Introduction: How to measure technical complexity? By modeling technology as a composite network, a paper proposes a new method of using structural diversity as a quantification of technical complexity. It is based on the improvement of the network diversity score of the complex network measurement, and can calculate the complexity index of different technical networks , And effectively distinguish between complex technology, medium technology and simple technology. The results of the paper prove many of the default facts that are usually related to technological complexity: such as technological complexity grows with time, complex technology requires greater R & D investment and cooperation scale, and high-tech with higher complexity is often more concentrated Space and so on. The title picture is from Visual China, This article is from WeChat public account: Jizhi Club (ID: swarma_org) < / a> , author: ten-dimensional

Illustration by French artist and writer Albert Robida in the 1892 novel La Vie electrique

Technology, this kind of fire that Prometheus deceived from the gods to help mankind in mythology, has now become the dominant force in the development of human civilization. If this is not the case, at least it is the default consensus. Since the Industrial Revolution, modern civilization has liberated the internal forces of matter like desire, stripped energy and information, and extracted, stored, and multiplied. No longer needs magic, humans have sinceTo be able to directly use the power of nature to control nature.

The myth disappears and the classical falls. Once the automaton switch is turned on, the modern giant machine begins to take shape. To be or not to be, human beings have no choice, all they can do is to respond to it and how to respond.

—— Tool? A medium? The strongest replicon? Or a new subject in the birth? Scholars often have divergent opinions on these essential tendencies, and each has their own opinions, which eventually turns into the deduction of various concepts and the conviction of belief.

To resolve conceptual disputes, it is better to do it first, just like the strategies that scientists have adopted for energy, information, life, and consciousness, start with the operation. That is to say, if we can find some indicators of technical measurement, we can continue to approach its essence from the operationally defined way.

In this way, we can not only judge the value of a specific technology, but also allow the country or enterprise to make better decisions on whether to invest in certain fields.

The question we should really ask is: How do you measure technology?

Thesis Title: Using structural diversity to measure the complexity of technologies

Thesis address:

Figure 1: Thesis author Tom Broekel

In 2019, a previous paper published in PLoS ONE, “Using structural diversity to measure the complexity of technologies”, proposed a new method of quantification technology: by modeling technology as a component composition network, you can get An indicator of structural diversity that measures the complexity of the technology, that is, the diversity of topologies in these networks and subnetworks. This indicator can not only effectively distinguish between complex technology, medium complex technology and simple technology, but also has been proved by the paper to confirm many of the default facts that are usually related to technical complexity: such as the complexity of technology grows with time, complex technology needs more research and development and Technologies with higher scores on cooperation and structural diversity are also in more concentrated spaces and so on. The author Tom Broekel is a professor at the Business School of Stavanger University in Norway and a member of the Regional and Innovation Economics Center at Bremen University in Germany. His research direction is regional innovation and technological complexity.

One, complexity measurement: Zhongli Xunhuaqianbaidu

Although it is difficult to question the ontology of technology, most scholars basically agree that technology itself is a hierarchical structure, which comes from a combination of lower-level technologies. For the complex economist Brian Arthur, the most primitive technique is the capture of natural phenomena and their effects [1]. Therefore, the technology is regarded as a kind of complex network, and there is not even excessive restoration. What really needs to be solved is how to effectively measure the network structure. However, this is a difficult problem.

Traditionally, similar statistical physics or information theory methods can be used to calculate the entropy complexity of an object or network [2,3] [4]. For example, the following figure shows six typical network structures: (a) star network (b) lattice network (c) tree network (d) small world network (e) fully connected network (f) random network.

Figure 2: Six typical networks

The information needed to describe the star network, lattice network, and fully connected network is very small. They are all simple networks. (c) The tree network is slightly more complicated, but only requires limited information. The most important thing is the comparison between (d) small-world networks and (f) random networks. Although small-world networks are typical complex networks, if calculated according to information theory methods, you will find (f) information contained in random networks The volume is even higher than the small world network.

Therefore, for traditional complexity measurement, whether it is a typical theoretical network or an empirical network such as a biological network, the most difficult problem to solve is how to distinguish a complex network from a random network and an ordered network . That is, an effective complexity measure distribution should be shown in Figure 2A instead of B:

Figure 3: Theoretical and practical distribution of effective indicators of complexity measurement

In the study of the actual empirical network, it is mainly based on chemical graph theory (Chemical Graph Theory) , And the various properties of ecological networks, scientists have sorted out 16 kinds of network complexity metrics:

Figure 4: Sixteen typical complex network metrics

However, Frank Emmert-Streib and Matthias Dehmer, two bioinformaticians from the United Kingdom and Austria, after verifying and analyzing these 16 complexity indicators [5], found that they can hardly distinguish between complex networks and Random network.

Figure 5: The performance of sixteen complex measurement indicators to distinguish ability under numerical test

The results are shown in Figure 5, showing the relationship between the probability density of the complexity value (y-axis) and the complexity value (x-axis). Most indicators are mixed with the distribution of ordered, complex and random networks, except that the non-diagonal complexity can be basically differentiated. But even it has a big problem, not only there are two distribution peaks, but also there is considerable overlap in the complex network (purple) and random network (red).

Second, network diversity score: the most beautiful one among complexity and randomness

A complex network can be regarded as a high-dimensional object. I am afraid that a single-dimensional index alone cannot effectively resolve and measure complex networks. What about comprehensive multi-dimensional indexes?

Thesis title: Exploring Statistical and Population Aspects of Network Complexity

Thesis address:

Along this line of thought, the same two bioinformaticians published a paper in 2012: “Exploring statistical and population aspects of network complexity”, which proposed network diversity indicators (Network diversity score, NDS) effectively solves this problem. Their methods are as follows:

Let G denote a network with vertex set V and edge set E. The number of vertices is n = | V |, and the number of edges is e = | E |. The indicator is calculated based on the following four variables:

where M is the number of modules in network G. The vector m = (m1, m2 …) is the size of the included module, arranged according to the number of nodes of the corresponding module, the size of the i-th module is mi. In order to identify the modules in the network, a method called Walktrap [6] similar to random walk [7, 8] can be used to find the modules. Its advantage is that it can directly estimate the computational complexity O (e * n ^ 2) .

The four variables in equations (30)-(33) respectively reflect different attribute information in the network structure: