- THE. But it is also written that:
“… , then it would be mathematically impossible for
of large collections of indistinguishable particles.”
- P. Phew, there is energy for so much grace! Now I'm like you, exhausted. Courage, let's continue some more. There must be a spectacular reason for this statement, let's see what it is:
“The usual math is strongly inspired by the experiences we have on the day.-The-day,
inconsistent with the apparent reality of the world of protons and electrons.”
For breathlessness, let us ignore the tranquility of the statement of the "apparent reality of the world of protons and electrons" and stick to the statement about mathematics and its inspiration in everyday life. Now it's too much! Patience has limits. Who are those who “have day-to-day experiences inspiring mathematics”? What is “everyday experience”?
- THE. This directly contradicts what you preach in your calculus classes. For example, when you claim that without the pure theory of calculus you have no way of knowing if the graph plotted on a computer screen is misleading. I mean, everyday life (computer graphics, for example) has to be inspired and guided by mathematics, not the other way around!
- P. Well, have you ever noticed that I risk my job in every holy (or demonic) class. If the school principal agrees with the article, he will have to fire me. Patience. But the life of a specimen in the Hoss net is a constant danger indeed. I have been studying mathematics and physics, perhaps not intensely and academically, for 35 long years, and I have never experienced a single experience in my life that would inspire any mathematical concept. (I insist that the possibility of me being a mere windsock is open.) On the contrary, quite the contrary, this naive and poor mortal (windsock?) Thinks for more than three decades that his daily life is inspired and illuminated by mathematics. and by physics. The most important concept of mathematics, the infinite, for example, has always inspired me and illuminated my experience with “countless” collections of objects and the “unobservable” part of the universe. We don't really know if the universe is "infinite" or if there are infinite "universes", nor do we know exactly how many stars are in them. The star collection is an “uncountable” collection, it resembles the collection of possible numbers obtained intuitively in counts. Imagine (you can't experience this!) Every possible count of things by any being in the universe, so you will need every possible natural number, that is, you immediately need an infinite set of natural numbers. This is straightforward in your study of mathematics. So what I cannot "experience in everyday life" is filled with the notion of "infinity." Without these wonderful math glasses, we would see absolutely nothing in everyday life. Didn't Popper teach me that "theory is prior"? Mathematics is the theory par excellence!
- THE. You are kind of excited.
- P. There's no other way. The concept of equivalence class inspires me and illuminates my experience with the various ways of representing a real number. It is unnecessary to continue to give examples in this line of reasoning, but it is worth remembering that my experiences with physical concepts are inspired and illuminated by mathematical concepts, just as many intellectual experiences (such as instantaneous rate of change) are difficult to classify as physically or mathematically inspired. although it is clear that they have absolutely nothing to do with everyday experiences: there is nothing in everyday life that remotely resembles the idea of instantaneous rate of change or instantaneous speed. This physical-mathematical concept is pure physical-mathematical imagination with enormous benefits for the Hoss species in its daily dealings. Fortunately that's the way it is!
- THE. At this point I think I am also crazy, I convinced myself of this in his classes on limits and derivatives.
- P. Precisely because they are pure abstract speculation, mathematical concepts have numerous applications in all areas of science and human knowledge. As Michel Serres says, it is precisely because he has no commitment to any particular situation that mathematics is available to be applied, in principle, in any situation, to any phenomenon. The abstract characteristic of mathematics is precisely what gives it so much power and so much beauty. It's tiring to have to restate this periodically!
- THE. Don't get too excited. You are past fifty. It can do harm to your heart organ.
- P. As one teacher I miss so much said, "Math is pure imagination." Who knows, now I say, that half the genomic difference between the Hoss and the chimpanzee is precisely the ability to abstract, generalize (go to the essence of things) and, with these glasses, "see the world". If not, we will strive to introduce this trait into the genetic evolution of the Hoss species. I was happy before you came to ask me about this article, thinking that mathematics is useful precisely because it is abstract, and because of that, it is able to "illuminate the world." I think I'm still happy about that, but now unhappy to see that this is far from obvious not only to most of Hoss's 6 billion specimens, but also to storytellers in excellent scientific journals.
- THE. I disturbed your calmness and emotional balance.
- P. I bet a real like Russian Yuri Manin, a great contemporary mathematician, did not and will never make, analogous or equivalent statements to those bombastic, hilarious, nonsense that you brought me and I dared to analyze. For example, I can't imagine Manin saying:
“One of the main lessons of non-individuality is to attack
the dangerous (though not necessarily undesirable) compromise that
the usual math has with the way
mathematicians perceive the so-called real world.”
I can only say, please, help !!! Quickly bring my high blood pressure medicine! After 35 years studying mathematics, I have not yet “realized” the “real world”. My mistake was to study a little bit of Knowledge Theory and get the impression that the "real world" is a bit complicated to be "known". But some seem to have no doubt about him: they must be much happier specimens of Hoss, with blood pressure 12 by 8 and, therefore, congratulations to them (mine must be 18 by 12).
- THE. Master, very calm at this time! Take the things that happen on Hoss's net in sports.
- P. I'm trying, but it's not easy. See this:
“Our usual view is that people and objects are individuals.
Each person, flower and number is unique.
Despite the widely held idea that
math deals with abstract concepts or structures
and generic, its link with the “reality” in which
the mathematician lives is not always questioned
with proper ownership.”
I thought that mathematics was a creation of some specimens of Hoss and therefore has no commitment to anything. Those who are committed to something are the few specimens of Hoss who seek the path of "reason" and find mathematics, such as Thales of Miletus and Euclid of Alexandria, or Albert Einstein, for example. Also dangerous are the commitments of some Hoss individuals to endless "unusual" mathematics, such as Fuzzy Mathematics, for example?
This idea of "usual mathematics" is not necessary. Mathematics is a certain mode of some Hoss individuals theorizing that includes infinite Logics and infinite Set, Category, and Factor Theories. Why, then, with one of them?
The infinite possible Mathematics are as abstract as Classical Mathematics (Zermelo-Fraenkel Set Theory & Classical Logic & Categories and Factors) and are only linked to themselves, their intrinsic structures and internal coherence, and nothing to do with fiction. illusory call "the reality in which the mathematician lives". On the contrary, it is precisely the infinite possible mathematics that provides the only rational chance to question any such invention. One caveat: beware of the stories that mirror the accountant.
Of course, this caveat is especially true of this poor naive mortal, calculating teacher about to be fired for his stupidity, puzzlement, avid reader of Sciam. =
- THE. Master, very calm at this difficult time!
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