# Zhang Shousheng’s speech before his life: the core of the block chain is In Math We Trust

This article comes from: large data digest, the author: the old, the Star daily is authorized to forward.

In December 1st, American Chinese physicists, lifelong professor of the Stanford University, academician of the American Academy of Sciences, and a foreign academician of the Chinese Academy of Sciences, the founder of the capital of Dan Hua and Zhang Cheng, an independent director of the United States, died at the age of 55.

In this paper, the speech of Professor Zhang Sheng Sheng in the open class of the chaining chain in Tsinghua is arranged.

Good evening, my classmates. I am a professor at the Stanford University and a professor from Tsinghua University. My usual lectures are about physics, but I have been very interested in the block chain.

The topic for today is In Math We Trust, the subtitle is Foundation of the Crypto-economic Science, which refers to the world economic science of virtual currency. I think that, in the era of monetary economy, economic behavior is built in mathematics. The most fundamental behavior of the economy is to trust each other, and the mechanism of trust is built in mathematics.

### View the block chain in the view of Natural Science

We first understand what is money from the point of view of natural science.

Money is a medium of exchange value, which is very similar to the concept of “field” in physics. High school physics tells that homosexual repellent, heterosexual sucking, although two charges do not have contact with each other, but also have a mutual force to interact with each other. It seems to be different from the experience of everyday life. In everyday life, we must have a force and must contact each other.

So with the concept of “field”, a charge produces an electric field and the electric field can act on another charge. So we have to study the interaction between the N charge and the electric field, and the interaction of the electric field in the near distance. This is a conceptual breakthrough in Physics: it is supposed to study the interaction between charge and charge, and now as long as the interaction between the charge and the field is described.

This is very similar to the emergence of money in economics. The beginning of human civilization is the time for things to change. The mode of object change is somewhat like the interaction between charge and charge.

But it’s very difficult to deal with things. You just need my fish. I just need your apple and the number should be corresponding to the deal. Later, we began to introduce money as the medium of value exchange, which was the generation of money.

In the age of money, change the goods into one currency, and then change it into another item in money, just like a charge produces a field, and the field acts on the other.

At first, people think that the concept of the field is a virtual concept, not a real physical entity.

What is the value of the existence of an object? In natural science, the only measure is energy. The introduction of “field” to a certain extent facilitates the mathematical description, but it has no energy in itself.

In fact, this problem is similar to the question of the block chain today, like a large number of physicists who think that the concept of the electric field is completely an empty mathematical concept, not a concept of real physical existence. The introduction of the field as a exchange media, if you do not agree, it is not worth. It is not until the emergence of Einstein’s theory that the concept of the field is really a physical entity, and we can measure its value accurately.

### Consensus is the recognition of value

Say back to money. What is the true value of money? Why do some things have the property of money in the process of human history, but other items have no property of money?

The real difference is the “consensus”. A consensus on value.

If we consider apple as a medium of exchange, our understanding of its value is a very broad distribution. Apples are red, green, ripe and raw, and everyone has a different understanding of the value of the apple. Especially in economic behavior, some people produce apples, some people consume apples, but most people do not produce apples or eat apples, and most people are not so deep in understanding an apple because he can’t distinguish the value of different apples at all.

But gold is not the same. Our understanding of an ounce of gold is very accurate, the consensus is very strong, and the distribution of its value consensus curve is very, very narrow.

Why do you have such a big understanding of Kim? It is mainly the contribution of two famous physicists.

One is Archimedes, a Greek physicist. One day the king gave him a crown and asked him, “does the craftsman replace the gold with cheap metal in the process of making the crown?”

Archimedes thought for half a day and finally called a Eureka at the last day of the deal when he took a bath. He came up with a very clever way to put a crown on the left of a balance scale, put gold on the right, balance the balance, and then put the balance scale into the water and find it no longer balanced: the weight of the crown is the same as gold, but the volume is bigger, and the buoyancy is related to the volume.

