A Man of Science and Engineering in Troubled Times Wandering in the Late Qing Dynasty

Chapter 352 The Infinitely Small Ghost
The Great God Newton can say that he touched the ceiling of classical physics two or three hundred years in advance, and then he couldn't figure it out.

Perhaps it was also one of the reasons why he engaged in theological research in his later years.It can only be said that Newton is too advanced.

Moreover, a bishop of Berkeley in England at the same time as Newton was not simple. In order to deny the calculus invented by Newton (it was called the method of flow at that time), he proposed the famous "Berkeley's paradox", which directly led to the second Math crisis.

Can you believe it!From a bishop!
The second mathematical crisis is not difficult to understand.

There is a very classic difference between physics and mathematics. In the matter of dealing with infinity, there are basically no infinitesimals or infinities in physics, because physics interprets nature, and there is no such terrible thing as infinity in nature. Especially after Planck, it is relatively The tricky infinitesimal doesn't exist either.

So infinity basically belongs to the concept of pure mathematics.

The introduction of infinitesimals in mathematics is the foundation of calculus.

Bishop Berkeley is really clever, and his spearhead is aimed at the infinitesimal—the ghost-like dx, or the more common Δx when he first started learning calculus in middle school mathematics, that is, "extremely small increments".

Berkeley is directly a super heavy punch:
He gave an example, for example, when finding the square of x, the derivative of this super simple function, it is first necessary to assume Δx, that is, there is an infinitesimal increment;
Then use the square of (x+Δx) to cut off the square of x, which is the increment of the function;

Then divide the increment of the function by Δx.This is a process of derivation.But here's the problem!Since Δx is in the denominator, that is to say it should be non-zero.Keep this conclusion in mind.

But after simplification, the formula is finally 2x+Δx.At this time, Δx can be zero again, so that the derivative of the square of x can be calculated as 2x.

(I posted a picture at the end, it is clear at a glance, it is very simple)

This is Newton's approach, but Berkeley found that in this process, Δx must be both 0 and not 0; sometimes it is 0, and sometimes it is not 0!

So weird!

Faced with this kind of operation that comes and goes when called, Berkeley uttered a very famous joke:

"The Ghost of the Infinitely Small".

After reading it, Newton had no choice but to avoid talking about it.

Although Berkeley's attack was aimed at defending theology, it really captured Newton's flaws, punching to the flesh.

Therefore, it is called "Berkeley's Paradox" in history, which is the beginning of the second mathematical crisis.

When the bishop is in this position, it is even a little touching. 0.0
Bishop Berkeley's approach is much better than many believers who stalked and slandered science later.

At least they really managed to know themselves and the enemy and win a hundred battles. Not only did they thoroughly understand Newton's theory, but they also found key mistakes in it.

This is simply the rigorous academic spirit most admired by mathematics research itself!
This second mathematical crisis caused by Bishop Berkeley lasted for more than 200 years!This person is also powerful enough that the history of mathematics must have his name.

It was not until the 19s that a large number of top mathematicians represented by Cauchy and Cantor finally established rigorous limit theory and real number theory after more than half a century, and completed the logical foundation of analysis. Solved the second math crisis.

They make the infinitesimal no longer a ghost.

But... Seeing the name Cantor, the founder of set theory, some people may have guessed the follow-up.

Just when everyone was about to raise their glasses to celebrate, the bad news came!
From the second mathematical crisis, set theory was born, and then... directly led to the third mathematical crisis.

The third math crisis is coming even more fiercely!
The core debate continued until Li Yu's time travel.To some extent, it is not an exaggeration to say that the third crisis of mathematics has shaped modern civilization.

Mentioning this matter, I also want to add: It was mentioned earlier that physics ushered in a window period at the beginning of the [-]th century because of Planck and Einstein, the two "leaders of the demolition of classical physics";
Mathematics in the same period is also difficult because of Russell's barber paradox in the third mathematical crisis, it is very uncomfortable!

In short, the two basic disciplines of mathematics and physics at this stage are almost the stage of rebirth from nirvana.

Fortunately, the level of Bishop Jason in front of Li Yu was obviously not as good as that of Bishop Berkeley 200 years ago.At least he must not understand the most cutting-edge mathematical theory, otherwise it would really make it difficult for Li Yu to parry.

