In details

The unreasonable effectiveness of mathematics (II)


Eugene Wigner believed that the miracle of the effectiveness of mathematical language in formulating physical theories was a wonderful gift that we neither understand nor deserve. For him, mathematics is the science of skillful operations with concepts and rules, invented for the same purpose. Such an invention includes generality, simplicity and beauty as inherent notions.

This view clashes with other dominant mathematics.

The realists of Platonism believe that mathematical entities exist independently of humans, as do trees and tables. Such entities inhabit a special world, the Platonic world. The reality of this world explains the universality of mathematical truth. The problem here is that we do not know how Platonic entities, which do not have spatial and temporal characteristics, can have contact with our physical world of spatiotemporal extension. In other words, how do humans access platonic objects?

For the MJVI, the assumption of the existence of Platonic beings is but a kind of dessert at the desire to exist dinner. In its way of playing the game of Being, the MJVI chooses the strategy of caution over the mermaid chant of "existence of the world and things", much less "platonic things."

The MJVI assumes that the "feast of existence" has no limits and easily goes beyond the size of the observable.

For MJVI, this is natural because self-awareness knows deep down that its greatest desire to exist does not rest on the “things of the world” it invents and, to remedy, or to try to save its project from existing, it desperately seeks an even riskier card, transferring to the slightly more protected dimension of the unobservable his “creations of things”.

Another dominant view of mathematics relates it intrinsically to logic. Gottlob Frege said that mathematics is nothing more than a systematic construction of complex deductive arguments. Bertrand Russell tried to show that mathematical concepts could be redefined in terms of purely logical concepts.

The problem here is how to understand the incompatible axiomatics of set theories under the same logic.

However, for MJVI logicism is a much more airy imagination. In fact, for MJVI, its fundamental axiom is purely logical. Its strategy in the game of Being, or in the game of the life of the individual, is purely logical, although classical logic is quite true. He is not impressed by the lesser mystery of being self-consciously endowed with classical logic because he is deeply surprised by the greater mystery of the instability of "NOTHING."

For David Hilbert's Formalism, mathematics is nothing more than a set of rules and formal manipulations of mathematical symbols and terms according to such rules. For the formalist imagination, there are no meanings glued to mathematical objects, equations, or operations over and beyond these meaningless formal manipulations, whether demonstrations or applications.

Math is like a chess game with its pieces and rules of movement. There is no meaning to mathematics other than the game that is played with mathematical objects according to given rules.

The problem with imagination “Formalism” is that it seems hard to accept math as just a game. Its applicability in the sciences, then, seems totally arbitrary and forces us to ask why chess does not apply to the "world" as mathematics does? For Frege, it is precisely this applicability that makes mathematics more than just a game.

For Godfrey Harold Hardy, a formalist, the applicability of mathematics is an offense and mathematics that has applications in practical uses is uninteresting and of little aesthetic value.

The MJVI feels very good in this formal gaming atmosphere that it finds most consistent with an environment of imagination. He observes, by the way, that imaginations are free beyond any imaginable limit. The Being game is a sophisticated chess game in which the rules are never all known and change continuously, and the rule of change is unfathomable.

The MJVI strategically considers the psyche-DNA analogy. Both can only replicate. The psyche, matter in the state of information, replicates through imaginations, but has no control or formula of complex patterns that can emerge in the game of Being.

Similarly, DNA replicates apparently without control, or obedience to genetic patterns that emerge in the biological game, which, in turn, evolves unpredictably in the larger biosphere game scenario.

These are apparently unfathomable mysteries, but smaller in MJVI's imagination than the instability of the "NOTHING". As for the mystery of “applicability,” the MJVI takes refuge in the strategy of imagining that everything is imagination. It robs Sartre of the strategy of imagining that consciousness is for itself, not itself, as Descartes imagined to be the case. That is, for MJVI, “I imagine, I just imagine” and never, “I imagine, therefore I am”. Although Descartes steals (or perhaps misunderstands) the analogical imagination “I imagine because, as much as I imagine I am not imagining, I cannot help but imagine that I imagine”; therefore, I am a possibility of imagination and nowhere near a "thing that imagines".

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