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On December 1, local time in the United States, Chinese-American physicist, tenured professor of Stanford University, academician of the American Academy of Sciences, foreign academician of the Chinese Academy of Sciences, founder of Danhua Capital, and independent director of Meitu Zhang Shoucheng died unexpectedly at the age of 55.

On December 1, local time in the United States, Chinese-American physicist, tenured professor of Stanford University, academician of the American Academy of Sciences, foreign academician of the Chinese Academy of Sciences, founder of Danhua Capital, and independent director of Meitu Zhang Shoucheng died unexpectedly at the age of 55.

This article is compiled from Professor Zhang Shousheng's speech at the Tsinghua Blockchain Open Class:

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

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Look at the blockchain from the perspective of natural science

Let's first understand what currency is from the perspective of natural science.

Currency is a medium for exchanging value, which is very similar to the concept of "field" in physics. As mentioned in high school physics, the same sex repels and the opposite sex attracts. Although the two charges are not in contact with each other, there is also an interaction force that makes them interact. This seems to be different from the experience of daily life. In order to have a force in daily life, it must be in contact with each other.

So there is the concept of "field", a charge generates an electric field, and this electric field can act on another charge. Therefore, we only need to study the interaction between N charges and electric fields, and it is a close-range interaction. This is a conceptual breakthrough in physics: it was originally intended to study the interaction between charges and charges, but now it only needs to describe the interaction between charges and fields.

This is very similar to the creation of money in economics. At the beginning of human civilization, it was an era of bartering. The barter model is a bit like the interaction between charges and charges.

But exchanging things is very difficult to deal with. You need my fish just in time and I need your apples just in time, and the quantity must be corresponding in order to make a deal. Later, we began to introduce currency as a medium of value exchange, which is the creation of currency.

In the era of currency, changing an item into a currency, and then using the currency to exchange it into another item, is like an electric charge generating a field, which then acts on another field.

At the beginning, everyone thought that the concept of field was a virtual concept, not a real physical entity.

In fact, this question is very similar to today's questions about the blockchain, just as a large number of physicists believed that the concept of electric field was a completely illusory mathematical concept, not a concept of real physical existence. The introduction of the field as a medium of exchange, if everyone does not recognize it, it has no value. It wasn't until the emergence of Einstein's theory that the concept of a field really became a physical entity, and we could accurately measure its value.

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To reach a consensus is to recognize the value

Back to currency. What is the true value of money? Why in the course of human history, some items have the attribute of currency, but other items do not have the attribute of currency?

The real difference is "consensus". consensus on value.

If we consider apples as a medium of exchange, our understanding of their value has a very wide distribution. There are red, green, ripe, and raw apples. Everyone has a different understanding of the value of apples. Especially in economic activities, some people produce apples, some people consume apples, but most people neither produce apples nor eat apples. Most people certainly don’t have that deep understanding of an apple, because they can’t tell the difference at all. The value of different apples.

But gold is different. Our understanding of an ounce of gold is very precise, the consensus is very strong, and the distribution of its value consensus curve is very, very narrow.

Why do you know so much about Jin? Mainly the contribution of two famous physicists.

One is the Greek physicist Archimedes. One day the king gave him a crown and asked him to answer the question "did the craftsmen secretly replace gold with cheap metals in the process of making the crown".

Archimedes thought about it for a long time, and finally on the last day of work, he yelled Eureka while taking a shower! He came up with a very ingenious way to put a crown on the left side of a balance and gold on the right, so that the balance was just balanced, and then put the balance in the water, and found that it was no longer balanced: although the weight of the crown was the same as that of gold, But the volume is larger, and the buoyancy is related to the volume.

Based on Archimedes' method, we can measure whether an ounce of gold is really an ounce of gold, so we have a very precise understanding of what an ounce of gold is.

Later, people were lazy and did not measure accurately every time they exchanged gold coins, so there were many fraudulent behaviors in the process of economic exchange. Grind a little on the edge of the gold coin secretly, and after a hundred times of grinding, a brand new gold coin will be produced. In this way, the value of gold coins is not easy to measure.

As a result, the distribution of the gold coin value recognition curve is very narrow. The narrower the value recognition curve distribution, the stronger the consensus. To treat items as general equivalents, first of all, everyone must have a consensus on the value of the item. This is the core concept.

