[time 545] Re: [time 535] Chu Spaces & Construction by Games

Matti Pitkanen (matpitka@pcu.helsinki.fi)
Mon, 16 Aug 1999 13:50:55 +0300 (EET DST)

Here are the bibliodata you asked below.

Gerard O'Brien & Jon Opie, A connectionist theory of phenomenal experience


It can be found from the page of Chalmers


which contains all kinds of interesting material.

I will reply later to the rest of posting. Computer has been down for
several days and I am in rather irritated state of mind! Must calm down


On Fri, 13 Aug 1999, Stephen P. King wrote:

> Dear Matti and Friends,
> Matti Pitkanen wrote:
> >
> > On Fri, 13 Aug 1999, Stephen P. King wrote:
> snip
> [SPK]
> > > I see "structure" or pattern recognition as a general type of
> > > bisimulation. I believe that this is modeled by Pratt then he discusses
> > > Chu spaces with K > 2 values. For K = 2, we have a binary situation like
> > > you ask: "familiar" or "unfamiliar", but this is easily seen to be vague
> > > as it tacitly assumes an absolute "standard" to distinguish the two...
> > > He proposes that QM can be represented by the behavior of Chu_K = C (C
> > > being the set of complex numbers)...
> [MP]
> > Interesting situation occurs when binary numbers Z_2 are replaced
> > with G(p,1): finite field with p elements. What one obtains
> > by the construction taking it to infinite is p-adic numbers with
> > norm not larger than one: also p-adic numbers infinite as
> > ordinary integers are included. Binary case would give 2-adics.
> > What differentiates between this construction and construction of surreals
> > is presumably that p-adic topology is introduced.
> [SPK]
> > > I think that the Pinary tree is a better model since it captures
> > > phylogenetic relations that a binary tree can not! Thus the "history" of
> > > a particular player has an effect on the possible moves it will make in
> > > a particular game... We skew (?)or weigh the moves as a function of the
> > > number of times that a particular move was successful for that player!?
> > > Since Chu spaces represent both the games and the players of the games,
> > > we can identify a player with a set of games and a game by an antiset of
> > > players. (I think, I may be misinterpreting Pratt!?)
> BTW, a game between two players (chu spaces) A and B is defined by the
> tensor product of A and B, which can be considered as a player of a
> "bigger" game... See pg. 5,6 of ratmech.ps
> snip
> [SPK]
> > > You make a very good point here, but I believe that Dennett is mistakes
> > > in thinking that the difference between, say "files of numbers" and the
> > > "mechanism of the reading head" are only differences in *degree* and
> > > that this is all there is to be said of the situation. If we are
> > > strictly talking about the information content of the physical
> > > embodiments of these informational structures, we can see that the
> > > difference in only in degree, but Dennett's material monism blinds him
> > > to the categorical difference in *kind* that exists between the "mental
> > > object" (information about) A* and the physical object A.
> [MP]
> > Yes, I understand you point.
> [MP]
> > > > Isn't the situation same in physics? To take example relating to previous
> > > > discussions. Could it be that spacetime geometry is tacit information?
> > > > The dynamics of spacetime surface defined Kahler action as dynamical
> > > > principle is tacit information not allowing representation in terms
> > > > of LS interactions: simply because it defines these interactions!?
> > > > Same would apply to unitary time evolution U: it would also represent
> > > > 'raw physics'. Explicit (DNA, short term memory?) and potentially
> > > > explicit (motor program in my brain realized as cascades of selves, long
> > > > term memory realized in terms of self hierachy and communication between
> > > > levels of hierarchy?) information would emerge only at the level when
> > > > selves emerge.
> [SPK]
> > > Given my comment above, I agree with you here! :-) (Does Dennett allow
> > > for "implicit" as the complement of "explicit"? I have read his book,
> > > but I can't remember...)
> [MP]
> > Probably: I think he divided implicit to potentially explicit and tacit.
> > (I read a paper about implicit learning yesterday and found the
> > definitions there).
> Could you send me the bibliodata on it?
> [SPK]
> > > In Hitoshi's LS theory, the "outsides" of LS are "physical" and the
> > > "insides" are "mental", I think!? We could categorize the information
> > > involved in the external behavior of LS in the way you describe here.
> > > :-)
> [MP]
> > I read the rathmech in train and I think I understand the general
> > idea and philosophy. Although the basic philosophy is quite different
> > from my stubborn beliefs, I find the mathematical idea beautiful. I hope
> > I could apply it in my own thought constructions. To put
> > it mildly, I am still far from any concrete model for cognitive
> > representations: in any case, cognitive spacetime sheets and material
> > spacetime sheets could replace mind and matter in TGD framework.
> > Perhaps the models provided by cognitive spacetime sheets for the
> > behaviour of material ones could be formulated in terms of
> > Chu pair somehow defined by cognitive and material spacetime sheet forming
> > self and K valued mapping |= would characterize the simulation
> > provided by cognitive spacetime sheet for the behaviour of material
> > one. Something like this...
> I have thought of your "cognitive and material spacetime sheets" as
> representable by Chu spaces! :-) The |= can be interpreted as the
> "payoff matrix of a von-Neumann-Morganstern two-person game"; it is a
> matrix whose entries range over the values of K... How this applies to
> your thought here I am not sure... The "self" is a "player" of the
> "information acquisition game" that I see bisimulation to be.

