Zhu Jiaming: Approaching Technical Singularity, Constructing Mathematical Foundation of Block Chain

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 Zhu Jiaming: Approaching Technical Singularity, Constructing Mathematical Foundation of Block Chain


There is a correlation between the development and growth of block chains and the diversification of applied mathematics, and this correlation will promote the evolution of block chains mathematics.

Around World War II, the regular Macy Conference attracted world mathematicians, physicists, sociologists and semanticians centered around the United States to conduct interdisciplinary discussions and cooperation. It laid the foundation for almost all major scientific and technological issues from the second half of the twentieth century to the present, including cybernetics, information theory, artificial intelligence, systems theory and complex science. Analysis and research ideas and framework.

From December 17 to 18, the Block Chain Mathematics Science Conference was held in Beijing. The purpose of this meeting is to learn the spirit of the Macy Conference and to provide an academic exchange platform for experts in the fields of mathematicians, cryptographers, computer scientists, economists and so on. The conference focused on exploring the paradigm of disassembling existing block chain mathematics, looking for mathematical fields related to block chain technology. Combination can introduce mathematical tools of block chain technology, and through analogy, analysis, induction, put forward block chain mathematical conjecture.

This conference is sponsored by Digital Assets Research Institute, with financial and economic support of pomegranate.

Zhu Jiaming, a famous economist, has analyzed in detail the relationship between block chain and mathematics, and the possibility of forming block chain applied mathematics. The following is a summary of Zhu Jiamings speech:

First, why should we carry out block chain applied mathematics research?

We are in an era of scientific dominance, mixed growth of science clusters and technology, and technological singularity is no longer a guess.

Descartes put forward the term imaginary number in the 17th century, which is believed to be a real non-existent number. Later, people found that the imaginary number can correspond to the vertical axis of the plane. The imaginary number exists in the conceptual world and is as real as the real number of the horizontal axis of the corresponding plane.

Parallel world has come into being, and applied mathematics plays a prominent role.

Parallel world has been formed, one is the concrete world dominated by material world, physical world, real economy and empirical science, the other is the abstract world dominated by conceptual world, non-physical world, virtual economy, pure science, social science and art.

Two parallel worlds coexist. They are not simply corresponding, but have their own structures and infrastructure. Applied mathematics connects the two worlds together.

We can see that applied mathematics plays an important role in the fields of materialization, engineering, IT and Internet revolution, especially in the field of economics.

Mathematics breeds block chain, and block chain promotes mathematics.

The basic function of block chain is: first, it is the infrastructure of the immaterial world and the non-physical world. Secondly, it is the bridge between the material world and the non-material world.

When we envisage the relationship between block chain and mathematics, it is such a logic that mathematics breeds block chain, block chain promotes mathematics, and mathematics may further transform block chain.

In exploring block chains and applied mathematics, we need Hilberts spirit of We must know, we must know.

2. What are the prerequisites for forming a branch of applied mathematics?

The important goal of this conference is to find the relationship between mathematics and block chains, so as to further deconstruct block chains and provide stronger mathematical support for block chains. In order to solve this problem, we must first understand the premises of establishing a new branch of applied mathematics.

I sum up four points:

1. Complete disciplines such as physics, biology and economics 2. Genes with mathematics 3. Architectures with mathematics 4. Tension in application scenarios

Based on these four conditions, there are usually two ways to generate new disciplines as far as possible in theory: one is to let mathematicians enter new fields of application. They focus on new areas and explore and apply well-known mathematical methods and tools, such as Turing and Church. Another is to let professionals in the field of application enter the field of mathematics. In order to solve the unique problems they encounter, they either introduce well-developed mathematics or creatively develop new mathematical methods.

Third, does the block chain have the condition of extending applied mathematics?

Do block chains have the basic conditions for extending applied mathematics?

The answer is yes for three reasons:

Firstly, block chains have sufficient interdisciplinary basis: cryptography and the mathematics behind it, big data and the mathematics behind it, network communication, computer science, programming language and so on. All these components are linked together to support todays block chains.

Secondly, block chain and mathematics have direct blood relationship, namely number and type. Block chain and mathematics have quite indirect, if not direct, relationship. The basic principles of hash function and elliptic curve, which are important components of block chain structure, are inspired by mathematics.

Thirdly, block chains show the possibility of introducing more mathematical tools: it is generally acknowledged that computer science is directly related to the following scientific tools, including mathematical logic, linear algebra, mathematical statistics, probability distribution, parameter estimation, group theory, integral variation, differential equation topology, etc.

If the block chain has the possibility of extending the branch of applied mathematics, it is obviously unique in its paradigm. Its greatest uniqueness lies in:

1. Block chains are a collection of science, technology, engineering and economics 2. Applied mathematics behind block chains is the superposition of groups. Block chains provide experimental platform for pure mathematics and stimulate mathematics.

Fourth, is mathematics embedded in block chains or block chains embedded in mathematics?

Now we are going to discuss an interesting question, is mathematics embedded in block chains or block chains embedded in mathematics?

In fact, I have no conclusion. I can only say that both possibilities exist.

From the historical process, block chains are embedded in mathematics, because all the mathematical tools supporting block chains have a history of about 20, 30 or 30, 40 years before the birth of block chains. It is their combination that gives birth to block chains, so block chains should be embedded in mathematics. But in a deeper sense, we see further development, where mathematics is embedded in the block chain, which is an obvious interactive process.

At present, the most closely related mathematical means to block chains is theory, multiplying prime numbers makes it more difficult to interpret and decompose them, which stimulates the development of contemporary cryptography, and in turn supports the security of block chains. However, current research shows that the mathematical basis of DAG has gone beyond number theory, and its mathematical basis is probably graph theory, that is, taking space, dimension and transformation as the research object, which may lead to block chains that have not been constructed before.

Fifth, what is the mathematical trend of block chain?

Finally, I want to talk about the mathematical trends of mathematical thinking and block chains.

A strong feeling is that in the development of mathematics, our country has made too little contribution. Lack of good traditional and mathematical ideas and even philosophical thinking behind them may be an important reason, in which we still have a big gap.

This passage comes from Xi Nanhuas article Some Past and Present Situation of Basic Mathematics. I think it is a relatively complete summary of basic mathematics by Chinese mathematicians so far. He put forward that in the development of mathematics, our country has made too little contribution and lacked good traditional and mathematical ideas, which is a big problem.

There is a correlation between the development and growth of block chains and the diversification of applied mathematics, and this correlation will promote the evolution of block chains mathematics.

Einstein said, When mathematics talks about reality, they are uncertain; when mathematics is certain, they do not involve reality. How do you understand this sentence?

Thats how I understand it. In Einsteins view, there are two worlds. One is the mathematical world, the other is the real world. The two worlds can not exist at the same time. The real world of mathematics must not be realistic. If it is realistic, it must not be mathematical.

This sentence essentially means the same thing as the two parallel worlds I mentioned at the beginning. One is the concrete world dominated by material world, physical world, real economy and empirical science, the other is the abstract world dominated by conceptual world, non-physical world, virtual economy, pure science, social science and art.

How does mathematics fit into another world? One of the most important means is to let mathematics be applied in the physical world. In this process, more and more widely applied mathematical systems will emerge.

In the applied mathematics system we have seen, the most promising one is the block chain. Therefore, the block chain will be the bridge connecting the material world and the non-material world.

Source: Babbitts Editor-in-Charge: Wu Mengyang_NBJ11200