Fox of France

At this time, not only Napoleon's heart trembled, but he yelled badly, even Laplace and the others were shocked. Why Dean Bonaparte already has a way to prove this weird geometry, but this is normal. If anyone in this world can solve this problem quickly, "Joseph who never makes mistakes" is of course the most possible The candidate is selected.

At this time, on the podium, Joseph greeted Fourier slowly: "Mr. Fourier, um, you can help me and distribute my paper to everyone to see. I can just take a break, too. Drink some water. When they finish reading, we will continue our discussion."

After saying this, Joseph slowly returned to his seat and took a cup of tea. At this time, Fourier also distributed a paper to everyone.

A Joseph's thesis was also sent to Napoleon in front of him. Napoleon lowered his head and saw an attempt to explain non-Euclidean geometry. He opened the paper in despair, trying to find out if there were any loopholes in this round of essays. Although he knew that the paper that Joseph threw at this time was in a loophole, it was more likely than he had brought a hundred thousand current law team to fight against less than one thousand Prussians in the field, and the entire army was wiped out. It may be smaller. After all, there is still a possibility that a few meteorites fell from the sky and hit them.

Napoleon's mathematics is actually pretty good. Although to be honest, he is far from the academician's level, but among ordinary people, it is definitely at the academic level. Therefore, he would not have the problem of not being able to read the paper.

Napoleon quickly read the thesis with a fluke. This paper is indeed a typical Joseph style, with rigorous arguments, no blank space, and buy one get one free, with a deduction of one or two new mathematical tools.

"This is using differential geometry. The whole argumentation process seems to be okay." Napoleon raised his head and looked at Laplace and the others next to him. He saw that all of them had their eyes wide open, but none of them seemed to talk.

"It's over, I probably don't see the problem. Joseph, this guy, really realized such a triangle on a hyperbolic surface. This, I'm so stupid, really, I actually ran to Joseph's base. Don’t show up with him. I thought he really wouldn’t retaliate. I forgot that this guy is always careful.”

Laplace and the others finally finished reading the paper. They looked more carefully than Napoleon, but like Napoleon, they could not find any errors in this paper.

"Joseph, who never makes mistakes." Many people have such a sentence in their minds, and at the same time they feel that the mountain that is pressing on them is a little heavier.

Joseph had finished drinking the tea in the teacup, and added two more cups. At this time, seeing everyone have basically finished drinking, they put down their tea cups and said slowly: "Everyone seems to have finished reading now, do you have any doubts about this Mr. Lucian Evans's paper?"

Everyone is silent.

Joseph said again: "In fact, in addition to my method, there is a more ingenious proof, which was also completed by my friend, Academician Gauss. You can also take a look."

So Fourier sent Gauss's paper to everyone.

This paper by Gauss is also called an attempt to explain non-Euclidean geometry, but his argument is indeed different from that of Joseph. His thinking is simpler and more special. He used the concept of projection to prove the compatibility of the new geometry with Euclidean geometry on the unit circle. If Euclidean geometry holds, then the new geometry must also hold

This kind of succinct derivation, beautiful proof, full of mathematics beauty, for Laplace and others, there is nothing more shocking than it.

"I think everyone should have no doubt about the paper by Mr. Lucian Evans, who is actually anonymous," Joseph said, "If so, I will announce the hearing The result is, um, I think Mr. Fourier made a correct evaluation in the review of this paper. Now, who of you agrees and who opposes"

So everyone, including Napoleon, all agreed.

"Very well, I am very happy to see that our Academy of Sciences is after all the Academy of Sciences, and everyone is willing to make sense. Right or wrong, everyone is willing to speak with papers. Well, Mr. Fourier, you are seeing perfect Before the proof, I made a judgment that passed the paper. And we all know that in this paper, there are many things that surpass our common sense and make us feel unacceptable. Now, I want to ask Tell me about it, why did you make the judgment to pass this paper before seeing the perfect proof."

Fourier nodded and stepped onto the podium.

"Dear academicians, in fact, when I first read this paper, I felt absurd and unbelievable. I was convinced that there must be some kind of error in this paper. It was just that I felt that the Although the creator came up with a ridiculous composition, the level of mathematics he showed in the paper is amazing. I think anyone who really restrains his disgust in his heart and reads this paper seriously Everyone should be able to discover this. I thought at the time: even if this paper is really wrong and absurd. It is also a higher level of error and absurdity, so I will never pursue Zeno’s paradox, Achilles. The last turtle a little before him is obviously absurd, but it is probably absurd with very deep connotations. It is absurd that deserves to be taken seriously. It is like the study of Zeno’s paradox has led to the finite The same as infinite, continuous and discrete in-depth study.

So I carefully studied this paper again. To be honest, this kind of research makes me very scared. My heart tells me that this thing must be wrong, how can there be such a truth in the world. But my brain tells me that this paper is mathematically correct.

This is really a terrible thing, because it almost means that our mathematics contradicts reality. It is possible that our mathematics is fundamentally wrong. At that time, I was so scared that I couldn't eat enough of my food. "

Regarding this statement, even Laplace couldn't help but nodded in agreement. Because this is really scary. It's almost as scary as the universe's 3k microwave background radiation suddenly fluctuates isotropically in amplitude between 1% and 5%, or the universe shimmers.