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Entropy, the consensus mechanism of nature

It is very difficult to reach a consensus in human society. It seems that only the central bank can do it. But is there a mechanism for reaching consensus in nature?

Many students will stick a photo on the refrigerator with a magnet. Why do magnets stick to refrigerators? Not only magnets are magnetic, but all objects are magnetic. All objects are composed of electrons, and each electron is like a small compass with a north pole and a south pole. The direction that the compass points for most electrons is completely randomly distributed, so the electron spins add up to have no total magnetism.

But there is a very, very wonderful phenomenon in nature. Under a special situation, such as a relatively low temperature, and in some special objects, all electrons point in the same direction at the same time, and this has reached a consensus. They do not have a centralized command, which means that they have reached a consensus.

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

If you think about it carefully, you must pay a price to reach a consensus.

When I was teaching the first class of statistical mechanics, I always quoted a quote from the literary master Tolstoy:

"Happy families are always alike, and every unhappy family is unhappy in its own way."

For example, the students' dormitory is very messy most of the time. Human language is very simple, we only use two nouns, tidy and messy, and it sounds like there is a 50% chance that it is neat and 50% that it is messy. But if you think about it carefully, there are many ways to be chaotic, but there is only one way to be tidy.

For example, there is a toothbrush, a pair of leather shoes, and a pen in the dormitory. The neat way is to put pens on the desk and leather shoes by the door, that's the only way. There are many messy ways, such as putting the toothbrush at the door, leather shoes on the desk, and so on. There are many more messy ways than neat ways. Over time, if the probability of each way is the same, the probability of chaos is far greater than the probability of order.

If the trend of nature is to become more and more disordered, why do these electrons all point in the same direction? This introduces the concept of "entropy".

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full classroom

Entropy is equivalent to measuring a permutation combination. The natural world always tends to be more and more disorderly, and no consensus can be reached. The only way to reach a consensus is to make the surroundings a little more messy and make ourselves tidy.

Life is such a phenomenon. Life is a highly ordered phenomenon, but life will inevitably make the surroundings a little more chaotic.

In some systems, it can become more orderly by itself and expel entropy. The total entropy is still increasing, but its own entropy is decreasing, and it becomes more orderly, reaching a consensus.

Bacteria have a mutual exchange mechanism. Each bacterium sends out some information. If a lot of information is collected around, it means that there are more bacteria around. Everyone immediately decides to start to shine together. This mechanism also exists in the biological world, as well as in the physical world. We see an inevitable trend, which makes us know that order is very valuable.

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Reaching a consensus will inevitably result in a decrease in entropy

In the era of blockchain, the first problem that everyone encounters is that when more and more computers start to become available, we need to form a network, which is a distributed computer system. For example, we need to have a common database, but who has the right to modify this database? What is the modification order?

Can these distributed computers have a mechanism to reach consensus? The first thing everyone thinks of is whether there is a deterministic algorithm to command all these distributed computers, or to do some commonly recognized things.

The current situation is like the perpetual motion machine in those days, when there were at least more than 1,000 patents on perpetual motion machines. You also know later that the perpetual motion machine has not yet been developed. This is the same problem encountered by distributed computers. Everyone wants to find a deterministic algorithm that can tell all computers how to do it. Afterwards, everyone worked for a long time, but no one could do it.

This is very close to the concept of physics. If you build a wall between moving molecules, divide it in half, and open a small hole, when you see a particularly fast molecule coming, open the door and see a particularly slow molecule. Molecules come over and close the door. Over time, the temperature here is very high, and the temperature there is very low. Once there is a temperature difference, you can build a machine and use it to do work. Obviously, this is impossible, a completely stable state, a state of thermal equilibrium, cannot be used to do work.

Similarly, it is impossible to have some central command mechanism that can use a deterministic method to tell these computers how to reach a consensus without increasing the entropy even more.

The reason for the ultimate impossibility is the second point of thermodynamics: the entropy of the whole system will always increase.

Great things in science always coincide. The concept of entropy introduced in thermodynamics is also introduced in computer science.

In the era of blockchain today, everyone needs to find a new consensus mechanism. In this way, if we look at it with high-level principles, we can see it very clearly:

To reach a consensus, it must be an act of entropy reduction, and a part of entropy must be discharged.

