# Re: Similarity of Structure (was Memory Merging Possible for Close Duplicates)

From: Mike Dougherty (msd001@gmail.com)
Date: Mon Mar 17 2008 - 19:14:00 MDT

On Mon, Mar 17, 2008 at 7:45 PM, Lee Corbin <lcorbin@rawbw.com> wrote:
>Suppose that by some *obvious* [1] isomorphism, today Lee is one bit string
> 11011011001110010110111111001010110100000011...
> and tomorrow I am
> 11011011001110010110011111001010110100000010...
>where two 0's happen to be changed to 1's. By all measures
>of similarity, those two strings are still very similar. (It would be
>easy to mention some particular measures used by mathematicians,
>but the ones I'm completely familiar with without having to go look
>them up aren't very applicable here.)

Perhaps I did not find that isomorphism obvious enough. My initial
confusion was related (i think) to the notion of your bit string in
Platonia - which made no sense that it should be a different string
from day to day. Now I realize that each byte position could be a
measure of separate dimensions, some of which might be temporal - and
that the string always represents a fixed point (Lee) measured from a
moving observer.

There also exist some cases of similar that are completely ambiguous.
Less Than (<) and Greater Than (>) symbols may be similar in that they
identical after a simple rotational translation. Depending on our
choice of font, the letters p and d share rotational similarity. d
and b share the same similarity as q and p. Is there a similarity
function for how p and b are first-order similar, or are they similar
through a two step transformation where first p -> d then d -> b ?
I'm surprised if you are still with me. It's completely fine if you
are not.

We could of course agree on the common usage of similar and trust that
the net ambiguity will cancel on either side of the conversation.

If we were to provide a greater measure of similarity (as in your
thermometer example) I suggest the function by which two candidate
entities are compared must necessarily be stated. I could define a
translation where
A) 10110010 <-> B) 01001101 are similar because they are binary
compliments of each other. The same strings could be similar because
generally F( A(n) ) = F( B( len(B)-n+1 ) ) for every integer byte
position n >= 1 to n <= len(B) aka the first string is identical to
the inverse byte order of the second. Now I have two definitions of
similar for the same strings. If I declare we are discussing the
strings' similarity, we may be in agreement until I declare that 101
and 010 are similar by measure 1 (binary compliment) and you are using
measure 2 (reverseability). Unfortunately if that declaration is not
made until after several further agreements along a proof, then it
causes a great deal of frustration and confusion when those agreements
are no longer valid and must be revoked.

I feel this point is relevant to this list because it illustrates a
type of problem that a general intelligence will have to face trying
to communicate with another intelligence. Not all isomorphisms are
obvious. If language (communication protocol) is something that must
evolve between two parties then it will be important to understand how
this mechanism works. I am unsure how to frame this thought as a
primitive function of learning. Until I am able, I feel it is
worthwhile to discuss examples (above) of a class of behavior I
haven't yet modeled well enough.

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