Based on Archimedes’s method, we can measure out an ounce of gold is not a real ounce of gold, so it has a very precise understanding of what an ounce of gold is.

Later, people are more lazy, not every time the exchange of gold coins are accurately measured, so in the process of economic exchange, there are many fraudulent behavior. Sly sharpen a little on the edge of the gold coin, and after one hundred times, it will produce a new gold coin. The value of the gold coin is not well measured.

The solution to this problem is Newton. Newton was a very great theoretical physicist, and when he became famous, the queen of England gave him a poor manure and became the director of the Royal Mint in England. He invented the way to avoid the counterfeiting of gold coins: a serrated mark on the edge of the gold coin, so that if a little was worn off, it could be seen immediately.

In this way, the distribution of the value identity of gold coins is very narrow. The narrower the distribution of the value identity, the stronger the consensus. As a general equivalent, first of all, there is a consensus on the value of the goods. This is the core of the concept.

### Entropy, the common understanding mechanism of nature

It is very difficult to achieve consensus in human society, as if only the central bank can do it. But is there a mechanism in nature to reach consensus?

Many students will stick a photo on the refrigerator with a magnet. Why can magnets suck on the refrigerator? It is not only the magnets that have magnetism, but all the objects have magnetic properties. All objects are made up of electrons, each of which is like a small compass, a North Pole, and an Antarctic. The direction of the most electronic compass is completely random, so the electron spin adds up to no total magnetism.

But there is a very very wonderful phenomenon in nature. In a relatively special case, such as low temperature, and in some special objects, all electrons point to the same direction at the same time, which reaches the consensus. They have no central command, which shows that they have reached a consensus.

Consensus is the core concept of money, that is to say, we must have a consensus that we can use an item as a medium of exchange. But in nature, it seems that there is no need for a central command, and these completely unconscious electrons can reach consensus.

Think carefully that it is necessary to pay a price to reach a consensus.

When I teach the first lesson in statistical mechanics, I always quote the words of a great master of literature, Tolstoy.

“Happy families are always similar, and unhappy families have their own misfortunes.”

For example, students’ bedroom, most of the time is very messy. Human language is very simple, we use only two nouns, neatly and disorderly, sounds like the probability of 50% is neat, the probability of 50% is disorderly. But think about it, there are a lot of methods, and there is only one neat way to do it.

For example, there is a toothbrush, a pair of leather shoes and a pen in the dorm. The neat way is to put the pen on the desk, and the leather shoes should be placed in the doorway, only this kind of practice. There are many disorderly practices, toothbrushes on the doorway, shoes on the desk and so on, and so on. The disorderly way is much more than the neat method, and over time, if the probability of each method is the same, the probability of chaos is far greater than the regular probability.

Nature has an inevitable trend, with the development of time, more and more disorder. There are many ways of disordering, and there is only one way of ordering.

If the trend of nature is becoming more and more disorderly, why do these electrons point in the same direction? This introduces the concept of “entropy”.

A full classroom

Entropy is equal to the measure of an arrangement. Nature is always becoming more and more disorderly and cannot reach consensus. The only way to achieve consensus is to make a little mess around and make yourself a little bit more orderly.

Life is such a phenomenon, life is a highly ordered phenomenon, but life is bound to make a little bit more chaotic.

In some systems, it can become more orderly and put entropy out. The total entropy is still increasing, but its entropy is decreasing, and it becomes more orderly and has reached consensus.

There is the same phenomenon in the world of biology. For example, single cell bacteria, they do some very interesting behavior at the same time, such as emitting light at the same time. A bacterium that sends out light can not be seen around, and a lot of energy is wasted. It’s not a good deal. So when you see a lot of bacteria around you, everyone shines together.

Bacteria have a mechanism of exchange, each bacterium sends out some information. If a lot of information is collected around it, there are more bacteria around it. Everyone immediately decides to begin to shine together. This mechanism is also in the biological world, the physical world also has, we see an inevitable trend, making us know that order is very valuable.