Today's Bitcoin blockchain system fully satisfies this point, at least qualitatively. Once there is a ledger, it is equivalent to having currency, but this will inevitably come at a price, that is, the surrounding entropy will also increase. So in the Bitcoin system, we need to calculate the hash function, and during the calculation process, entropy is generated. After generation, the consensus of the subsystems will be reached, and the entropy will decrease, but the entropy of the overall system will increase.

This is a qualitative result, not a quantitative result. To reach a unit consensus, some entropy must be consumed, but does Bitcoin consume too much entropy?

This is a very, very interesting question. Is there a lower limit of entropy, that is, the minimum amount of entropy that must be consumed to achieve unit consensus, and then compare the current entropy consumed by Bitcoin with the lowest standard to see if this system can evolve.

There is a similar result in computer science: the energy consumed to do a bit operation is converted from room temperature into energy units. But all computers now consume a million times as much energy as this result for each bit operation. From this point of view, it is very possible that computers will consume less and less energy in the future.

In the blockchain system, we face the same problem. Don’t think that the blockchain is just for issuing some coins. In fact, there are very, very profound knowledge in it. If you are really a smart student, can you try to prove it? The lowest lower bound, that is, how much energy must be spent to reach consensus.

The same is true in the blockchain. Everyone is trying to prove theoretically how much energy must be spent to reach a consensus. Is there a lower limit. If it proves, maybe it can also reduce the energy consumption of Bitcoin.

Now there is a way to sow a lot of random numbers in the hard disk like sowing seeds. If everyone buys a hard disk, just compare and generate a new random number. Closest to who has the right to vote. This is a very smart approach and is a truly green virtual currency.

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From AT&T to Google to the blockchain, the long-term must be divided

Let me share with you the trend of the blockchain world and the history of the online world. Just like the history of human beings, the history of the Internet can also be summed up as "the long-term division must be combined, and the long-term unity must be divided".

When I went to the United States to study in 1983, there was a giant named AT&T, which seemed to never fail. My biggest dream at the time was not to become a professor in a university after graduation, but to work at Bell Labs, because here Has produced 30 Nobel Prize winners. AT&T spends so much money to raise so many Nobel Prize-winning scientific researchers just to monopolize all network resources.

Slowly, a new protocol emerged—the network protocol. It is completely a decentralized protocol that enables completely arbitrary communication between peers. I can take this path, or I can take another path, all paths lead to Rome, and I can finally reach the result, no longer needing the monopoly of the center. Overnight, the company that I thought would never fail disappeared. AT&T's monopoly has been completely destroyed. This is called long-term cooperation and division. In the past, AT&T appeared after competition, but when a new network technology appeared, it was the time when the long-term cooperation must be divided.

This era of long-term unity is not so long. If everyone can communicate, everyone can create communication content, and this content is widely scattered on the peripheral Internet. Then I will find a piece of information, and it will become It is very, very inconvenient, so in this case, long-term division must be combined, and some very neutral new monopoly platforms have emerged, which are called Google and Facebook in the United States.

In fact, what Google and Facebook do is to reassemble everyone's information. Think about it carefully, all the great companies in human history must not create something themselves, but rearrange and combine existing things. For example, oil companies and chemical companies, what do they do? Crude oil is made up of atoms and can be dug directly out of the ground. The only thing they do is to rearrange these atoms and turn them into other chemicals, such as refined oil.

What do monopoly platforms like Google and Facebook do? It is to rearrange and combine everyone's information. For example, the only thing Google did at the beginning was to make an arrangement to make it very easy for us to find information. What these centralized platforms do is centrally reorganize the content we spread on the Internet.

The blockchain technology emerging today will also lead to a new era. The intensity of the revolution in this era may be ten or a hundred times that of the Internet revolution. This new era allows all the information we generate to be in our own personal possession. The era of the Internet is only the era of information exchange, and the era of blockchain has the exchange of value, we can generate a data market, everyone owns their own data, and then generate new value in the process of exchange.

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Trust mechanisms are built on mathematics

In this great era, I use a slogan to describe it, which is In Math We Trust. We all understand that the value of currency lies in consensus. Then ask a question, among all the knowledge of human beings, which one is the easiest for everyone to reach a consensus on? Obviously not economics, not law, not political science, not chemistry, not biology, not even physics, the easiest to reach consensus is mathematics.

