I tried to comment your post as much I could, it's nothing very systematic though but I hope that it may still be useful as some kind of explanation.
> In a mutual word definition-space: the structure COULD be constantly changing; if mapped in a minimum math-way it would appear to be constantly changing.
It can if definitions change when something changes.
> Of course we are talking about mutual awareness of specifying and generalising characteristics in defining something; so such a definition-space implies a mutual awareness among items. The structure overall may seem like it is "conscious" due to the inter-dependent relations.
Inter-dependent relations are necessary but not enough, many things must be possible to haappen.
> By holding each "knot" or "link" as unchanging (equates to Dr. Dick's "conservation of center of mass?) seems to be like saying that any additional detail introduced to the definition-space (such as adding category "D" say: "with tyres" to the aeroplane/wheels/wings interaction) does not change the knots (overlaps of overlaps projecting potentially new space) and links (overlaps) among categories. But the structure itself changes.
> This triple effect of three categories meeting might be called "time".
? Time comes from that every generation of new knots would generate new generation of new knots, this may thought to happen instantaneously everywhere.
> By introducing a fourth category "things with tyres"; you still can have the three knotted as before and linked as before but you can generate a new space or new dimension on this it appears say:
When whe had "things with wheels" then we would have new knot what means "wheels and tyres", this is association because "things" is common :-)
> (Double-slit experiment: two views of three categories may be called "photon"? Pass this through double-slit is like asking "which two is which? Two that defines photon or two slits? So you lose track of the photon? It becomes "everywhere" in the experiment? But if you specify "past" and "future" you get "where is which?"? So you get "offer wave" and "confirmation wave" as in John Cramer's interpretation of quantum mechanics?)
> Introduce a fifth category and "space-time" is uncertainly allocated; which of five are the four and which is the extra dimension in space?
Time is not category and space is not category. To simulate space with ADS there must be some nodes where angles between connections are somehow determined (or marked with patterns if process interprets them in a proper way). Now if angles are determined as in 3d space, this is 3d space, if as in 4d space, then this is 4d space. Yep, in fact in any such system would emerge some "processing nodes", relatively independent structures what are connected to each other, though connections may change. These may even be "particles" :-) These nodes may also join, split, new ones may be created, whatever.
> It is the existence of that "possibility space" of two other options that makes the "three quark anti-colours" of your ONE choice of three options into a "three-affected" choice. Perhaps this is why "anti-colours" are regarded as "going backwards in time" if "time" is "triple-ness" (self-referent reference like pendulum self-refers by retrace alleged same path)
Don't know enough to comment this. There would always be iterations when a process or sequence of processes cause itself. This may also be as a kind of dynamic memory.
> Is the very definition of "number" entangled here? Or rather, is the definition of "category" caught up with "base" in which numbers are counted ? What is going on?
Ha, what would numbers look like in ADS? Like first position is connected to pattern three and second position is connected to pattern seven...
> It seems like a "space-expansion" system?
Like space-creating system :-)
> This is just like my "discussion model of physics": I call it "transparency" where everything is built from mutual-agreed space so all constructs are built of pure consciousness.
ADS may not always implement artificial consciousness, they may also implement a very "mechanical" system.
> May I suggest you have inverted the usual arrangement: instead of a rigid geometry in which events are played out; you have made rigid events in which geometry is "played out"?
Maybe, Heraclitus said something that the rivers don't change, but they are a result of change.
> Maybe your computer programme is an inversion of "cellular automata":
Or cellular automata in space with limitless number of connections from every point :-)
> What if "the law of non-contradiction" is the only fixed reference in a dictionary?
Laws are rather something like association and natural selection.
> "knot" becomes "category overlaps with category overlaps with category", so A:B:C
You may consider knot as a set what consists of connections to other knots, this is how sets are represented in ADS.
> (IN QED: the direction of the arrow may be D:E and the length of the arrow may be A:B:C.)
The links have no direction, any direction must come from the process itself.
> Like dissapearing Chess-move-options which have no logical-compatibility common ground with a new move made by a player?
Like dissapearing the parts of the system what don't fit into the rest of the system. This enables trying the possibilities and association enables generating every possibility in the environment.
> to Chess-move options not yet available as spaces occupied
These are just possibilities considered in derivation, in ADS new knot shall be created only from links what are different to two knots because only this possibility doesn't cause system to constantly increase or decrease.
> If new moves in Chess point to non-common spaces (ones that are not in your game-plan of moves) you have a constantly changing game-plan so "an absolutely dynamic way to play Chess" where you never rule out any move? Like a discussion where every view gets a hearing and no one is left out...
Yes, this way we create something new.
> Like a few cellular automata with no grid to play on?
Almost. In what ADS are similar to cellular automata is that both are self-developing.
> You get a rapidly built grid that keeps changing?
> Then it settles down as the grid stabilises? Due to feedback loops between the cells and their new environment?
Yes, because only these parts of system remain what can maintain themselves in certain environment.
> I see why you say it looks like it is conscious.
To satisfy the criteria of artificial consciousness, more about that in my forum.
> Would it not tend towards a Bose-Einstein condensate type state? Eventually it would generate so much feedback that it would break up into a whole lot of individual cells and die?
May happen, it shall collapse when constantly more knots shall be deleted than created, this doesn't suppose to happen when the system is well-developed.
> (The static starting state might cause problems by speading "background noise" through the system? Or ? Not sure...)
If starting structure is minimal then very soon after some interaction the starting state shall have almost no influence and almost all system is only determined by interaction. But yes, a single thing may influence a whole system, this is why such system has some "holographic" properties"
> And the kind of BEC death your model might experience: why ! Cellular division! Runaway cellular division! Cancer!
Yes, at least in theory it can model cellular division. Equations cannot do this well because they cannot directly model changing structure.