Due to embedded agency, no embedded map can contain the entire territory.
Hm, this depends on how large of a territory you are claiming, but while I think this is probably true in a whole lot of practical cases, in special cases you can have a map that is both embedded and yet contains the entire territory, albeit the natural examples I’m thinking of only really work in the infinite case, like infinite state Turing machines, or something like this:
I think the basic reason for that is that in the infinite case, you can often abuse the fact that having a smaller area to do computations with still results in you having the same infinity of computational power, whereas you really can’t do that with only finitely powerful computation.
That said, I agree with this:
So no map alone constitutes the territory, but the territory does not exist without its maps, and the collection of all such maps (and the interrelationships between them) is perhaps all that the “territory” really was in the first place.
In practice, I think this statement is actually very true.
Note that it isn’t intended to be in any way a realistic program we could ever run, but rather an interesting ideal case where we could compute every well-founded set.
Some comments on this post:
Hm, this depends on how large of a territory you are claiming, but while I think this is probably true in a whole lot of practical cases, in special cases you can have a map that is both embedded and yet contains the entire territory, albeit the natural examples I’m thinking of only really work in the infinite case, like infinite state Turing machines, or something like this:
https://arxiv.org/abs/1806.08747
I think the basic reason for that is that in the infinite case, you can often abuse the fact that having a smaller area to do computations with still results in you having the same infinity of computational power, whereas you really can’t do that with only finitely powerful computation.
That said, I agree with this:
In practice, I think this statement is actually very true.
Interesting, I’ll check it out!
Note that it isn’t intended to be in any way a realistic program we could ever run, but rather an interesting ideal case where we could compute every well-founded set.