**From:** Stuart Armstrong (*dragondreaming@googlemail.com*)

**Date:** Wed Apr 02 2008 - 05:45:36 MDT

**Next message:**Stathis Papaioannou: "Re: The GLUT and functionalism"**Previous message:**Stuart Armstrong: "Re: Memory Addition and The Clock/Torture Experiment"**In reply to:**Lee Corbin: "Mathematical Model of GLUTs and Lookups"**Next in thread:**Lee Corbin: "Re: Mathematical Model of GLUTs and Lookups"**Reply:**Lee Corbin: "Re: Mathematical Model of GLUTs and Lookups"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

Hum, my understanding of a GLUT was that you fed it the state of a

system, and it would give you the next one. Thus a GLUT is a function

on the states of a system; you feed it one state and it gives you

another.

So S is my set of states (taken to be polynomials, for this example),

and G is a GLUT on S - a function from S to itself.

(note: I don't actually want G to be full GLUT, but actually a simpler

rule, like differentiation; but we'll have to start with G being a

GLUT).

G is therefore a collection of ordered pairs of elements of S (the

pairs are (initial state , resulting state). The KC of such a

collection is well defined.

Now R is a rule, i.e. a restiction that the function G must obey. It

is given by an ordered collection of sets (P(n) = the "n-th degree

polynomials"), and the rule that G must map P(n) to P(n-1)).

Now the maximal KC that G can have, given this rule, is huge.

Formulating the rule R itself is of trivial KC; the process of taking

a polynomial and sending it to its degree is also of trivial KC. In

fact I have just, completely defined it in a few sentences, no matter

what the cardinality of S is.

Now we have a hash function f, mapping bijectively to the set f(S). By

the composition f G f^{-1} , we have a function (a GLUT) mapping f(S)

to itself. I called it f(G).

We also have the "rule" f(R). This is given by the requirement that

f(G) must map f(P(n)) to f(P(n-1)). That statement is of trivial KC.

But given an element p of f(S), knowing whether it is in f(P(n)) is of

very high KC: to do so, we need to calculate f^{-1}(p), and the KC of

f is maximal.

Thus the rule f(R) is of high KC, as it requires a lot of information

to describe.

With me so far?

Stuart

PS: will continue in a later message

**Next message:**Stathis Papaioannou: "Re: The GLUT and functionalism"**Previous message:**Stuart Armstrong: "Re: Memory Addition and The Clock/Torture Experiment"**In reply to:**Lee Corbin: "Mathematical Model of GLUTs and Lookups"**Next in thread:**Lee Corbin: "Re: Mathematical Model of GLUTs and Lookups"**Reply:**Lee Corbin: "Re: Mathematical Model of GLUTs and Lookups"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ] [ attachment ]

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