If you look at the deepest mysteries of the entire universe, then the core formulas and standard models of the entire universe in physics are also described with very, very delicate mathematics, most of which are also created by Mr. Yang Zhenning of.

If you look at the deepest mysteries of the entire universe, then the core formulas and standard models of the entire universe in physics are also described with very, very delicate mathematics, most of which are also created by Mr. Yang Zhenning of.

Since the most fundamental laws of nature are described by mathematics, can we make the rules and trust of human society also be based on mathematical blocks?

Since the most fundamental laws of nature are described by mathematics, can we make the rules and trust of human society also be based on mathematical blocks?

The combination of public key and private key is based on number theory, and it is based on a higher-level number theory called elliptic curve. As you may know, one of the biggest conjectures in mathematics - Fermat's last law, has been proved recently, and this proof is based on elliptic curves. This sounds like very, very abstract math, but today we use fantastic math every time we shop online.

The other is the hash function. It has a unidirectionality, anything that goes in, comes out as a string of random numbers. This is very similar to a black hole, where any input is made into the black hole, and all random numbers come out.

The other is the hash function. It has a unidirectionality, anything that goes in, comes out as a string of random numbers. This is very similar to a black hole, where any input is made into the black hole, and all random numbers come out.

There is also a zero-knowledge proof (zero-knowledge proof). For example, I have solved a difficult problem, but I don't want to tell you my answer directly, but I want to convince you that I have indeed solved the difficult problem. This is also a very wonderful mathematical problem, but there is a solution. I can give you one bit of information, I solved the puzzle, but not tell you anything else. This will be very, very useful for the entire data market. I can give information bit by bit instead of giving all the information at once.

For two millionaires, one may be a billionaire and the other may be a millionaire. They don't want to disclose their wealth, but they want to know who is richer. This can be calculated using the method of Tsinghua University professor Yao Qizhi, who can know who is richer by giving only one bit of information.

If the data is owned by myself, I will never learn the wisdom of big data. But I want to understand statistical data, and others want to protect personal privacy, so there is a very simple way-intentionally add some noise to personal privacy data, these noises make it impossible for you to tell whether the data is your own or not data. After collecting these data, in the environment of big data, these noises will cancel each other out, and the statistics I get are still completely accurate. This method is called differential privacy.

These wonderful mathematics can all be used on the blockchain and can be used for Formal verification. Because today we are in the era of open source, and our smart contracts on the blockchain today are completely open source. But after the open source is written, ordinary people can't understand it, and even experts may not understand it. So is there a mathematical program that can tell you whether the smart contract is in line with what you want to do in the white paper? This is a very wonderful idea, using logic in mathematics.

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Blockchain Brings Social Justice

AI requires smart students here to come up with the latest algorithms, but the biggest bottleneck everyone encounters in universities is that we don't have data. We have smart brains and smart algorithms, but the data is monopolized on the central platform. In this case, it is not easy for AI to learn. You come up with an algorithm and don't know where the data is. But once there is a blockchain and a data market, it will return to the era I just mentioned, and we can personally own all the data.

In this way, I contribute part of my personal data while protecting my personal privacy. In the era of blockchain, I can get a certain return, and everyone will have the motivation to protect their privacy. With privacy, there is value, and once there is value, if I contribute this data for AI to learn, it will inevitably bring about rapid changes in AI.

In this way, I contribute part of my personal data while protecting my personal privacy. In the era of blockchain, I can get a certain return, and everyone will have the motivation to protect their privacy. With privacy, there is value, and once there is value, if I contribute this data for AI to learn, it will inevitably bring about rapid changes in AI.

In addition to making rapid changes to AI, it can also make society advance by leaps and bounds.

What is the contribution of blockchain to society? At least I see it can lead to greater justice in society.

What mechanism is this? The injustice in our society today is mainly due to our discrimination against minorities. In the Nazi empire, it was discrimination against Jews.

First of all, the data I want to learn cannot be the same as the data I learned before. If it was 99% of the data before, they already represent the majority, but to be more accurate, if 99% becomes 99.9%, What needs to be learned is the data that is completely different from before. The more different it is from before and from the public, the more valuable the data will be.