> > What troubles me that that the causation from mental to material
> > was replaced by a K-valued function. And interpretation
> > of the values of |= as complex time or logical value.
> > If K=Z_2 this everything is ok but
> > K=C? I did not quite understand the construction of left and
> > right residuations in case of QM.
> > I understood right residuation in general case.
> No, causation is not "replaced by a K-valued function", as I understand
> it, it is a matrix of relations. Look at the 4th paragraph on pg. 3, 4th
> paragraph of page 6, 3rd & 6th paragraph of pg. 8, 8th paragraph of pg.
> 9 of ratmech.ps, for various discussions of causality.
> The last reference is particularly telling: "...we find that two
> events, or two states, communicate with each other by interrogating
> *all* entities of the opposite type. Thus event a deduces that it
> precedes event b not by broaching the matter with b directly, but
> instead by consulting the record of every state to see if there is any
> state volunteering a counterexample. When none is found, the precedence
> is established. Conversely when a Chu space is in state x and desires to
> pass to state y, it inquires as to whether this would undo any event
> that has already occurred. If not then the transition is allowed."
> I am arguing that Pratt's idealized definition, presented here, can be
> weakened to take into account computational error, entropy and the
> "duration" or "granularity" of a transition, which is equivalent to your
> q-jump. I am have only philosophical arguments and not mathematical ones
> so I beg your patience and ask for your help to formalize the idea.
> (Hint: entropy is generated in computing by erasing memory)
> I think that we need to also read
> http://boole.stanford.edu/chuguide.html#ph94 to see more of Pratt's
> ideas of how the construction works for QM. He does identify, on pg. 10
> of ratmech.ps, right residuation with the inner product of a "mixed
> state" and left residuation with the outer product.
> > Chu spaces involve the
> > assumption about *given* spaces A and X: isn't this assumption
> > very similar to the assumption 'spacetimes are 4-surfaces
> > of 8-dimensional H', which assumption in turn induces
> > the concept of configuration space and its spinor structure
> > crucial for quantum theory?
> I am not sure that we could really say "*given*", remember that there
> is no notion of absolute initiality (or finality) of the spaces A and X,
> they are constructed by constructions which are constructed themselves.
> We are no longer using the naive classical notion that there is an
> absolute "beginning" to a space. This notion can be see to derive from
> the way that observations ("results of information acquisition games" in
> Frieden's thinking and "the tensor product of Chu spaces" representing
> observers in Pratt's thinking). An observation is a finite sampling,
> like Robert Fung's "bucket" that scoops up a finite distribution of
> spectra. Umm, I am not clearheaded right now, I'll try to elaborate more
> on this some other time.
> Onward,
> Stephen

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