Translated material
Two cultures-2
"Banner", # 12, 2007. Mathematical and humanitarian: overcoming the barrier.
From the moment Charles Snow published his famous manifesto “Two Cultures”, quite a lot of time has passed. "Two Cultures" were published in the article in 1956, and then a separate publication in 1963. Snow's work had a strong resonance - both critical and sympathetic. And still researchers - both humanities and scientists working in the natural sciences - return to the ideas expressed by Snow more than 50 years ago.
I want to recall the main thesis of this work before I turn to the main topic of this note - the articles of Vladimir Uspensky (1) , published in the latest numbers of the New World magazines and the Banner (2) .
Two cultures-1
Charles Snow described the paradoxical situation that developed by the middle of the 20th century: “By education, I am a scientist, by vocation - the writer <...> very often - not figuratively, but literally - I spent the day with scientists, and evenings with my literary friends. It goes without saying that I had close friends both among scientists and among writers. Due to the fact that I am closely that I am closely I contacted those and others, and, probably, even more due to the fact that all the time I passed from one to others, the problem that I called me the “two cultures” began to occupy me even before I tried to state it on paper. different in social origin, having approximately the same means of existence and at the same time almost lost the opportunity to communicate with each other, living in such different interests, in such a unlike psychological and moral atmosphere, which seems to be easier to cross the ocean than to make the path from Berlington House or South Censington to Chelsea. "
Snow writes that if “physicists” are still able to perceive humanitarian knowledge (Hamlet is still considered indecent among physicists), then the humanities are not at all embarrassed that they have not heard anything about the second beginning of thermodynamics. From the point of view of Snow, the situation is even worse: this is not just a misunderstanding, but an aggressive misunderstanding - he calls the artistic intelligentsia “new Luddites” who are ready to destroy science in fact only for the reason that they do not understand it.
The article by Snow is rather openly Alarmist in nature. He tried to pose the problem as much as possible, not solve.
Physics lyrics
I feel quite sharply the problem of two cultures, because I received a scientific (mathematical) education, but throughout my life I was engaged in literature. Among my friends there are enough scientists and writers. But the following should be noted. Among the writers I know, there are people who do not just not scare the words “second beginning”, but there are those who are well familiar with such non -trivial scientific fields as quantum mechanics or general theory of relativity. I can call two laureates of the “Russian Boker” - Mikhail Butova, who graduated from Meis (Institute of Communications), and Alexander Ilichevsky - graduate of Fiztekh.
Probably, such a situation arose as a result of total mixing that has occurred over the past ten to twenty years in the USSR and Russia: many people abandoned their professions (including scientists) due to external circumstances.
Nevertheless, the problem of two cultures remains, and how to solve it is not clear.
Crisis of trust
In recent decades, another problem has been manifested that exacerbated the traditional misunderstanding of naturalists and humanities - this is a crisis of trust in science in general, a crisis that led to an avalanche -like growth of pseudo -scientific and pseudoscientific theories. The reasons for this crisis of trust here in detail do not make sense, but it is necessary to state it.
The vast majority of people today know very little about science and are doomed to believe the word to the first counting charlatan. And these charlatans use still high (no matter what) the authority of scientific knowledge, and often use it for their selfish purposes, which inflict severe damage to science.
This kind of false projects, of course, include the "new chronology" of Fomenko and his followers. Here we are faced with the other side of the same problem: complete ignorance by scientists (in this case by mathematicians) of the basic principles of humanitarian research. To trust the "new chronology", you just need to know nothing about history, about linguistics, about scientific methodology. Andrei Zaliznyak in his article (3) , dedicated to the linguistic analysis of the arguments given by supporters of the "new chronology", it seems, quite convincingly demonstrated its complete failure, but his arguments were not heard by either authors or readers. This is the state of mutual deafness.
Mathematics without formulas
And against the backdrop of misunderstanding and crisis of trust, the work of both his task and execution of Vladimir Uspensky, dedicated to the attempt to demonstrate to modern humanities and just people inquisitive (engineers, programmers, businessmen), that there are modern mathematics.
