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A comment on Add extra stuff to a “standard” encoding? Sure, why not. Parent comment

Re:Add extra stuff to a “standard” encoding? Sure, why not by layer8 on Wednesday September 20, 2023 @08:50AM (#37583509)
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.

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Re:Add extra stuff to a “standard” encoding? Sure, why not by spacebanana7 on Wednesday September 20, 2023 @09:20AM (#37583773)
> 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.

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Re:Add extra stuff to a “standard” encoding? Sure, why not by ruined on Wednesday September 20, 2023 @09:51AM (#37584104)
all expression is reference
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Re:Add extra stuff to a “standard” encoding? Sure, why not by carapace on Wednesday September 20, 2023 @10:03AM (#37584269)
You might enjoy:

"Measuring the intelligence of an idealized mechanical knowing agent" https://philpapers.org/archive/ALEMTI-2.pdf

"Intuitive Ordinal Notations" https://github.com/semitrivial/IONs

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Re:Add extra stuff to a “standard” encoding? Sure, why not by bee_rider on Wednesday September 20, 2023 @10:30AM (#37584622)
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

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.

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