything is a pretty well defined concept.
- layer8 3y ago
  Depends on what you mean by “expressed”. E.g. you can represent a busy beaver that expresses the length of its output. We don’t know if there is only a finite number of discrete states in the observable universe. The Planck length is not a discretization.
  - spacebanana7 3y ago
    > Depends on what you mean by “expressed” I'll have to think about this. I want a very physical meaning of the term using values rather than references. One where the largest number that can be expressed using up/down fingers with two hands is 1024, not a sign language reference to a googolplex.
    - ruined 3y ago
      all expression is reference
    - carapace 3y ago
      You might enjoy: "Measuring the intelligence of an idealized mechanical knowing agent" https://philpapers.org/archive/ALEMTI-2.pdf https://philpapers.org/archive/ALEMTI-2.pdf "Intuitive Ordinal Notations" https://github.com/semitrivial/IONs https://github.com/semitrivial/IONs
    - bee_rider 3y ago
      If you are OK with a sum constants times powers of two, would you be ok with other hyperoperations on two? https://en.m.wikipedia.org/wiki/Hyperoperation https://en.m.wikipedia.org/wiki/Hyperoperation I wonder if it would be helpful to restrict the question a bit, maybe something like: what is the largest number for which the number, and also all smaller magnitude integers, can be expressed.

benj111 3y ago

Tbf though, I'm sure the number of cat pics floating about the internet dwarfs this number, so it depends on the data I suppose. Plus rather simple things like pi could create rather a long message.

gumby 3y ago
I suppose pi has a cheat code: if you made the largest possible circle in the universe you only need enough digits to distinguish points on its circumference that are a Planck distance apart. Then you can either ignore any digits beyond that or even simply make them up, as there would be no way to measure the difference.

spacebanana7 3y ago

I wonder whether there’s an upper bound on the largest number that can be expressed in the observable universe. All digital representations rely on discrete states in hardware, and there’s a finite number of those in the observable universe, so there should a finite maximum number for computers.

chaxor 3y ago
Related to https://en.m.wikipedia.org/wiki/Berry_paradox https://en.m.wikipedia.org/wiki/Berry_paradox Just as a quick example of why it's a bit absurd - I name that number you just defined $zeta$. Now I make $zeta'$ = zeta^zeta. Or whatever manipulation you like. Adding constraints is addressed in the link.
- marcosdumay 3y ago
  And zeta' can not be expressed by any state of the visible Universe. The GP question was not about encoding, and thus is not subject to compression. The largest number we can measure of anything is a pretty well defined concept.
layer8 3y ago
Depends on what you mean by “expressed”. E.g. you can represent a busy beaver that expresses the length of its output. We don’t know if there is only a finite number of discrete states in the observable universe. The Planck length is not a discretization.
- spacebanana7 3y ago
  > Depends on what you mean by “expressed” I'll have to think about this. I want a very physical meaning of the term using values rather than references. One where the largest number that can be expressed using up/down fingers with two hands is 1024, not a sign language reference to a googolplex.
  - ruined 3y ago
    all expression is reference
  - carapace 3y ago
    You might enjoy: "Measuring the intelligence of an idealized mechanical knowing agent" https://philpapers.org/archive/ALEMTI-2.pdf https://philpapers.org/archive/ALEMTI-2.pdf "Intuitive Ordinal Notations" https://github.com/semitrivial/IONs https://github.com/semitrivial/IONs
  - bee_rider 3y ago
    If you are OK with a sum constants times powers of two, would you be ok with other hyperoperations on two? https://en.m.wikipedia.org/wiki/Hyperoperation https://en.m.wikipedia.org/wiki/Hyperoperation I wonder if it would be helpful to restrict the question a bit, maybe something like: what is the largest number for which the number, and also all smaller magnitude integers, can be expressed.