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Xiao shengchu's mathematical folding problem
The college entrance examination has just ended, and many students have put down their tired camouflage these days and tried to return to innocence. Staring at the newly-released Chinese topic in the college entrance examination, my thoughts returned to the era of liver questions a few years ago and the Chinese exam at the beginning of Xiaoshengchu.

I remember that on the eve of the exam, the teacher told the students with better grades in our class that we should try our best to help other students understand the meaning of the composition during the exam to prevent digression. At that time, the articles were inseparable from the topic, and because of the profoundness of the language, many students often misunderstood the teacher's intention. So with the consent of the invigilator, I asked aloud whether the Chinese topic refers to A or B. I can't remember the specific topic for a long time, but as long as the students who are not stupid hear these two meanings, they will not hesitate to choose A, so there will be no digression in choosing B directly. The teacher didn't answer directly, but asked me to continue the exam, but from the whispers of the two teachers, I seemed to hear that the exam was not difficult.

Of course, now I feel that I am still praising my wit at that time. It seems to be a retarded question, and I didn't get a definite answer, but all my friends got the answer they wanted. At the same time, a concept that I have been playing for a long time resurfaced in my mind-one good question is better than ten good answers.

Before Jarinik, people thought speech recognition was an intellectual activity. For example, when we hear a string of phonetic signals, our brain will first turn them into syllables, then form words and phrases, then understand their meanings in the context, and finally eliminate the ambiguity of homophones and get their meanings. In order to do this, scientists try to make computers learn word formation, analyze grammar and understand semantics. But it turns out that it is not feasible.

Jarinik, a famous expert in information theory, came to IBM and found the equivalent problem of speech recognition and machine translation, that is, communication problem, so as to solve the above intelligent problems by solving communication problems. This is his view on this issue. When a speaker speaks, he encodes his thoughts in words and characters, which becomes a problem of information theory. Language and characters, whether spread through the air or telephone lines, are all an information dissemination problem, and there is a set of corresponding channel coding theory in the dissemination. At the receiving end, the sound waves in the air are decoded again, and then the meaning is obtained by decoding the language characters.

Before Jarinik, the whole world had worked hard for more than ten years and could only recognize hundreds of English words, with an error rate as high as 30%. It took dozens of scientists five or six years for Jarinik to recognize 22,000 English words, and the error rate was reduced to 10%.

Jarinik not only answered the question of speech recognition well, but also raised a new question to the world. Is speech recognition a communication problem or an intelligent problem? Based on this, Jarinik actually promoted the solution of a series of equivalence problems.

For example, Professor Salzberg, Jarinik's university colleague, adopted a brand-new perspective to look at the problem of gene sequencing. He believes that the human genome is just a special book, and there are only four letters, A, G, C and T, so any algorithm for recognizing languages and characters, such as speech recognition and OCR algorithm, can be used for gene sequencing. With this idea, he left the university, went to TIGR, a research institute specializing in gene sequencing, and turned to gene sequencing research, and later won the highest award in that field. He took this as the key to solve the problem and created a new chapter in human gene sequencing.

There are many other similar equivalence problems. Simply put, they can be summarized into two categories: the first category is direct equivalence, including the analysis and prediction of the stock market; The second category is indirect and generalized equivalence problems, including many image recognition problems today, especially face and medical image recognition problems.

Let's take a look at the story of the space telescope told by Luo Pang a few days ago. Space telescope, the larger the mirror, the stronger the receiving ability and the better the effect. However, the carrying capacity of the rocket is limited. The bigger the reflector, the bigger the rocket and the limited size of the rocket, which limits the development of space telescopes.

In response to this question, if you are asking, how to design a space telescope? Just talking, I can't get a reliable answer.

If your question is improved to, how to solve the contradiction between the aperture size of space telescope and the feasibility of transportation? This problem is much better and can be solved.

However, the problem can be further narrowed. How to design a space telescope with foldable structure by using origami method for reference? Just like a math problem, it is possible to solve it in the end.

Achshuler said: "Creativity is the skill to express problems correctly."

Yes, creativity is not a mystery. Its starting point is to correctly express the problem. A good question is to see the contradiction, admit the contradiction, and then look elsewhere for the answer. This is really better than ten good answers.