# Technology or Monetary System: What is the key to progress? — Part I: The case for Technology

## Is money really the most important innovation of society?

*This is the first of a series of posts where I debate whether a monetary system or technology is the key to growth in society.*

It seems today there are two competing narratives regarding the question of growth. The first regards technology as the key to our economy, our wealth, and our way of being. The second claims that a proper monetary system is foundational for being able to freely invent and build layers of complexity within our society. In particular, we generate technology inside a society with a monetary system, that values and influences it. However, money itself can be regarded as a social technology, so we are inside a sort of Chicken and Egg problem displayed in the cover image.

Historically technology comes before money, however, societies without money don’t look like anything we are familiar with today. Was money the key innovation that unlocked the power of modern society? Was money the fundamental element to extend the principles of natural selection to markets? In this series of posts, I’ll explore some ideas that argue in both directions. First I’ll argue why technology is the key to economic growth and how it's dependent and independent of a monetary system in part I of this series.

` 1. Combinatorial Evolution of Technology `

1.1 Layers of Creativity

1.2 Combinatorial Evolution in Mathematics

# Combinatorial Evolution of Technology

Ever since the publication of Darwin’s Theory of Natural selection, people wondered if Technology evolves, and if it does, what is the mechanism behind its evolution process? I’ll follow here the ideas of Economists Paul Romer and W. Brian Arthur. The main ingredient for both of them lies in the concept of **Combination.**

The theory of combinatorial evolution of technology states technology works a bit like a very strange Lego set. You make combinations and if they happen to repeat and be extremely useful, you heat those combinations, fuse them together and throw them back in the Lego set for yet further combination. Moreover, the instructions of combining the legos are what we define as **ideas**, more precisely, ideas are the instructions that let us combine limited physical resources in arrangements that are ever more valuable.

Therefore we can think of the invention of new technologies as a combinatorial evolutionary process where we don’t mutate the current technology to generate a new one, but rather we combine and reuse other technologies to generate a new one. This sounds very compelling, but how does this work in practice? Let’s take the example of building a battery pack for electric vehicles.

Clearly, a car battery is made from a lot of different components, the point here is not to learn about the specifics of car batteries but of the role of combinations in technologies. Each of the pieces of the battery itself is made from different parts themselves, in fact, we could go so far as to end up in the raw materials used to build the battery. Is this decomposition in the fundamental building blocks useful at all? We let Elon Musk himself answer this question:

So it is clear that a clever combination of materials is not only important for generating new technologies but also for massify and decrease their monetary value. However, this example is not only interesting because it shows the combinatorial mindset in practice, but rather because, Elon mentions London Metal Exchange. Therefore the price of the materials is not only fundamental for mass-producing the invention but rather influences the possible combinations he is willing to create. However, we can think of decreasing the price as just one possible problem that Elon is trying to solve.

In general when we create technologies we not only are thinking about how to minimize the mass-produced prize but we can consider any kind of human problem and this is precisely the second component of the theory of combinatorial evolution, we generate technologies for solving a Human problem. A Human problem can be monetary, scientific, social, survival, etc. These problems can be strongly, lightly, or totally uncoupled from money or the monetary system.

However generating a specific device to solve a problem does not immediately amount to mass adoption, one has to convince other people to use it. Moreover one has to teach how to use this correctly, and it will only persevere when it has found a stable socio-economic niche. These elements are foundational to the adoption and permanence of the technology, however, the recipe to create the device is well described by the combinatory theory.

Having said this, not all technologies need such an awareness process, many technologies are developed just to improve a very specific problem, in the case of the batteries, it is clear that a much better battery has already an uncountable number of uses. Nevertheless, there is a gradient of awareness from total novelty to incremental innovation on a well-established product.

All these elements that are generated after the technology has been conceived can potentially be linked with money sooner or later, moreover, they are inherently dynamic. Although this is quite clear, the contemporary Economics paradigm is static, exemplified in the seminal paper De Gustibus Non Est Disputandum, where the authors argue that tastes should be treated as the same for all men, and do not vary over time, comparing them to the Rocky Mountains. This static picture is very misleading because the world is constantly changing, moreover the picture of combinatorial evolution we presented before is also static !!, a way to make it dynamic is described next.

## Layers of Creativity

Sometimes when faced with a problem, we are not able to solve it within the same framework where the question was asked. A classic example is: What are the integers m and n such that √2=m/n. It turns out that there are not m,n integers such that √2=m/n, we have to go one level above, to the irrational numbers to solve this problem. Within technology sometimes we also need to enhance our framework to solve a problem. One way to see this is not to see the decomposition of atoms in the battery as the last layer, we can for example also consider at the atomic level, how do we engineer these materials.

