Off Topic — HabitableZone

Off Topic » in reply to A + B = infinity

SDAI discovers formal generative grammar!

Actualy, you can get an infinite set with just 1 symbol in a language and two re-write production rules:

S->aS
S->a

so:
from a base case S:

S-->a
S-->aS-->aa
S-->aS-->aaS --> aaa

etc.

And what you're talking about properly is not a universe, nor anyting that is analogous to evolution. Something analogous to evolution would have the production rules altering as part of the process of generating the rules. IE, movement through a proper metaspace, not through a defined statespace. IE: the statespace of this grammar is infinite yet enitely determined by the operators

a, S-->aS>

If we had some sort of nondeterministic change in the operators... Suppose a rule that went something like this:

f(On)-->On+1 where O is an operation from the set defined by the function f.

so, in other words, our set of grammatical operators would go from:

a, S-->aS>
to
a, S-->aS, S-->bS>

Then you would, by changing the metspace state, end up with a new phase space. I don't think just adding strings to a closed language is analgous to evolution- you have to change the closure operations.

DL

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