So if in a completely private data market, everyone will pay more tokens for the 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 just different from others, but in this world, the more different it is from others, the more it will get.

So if in a completely private data market, everyone will pay more tokens for the 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 just different from others, but in this world, the more different it is from others, the more it will get.

For example, what we most want to know is what gene mutations correspond to certain diseases, but once we let individuals own all personal genetic information and medical information, we will generate a very effective data market.

For example, what we most want to know is what gene mutations correspond to certain diseases, but once we let individuals own all personal genetic information and medical information, we will generate a very effective data market.

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One-to-one correspondence between blockchain and currency system

The virtual currency on the entire blockchain can correspond one-to-one with the current currency structure in society. The current currency structure includes M0, M1, M2, M3, etc., and derivatives can be continuously established on the bottom layer.

I think the Lightning Network is in line with this nature. The two of us conduct transactions and have a certain degree of trust between each other, but we still need a trust mechanism to strengthen it. After we sign the contract, we mortgage some currency on Bitcoin and the blockchain, and every subsequent transaction, it is enough to publish it on the blockchain periodically (such as every month). The development of the entire virtual currency will inevitably be the same as the development of the current world currency. On M0, or Bitcoin, or a greener Bitcoin, a lightning network can be established, and there will also be a prediction market.

Among our current financial products, one is futures. Futures are predictions of the future, but now futures have to go through the courts to really guarantee us, and after we use the blockchain, Internet users all over the world can testify for us.

All these network systems help each other to make it more efficient, but the current billing system is not very effective, I give you some bandwidth, and I don't get enough in return. With the blockchain, very fair and relatively accurate records can be achieved, so that the operation of the entire network will become more and more effective. I have a prophecy that we will move from the 4G era to the 5G era, and then to the 6G era, and there will inevitably be network operations in it.

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The era of great unification of natural science and social science

I think of several slogans about the blockchain. If we talk about the law, there is a saying: "Code is Law", the original code is the law. Code originally meant codes and regulations. In today's world, this Code has a new meaning: computer programming, the code of coders. Now the code farmer has become a judge.

My favorite is Newton's Mathematical Principles of Natural Philosophy, which I personally own the first edition of which was published in 1723. Using the principles of mathematics to understand all natural sciences is Newton's greatness.

My favorite is Newton's Mathematical Principles of Natural Philosophy, which I personally own the first edition of which was published in 1723. Using the principles of mathematics to understand all natural sciences is Newton's greatness.

Social science has never been able to find fundamental mathematical principles, and it may indeed be difficult to find them, because many economic behaviors are based on human irrationality. In the era of blockchain, the most fundamental economic behavior is the mechanism of trust, which is based on mathematics.

I see a new era where the natural sciences and social sciences are unified. The style of my report today is also to use the language of natural science and the analogy of natural science to understand the new thing and this new era of blockchain. Once we have mathematics, we must be able to sum up an eternal law, making our economic system more effective, and enabling our social science and natural science to achieve a state of great unity.

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Part of the live Q&A

Q: What do you think is the most insecure place in cryptocurrency?

A: It is man-made entropy, which is the mistake people make when writing programs. Originally, it didn’t matter to write a program, but now it is very, very dangerous if it is related to many currencies. Of course, some markets will gradually emerge to automatically block this risk. Formal verification can automatically detect whether the smart contract is what you want to describe. The mathematics in it is very wonderful, which is the mathematical logic I just mentioned.

Q: In the blockchain, 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. It seems that using the understanding of physics to help us understand the blockchain, but can it be reversed? Have a major impact? I've been thinking about this issue recently, and I think it's possible. The core is everyone's concept of time.

Back then, from Aristotle to Newton, they believed that time was given by God, and there was nothing to discuss. Einstein said that the concept of time is how you measure time, and the time measured at different points is different. Using the principle of the constant speed of light, he discovered that the concept of time is different, and the time measured in different frames of reference is completely different.

And this definition often violates the physical world. For example, a transaction between me and him happened first, but our network node is very slow, and your transaction with him happened later, but the network node is very fast, and the whole world will know it at once. In the blockchain, time is not necessarily the same as the time in the physical world. But in a random system, there is no other better way to reach a consensus on time, so this may be the most neglected problem in physics. To reach a consensus on causality, it may be necessary to burn some entropy .

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