### Consensus is bound to lead to entropy reduction

In the era of block chain, one of the first problems you have encountered is that when the computer is getting more and more, we have to form a network, a distributed computer system. For example, we want to have a common database, but who has the right to modify the database in the end? What is the order of modification?

Can these distributed computers be able to have a mechanism to reach consensus? The first thing you think about is whether there is a deterministic algorithm to command all of these distributed computers, or to do something common.

The situation is like the perpetual motive of the year, with at least more than 1000 patents studying perpetual machines. And then you knew that there was no perpetual motive. Like a problem with a distributed computer, everyone wants to find a deterministic algorithm that can tell all the computers how to do it, and then it’s been half a day, no one can do it.

This is very close to the concept of physics. If a wall is made between the molecules of the movement, it is separated into two halves, and a small hole is opened. When a particularly fast molecule comes in, it opens the door and sees a very slow molecule coming over and closing the door. Over time, the temperature here is very high, the temperature is very low, once the temperature difference, you can build a machine, use it to do work. It is obvious that this is an impossible thing, a state of complete stability that reaches a state of heat balance and can not be taken out to do work.

Similarly, there can be no central command mechanism that can use a deterministic approach to tell the computers how to achieve consensus and not to increase the entropy.

The reason for the ultimate impossible is the second point of Thermodynamics: the entropy of the whole system is always increased.

The great things of science are always the same. The concept of entropy is introduced in the thermodynamics, and the concept of entropy is also introduced in computer science.

Today, when we come to the era of block chain, we need to find a new consensus mechanism. In this way, if we look at the high level principle, we can see it very clearly.

To achieve consensus, it must be an act of entropy reduction, and a part of entropy must be put out.

Today’s bitcoin block chain systems are at least qualitatively satisfied. Once you have an account, you have a currency, but it is bound to have a price, that is, the entropy is increasing. So in the bitcoin system, we have to calculate the hash function, and in the process of computing, the entropy comes into being. After that, the consensus of the subsystem, entropy reduction, but the entropy of the overall system is increasing.

This is a qualitative result, not a quantitative result. To reach a consensus of a unit, it is necessary to consume some entropy, but is the bitcoin too much entropy consumed?

This is a very, very interesting question. There is a lower limit of entropy, that is, how much entropy is necessary to reach the unit consensus, and then compare the entropy consumed by the bitcoin to the lowest standard, to see if it can evolve in this system.

There is a similar result in Computer Science: the energy of a bit of computing consumption is the conversion of the temperature of the room at room temperature into a unit of energy. But now all computers, every bit of a bit operation consumes one million times as much energy as this result. From this point of view, it is very possible that the computer’s energy consumption is getting lower and lower in the future.

In the block chain system, we face the same problem. We don’t think the block chain is only a few coins. In fact, there are very, very profound knowledge in it. If you are really a smart student, can you try to prove the lowest lower limit in it, that is, how much energy it will cost to reach the consensus.

The same is the same in the block chain. We are trying to prove theoretically how much energy it will cost to reach consensus, and there is a lower limit. If it is proved, it may also be able to reduce the energy consumption of bitcoin.

The most wasted resources in the whole computer system are actually stored resources. I bought a hard disk at home, 10TB size, but my photo only took up the space of 1TB. At least for a very long time, the rest of the hard disk space is useless.

Now one way is to sprinkle a lot of random numbers in the hard disk, and if everyone buys a hard disk, just compare it, and create a random number, with the random number stored on the hard disk in the seat, who is the closest who has the right to vote. This is a very smart way, the real green virtual currency.

### From AT&T to Google to block chain, it’s a long time to divide

Let’s share with you the trend of the block chain world and the history of the Internet world. Like the history of human beings, the history of the network can also be summed up by “a long period of time.”

