Firstly, l define what I mean by structure equation. The solution of an algebraic equation is a number. The solution of a functional equation is a function, for instance, differential equations. The solution of a structure equation would be a structured set ,say, a geometry, a differentiable manifold, an algebra etc.
As far as I know, the only structure equation that has been widely investigated is the Einstein one, the solution of which is a differentiable manifold determined by its connection coefficients.
A learning system, modifies its own structure as he is learning new topics and handling new information. Thus, the unknown of a learning system theory is its structure sequence determined by the acquired information. I think that this topic must be investigated.
Because it may be argued that structure (e.g., the double helix of DNA, etc.) determines and thereby predicts processes (e.g., leading to gene therapies), (i.e., function instead follows form), both structure and processes need be taken into account for science, or knowledge, to be complete and advance. Such a theory may unfold in the existing literature or branches of mathematics, particularly, Abstract or Fractal and Hyperbolic Geometries, Clifford or Weyl Algebras, if not all branches (or techniques) of mathematics combined for arriving at this same solution that is complete, I would emphasize. In turn, such a unified mathematical approach would also help fractal geometrically (self-similarly) to bring about a unified physical theory between gravity and quantum theory, etc., as well.
Dear Cj Nev
I have voted up your answer, because you have pointed out the core of the intelligent system structure, but this fundational matter is extended by experience together with learning processes via neuron conections and conditioned reflexes- (Paulov).
These conections form a scalable struture. Finding out those equations ruling these processes, in my opinion, is a fundational question.
Dear Juan-Esteban
Indeed, agreed, finding the equation or equations ruling these scalably-structured and I would add importantly self-reflective or -similar (that yes does include or extends from neuron connections to experience and learning) processes, or true, the key foundation, is of the essence. Without such a fundamental, foundational equation or equations, I personally would have no ability to comprehend or incorporate any of the existing branches of knowledge. As I gather this knowledge from here and elsewhere, I intend to publish that equation (or equations) by next year. I have great admiration of those like yourself and others who without such a fundamental equation have nonetheless forged ahead and acquired this knowledge first so very well and insightfully.
Dear Cj Nev,
Indeed, investigating human mind structure is a complex issue. However, focussing on some functions, the task can be simplified.
For instance, consider memory associations. Any student knows that, to remember some topic, repeating it again and again increases the probability of occurence, that is to say, frequency occurrence increases its probability. Notice, that frequency depends on probability; however in memory processes the converse statement is also true: probability depends on frequency.
Investigating those probability distributions satisfying both conditions is an interesting topic. As far as I know, nobody has investigated this kind of probability distributions. Perhaps, this kind of research would improve our mind knowledge.
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