MY ART MANIFESTO 9
In the previous part, I asked “If energy did not exist, would there be mathematics?” and briefly gave possible answers. I continue from there.
It turns out that for the physics to begin, the energy in singularity state definitely requires mathematics, so that Bigbang is formed. This can happen in two ways. First, all mathematical codes and variations are inherent in pure energy. There is already mathematics in energy and it has created the universe. Second, energy met mathematics in a way outside of itself and started through a method under the control of it, and formed the universe. There is not another way for the universe to exist.
A problem arises in the statement “Mathematics was existing in energy”. Energy is concrete, mathematics is abstract! Therefore, it is a handicap that there is already mathematics in pure energy because they have no similarities. Everything we know as concrete, the entire universe is made up of energy. That is, energy is concrete, it is the basis of concrete, but mathematics is certainly abstract. Therefore, it is unnecessary and meaningless for them to be together when there is nothing but energy in the beginning. And why, for what reason should they be together? As a matter of fact, another question arises here: why do we expect mathematics, what makes us think of mathematics? The reason is this; we know that the Bigbang started with the laws of physics, which are mathematical. This means that for the formation of universe, either the laws of physics must potentially exist within the energy, or mathematics must have existed before the laws of physics, or at least at the time of energy’s coming into existence, so that it could create laws according to the properties of energy. One of those is necessary for the formation of the present universe.
That’s why we think through logic of deduction, starting from the fact that the laws that make up the universe are mathematical. In other words, because of the states of energy after it is activated by the laws of physics, we evaluate and think that mathematics is necessary. Because of this reality, we are looking for mathematics as well as energy.
However, there is something overlooked here too! It has a state called singularity, in which energy has not come into action yet. This means that what will happen when energy is activated is unknown because it is not clear what will happen or what will emerge out of this energy. In other words, energy is in a state that cannot be evaluated in any way. Even there might not have been the Bigbang; it might have kept its current state forever. So, no mathematics would be needed. Therefore, for the beginning, mathematics cannot be expected or mentioned, and mathematical intervention cannot be foreseen. So, the spontaneous mathematical behavior of indefinite energy is not plausible. As such, the mathematical rates in the transformations of energy, the laws of physics cannot exist in the singularity. If it doesn’t exist in the singularity then it shouldn’t be either, but it has been. Then, if the mathematics wasn’t inside, it was outside.
A more interesting question arises when it is said that mathematics was outside of energy! Pure energy is said to be small in atomic dimensions. Wherever and how did it encounter mathematics? If there was no space yet, and mathematics was not in energy, where was mathematics? Let’s say we somehow said mathematics was over there, this time the question is, how did it come into existence? If it was independent of energy or any other element, why and how did it exist? In addition, if there was no element that can use mathematics, why did mathematics, which had a regulating feature exist? Because, as I said, it is totally abstract!
Because of this situation, we can say that the pure energy that brought physics into existence somehow came into existence. However, we cannot say the same for mathematics. Because it is abstract, it is not possible for it to exist somehow or randomly. For it to be random, a sample space is necessary. In other words, there must be other elements that will be options other than mathematics in the same place so that mathematics can enter the field of random!
Another important point: since we do not know how energy came into existence, we can say that it might have come into existence out of nothing. But we cannot say that for mathematics because mathematics is a work of reason, it is a structural order. Therefore, we cannot say that mathematics came into existence out of nothing. Because orders have to be structured.
There is another important issue within this regard. As it is known, the universe transformed from state to state while it existed out of energy, and the universe was formed after many years passed. Well, can we talk about a similar process for mathematics? Like the initial state of energy, did mathematics have an initial period? No! Because we know that there is a continuous development in the universe, but there is no such development in mathematics! Since the beginning of the universe, mathematics has preserved the same structure as whatever it is. In other words, it is impossible and illogical to state that it has made progress. Because if mathematics changes, the system will collapse. That is why the mathematics we have discovered so far, and all the mathematical and structural orders that humans or other intelligent beings will discover from now on, have existed from the very beginning and have not changed.
The point I want to explain is this: during the transformation of energy from state to state and the creation of the universe, mathematics did not change from state to state alongside energy. Because all state-to-state transformations in the universe are already the result of physical laws. All of the laws have to be present at the time of the event or on the condition of the situation so that creation continues. Otherwise, this universe would not exist.
As a result, all the mathematical states that we humans have discovered and we or other intelligent beings will discover until the end of the universe were already present at the beginning of existence. It has neither improved nor weakened. (On the other hand, as the energy expanded, its temperature dropped and the universe was able to form.) But mathematics kept its condition as whatever it was.
So far, we have talked about the absolute and certain effects of mathematics on the formation of the universe. So now let’s take a look at what mathematics is, what its definition is. Let me first give the official definition.
“Mathematics: the science that examines the structures, properties and relations between forms, numbers and multiplicities through logic and is divided into branches such as number knowledge, algebra and spatial knowledge.” (Turkish Language Institution)
“What is math?” The common definition of the question in the literature is that mathematics is a universal language. ” Here, let me repeat the excerpt from the book of Nobel Prize-winning physicist Richard P. Feynman that I gave in the previous section.
Physicists cannot turn to another language. If you want to learn about nature, to understand it, you need to understand the language it speaks. This is the only way nature delivers its messages. (Richard P. Feynman, On the Laws of Physics, pp.67-68)
As you can see, mathematics is explained as the language of the universe or it is stated that “mathematics is a language”. However, there are various handicaps in these explanations! Because language is a structural element formed on an order by those who use it. For mathematics, in order to be a language or resemble a language, it must be structured on a common system by at least two users so that it can be included in the definition of language. Accordingly, if mathematics is a language, then the only element we have available to compose that language is energy. There is nothing but energy! In this case, can we say that the language we call mathematics must have been developed by energy? No, we can’t say! Because the Bigbang, the universe, started with mathematical ratios at the very beginning and could exist within the definite and obligatory limits of mathematical laws. Therefore, energy cannot have created or developed the language of mathematics.
As can be seen, both academicians and many people who are not familiar with the subject easily say that “mathematics is a language”. However, it is not that easy and simple! After all, mathematics is an invention of human mind. It is a set of discoveries that explain the development in nature by means of a number of methods and calculations. However, according to science, nature cannot make plans for future. That is, it does not calculate. All developments happen in their own conditions. That’s why I said nature does not use math. Anyway, there are very interesting dilemmas and paradoxes within this subject. I will continue in the next part.
(Translated from Turkish by Semih AYDIN)