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Mazes~Minds
a Paper about ThoughtSpace
June, 2000

Thought space, physical space, the natural and the artificial.  Decisions and choices, open and closed.     We move through opportunities and events as if they were places, and they very well may be.  In a more profound way than we realize.  In analytical terms, every choice is a 'dimension', every option a whole new and independent 'direction'.  And when encountered and put together, form conditions that make some decisions - paths - easier than others.  There are hills and valleys, even convenient roadways that course like rivers.

We live in dimensions embedded and blended with other dimensions .. enormous quantities of them .. that we handle with greater ease than any computer.  Many coordinate into waves and sheets of energy-like relations that we can talk about using the same ideas and terms as we do energy.   Like 'entropy'.  Even when what we are really involved with is hopes, dreams, guesstimates, and aspirations .. dealing with the everyday and mundane, surviving in the here and now and behaving in ways that mean we value the future and do everything we can to see more of it.

Previous science has told us we live in three or four 'dimensions' of space and time.  New physics is exploring space~time dimension counts of 8, 10, 11, 26.   I'm here to tell you there are more.   This paper covers a few of the simple basics of how we/they work.

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Where do we begin recognizing the extent and implications of "option spaces", domains of relations which are pertinent to life and survival? 

We first experience "option spaces" while we are developing in the womb.  Limitations of movement, restrictions on physical enactions as we float blind yet sensate in the amniotic sea.   Jerky inadvertent muscular contractions that develop procedurally into coordinated muscular behaviors - because of the bio-environmental feedback - inform our neuro-anatomy that there is companion "else" surrounding us.   Even the stimulating fluid that graces our skin.   It is with events on that order of activity where it really begins. Where, quite bluntly, we float/bump/run into-things, and experience sensoriums of tactile extensions, resistances to progression, to momentum, and experience first hand all swarms of relationships to this 'space-of-being' - and through repetition/reinforcement retain else-self behaviors - establishing "pure cognition" models of space and how it/we perform together. 

Pre thought.  Pre language.

Later on, we expand that sensate comprehension, mapping it into cognitive awarenesses that we can draw from, and, after even that, into alert accessible "understandings" in models become the principle mode of communication with one another.   In fact, we revel in improving that clarification, even raising it to the level of science and philosophy.  Only here we call it Set Theory.   We become definitively fixated on 'limitations', 'boundaries', and all the sundry implications involved.  Even in high science, where Fuzzy Logic (Zadeh Logic) challenges the normalized boundaries of conventional statistics, where Bohm's Implicate Order challenges accessibility of 'normal space', and where the Integrity Paradigm challenges the artificial strictures of Gödel's Incompleteness theorems.

At issue in those venues is the necessity to deal - now and inside - with information that exists in the elsetime and on the outside of variously defined boundaries, of events and situations. Dynamics which are more open and more complicated than conventional simple models take into account.

Helpfully, there is a situation that can enlighten us.   If existence is sequentially deterministic, then how do neighboring space, subsequent opportunities and the like "frame" how things progress?  Let's take a look.

As a youngster, I loved doing puzzles. As I did, I noticed something fascinating about solving mazes. Trying to find the correct path by starting at the "beginning" wasn't always easy without a lot of trial and error, or previous experiences, or intuition.  But, I noticed that if I took a large overview, starting at the "goal" and working backwards, the solutions were usually very easy to find.  Now typically, every child who does something like that, and I assume everyone does, is usually told by adults/teachers, "That's cheating, don't do it." or something equally absurd because of other social agendas involved.

But, those chastisements didn't hold water for me, because I readily saw that if a path could go one way, it goes the other way too, and to label one entrance as "start" and the other "finish" was only a random choice.  The thing is, why weren't mazes as difficult or as easy in one direction as the other?  Something else, quite fundamental, was involved, independent of human ingenuity.