When I went to study in the United States in 1983, there was a giant called AT&T, which seemed never to fall, and my greatest dream was not to be a professor at the university after graduation, but to work in the Baer laboratory, because there had been 30 Nobel winners. AT&T, who spends so much money on such a prize class, has monopolized all network resources to monopolize it.

Slowly there was a new protocol, the network protocol. It is completely a centralization protocol that can make it possible to communicate completely between points and points. I can walk this road, I can also take another road, the road through Rome, the end can reach the result, no longer need the monopoly of the center. Overnight, I thought the company that never fell down, disappeared. The monopoly of AT&T is completely destroyed, which is called long term. It was once again after the competition that AT&T appeared, but when a new network technology appeared, it was time to score.

This time is not so long, if everyone can communicate, everyone can create the content of communication, this content is widely spread on the peripheral Internet, so I want to find a message, it will become very very inconvenient, so in this case, a number of very neutral, new monopoly platform, in the United States called Google and Facebook.

In fact, what Google and Facebook do is to recombine each person’s information. Think carefully that all the Great Companies in the history of human history are not doing something by themselves, but making a rearrangement of what you already have. For example, oil companies, chemical companies, what do they do? Crude oil is made up of atoms and can be dug out directly from the ground. The only thing they do is to rearrange the atoms and turn them into other chemicals, such as the oil that has been refined.

What are the platforms of the Google and Facebook monopolies? It is to rearrange each person’s information, for example, the only thing Google does at the beginning is to make an arrangement that makes it easy for us to find information. What these central platforms do is to restructure the content of the network and centralization.

This is a time for a long time, because of the new network agreement, AT&T fell, the emergence of CISCO, and the distribution of network resources, and the emergence of a huge platform, huge faucet.

The technology of the block chain that appears today will also lead to a new era. The strength of the revolution in this era may be ten times as many times as the Internet revolution. This new era makes all the information we produce, and we can own it personally. The age of the Internet is only the time of information exchange, and the era of block chain has value exchange, we can produce the market of data, each person has its own data, and then produce new value in the process of exchange.

### The trust mechanism is set up in Mathematics

This great time, I use a word to describe the slogan, that is, In Math We Trust. We all understand that the value of money lies in consensus. Then ask a question, which of the human knowledge, which one is the most easy to reach the consensus? Obviously not economics, not law science, not politics, not chemistry, not biology, nor even physics. It is mathematics that is most likely to reach consensus.

It is the most natural way to use mathematics as a mechanism of trust. The time of the real block chain is to make our mutual trust building on the basis of mathematics.

If I make a cube myself, it’s definitely not perfect. But if it is a mathematical form, the cube is fully symmetrical, every corner is exactly the same, each side is exactly the same, and each face is exactly the same. The mathematical form is the most accurate, and in the precise sense, it is also the easiest to reach the consensus.

If you look at the deepest mysteries of the whole universe, then the most core formulas and standard models of physics in the universe are described with very, very, very subtle mathematics, most of which is created by Mr. Chen Ning Yang.

Since the fundamental laws of nature are described in mathematics, can we make the rules and trust of human society on the block of mathematics?

So what math is it? All of you here, I hope you will learn these wonderful math.

The combination of the public key and the private key is built on the number theory, and is built on a higher level number theory, called the elliptic curve. As you may know, one of the biggest conjectures in mathematics, the law of ferma, has recently been proved to be based on the elliptic curve. It sounds very, very abstract mathematics, but every time we go shopping online today, we use wonderful math.

The other is the hash function. It has a unidirectional, anything that comes in and comes out a bunch of random numbers. It’s like a black hole, and the black hole is lost in any way, and all of them are random numbers.

Another is zero-knowledge proof. For example, I solved a problem, but I did not want to tell you my answer directly, but to convince you that I did solve the problem. This is also a very wonderful mathematical problem, but it is solved. I can give you a bit of information, I solved this problem, but I don’t tell you any other information. This is very very useful for the whole data market, and I can give it a bit of bits and one bit, instead of giving it all out.