"However, at this moment, I suddenly remembered something. It was the Bonaparte bright spot experiment of the Dean, which seemed completely contrary to common sense. Doesn't that experiment sound completely unrealistic but as long as the conditions Appropriate, it will really appear in reality. So I got a little comfort, I thought, maybe neither the mathematics is wrong, nor the reality is wrong, but my own understanding of reality is wrong. The real world is like this The grandeur, the scope of our contact is so limited. On what basis do we decide, what is in line with reality, and what is not in line with reality? Maybe, under certain special conditions, this strange geometry It can really be achieved, just as long as the conditions are right, we can really see a bright spot in the shadow of an opaque object.

Therefore, I discussed this thesis and my thoughts with the dean and Academician Gauss. They all agreed with my ideas and worked with me to try to find in reality the conditions that would allow this strange, different geometry to be true. The final result is the two papers you just saw.

This incident touched me a lot. "Fourier listened and continued, "We'd better be more cautious about what is reality." Don't think we really know what reality is. In many cases, the real world is different from what we think. In contrast, I feel that the things introduced in mathematical deductions may be more reliable than the reality we have seen. I remember Dean Bonaparte said before that our eyes will deceive us, our ears will deceive us, our imagination will deceive us, but mathematics will not. This is what I think, thank you all. "

So everyone applauded.

At this time Joseph also stood up. As the host of the meeting, the dean of the French Academy of Sciences, he will give a summary speech.

"Gentlemen, Mr. Fourier’s speech just now gave me a lot of inspiration. I suddenly remembered a pagan story. In faraway India, there is such a story. It is said that there was a king who took the lead. Elephant, come and touch a few people who are born blind. Then ask them what an elephant looks like. One blind man who has touched the elephant's body said: The elephant is like a wall. The other one touched the elephant. The man with the legs said: The elephant is like a pillar. A man who touched the elephant's trunk said: The elephant is like a snake. But we know that they are all wrong.

As for us, when we laugh at blind people who touch elephants, have we ever thought that the universe is much larger than elephants, and we are far inferior to the universe and even bacteria. The area that the blind can reach with their hands is much larger than the ratio of the area that all humans can see in all our ways to the universe itself. Our situation is actually more difficult than that of blind people. Blind people cannot see light, but we also cannot see all light. A lot of light, a lot of sounds, obviously exist, but we can't see or hear. In this sense. Are we blind too? What we have to face is a universe much larger than elephants. In this case, we use our own limited sense of touch as a basis for judging reality. Isn’t it ridiculous?

Therefore, in front of nature and in front of the world, we must be humble. Don’t think that we really understand what the real world is. Otherwise, it may explode our heads with a phenomenon that we temporarily cannot understand at any time. .

Therefore, we must reduce our prejudices as much as possible, reduce those self-identified rules, and do not pretend to prescribe what the world is like.

Finally, Mr. Fourier mentioned earlier that he felt that mathematical deductions might be more reliable than our visual and auditory senses. This also makes sense. After all, our eyes will turn a blind eye to some light, and our ears will turn a deaf ear to some sounds. Our sense of touch has no sense of vibration below a certain threshold. Our sense of smell also has a limited range. Only mathematics seems to be The truth of the universe. "Speaking of this, Joseph paused, then smiled and said, "But at the end, please allow me to tell another story, so as to scare everyone.

There is a chicken who has discovered a pattern through countless observations. That is, every time a peasant woman appears, there will be delicious grains that will fall down to make him full. He has observed countless times, without exception, so that he is sure that this can be used as a basis for understanding the world, an axiom. That is, when the peasant woman appears, there will be grain to eat. As a result, one day the peasant woman appeared again, but instead of bringing grain, she brought a knife. The chicks that greet them according to the axioms become chicken soup.

The axioms of our mathematics ~www.readwn.com~ are not based on the so-called intuitive laws discovered over and over again? Who knows if we are the little chicken? The real world may be very different from our hearts . Therefore, we must be cautious, must have more suspicions, must not have too many prejudices, and we must rely on actual reactions in the real world to judge. "

So everyone applauded.

"Today's hearing is really inspiring." Mr. Monge sighed beside Napoleon. "I think I should share today's story with my students so that they can also be educated."

Napoleon curled his lips and thought: "Joseph will definitely tell this story in the new issue of Mathematics. How could he not publicize such a thing? Well, the various factors in this story are really too Much more. People who are self-righteous and bound by old opinions; people who are modest and prudent, who can overcome their own prejudices; people who wake up and can change past mistakes; people who insist on the truth and are not afraid of power are better than this story. Does it reflect the scientific spirit of the French Academy of Sciences and the Academy of Sciences of Rome? The only painful thing is that I have to be a counterpoint in this story. No, my image in this story must be respect for science, respect for truth, and be brave to correct. Wrong, broad-minded"

Thinking of this, Napoleon quickly raised his hand and said: "President, I have something to say."