For example, many of these elements are conductors, these conductors are crystals of atoms with few outer layer electrons, assembling these atoms in a solid phase in a particular arrangement allows us to generate macroscopic phenomena of conductivity.

Similarly, If we have an electron-hole, for example in silicon doped with boron, we can arrange these atoms in a particular crystalline structure to generate a P-type semiconductor. Doing this at a large scale is what I roughly call the manufacturing process of a Silicon Wafer. So we see that at this scale we are still doing some combinatorial process, we are gluing legos(Collective Excitations) in a particular fashion(Phase of Matter) to generate newer technologies(Materials).

For example, we could in principle try to combine different conductor atoms in order to create an alloy, we can smelt them to combine them and then do some sort of annealing to increase the strength of the alloy. So we are combining different attoms with different collective excitations, in different arrangements in a particular phase of matter to generate a particular material. It just so happens that sometimes in nature we find some of these materials around as raw materials, however, in most cases we need to purify them or even create synthetic materials.

Furthermore, we can go even deeper and think about how are these collective excitations made out of, and go to the elementary particle stage. In this realm, we find exotic collective excitations or quasi-particles made of elementary particles in exotic arrangements. Some examples might be, anyons(2D particles), Polaritons, Fractons, etc. Although one can argue if these excitations are engineered or intrinsic to nature, they can also be thought of as new pieces of lego that we can put in our lego set.

This last layer is the Standard Model of Particle Physics and it is our current state-of-the-art model of nature since the 1970s. If we think about technology in this fashion, digging deeper and deeper into the atom has allowed us to solve newer problems in engineering. In some sense doing combinations in all layers of this space has allowed us to solve more and more difficult problems. This process is represented in the following table.

As a simple example, we can think of both nuclear power and semiconductor technology as combinations that came out from the atomic scale. The atomic scale opened the door for many problems that were believed to be impossible, even Einstein in 1933 said:

‘’There is not the slightest indication that nuclear energy will ever be obtainable. That would mean that the atom would have to be shattered at will.’’ Einstein(1933)

Manipulating objects at the atomic scale now not only give us nuclear energy but has lead to many innovations in the Information Technology domain, but also in medical, defense, etc. This expanding framework of technology was led by the expanding knowledge of physics, starting with the macroscopic world Newton established the laws of Mechanics leading the way of mechanical machines, then at a smaller scale, Maxwell and others established the laws of Electromagnetism, giving us the power of electromagnetic spectrum(Radio, Microwaves, etc). Later Kelvin and others with the discoveries in Thermodynamics allowed us to understand the power of heat engines and to some extent the power of Coal and Gas.

Next starting with Einstein's discoveries in the fundamental nature of matter, Quantum Mechanics was born, and with the breakthroughs of Bohr, Heisenberg, Schroedinger, and others we have obtained the power the Quantum. The understanding of the quantum was fundamental for the development of the Semiconductor opening the door for computer technology.

“In modern computers you need semiconductors, and the whole theory of solid state physics (band structures, doping, etc) is based on a foundation of quantum mechanics — since electrons in semiconducting solids behave in a manner that is more wave-like than particle-like, with each electron occupying its own distinct state. Making a semiconductor work well requires in depth understanding of these things.” (2015)Floris.

Next we can go further to Quantum Field Theory and how quantum relativistic analogs have been used in building novel materials like graphene and possible technologies with it. At each layer, we go smaller and smaller in scale and he enhances our framework and possibilities inside what technologies can be generated. So this graphic not only shows the evolution framework but also the evolution of what kind of problems are considered important in Physics.

The fact there has not been more enhancement of our view after the 1970s with the standard model has led some pundits and futurists to worry about the growth based on science-driven technology for the future. We are still developing ideas that came before the 1970s, however, new economic domains based on science fiction ideas like starships and intergalactic travel based on new physics seem at this point impossible.

This is a very strong claim, however not totally unsupported. One possible support for this claim is that the monopoly of the scientific domain in computation has led completely to the growth of the US in the 20th Century. Recall that the foundations of computation, both physical and mathematical were done in the 1930s, the growth has been a development from that point. We can see this easily in the fact that Most of the Turing Award Winners(Nobel prize in Computing) are Americans. And the gap is huge !!!

This monopoly is what in my opinion led the US to be the most prosperous country in the 20th century. Therefore technology seems to be fundamental for the growth of a country, regardless of the monetary system. Moreover, the stagnation in Theoretical physics since the 1970s seems to be independent of how much money and support we put on the economic system, moreover, this had led some scientists to believe that we have reached the end of physics.