Two millionaires, one may be a billionaire, a millionaire, and a millionaire who do not want to publish their own property, but know who is more rich. This can be calculated by Yao Qizhi, a professor at Tsinghua University, who gives only one bit of information to know who is richer.

I can never learn the wisdom of big data if I have the data. But I want to know the statistics, and others want to protect personal privacy, so there is a very simple way to put some noise on personal data, which makes you don’t know if the data is your own personal data. After collecting these data, in the environment of large data, the noise counteracts each other, and the statistics I get are perfectly accurate, which is called differential privacy.

The last concept is called formal verification. What was the greatest mathematical discovery of the last century? It is a proof of the incompleteness of mathematics. If I want to recommend a book to the students here, I think it is an ancient odd book, which tells the mathematical incomplete theorem, the artist’s painting and the composer, and the commonality between the three. This book is “Godel, Escher, Bach” (G.E.B).

These wonderful math can be used on the block chain and can be used to do Formal verification. Because today we are in the era of open source, our smart contracts on the block chain today are entirely open source. But when the open source is written, people don’t understand it, even the experts don’t understand it. So is there a mathematical program that tells you whether an intelligent contract is exactly what you want to do in your white paper? This is a very wonderful idea, using logic in mathematics.

### Block chain brings social justice

There are two important trends in computer science, one is AI, one is block chain, and there is an inevitable coexistence relationship between them. I think today’s AI is not so good. Why?

AI needs to come up with the latest algorithms from smart students here, but the biggest bottleneck in college is that we don’t have data. We have smart brains and smart algorithms, but the data are monopolized on the center of the platform, so that AI is not easy to learn. You’ve come up with an algorithm, and you don’t know where the data is. But once the block chain, with the data market, comes back to the time I just said, and we can own all the data.

In this way, I have contributed part of my personal data in the case of protecting my personal privacy. In the era of block chain, I can get a certain reward, and we also have the power to protect its own privacy. Having the value of privacy, and if I have a value, I will make a contribution to the AI learning, which will inevitably bring about a sudden change in the AI.

In addition to a sudden change in the AI, the society can also make a rapid progress.

What is the contribution of the block chain to the society? At least I see it can bring greater justice to society.

What is the mechanism? Our society today has an unfair place, mainly because of our discrimination against the minority, in the Nazi empire in that year, the discrimination against the Jews.

And if we come to the data market in the era of block chain, this will be completely different. For example, I have a AI algorithm, which is 90% accurate, I want to make it more accurate, 99% precision, it needs machine learning. So what do I need to do?

First of all the data I’m going to learn is not like the data I’ve learned before. If it was 99% before, they had represented the majority, but to be more accurate, if 99% became 99.9%, it was the data that was completely different from the previous ones. The more different from the previous, the more different from the public, the more valuable data.

So if in a fully owned market, people will pay more tokens to those minority data, which will bring social justice and turn the ugly duckling into a white swan. Because the ugly duckling is not ugly, it is not the same as other people, but in this world, the more different from others, the more it gets.

Another great ideal is to have all the individual data to be owned by the individual.

The most important data for individuals to have is genetic data and medical data. The data is owned by a person and must be a supreme standard. After individuals have data, they are worried about nothing, just to protect their privacy all day, and not to learn the concerns behind genetic data through large data and artificial intelligence.

What we want to know, for example, is that some of the diseases are based on a mutation of what genes, but once we have all the individual’s genetic information and medical information, we have a very effective data market.

### The one-to-one correspondence between the block chain and the monetary system

The virtual currency on the whole block chain can correspond to the current monetary structure in the society. The current monetary structure is M0, M1, M2, M3 and so on, and the derivatives can be established at the bottom of the bottom.

I think the block chain like bitcoin, because it corresponds to gold, corresponds to one of the most universal values, that is, the currency of M0, equivalent to saying that under this system, any two unacquainted people in the world can form a transaction. If you’ve been acquainted for ten years, and not two people that don’t know each other, we can trade with M1.