Li Yu said to Bishop Jason: "Mr. Bishop, since you put forward Newton's argument, you should naturally understand that science has greatly improved its theory in the past 200 years. And the development of scientific theory has not stopped, even like an explosion. It is growing rapidly, and it won’t be long before all the unknown areas of nature will be illuminated by the light of science. This is the general trend, I think the church will not feel it? Even if you don’t feel it, don’t you have received God or the prophet? warning?"

Jason said: "What the Holy See means is that science will never explain the entire universe from the past to the present."

Li Yu said, "One day it will."

Jason laughed and said, "How is it possible! Can human beings go that far away?"

Li Yu said: "There are too many scientific methods. Even if it is not millions of light-years away, you can still use the spectrum to know the age, composition, temperature, and many other information of distant stars. So many things can be done, isn't it? Doesn’t the bishop think that human beings themselves are God?”

"Oh, my God!" Jason quickly held the Bible, "It's disrespectful for you to say that! It's even more impossible! As far as I know, humans can't even measure the diameter of a star, because its hot brilliance cannot People who look directly at it are like those who want to blaspheme the Lord."

Li Yu said casually: "Nothing is impossible. If Mr. Bishop can keep paying attention, I can quickly find out the diameters of dozens of stars."

In fact, in the history of astronomy, it was not until five or six years later that astronomers such as Wilson used Planck's law of thermal radiation to calculate the diameters of some stars from their temperatures.

It can be seen that it was not until then, five years after the theory of relativity had been published, that Planck's very brilliant work was taken seriously.

But Li Yu did not have these shackles.

And it was very easy for him.

Jason disagreed: "It's just some small things in the telescope, how do you know the size?"

Li Yu spread his hands: "I have already said that there are many methods of astronomy. You can pay attention to my thesis. Not only the diameter of the star, but also more content. For example, it takes 2 million years for the sun to go around the Milky Way. Waiting around for data that you will be very interested in."

"What!" Bishop Jason turned pale in shock, "2 million years? Are you talking nonsense?"

Li Yu said: "It's about the same, roughly in this order of magnitude."

“不可能！绝对不可能！”杰森大声说道，“明明是上帝在公元前4004年10月18日创造了世界，然后在10月23日创造了人类！”

"Good guy, do you even have a specific date?" Li Yu was even a little surprised.

Jason said firmly, "That's right!"

Li Yu had a black line: "It seems that Bishop Jason didn't pay attention to the Nobel Prize in Physics that was just awarded last year."

"Of course I am concerned. You are talking about radium?" Bishop Jason said.

Li Yu said: "Not only that, but also radioactivity. You may still read too little of the latest scientific papers. The discovery and application of radioactivity have greatly increased the age of the earth of 1 million years estimated by Lord Kelvin half a century ago. At least for more than one billion years, maybe even longer."

Li Yu didn't dare to scare him, and he couldn't say that later generations discovered that the age of the earth is more than 30 billion years.

Jason did study science and engineering, but it was ten years ago, and his knowledge hadn't been updated.However, he knew that Lord Kelvin was a leading figure in the field of physics today, and he was also a figure that the Holy See could not afford to mess with.

Well, although it sounds a bit sad to the Holy See, since everyone knows that Bruno died unjustly and Galileo was wrongly sentenced, the Holy See really dare not accuse great scientists casually, let alone summon or even pronounce a sentence.

Bishop Jason was shocked: "So, the earth and the entire solar system have circled the Milky Way many times?"

Li Yu laughed and said, "When I was in this position last time, the earth was still full of dinosaurs."

"You mean the bones of that horrible reptilian lizard?" Jason said.

Dinosaurs are currently regarded by people as very terrifying prehistoric creatures, and they have little respect for dinosaurs. They regard them as a failure of evolution, otherwise how could they disappear?Some literature even portrays them as slow, lumbering beasts.

Li Yu pretended to be helpless and said, "I don't know if they were created by God."

Jason felt that his brain circuit could not be turned around, and the CPU was about to burn. After thinking for a long time, he could only give up and continue to ask. Instead, he asked directly: "Mr. Academician, do you think that science and religion should coexist peacefully?"

Li Yu immediately said: "It should be so."

