[time 269] Re: [Time 267] and [Time 83] and [Questions about Time and fuzzy hypersets]

Stephen P. King (stephenk1@home.com)
Mon, 03 May 1999 06:32:10 -0400

Dear Ben,

        I am thinking of your last post: [time 267]

>Primally, space and time are basically two kinds of ~separateness~.

>Space is what allows two identical objects to coexist but be ~different~.

>Time is what allows one object to be ~different from itself~ (because existing
>at different times)

>Space is the movement from X not= X to X=X
>Time is the movement from X=X to X not= X

>They are two directions of movement of the same paradox, X=X but X not= X

>Indian logic distinguishes 4 truth values,
>true, false, both true and false, neither true nor false

>Similarly, we may say that any two entities are either
>same, different, neither same nor different, both same and different

>Space and time both allow entities to be both same and different
>Space is the movement from difference to sameness; time is the movement from
>sameness to difference

>I suspect that this ontological observation can be used to deduce from
>first philosophical principles the fact that time is measured using imaginary numbers whereas
>space is measured using real numbers. But I don't have time to work this out right
>now (good excuse, huh?)
        How space and time are dynamical inverses is somewhat like a thought
that I have been mulling over for a long time! :) But I never thought of
it this way! ({X = ~X} -> (X = X}) <-> ({X = X} -> {X = ~X}) I think
that a infomorphism can be defined here! We just need to figure out the
        Peter, do you have any ideas? ;)

Re: [time 83] Re: [time 81] Entropy, wholeness, dialogue, algebras

Ben Goertzel wrote:

> It is very different,if my recollection serves. Fuzzy set theory is not
> the same as entropy or algorithmic information theory.
> It is based on the Min() and Max() operators which preserve distributivity
> but are not at all psychologically realistic. My preference is for probabilistic
> logic. So I agree that fuzziness is needed, but the min/max algebra on fuzzy
> sets I have always steered away from in my AI work.

        Could you explain your reasoning of why the Min() and Max() operators
of fuzzy logic are "not at all psychologically realistic"? This is
driving me nuts! ;)

Subject: Re: Questions about time and fuzzy hypersets
   Date: Thu, 14 Jan 1999 16:23:24 -0500
   From: "Ben Goertzel" <ben@goertzel.org>
     To: "Stephen P. King" <stephenk1@home.com>
    CC: "octonion@dialog.net \"octonion@dialog.net\""
        "Hitoshi Kitada" <hitoshi@kitada.com>, "Robert Fung"

>>Re: "Primal time is the result of resolution of contradictions."
>> Are we thinking of "contradiction resolution" in terms of
>>constructing/computing logical consistency chaining in information
>>databases? Like constructing Markov chains or Hasse diagrams or word
>>relation graphs. Umm, I am not sure what are the right words to use,
>>that you would be familiar with.

>I know about Markov chains, not Hasse diagrams. I am thinking more
>in terms of Spencer-Brown's "Laws of Form", which is a great book that
>you should read if you never have. It is written up on the Web in several

>The basic contradiction "this sentence is false" unravels itself
>as True, false, true, false,... ad infinitum

>presto- time!

        I am beginning to understand this line of thinking! :) But, as above, I
still see B. Kosko's formalism as the best. Perhaps it is his use of
"sets as points in hypercubes" that biases me, since I think in
pictures. But Kosko does not seem to think of the vicious loop of the
contradiction as a dynamical flow... :( I, as you, do! I think that the
"streams" that Peter uses -which are hypersets- lend themselves readily
to thinking about this! I am thinking of stream as time flows, plural,
in the sense that each is a different ordering of events.
        On a related note: What relation do you see between ensembles and
time-trials? I see ensembles S as "space-like" (Minkowskian sense)
distributions that can be identified -tentatively- to R^N : n >/= 2 and
time-trials T as "time-like" (ditto) distributions identified to R^1.
Pictorially, we can think of S as a hypersurface with T orthogonal, if
we identify a common point and order T with ">/=" (greater or equal to)
points and order S ">/=" concentric spheres R^N-1. I believe that this
reduces to a classic light-cone structure if we introduce the
appropriate metric...

Since we observe time as "flowing", I conjecture that this is so because
of the stream like nature of orderings, but given that the computation
of least action / greatest extrema is an NP Complete problem
computationally, this flow is not a priori but is contracted by an
ongoing interactional computation among LSs. This make sense? ;)



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