I think the lightning network is in line with this kind of nature, we two people trading, mutual trust between each other, but still need the trust mechanism to strengthen. When we sign the contract, we mortgage some of the money on the bitcoin, the block chain, and every transaction after it, on a regular basis (for example, every month) to the block chain to show it once. The development of the entire virtual currency is bound to be like the development of the current world currency. In M0, or bitcoin, or greener bitcoin, the lightning network can be built, and the market can be predicted.

One of our current financial products is futures. Futures are the prediction of the future, but now the futures will be able to really guarantee us through the court, and after we use the block chain, we can testify to the Internet users all over the world.

All of these network systems help each other to make it more effective, but the current billing system is not very effective, and I have provided you with some bandwidth, but not enough return. With a block chain, a very fair and accurate record can be made, so that the entire network will work more and more effectively. I have a prophecy that we go from the time of 4G to the age of 5G, and then to the age of 6G, which is bound to be in the network.

### The era of the great unification of natural science and Social Science

In the period of the whole block chain, I think the most needed talent is the best. In the block chain, the bottom is mathematics, the upper level is the law, and the upper level is the economic behavior.

I think of a few slogans about the block chain. If you talk about the law, there is a saying: “Code is Law”, the original code is the law. Code had the meaning of laws and regulations. And today’s world, the Code has a new meaning: computer programming, code farm code. Now the yard has become the chief justice.

I like Newton’s “mathematical principles of natural philosophy”, and I personally have the first edition of this book, published in 1723. To understand all the natural sciences with the principle of mathematics, this is the greatness of Newton.

Social science has never been able to find fundamental mathematical principles, and it may not be easy to find, because many economic behaviors are irrational in human beings. In the era of block chain, the most fundamental economic behavior is the mechanism of trust, which is based on mathematics.

We can imagine that the whole economic order will be changed and the whole relationship of production will be changed, but the core of it is that there is a cornerstone, the principle of mathematics.

I see a new era, the great unity of natural science and social science. The style I report today is also a new era of understanding the new things of the block chain, by the analogy of natural science and natural science. Once we have mathematics, we can certainly sum up an immutable law that makes our economic system more effective, so that our social science and natural science can reach a great unity.

### Part of the field question and answer

Q: where do you think the most insecure place in the encrypted currency?

A: it’s human entropy, the mistake you make when you write the program. It doesn’t matter to write a program, but it is very, very dangerous now that it is related to a lot of money. Of course, there will be some markets that will automatically block the risk. Formal verification can automatically detect intelligent contracts if you want to describe it, and the math in this is very wonderful, the mathematical logic that I just talked about.

Q: in the block chain, how does the time factor combine with entropy?

A: This is a very good question. Today, when you listen to my speech, you may ask such a question as if it helped us understand the block chain with the understanding of physics, but can we understand the block chain in turn, and will it have a significant impact on the fundamental concepts of physics? I’ve been thinking about this recently. I think it’s possible, and the core is the concept of time.

From Aristotle to Newton, it was thought that time was a day, and there was nothing to discuss. Einstein said that the concept of time is exactly how you measure time, and that time is different at different points. He uses the principle of constant light speed to find that the concept of time is different. In different frame of reference, the time of measurement is completely different.

The core of the depth of time is causality. In the block chain, the solution is cause and effect, because the most important thing is which is the first, which is the cause, which is the fruit. In a more random system, time is not very well defined, so in a sense, the block chain is a definition of a time, or more accurately, to give a definition of a causal relationship.

This definition is often contrary to the physical world. For example, I have a deal with him, it happens first, but our network nodes are very slow, you have been trading with him later, but the network node is very fast, the world will know. In the block chain, time is not necessarily the same as the time in the physical world. But in a random system, there is no better way to reach the consensus of time, so this may be one of the most neglected problems in physics. To reach the consensus of causality, it may have to burn some entropy.

A tutorial certificate issued by Tsinghua X-lab block chain open course