Jason breathed a sigh of relief. Fortunately, Li Yu's attitude did not embarrass him, "I will report to the Pope as soon as possible to discuss how to further promote this matter. I hope you can understand that the Holy See definitely needs the opinions of today's well-known scientists, and must Continue to communicate more forcefully."

Li Yu replied, "Don't worry, I can understand."

The current Holy See has really begun to think hard about how to deal with the relationship between science and religion.

The current state can only be said to be okay. In later generations, the Holy See will recognize whatever science says.

Can DNA be sequenced?I think!
clone?Solitary breeding?OK, I agree too!
The Big Bang Theory?I... I still admit it!

Anyway, all kinds of things that completely subvert theology, from the composition of man to the birth of the world, are accepted by the Holy See, and they only seek to coexist peacefully with science.

However, the Holy See did not completely lie down, and kept looking for "evidence" in the works of the most famous physicist in the world.

The early target was Einstein, and later the most typical one might be Hawking. Theologians once praised his "A Brief History of Time" as "repeatedly mentioning God, even the last word of the text is God", so Hawking was regarded by them as a search God's scientist.

However, "A Brief History of Time" is too famous, and the sales volume is extremely high. When I really opened Hawking's book, what I saw was: "As long as the universe has a beginning, we can imagine the existence of a creator. However, if the universe is indeed completely Self-contained, without borders or edges, it has neither beginning nor end—it just is. Is there, then, any place for the Creator?"

Although Hawking met the Pope and repeatedly mentioned God in the book, even the last word is God, but after reading it through, he knows that this is just a metaphorical usage.

Hawking's God is actually nature.

From this point of view, the fact that religious scholars continue to cite famous influential scientists such as Einstein and Hawking on religion and God has objectively proved that religion has lost its former supremacy.

But the decline of theology is inevitable.

If you have time to travel to Europe, you can see many famous cathedrals, but when you go in, you find that there are not many people.Of course there are still believers, but it is no longer the situation where all people believed in it in the Middle Ages.

A survey was done in the 1960s. In the UK, only half of the British people still believe in God of Humanity (note the prefix), but less than 3% of them know how to worship.

In Germany, where there are so many churches, one-third of the [-] to [-] churches are already unsustainable.

-

After Bishop Jason left, Li Yu looked to the north, and it seemed that he had to go to the Harvard Observatory.

Originally, he didn't want to do this kind of "simple" astronomical measurement, but the situation forced him to do it.

Just as Li Yu was about to leave, it suddenly occurred to him that he didn't need to go. The Harvard Observatory had a lot of data, so he had to send some telegrams.

Director Pickering was very willing to help after seeing Li Yu's telegram. Li Yu originally only wanted a dozen or so simpler and closer-distance stellar data, but Pickering sent fifty of them at once.

Li Yu brought out the invincible calculator and completed the calculation of the diameters of twenty stars in a few hours.

Together with some data about the rotation speed and period of the solar system around the center of the galaxy, it was sent to "Science".

With the current observation capabilities, these results are already very good.

In fact, human beings really know the whole picture of the Milky Way (mainly the bar-shaped structure in the center), and we have to wait half a century later, after the development of radio astronomy, there is hope. Otherwise, interstellar dust is an obstacle that optical telescopes cannot cross.

Jason and other bishops felt that it was impossible to know everything about the universe, so they probably also investigated telescope technology.

But they certainly didn't expect that the telescope technology itself is also developing, not to mention that the telescope can be thrown directly into space in the future.

Of course, no matter what, the shape of the Milky Way is still deduced through science, not really photographed.

If the Oort Cloud is used as the boundary, it will take at least tens of thousands of years for Voyager 1 to fly out of the solar system.

As for the Milky Way, even if it is a disk, the thickness of the disk is 1000 light-years.Even if Voyager 1 can reach the fourth cosmic speed (that is, the speed of escaping the Milky Way), it will take 10 years to fly to the disk of the Milky Way.

We can't wait!
Since the last two issues of "Science" had important content published, the sales volume was very good, and Bishop Jason spent a lot of effort to buy an additional copy.

Seeing the above data, he was completely desperate, the amount of information was too much, and he couldn't get it right!

Bishop Jason had no choice but to write a letter to the Holy See Vatican, hoping that they would come up with some truly effective measures.Don't talk about science and religion anymore, just take practical actions to win over scientists, otherwise it will be too painful for them to slap their faces!
(End of this chapter)