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The unreasonable effectiveness of mathematics (III)


MJVI uses in the game of Being the strategy of considering your self-awareness as something that is for you. Therefore the whole Being is something to itself, and never, by far, something in itself as an "independent real thing."

Another dominant view in mathematics is Brouwer's intuitionism, which accepts the "trueness of mathematical entities" and treats them analogously as real-world objects, for example, "chairs and tables" (MJVI quotes).

Intuitionists find the idea of ​​infinity problematic, and Brouwer claims that the approach to infinity and the transfinite theory of set theory is meaningless because they are beyond the limits of mathematical intuition. For intuitionists, mathematics is something to be created and not to be discovered, and the role of the “creator” is best presented when the mathematician has to demonstrate his assertions of “existence of mathematical objects” (MJVI quotes).

For MJVI, infinity is the key imagination for the imagination "argument of the impossibility of creation." The question “who created the creator of the thing” is, for MJVI, his greatest strategic move in the game of Being. For himself, or for his own self-awareness playing the game of Being, it is a movement that balances his feelings against imaginations such as "death", "living forever", "owning the truth of existence and the world of things", etc.

There are those who see mathematics as a product of the human imagination and assume that it is founded on their experience with the world and functions as a language.

The real world catalyses mathematical ideas including entities such as numbers, sets, functions, etc.

Part of the mystery of mathematical unreasonable effectiveness lies in the relationship between two different types of worlds - the physical and the mathematical.

If, however, we admit that mathematics comes from the physical world, then the mystery is diluted!

Already for the MJVI, everything is imagination, because everything is the product of his psyche, but experience with the world of things justifies a deep distrust of “his existence”, a total lack of credibility of “real existence independent of his psyche”. .

Any language is but a particular collection of imaginations, albeit a second level, that is, imaginations of imaginations.

There is confusion between what mathematics is and what its applicability is. Mathematics is a particular kind of description of the world. Description is an activity of language. Language describes the “world around us” (MJVI quotes). Different languages ​​offer unique descriptions according to their characteristics. Elements of a language include the types of language concepts, their grammatical structure, their vocabulary, and their meaning.

The ability of language to describe the world is already mysterious. Suppose the world is given to us. This is nothing more than a collection of "objects and events" (MJVI quotes). Language comes from learning to talk about such objects and world events.

Language not only seems to give us a proper description of the world, but also allows us to "negotiate and intervene in the world" in various ways (MJVI quotes). Thus, natural language, like Portuguese, is expected to emerge with the emergence and evolution of the world and therefore should describe the world well.

Mathematical objects are not seen as belonging to the natural world. However, mathematics works similarly to natural language, as it is also language and describes the mathematical world. The surprise is that mathematical objects, which presumably exist independently of the physical world, are apt to describe the physical world. And even more, mathematical language is better than natural language.

The predictive ability of science due to mathematics is the most important validation of mathematics. The mystery of mathematical effectiveness is emphasized by the fact that physicists find the best terms for a physical description, ready and elaborated by mathematicians such as groups and symmetry, gauge theoryor the theory of bundles.

The MJVI again uses the imagination that the opposite also occurs. That is, the mathematician is surprised by physical solutions to extremely difficult problems that he perhaps could never solve, or by unexpected mathematical links between mathematical theories glimpsed by theoretical physicists and hitherto invisible to mathematicians. Moreover, there is no mystery to MJVI in language's ability to describe the world, since language is but a private collection of imaginations that imagine new imaginations and this mystery is no greater than the mystery of self-awareness, that is, conscious self-consciousness, but always supposing this whole scenario in the game of Being and not in some kind of "game of existence."

In other words, the MJVI always imagines itself immersed in the game of Being, while the other self-consciousness considers itself immersed in a “game of existence”. They cling fiercely to "concrete and solid things." Phrases such as "all that is solid melts into the air" seem to make no sense to them. Much less the evidence of the "immediate cancellation of their creations" that time imposes on them continually and relentlessly. They seem immune to the imagination that time may just be the immanent cost of the pretentious adventure of existing. Or they seem far from the imagination that time may be nothing more than an automatic cancellation of any reification initiative.

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