If we look at the school textbooks of mathematics, we will see that the knowledge that is discussed in the school course was the front line of science at the turn of the XVII-XVIII centuries. Has nothing changed since then? Almost everything has changed. This state of affairs led Alexander Kharshiladze to the idea of the need to fully revise the school mathematical course: he proposed to exclude mathematics from the school course for ten years in order to completely reform it .
Uspensky is not so radical. He writes: “So, there is a certain amount of impractical knowledge, mandatory for any cultural person. <...> We believe that this volume includes some of those mathematical representations that are not related to the utilitarian use of mathematics. These ideas consist not only of facts, but also of the concepts and methods of operating with these concepts. <...> In this essay, we are going to talk about mathematics as part of culture spiritual ".
This kind of statement is just a "protocol about intent." But then the most interesting begins. Uspensky takes one after another mathematical problems and shows what they really mean for universal culture. And the first thing to do is the problem must be outlined, almost without using neither formulas nor terms. How to do it? There is no general solution here. Each time, considering a mathematical problem or introducing a new concept, you have to look for the necessary visual material, look for metaphors to make the presentation visual and clear. But at the same time, you still need to somehow not lose either in the depths or in content, and still do not make mistakes.
One of the difficulties in writing this kind of article is the ultimate attention to the correctness of the presentation. If in an article published in a mathematical magazine, an error (for example, a typo) is clear to any reader, then a typo in a popular science article by the reader can be accepted as truth: he simply does not have enough qualifications to notice this typo. At the cost of serious efforts, Vladimir Uspensky managed to cope with this problem.
"Tsarist path in mathematics"
Uspensky starts with a natural series. He shows that such a seemingly familiar object is actually not at all simple, and it is full of riddles and in itself is a high -level abstraction. Uspensky writes about the geometry of Lobachevsky and the quadrature of the circle, about insoluble mass tasks and urgent infinity, about topology, about the hypothesis of Poincar, which Grigory Perelman managed to prove.
Uspensky quotes the following words: “This is what the outstanding mathematician, the teacher of the great Kolmogorov, Nikolai Nikolaevich Lusin (1883-1950) wrote:“ Mathematics are amazed at the harmony of numbers and geometric forms. They come to awe when a new discovery opens up unexpected prospects for them. And the joy that they experience, unless it is the joy of aesthetic order, although the usual feelings of vision and hearing do not participate here. <...> The mathematician studies his science not at all because it is useful. He studies her because she is beautiful. "And mathematicians sometimes want to share this vision of beauty. But, alas, it is extremely difficult to do.
What the Uspensky gropes in this article can be called "royal path in mathematics", which, as you know, does not exist. Uspensky attempts to show non -dummerism the depth of modern scientific activity, not burdening him with a strict need to move step by step along the steep steps of abstraction, that is, along the path along which any normal mathematician is coming. The most amazing thing is that Assumption succeeds. His work, perhaps, is the first intelligible attempt to really break through the wall between two cultures. She shows that there is no impassable border between them, if the reader has enough attention and patience if the author is inventive and thin.
This gives hope that two crops, if they do not merge into one, then, in any case, they will stop scaring and avoiding each other. And if the reader understands at least part of what Uspensky writes about, he will not only enjoy contemplation of high abstractions, but will also be armed to confront pseudoscience.
Notes:
1. Uspensky Vladimir Andreevich-doctor of physical and mathematical sciences, professor, head of the department of mathematical logic and theory of algorithms of the mechanical and mathematics faculty of Moscow State University named after M.V. Lomonosov. Born in 1930. The author of numerous scientific papers, as well as philological and cultural articles published in the magazines "New World", "New Literary Review", "Unaccounted Reserve" and other publications.
2. "New World", # 11, 2007. "Apology of mathematics, or about mathematics as part of spiritual culture." Part 1.
"Banner", # 12, 2007. Mathematical and humanitarian: overcoming the barrier.
3. Article of Andrei Zaliznyak "Linguistics according to A.T. Fomenko."