It was then that I realized that nearly every maze-puzzle has some sort of bias built in to its design ... either because of its designer's personal tacit perspectives, or, because of the nature of "junctures" (intersections, intersection angles, increasing or diminishing geometric placement possibilities) ... whereby it is easier to back-track the various patterns and causal connections in a goal-to-source direction than in the source-to-goal direction, of typically designed mazes.  There are just so many turns or options that can be fitted into an area, and as space is used up, what remains is an even smaller area to make choices in.  Ergo - typically but not absolutely - a performance/design bias.

The number of options near the end is fewer, being .. in the vernacular of modern science .. more 'ordered'.  There is a lower entropy architecture present at the end of a maze than at the beginning.    Thus, there is an "entropy" gradient in the design so to speak.    As I was beginning to appreciate the relations of things and process, here was one reason why typical mazes are easier to solve and get through in the overall from the 'goal' to the 'start'.

Collaterally, an important technique I also used in finding solutions was being able to constantly maintain an overview of the flow and design of the options available at each juncture - being able to quickly evaluate side paths out to some peripheral distance, and then come back to the main task ... complete the path. 

In working backwards, side paths tend to be shorter in length (and therefore quicker to evaluate) because of "environmental" competition that exists .. what I mentioned earlier about diminished areas into which the maze can go.  The residual design-space - which back-to-front is encountered first rather than later - is smaller and therefore easier to evaluate.  

In biological terms ... it is a competition for limited econiche space. 

Physical spaces in which to draw new paths are already used up by previous original-path extensions.  That is, in any closed-bounded domain, as the number of options present when any juncture is progressively reached and available optionspace is used-up --  then the remaining space available to create additional separate paths is diminished. That alone is enough to create a "decision differential".  Each use of space within-a-boundary reduces the subsequent choices left available in the remainder of the construction..

The same holds true for spacetime in general, and closed systems which are held fixed and not free to re-order, specifically

The same holds true in non-quantum, thermodynamic/relativistic systems with non-zero motion - in regard to the whole space around them.  From a stationary position it's possible to reach an infinite number of "next" locations that are accessible around you (using ultra-fine partitioning of the space you exist in).  If you are in motion with some momentum heading towards that a 'next' location, it becomes more difficult and in some cases impossible to reach the same set of "next" locations once you get to the new-point.  Having a prior momentum imposes a limiting condition which reduces the overall "next" options that originally existed because some options are receded from.   In a similar way, a channel corrals its content, reducing "next" options, especially along lengths of path with no junctures.

Absent some additional mechanism or force or path option, water won't come out of a down angled spout and then suddenly turn to the side or rise up to the ceiling.

The 'design space' of predominantly closed systems is more deterministic and simple to model.  The behavior gradient narrows, simplifies, organizes, and focuses - in opposition to any dispersive trend of entropy.

Contrarily, open systems have increasing 'opportunity' junctions and events.

Biased Maze 1		Neutral Maze 2

What significance does this have for human life?  I would suggest it is crucial for all holistic sentient systems. The Global Workspace of the Mind (Baars) operates with both of these dynamics (trace forward | back trace) engaged and is a case in point. 

"Original experience" typically proceeds slowly by the source-to-the-goal constraint.    Yet, once the information net is expanded ... and thought space or process space is defined (retained) ... the connections become relational and are forever perceived and evaluated "in larger contexts", where all stored information is, by re-enforcement, linked closer quicker and more directly...indeed, improved by re-iteration.  Benjamin Whorf observed in the 1930's that "experience becomes perception (expression), which in turn, becomes "experience" ".  So the paths and access connections that enable new actions and subsequent uses of prior 'experiences' are re-enforced and used more often.

Mental operations, then, function primarily in a sort of time-reversed mode - sequence reversed access -  because that activity is supportive of quicker response times and therefore greater security-stability, i.e., Integrity.  It is "Recall".    Everything universal proceeds "time-forward".   Yet information retention in quantities over-and-above minimal "stasis" requirements permit the re-use of that information, "retrieved" in paths that are basically directed contra to the paths of acquisition.   Over and over again.

