The Mathematical and Physical Theory of Rational Human Intelligence: Complete Empirical-Digital Properties; Full Electrochemical-Mechanical Model (Part I: Mathematical Foundations)

Abstract

The design of this paper is to present the first installment of a complete and final theory of rational human intelligence. The theory is mathematical in the strictest possible sense. The mathematics involved is strictly digital-not quantitative in the manner that what is usually thought of as mathematics is quantitative. It is anticipated at this time that the exclusively digital nature of rational human intelligence exhibits four flavors of digitality, apparently no more, and that each flavor will require a lengthy study in its own right. The four flavors are as follows: 1) Selection Digitality (SelDi); 2) Nexus Digitality (NexDi); 3) Certification Digitality (CerDi); and 4) Supplement Digitality (SupDi). The provisional title of the forthoming second installment is "The Mathematical and Physical Theory of Rational Human Intelligence, Part II ("SelDi"): Selection Digitality and Probability as Its Perfect Analogue; Probability Redefined and Inverse Probability Inverted, or from Numbers of Balls to Numbers of Urns". The following account will be as explicit as possible in order to afford access to those who have only limited prior acquaintance with the overall topic. Succinctness has many virtues. But these virtues only go so far. The theory at hand describes the operations of a physical tool, the brain. In that regard, the theory is not only mathematical but also physical-more or less in the same way that, say, the theory describing the operations of an electric motor is both mathematical and physical. To the extent that it is designed to fully explain a physical phenomenon, the proposed theory of rational human intelligence can rightly be called a theory of physics and has been called so in the title of this paper. Then again, the physics involved is theoretical rather than applied. As a theory of physics, the theory of rational human intelligence contains a dominant mathematical component in the sense that J.-L. Lagrange's application of partial differential Equations to mechanical phenomena and J. C. Maxwell's application of such Equations to electromagnetic phenomena can be said to be purely mathematical. In fact, the Equations in question say nothing about what the actual phenomena that they describe really are. In that regard, J. C. Maxwell's theory of electromagnetism is not directly and bodily empirical. Nor is the proposed theory of rational human intelligence bodily empirical. Still, the intention at this time is that a future installment of the present description of rational human intelligence will include reflections on the empirical and bodily-which, in the case of the brain, means electrochemical-nature of rational human intelligence. What is more, as the description of a tool, the theory of rational human intelligence should be relevant to a practical side of physics, namely engineering. Since the tool in question is biological, the theory pertains more specifically to bioengineering. What follows in this first installment is not the theory of rational human intelligence itself. This installment ...

Chapter Five : The Prime Sequence: Demonstrably Highly Organized While Opaque and Incomputable (with Remarks on Riemann��s Hypothesis, Partition, Goldbach��s Conjecture, Euclid on Primes, Euclid��s Fifth Postulate, Wilson��s Theorem along with Lagrange��s Proof of It and Pascal��s Triangle, and Rational Human Intelligence)

“…The main design of the present chapter is to determine the true nature of the sequence of the prime numbers, or primes, that is, of the sequence 2, 3,5,7,11,13,17,19,23,29, and so on.…”