The rules of grammars are obviously anti-entropic devices, imposing order and diminishing ambiguity given the set of objects and agents that comprise the object of thought. I believe that the anti-entropic "vector" can be measured both internally using an algebra of grammatical objects, and externally in a probabilistic framework. There are two forces at work:time and grammar. Start at time=0, when the listener/receiver starts receiving the first object (word at the lowest level, the string with no cultural association, etc., no inflection, no expectation given a context, no other clue ), and the first part of the grammatical structure (In many cases the part of speech can be determined with a high degree of certainty). From there, time and grammar almost compete to see which can form the final "other person's thought" first. During this time the possible ambiguities vary both in value and in their domain. By varying in their domain I mean that the grammatical rules pare more of the possible branches of ambiguity than do the objects received. By varying in value I mean the content of the words themselves' meaning. I see there being oscillations in the contribution to anti-entropic forces between the grammatical structure and the word-objects, or phrase-objects, etc... or whatever structures. What we call a sentence is then that structure whose object structure and grammatical structures have reached an equilibrium. The sentence then is a localized diminution of entropy within the wider context, for example, a sentence embedded in a paragraph has local and supra-local(whatever the next unit up is) anti-entropic force. The effect of the force is anisotropic, affecting the structures before t(s(n)) [structure n at time t] less than that after, etc... . The Anisotropic effect is caused mainly by the object value, but the structural component is not negligible. That local force can be measured, and is equal to, but opposite in sign to the normal to the tangent on the entropy curve at that time t(n) [when structure n occurs].
Grammar as a function of Memory.
Deep Structure as the intermediate layer in the mapping of "objects of thought" to language. Deep Structure and memory types
Rules of Grammar in a Hierarchy.
Experiments to determine the hierarchy.
The Topology of Linguistic Structures
I see the understanding of a natural language as a function of time, with dependent variables:
1: objects structures
2: Grammatical structure,
There are two related topologies, one of grammatical structures, and the other of object structures. The Grammatical topological object is a finite multiply connected topological structure, with a kernel and extensions. The kernel is that part which is closest to the deep structure
The topological object of the object structures can be determined as follows, (approximately): take the words in a dictionary that appear on the left hand side, and make them vertices of a polyhedra. Connect them to the words that appear on the right hand side making sure that in the figure no exterior vertices that do not have associated right-hand subsets in common do not form common interior nodes. This (might start to) give some information of the structure of the objects, the figure appearing as some n-dimensional object with related interior islands, hooks, and possibly directed edges.
The duality of object structures and grammatical structures.
Can grammar be treated as an application of K-lines? Yes. There is definitely therefore a relationship to the deep structure referred to by Chomsky.
K-lines, Deep Structure and Grammar
Grammatical 'agencies', (as the word 'agencies' is described by Marvin Minsky in The Society of Mind), obviously seem to be present in a grammar. The same way that Agencies associate a 'trace' of its 'learnt behaviour' a grammar can be viewed as the rules or functions that govern the way the multiple pointers of the objects [data structures themselves] map from the domain of the mental expressions to the 'deep structure, and then to the surface structure... . . The recursive function of the pointers' behaviour may then be mapped to a grammar. The Agencies, from this point of view, will associate the 'trace' from the mental expression, which may be a simple object, or a compound object, to the corresponding pattern.
What all grammars have in common is the meta structure of the data structures.
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Self configurable architectures using AI and Genetic algorithms.
The problem of talking with a machine, no matter what the input, is the discrimination between the signal and the noise. By this differentiation I do not mean necessarily the discrimination between linguistic and non-linguistic elements, but more between what a human receptor understands, thanks to grammar and object content, of what the 'goal' is, and what is instead linguistic 'noise'. The reason for the question arises from questioning the necessary linguistic precision required to program a computer, compared to the much vaguer language needed to convey the same information to another person. The causes are many, but finite and computable. One obvious barrier is the balance between the knowledge (preassure) of both systems, the knowledge content of the message, and the amount of entropy of the channel. Language may then be regarded as a difference machine that automatically configures two objects, (the two minds) so that the difference between the two is minimized. (That is why I used the "preassure" analogy, communication here is the tube connecting two containers of liquid, at different heights, or filled to different levels.) Another barrier is the great amount of 'energy' (anti-entropy) necessary to overcome the different state of entropy (The ordering magnitude may be independent of the relative entropy) of the system 'receiving' or 'opposing', in the sense of having to climb a gradient, the action on the target. This amount of 'energy' is directly proportional to the difference in the 'information structure' between the sender and the receiver. If we take the sum of the receiver's components' contribution to the diminution of entropy in the system, these components identified for now as hardware and software, then the barrier that must be overcome must be less than this amount, or the operation will not be successful. I separate the hardware and the software, as I do time and space of the complexity, because I find it insightful to compare the "hard-wired Vs.'learned behaviors (behavior meant here to convey the relation between an input, and the subsequent modification of an act (such as processing the signal, then understanding it, then 'reacting'), which is the only way the sender can know whether he has been 'understood').
Linguistic rules have a 'goal' awareness.
When a person formulates a sentance, he has a goal in mind. That goal is implemented through grammmatical rules. So the grammatical rules have a "goal awareness" or a Goal encoding in them when they are recaptured at the receiving end. This encoding, and its degree of redundancy, is what what permits us to understand. (This is what I want to prove!)
(The Computer as an Anti Entropy Machine )
The more powerful the machine, the better it can be in discriminating between The Goal and the obstructions to its attainment. The anti-entropic nature of the computer (its ability to filter out noise from the minimal goal path) means that the more powerful the engine, the steeper the gradient of entropy that can be overcome, the energy coming from the 'engine'. 'understood'. This can also give a measure to algorithmic power.
Thank you for you attention and consideration, I look foreward to your comments.