Other scientists remain skeptical of this fact, for me is quite clear Theoretical Physics is in a deep crisis. A big part of this effect is independent of more diversity of ideas or better funding. It is the fact that to explore nature at a smaller scale we need much larger energy scales and this is almost unfeasible in our current century. So for this part, Technology seems to be much more important than the monetary system.

However, is physics the only source of technology? This is absolutely not the case, equally as important as the transistor for the creation of the computer was the mathematical idea of the Turing machine from mathematics, we’ll discuss the relevance of mathematics in technology in the following section.

## Combinatorial Evolution in Mathematics

Although mathematics seems to be a completely different monster, mathematicians act more as priests rather than businessmen, at its heart it is a human endeavor and it is evolving in a combinatorial way. Moreover, the temporal picture we say for the evolution of Physics and Technology is very much replicated in mathematics.

For starters the devices created by mathematicians are Theorems, these statements are very related to physical technology. First In order to generate a new theorem you combine previous theorems, lemmas, mathematical objects(legos), we follow a precise logic with each of them(fuse them and combine them) in such a way that we get the new theorem.

Moreover, today similarly as we have mass assembly robots, or unintelligent robots to manufacture an object following well-precise instructions, we can verify mathematical statements using computational theorem provers. These two “robots” are not intelligent, they are just following a recipe on how to combine certain statements(pieces), and how to fuse them(logical procedure). Science on the other part is much messier and is more similar to the process of creating the algorithm or the proof the robot and the theorem prover used respectively.

Similarly, as with technology, the question we pose might not be answered within our current framework of thinking. In fact, we started this discussion with the question behind the irrationality of √2, although this is a fundamental case of elementary mathematics, let's consider a more contemporary example. One such example is the question regarding the Hilbert’s Program.

In the year 1900, Hilbert presented the mathematical community the continuum hypothesis problem of whether there is a set whose size is strictly between that of the integers and that of the real numbers. The framework of this question was enhanced by Goedel in 1931 when he proved that there are mathematical statements that cannot be shown to be true or false inside a given axiomatic system. In fact, this statement was the fact that Paul Cohen proved in 1963 that this question impossible to prove or disprove within the axiomatic system of Zermelo–Fraenkel set theory.

This is a typical example of obstruction and opening inside of mathematics. However, the framework enhancements are constructed by mathematicians themselves and very rarely by outsiders. Moreover, these enhancements in mathematics are also fundamentals inside technology(computers are directly related to Turing’s 1936 paper, an externality on Hilbert’s program). Hence similarly we can consider a similar time graph as in physics, where each era contributed to the technology of the time.

We start with the invention of mathematics by the Greeks, whereby the use of geometry they were able to build the ancient structures of antiquity. Then after the breakthroughs of the Arabs in accounting, we arrive at the Classical period where Calculus was developed and that gave rise to all modern physics and engineering. Perhaps the biggest breakthrough then comes in the Modern era with Galois and Rieman that generated Algebra and Differential Geometry respectively. Algebra today is used for cryptography in the study of elliptic curves, and Differential Geometry is the basis of all modern formulations of Robotics.

Next comes Hilbert with the development of Functional Analysis, which is the basis of Quantum Mechanics among many other things. Next, we have contemporary mathematics that is much more abstract, where we have Alexander Grothendieck algebraic geometry, Saharon Shelah model theory, and Grigory Perelman Ricci Flow. Each of these mathematical theories has applications, and still pushes the developments of new technologies and science.

Moreover, unlike physics, mathematics is in a sort of golden age, unbelievable breakthroughs have been produced in the last 50 years. I could spend all day mentioning the novel ideas in Optimal Transport, Analytic Number Theory, Knot Theory, Group Theory, Differential Geometry, … Many of these ideas have been translated into science and technology, for example, there are the novel fields of Computational Optimal Transport, Discrete Differential Geometry that have both scientific and technological breakthrough already.

So unlike physics, mathematical progress doesn’t seem in any kind of stagnation, moreover, it seems to be in a very fruitful era. This is not very surprising since the advancement of mathematics does not depend on the energy scale of our age. Furthermore, mathematics seems to be for the most part infinitely rich, so in some sense mathematics is the future of the economy. Since technological innovations seem to be more and more tied to a field with continuous growth.

In this part I mostly talked about the case of technology, however, this picture is incomplete since combinatorial evolution seems to be sterile to the problems and trends in society. Much more robustly it seems that money is what is behind many of the strong innovations in society. However, this is a story for another time.