Splitting of the billiards

On January 25, Russian President Vladimir Putin, on the occasion of Tatyana’s Day, despite the obvious aggravation of international tension, or maybe because of it, met with students via video conference. Special QR “b” Andrey Kolesnikov draws attention to the fact that for some reason Vladimir Putin was given only mathematicians who explained to the president even the inexplicable laws of billiards.

Against the backdrop of events that excite the world community in connection with Russia (it seems that in connection with the impending invasion, only one question really remains unanswered: to Ukraine or to Ukraine?), An innocent meeting with students on Tatyana’s Day looked, one might say, even bold. That is, it looked the way it should have looked according to the thoughts of those who would like to make it clear that war is war, and lunch is on schedule.

Moreover, it is not very clear why so much was said about mathematics. Such a number of mathematicians gathered at a videoconference with the president that it could already be mistaken for the International Congress of Mathematicians, which in fact will be held in St. Petersburg only in mid-July.

Mathematics students were very proud of themselves, they talked about probability theory, mathematical analysis and logic, and about the fact that they were invited to the congress as speakers.

Indeed, a sense of inferiority was already beginning to haunt you because you were not invited to this congress even as a journalist.

But on the other hand, I liked these mathematical games of the student’s mind with a sincere attempt to captivate the president with them, because finally not only experts on the use of the teenage vaccine against SARS-CoV-2 and not members of the government with their incessant deputy prime ministers spoke publicly here about absolute records of the increase in the incidence of COVID-19, and normal people with an overdue conversation about the modernization of the maximum likelihood method and the possibilities of subadditive measures, as well as decision-making in conditions of fuzzy information.

Vladimir Putin, in response, promised to at least try to attend the opening ceremony of the International Mathematical Congress and admitted that “everything is mathematics one way or another”, and also expressed the hope that “it will help us”, although, of course, apocalyptic doubt has been creeping in for too long in that something will help us.

Mathematical statistics and probability theory, in fact, have become routine tools for physicians and sociologists, a mathematics student explained to the president and encouraged that “it was mathematics that always helped to withstand the difficult challenges of the time.”

She seemed to hint: we are here, we, if anything, will help:

– During the Great Patriotic War, Academician, Professor of Moscow State University Andrey Kolmogorov developed special tables for artillery, creating a unique statistical apparatus for this, which made an undoubted contribution to our victory!

It was clear: and now we will create what is necessary and how it is necessary! 31 medals at the World School Olympiads in a year… Can’t we create one!

“Interdisciplinarity has always been important, at all times,” the president agreed, “but today it is especially important! We all understand this very well: discoveries are made at the intersection of sciences … And mathematics, as a rule, acts as a link … Viktor Antonovich (Mr. Sadovnichy, rector of Moscow State University named after M. V. Lomonosov.— A.K.) told me a lot about this!.. He, as a mathematician, certainly supported and will continue to support this direction at Moscow State University… I don’t remember… Galileo Galilei, in my opinion, said that it was in the language of mathematics that God wrote the Universe.

Galileo Galilei said so, but now it was a little insulting for the students of the philological faculty. Everything that day went to mathematicians. (He and Mr. Putin had already discussed whether the students of the Mekhmat of the University could teach students at school … No, I got a vengeful satisfaction from the fact that they still couldn’t at least do something …) But at least the Bible was written in the language of letters. (Although here, for those who wish, there are, of course, fatal mathematical patterns. And the very selection of these letters in the end will turn out to be high, although hardly higher mathematics. At least Academician Kolmogorov himself did this in his famous work “Proceedings in Poetry” .)

That is, to make it completely clear: the first six students who spoke were mathematicians. And only then came physics.

One Moscow State University student thanked for the construction of new dormitories, in one of which he already lives and from time to time looks out of the window at the foundation of the other, “the construction was a little delayed and stopped.”

Mr. Putin asked the rector of Moscow State University why this was so, and he first said that “today we have a holiday, Tatiana’s day, they are waiting for me-do-woo-hoo” …

The hint was clear: it’s time to roll up.

“I see…” the Russian president nodded. “Everything is good only in moderation. You can’t do without mead, but…

Vladimir Putin may have forgotten how in 2005, in the pre-Covid era, he himself, surrounded by dozens of students in the new fundamental library of Moscow State University, drank mead without measure from a huge mug with a double-headed eagle.

“Well, as soon as they heard about the mead, the questions disappeared,” he then told the students.

Now he asked them himself:

What about the campus…

– There are your instructions on the board of trustees (MGU. – A.K.), – Viktor Sadovnichy assured him, – and Dmitry Nikolaevich Chernyshenko (Deputy Prime Minister of the Russian Federation. – A.K.) is doing a lot, but the question remains in place …

There was some contradiction in the last sentence.

“The foundation has been built,” added Viktor Sadovnichiy. A.K.), build a dormitory for 3 thousand people … The guys from other cities would be very grateful … It would be a holiday …

And Dmitry Chernyshenko would finally breathe a sigh of relief.

“Well, we will call you then and see what practically needs to be done to push it all,” Vladimir Putin completed the construction of the campus for the anniversary.

Here again, mathematics students with coming-outs took over the conversation about the fact that they had “a calculator in childhood was a favorite toy.”

One mathematics student decided to talk about “what important practical results pure mathematics gives, using the example of non-standard use of billiards.”

— Billiards? Mr. Putin asked incredulously.

– Billiards in mathematics is a game of the mind that promises unexpected results. The billiard ball moves simply. The angle of incidence is equal to the angle of reflection. However, if we change the shape of the table border… Well, suppose that the border consists of ellipses and hyperbolas with a common focus, a world of rich internal symmetries will appear,” the student encouraged. . This is when several billiard tables are glued together along the ribs-backs, and the ball moves from one table to another. It turns out that this approach perfectly models many approaches, important actual systems from physics, mechanics and geometry!

The student was visibly inspired by his own story and looked invitingly at the president, but so far, apparently, Mr. Putin has not experienced reciprocal enthusiasm and has not even tried to portray it.

“For example, in space, heavy tops-gyroscopes,” the student continued, “suddenly change their stable and unstable regimes!” This difficult to explain phenomenon bears the name of our wonderful cosmonaut: the “Dzhanibekov effect” (Vladimira Dzhanibekov.— “b”)! As we unexpectedly found out, such an evolution of complex gyroscopes is completely modeled and predicted with the help of billiards!

Well, is it really possible not to admire this, said the whole look of a capable student.

And Vladimir Putin could not let him down and decided to take part in the conversation.

— Gleb, — the president turned to the student, — what if we just increase the size of the holes and their number? ..

– No no! the student laughed condescendingly. “It’s a little different there!” We are not interested in hitting the hole. We are interested in the structure of the trajectory!

And he laughed happily again.

“I understand…” Mr. Putin sighed.

He is interested in getting into the hole, that is, not the process, but the result.

And for this you just need to make more holes (not to be confused with funnels). And wider, wider.

Because this is what works. And not the structure of the trajectory.

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