We live in a world in which analysis is performed in a logical framework. Every question which we can answer is answered with a unique answer. On a Quiz, papers that have answers that agree with those on the answer sheet are right; the others are wrong. Logical systems satisfy closure; every proposition has a unique conclusion.
This same world is one in which rationality holds sway; many conclusions are expected. Solutions are contradictory. For every one who sees clearly that a stock share should be sold, there is another one to whom it is obvious that the shares should be bought. For every Pro there is a Con.
The question thus arises: Would it be worthwhile to forego logical, deterministic, solutions to questions about the world, and use rational, non-deterministic solutions instead? Are there advantages to be found in such an approach? Computer power is so great now so that one can fumble around for a solution and still rapidly complete the process. Probabilistic situations are non-deterministic. But physicists have converted those problems to deterministic ones by restricting answers to descriptions of the range and frequency of those results. Darwinian Laws or Mendelian Laws of genetics appear as deterministic tools, but they are broken if they are taken to apply in single instances. The parents of six daughters who want a son know full well that genetics is non-deterministic. Mathematicians are interested in the role randomness plays in the world of analysis. The number pi appears to consist of a random sequence of digits; the numbers 0 through 9 each appear in it 10% of the time in a decimal representation. But the information the infinity of digits that pi represents must be trivial for the sequence of those digits can be compressed into a concise computer algorithm. And Godel proved that a formal axiomatic system containing simple arithmetic is consistent (free of contradictions) yet incomplete (it does not represent all the truth). To summarize: Using non-deterministic, say, random, processes, and some metric associated with the problem, one can construct an ensemble of pretty good solutions to a problem; probably a denumerable infinity of them. Are the best of these pretty good solutions usable? Does the ensemble, possibly, contain solutions of special value?
I am exploring the potential of non-deterministic analysis by applying it to the processing of the audio used by a hearing aid. It turns out that this approach yields unexpected benefits. For example, signals from an array of two or more microphones can be processed so that the sound from various sources in the sound field can be factored from the total signal. Each individual source can thus be channeled to a hearing aid, and so provide a solution to the cocktail party effect hearing aid users complain about. I am of the opinion that the non-deterministic system supplies some of the truth, or pseudo truth, that the deterministic system lacks.
A digital process has been demonstrated in principle and in concept which serves as a non linear filter to factor the merged field of several or many sources into their individual source fields. An array of miniature microphones, spaced at a distance much less than the median wave length, senses the merged field. The array used with a speech sound field could be mounted on a barrette pinned to the users clothing. In use as a filter for a hearing aid, the speech from the source directly in front of the wearer which the non linear digital process produces as one of the factored sound sources, could be sent to the wearer's earphone.
Work at the present time is directed at producing a processor package that could be carried in the users pocket or purse.
The principle is applicable to all types of wave fields, and situations other than hearing prosthesis. For example, it would be valuable in voice recognition implementation of computer input, or for speaker selection in video conferencing.
Of continuing interest and in need of future effort is the application of canonical thermodynamics to biological processes. In particular the nerve action potential is an ideal subject for a rigorous study of entropy generation during its excitation. The process allows a fruitful study of the effect of the other extensive parameters such as pressure and the chemical potential of anesthetic agents on the process.
The text for studies of Mendel as a physicist have been on file for a few years. He was a trained physicist doing work at the cutting edge of genetic research that depended heavily on an understanding of statistical sampling theory. His work was of interest to naturalists who had not the slightest idea of what he was saying.
An outline exists for an article on Wages: What We Do Not Teach in School In Spite of Its Overwhelming Importance. It is framed up on the uthor's own history of earning and rewards.
This is the weekday effort starting with running, weight room, and a 'Net fix on Athena, MIT's network. And topping this off is a lot of effort on food preparation -- a measure of self protection, for I am quite sure of what I am eating, and that it includes all the food groups and no supplements in little bottles!
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