We "go forward" into our pasts, to deal with "now", and apply it, endorse it, to anticipate the future. The improved ease of retrieval - defined by constant and quicker positive feedback to whatever Integrity states are involved - is achieved by constant re-processing of those success-loops, and are known to psychologists as "reinforcement" behaviors.

Artificial Intelligence research to date has reached an interesting plateau, in this regard.  The micro- and nano- circuitry available, combined with co-processor redundancy, is producing some spectacular results.but there are limitations. I suggest it would be worthwhile to go one step further.   Besides using self-educating neural nets, besides using Zadeh Logic, it would be wise to use the computer architecture strategy similar to what was developed in the machines that play Chess. Those programs already function as Recall operations in evaluating moves and strategies. They use "probability for success" evaluations - several moves deep - for each initial response choice, and see those options in terms of the move-space available.

Some routes are open ended. Some close off rather quickly. Others lead to obvious failure vis a vis some "goal". The choice-set improves as the game continues. The menu of action choices improves as the game progresses. In the closed environment of chess, this leads to winning strategies. But the same process can be applied to holistic open-environments. In this case there is a duality of options that can be developed: safe conservative choices that re-enact and re-enforce past behavior choices, and, adventuresome behaviors ... keeping and applying the repertoire of other infrequently used choice-options which might find new appropriateness as new situations and conditions arise as the environment continues to expand.

Applying this to artificial intelligence would give it a significant increase in desired performance, by "evaluation synchronization" of input from several distinct parts of the electro-magnetic spectra. Each evaluated separately, then internally in synchronous coordination. Each choice-moment evaluated under the synchrony of Zadeh Logic.

The cept and realization that becomes most obvious is that it is right here that we find the true difference between living and non-living systems.    Human-contrived artificial systems are close-bounded, where as "natural" systems are open-bounded - on all levels. A "robotically" devised system has some framework architecture that is distinct and separate from the programming. That framework will always ƒfunction as a boundary limit of possible behavior. A static chess board is a closed-field of 64 locations. A conventionally robotic AI will always have 'x' number of circuits, gates, connectors and processors - no matter how large that number may be. And the "programming" will only be as applicable as that constraining number allows... and the routing design dependent upon a static architecture. "Living" systems will always be distinguishable because every level will never be limited by those restrictions.   They are reformable, self-repairable in situ (at the site) using local mechanisms - not dependent upon extraneous incursions.

Corresponding dynamics in "concept space" illuminate the physiological underpinnings.

My youngest daughter - by age twenty months - had been shown and exposed to a variety of experiences and concepts. Among other things, she had been taught "in", as in you can put things "in" a cup. Among her toys - dolls, whistles, bells, books, rollers, etc - was a single soft cat figure. It was the only one open on the bottom and we had shown her how to put her hand up inside, and we called the thing "puppet". An obvious thing to older humans ...a figurine that could be manipulated to resemble a living creature. Well, I walked in to her room one morning to take her out of her crib. She was sitting toward one end of the crib, back resting on the spokes, holding and playing with her milk bottle. As I walked in, she glanced up at me, then very matter of factly turned to look down at her feet again. Without a moments hesitation she took her bottle, which was the disposable insert type (open on the bottom)...and put it on her foot. "Puppet", she announced, very proudly.

There it was. No face, no figurine likeness. It didn't matter that it was a foot up inside this thing and not her hand. Out of all the experiential information she was capable of processing, she was open enough to recognize what another essence of "puppet" was...from among all the other noise/data she had experienced, and whether we adults focussed on that aspect or not...and apply that special real version and meaning to the world around her. Would even the most astute AI programmer be able to include every potential option to account for all known and unanticipated interactions and viable Integrity responses? Are past experience or practiced biases truly the sole reliable guides for designing the future?

