3 ms·
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 st
by 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 agoRelated 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 agoAnd 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 agoDepends 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 agoall expression is reference
- carapace 3y agoYou 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 agoIf 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.