BIT Mathematics

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The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with mathematics, that they have become almost a part of its structure under the generic title of Applied Mathematics. But with the progress of time, more and more branches of Science are getting quantified and coming under its ambit. And once a branch of science gets articulated into a mathematical structure, the process goes beyond mere classification and arrangement, and becomes eligible as a candidate for enjoying its predictive powers! Indeed it is this single property of Mathematics which gives it the capacity to predict the nature of evolution in time of the said branch of science. This has been well verified in the domain of physical sciences, but now even biological sciences are slowly feeling its strength, and the list is expanding.

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“Perhaps the biggest asset of (pure) Mathematics is its capacity to predict an outcome by virtue of its closely knit logic. For, once a branch of science gets articulated into a mathematical structure, the process goes beyond mere classification and arrangement, all the way to the fruits of its predictive powers ! Indeed it is this single property of Mathematics which gives it the capacity to predict the nature of evolution in time of the said branch of science. And since this power stems from its logical structure, the issue centres around the very process of mathematical thinking which in turn presupposes the existence of order as the very basis of mathematical logic. In this respect it has been argued that the boundary between order and disorder is the realm of reason, the playfield of creativity! As to the precise relation of Mathematics with creativity, however, a formal consensus seems to be lacking.” -bottom of page 2.

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“He could resolve this vexing problem only after postulating that the vacuum (the state of lowest energy) is already full of negative energy states, so that a positive energy electron cannot directly make a transition to a negative energy state–thanks to the Pauli Exclusive Principle characteristic of spin-one-half particles. It is only when a ‘hole’ is created in this sea of negative energy states by one of these negative energy particles acquiring enough positive energy (given from outside) to jump out of the vacuum, that a transition to a negative energy state by another positive energy particle becomes possible.” -bottom of page 6.

gld: Dirac’s ‘negative energy state’ of the vacuum sound surprising close to my ‘Opportunity.’  Where there is something, a new thing is less likely.

Natural Laws travel instantaneously throughout all of space-time. This is proven by Einstein's equations. The Natural Laws exist constantly everywhere, always. This is really a truism, an ideological tautology, a postulate of Relativity.

Therefore, one material energy change here, affects all space-time points, instantaneously. Therefore the opportunity to become evolves, all where's and in each time, mutually recursively. This function, that opportunity to be, is energetic. This is the energy found experimentally in the quantum anomalies. I call it Opportunity. Dirac calls it the ‘varying negative energy state’ found in the vacuum. The ancients called it the Logos of God. These are three synonyms for the same physical thing. -g

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“All that was needed was that the parameter of energy be replaced by the parameter of probability density.” Another synonym for Opportunity.

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Quantum Field Theory: Its mathematical language being that of the harmonic oscillator (HO) , QFT may be regarded as a collection of harmonic oscillators which must be systematically classified and put to different jobs. Now for a single HO, the total energy is half kinetic and half potential, so it is convenient to define its basic variables as 50 -50 ad mixtures of momentum (p) and coordinate (x) variables whose basic commutator [x, p] has the value ih¯ by virtue of their Poisson bracket structure (see Dirac above).

gld: harmonic oscillators are male/female forms that copulate, creating material being. They do so to live more, for less. Think of them as standing waves. This is the formative Opportunity for becoming more. It is what awareness seeks and acts upon. It’s an artful, not entropic, process. This creative force is named artropy.

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It is fair to ask, “What is the mathematical structure that supports BIT (Bouton Ideation Theory).” The answer is twofold. First boutons ideate physically. This means all of the proven physical, particle mathematics apply to BIT.

Second, and this is the BIT mathematical innovation, the past-forward math of QFT must be complimented with a simultaneous future-back mathematical structure of OFT – Opportunity Field Theory. BIT sits between these two.

More on this future-back mathematics latter. -g

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