Fourth article in the series, covering the conference that took place on Monday, May 19 on the occasion of 60 years of science in Israel, with the participation of ten Nobel laureates
According to Professor Uman, pure science and applied science are actually the same thing. Science is one entity that cannot be separated into different categories. In order to illustrate the point, Uman told about the XNUMXs, in which mathematicians focused mainly on pure mathematics, out of a sense of contempt for everything that was applied.
In accordance with the spirit of the time, Bauman also decided to focus on simplified mathematics and initially concentrated on number theory. This Torah is particularly interesting because the problems in it are very natural in nature and easy to express and formulate. As Oman says, "Often even children in school can explain the problems in number theory." At the same time, it is often difficult to present a sufficient proof for the solution of the problems in the Torah. But all these were only appetizers in the eyes of Uman, since his main attraction to the theory of numbers stemmed from its utter uselessness. It was, to his taste, the most perfect and beautiful mathematics.
When Uman reached the period of his doctorate, he decided to switch to another subject, which was also completely useless. Uman studied the theory of connections, based on alternating and non-alternating connections. Alternating knots, by definition, are knots in which one thread passes under the other thread, then over it, then under it again and God forbid. A craftsman was able to prove that when two threads (each of which is part of a circle) are tied together in alternating knots, they cannot be separated from each other. When two circles are tied with non-alternating knots, on the other hand, there is no problem pulling and separating them.
This problem, as Oman emphasized, is very natural and easy to formulate. It is very difficult to prove, and he was the first to prove it, but the real icing on the cake is that it is completely useless.
A long jump forward brings us to the year 2004, in which the artist suddenly learned that the theory of connections that he himself had helped to develop and promote, had become a useful and important subject in biology. The DNA present in our cells also consists of two parallel threads - or fibers - wrapped around each other. In many cases the two strands of DNA have to separate from each other in order to allow the DNA to be copied. Problems in opening and closing DNA can lead to various health deficiencies, including cancer. And here it turns out that the theory of connections makes an important contribution to understanding the mechanism of opening and closing the DNA, and as a result - also to the fight against cancer.
Oman describes the shock he felt when he realized that his grandson is now studying at the medical school in Be'er Sheva the subject he worked on 50 years ago, which was completely useless at the time. He excitedly explains that there is no pure science and no applied science. Any 'pure' science will become applicable once people take it and use it to fight cancer, or for any other purpose.
A similar process, according to Uman, also went through game theory. It also started with a mathematician - von Neumann - who proved its first principles without any practical use. But when von Neumann met the economist Morgenstern, the two understood how the method could be used to solve economic problems. Since then, game theory has become a cornerstone and the basis of the economic theories used today.
At the end of his remarks, Uman repeated the key line that he repeated as the second thread in his lecture, "There is no such thing as pure science and applied science," he said, and added a final piece of advice to the hundreds of researchers who crowded the hall. "You have to follow the path where your curiosity leads you."
9 תגובות
lion:
The short answer is no.
As you will see in http://en.wikipedia.org/wiki/Complex_number#History
The geometric representation of the complex numbers was invented only in 1799.
An interesting process: in my first response I said that I did not know the history of the narrator but now - in light of the questions - I went and studied it - at least partially.
Michael (or someone else)
Do you know if when the imaginary (and complex) numbers were invented, they were already defined on an axis vertical to the number axis (or on a plane)?
Levi:
The fact that there is one religious scientist in 100 (that's roughly the ratio) doesn't prove anything of what you're trying to deduce from it. It just proves that humans can live with internal contradictions.
lion:
All uses in the field of electronics are much later than the invention of complex numbers. The number I was invented (literally!) so that even negative numbers would have a root - just as negative numbers were invented so that any number could be subtracted from any other number.
The uses in the field of electronics are much later and are based on the presentation of the complex numbers as a real multiplied by the power of e - a presentation which itself is later than the invention of the complex.
lion,
I highly doubt the original usefulness of the complex numbers. If I remember correctly, there was a course at the broadcast university where they talked about the history of numbers. It turns out that there were certain periods when i was considered a broken and unnatural number (from a moral point of view). I don't believe it was used in ancient engineering.
Another example of pure mathematics that has become applied is the Euler function, which plays an important role in explaining superstring theory (the application here is to a theory that itself is currently not applied).
Michael
I am also not familiar with the history of the imaginary and complex numbers, but I believe that when they were defined they already had at that moment an application in the explanation of various physical phenomena.
I noticed that this scientist is religious...so apparently there are answers to all the difficulties of science about religion,
Maybe then it's time to develop a mathematical theory that can predict what future connections a mathematical subject has that is useless to other fields as well as for any subject that is useful in certain fields how to relate them to other fields
I don't know the full historical story of the number I (the root of minus one) but I guess whoever came up with the nickname "dummy number" did not imagine that it would become one of the most useful numbers.