All energy transfers - and components of such transfer - are information.  The only "apparent" difference is ƒfunctionality. "Useful" energy is information. Energy which seemingly has no use, purpose or pertinence, is categorized "noise". This is the limitation inherent in whether a given organization is "open to making connections" or not - from the flurry of all possible information. An openness which "artificial" systems cannot exhibit, that living systems can. Within the capacity of every life form is the ability to encounter and respond to all energy as potential information. Artificial systems are constrained by the imagination and awareness limitations of their creators. And deficiencies or inadequacies in preplanned preparation end up being displayed as limited-
performance-operations. Closed-boundedness. Living systems are open-bounded. Gödel is closed. Integrity is open.

In computer hardware, one of the primary limitations of size reduction (as a measure & technique for improved performance) is the amount of heat produced by the movement of so many electrons through the circuitry. In living systems, heat removal has been co-developed along with the information processing structures. For some life forms, the general environment it exists in is the "heat-sink". In others, such as ourselves, circulating fluids (blood, e.g.) are a co-ƒfunctional system for conveying energy containing molecules into where they are needed, removing waste byproducts out, and heat-removal. All (and more obviously) dynamically interactive in accomplishing several requirements simultaneously. (This being another indicator that several entropies are co-operating in any given process.)

This is the difference between a Biota or Gaia, and what humanity has created "artificially". We haven't yet been able to pre-plan for the extraordinarily wide spectrum and interconnectedness of information and energy transfers....the integrated integral Integrity co-dependence. Fuzzy Logic is one of the steps in the right direction, because it opens up the channelizations and connections of possibility. It enables a mutually singular-coordination of information, energies, ideas, and potential. Dynamically focussed toward the smooth ƒfunctioning of some identifiably unique organization - which is open to balanced adjustments by a spectrum of inƒfluences. In a way, this is a window toward appreciating just how extraordinary Creation is. Just as AI entities are insufficient models for us and our conscious-ness, we too, ...all life... are insufficient models for the Essence behind Creation. I can't help but sit back and laugh, thinking that we ... all of us ... everything in the Universe ... just might be the God-head's idea of "Artificial Intelligence"!! As incredible as all of the Universe is, it still pales in the light of that Essence. Absolutely fantastic and awe inspiring.

The ƒfunctional mechanics of Fuzzy Logic - which is the predominate process for handling information - comes into strong focus here. In the current state of analysis about Fuzzy Logic, there is a strong requirement to re-evaluate existing (read: human expert interaction with subtle system controls and manipulations) procedures, and code/translate them into a spectrum of weighted and interaffective rules. ( In one sense, this re-establishes the smooth informational continuum of the Calculus... designating a finer and finer mesh netting of information "infinitesimals" that blend into continuous but alternative options) In the primary analysis though, the "bounds" and "goals" must be predetermined, the language and choice options pre-evaluated, and the Fuzzy control deployments built around that knowledge. As the control process continues it must constantly refer back to such "net-goals" and "bound parameters". The re-loop is a RECALL process.

In addition - but more for those deeply interested in analytical reasonings dealing with other aspects about the architecture and idea/reality relationships of this improved dimensional and infinite-dimensional house of existence - I refer you to a paper by Kevin Johnson and Reasoning in a Transfinite Cantorian Universe, presented to the ISSS conference in July 2000.

Life is a persistence of encounters, reactions and choices.  Blends of 'dimensions of opportunity'.  Mazes and minds, unceasingly to be dealt with and uncompromising in their presence.   We suffer outcomes and reap rewards .. the chance to continue existing .. ourselves and our posterities.   Adapting and creating simultaneously, for that is the way of things.    Experience and knowledge.  Essence and purpose.  The great hunger.   We are steeped in it, infused of it, and we act our existences accordingly.   Mazes and Minds.

 

November, 1999
June, 2000

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