What is mathematics unsuitable for in learning about nature?

Mathematics is a wonderful science. That seems to be the essence of all science. Mathematics is the language of nature. Nature works acco...

Mathematics is a wonderful science. That seems to be the essence of all science. Mathematics is the language of nature. Nature works according to the rules of mathematics. We think we understand nature when we can also describe it with mathematics.

However, the appearance of the perfection of mathematics hides a dangerous trap. It suggests completeness. It gives the impression that you can get to know nature perfectly with mathematics.

This trend is especially evident as we get closer and closer to the foundation of nature. Space, elementary particles, interactions only exist for us in mathematical formulas. The reality of nature becomes an illustration of mathematics. Curved space, point-like and virtual elementary particles, and many more realistic models are models created from applied and well-functioning mathematics, and we relate these models to reality.

However, such an application of mathematics to reality makes mathematics not only a tool of learning about nature, but also an obstacle to learning about nature. It gives the impression that mathematics is an omnipotent tool of learning about nature as if everything could be solved with mathematics. Nevertheless, many times we get stuck in getting to know nature. When we see that mathematical formulas are accurate, but yet it doesn’t make sense, that it cannot work that way, if we don’t see where and how to go about getting to know nature, we may be at a dead-end in math.

Why can the cognition that based on math leads to a dead end? Math tells how nature works, but it tells nothing about what is it that what works that way. It is precisely mathematics that cannot show the reality of the foundations of nature. To understand nature, we must also know the reality of the foundations of nature. Mathematics is not a tool for recognizing the reality of the foundation of nature, no matter how hard we want to use it. Mathematics leaves a blankness in our knowledge that cannot be filled by mathematics.

We disguise the lack of our knowledge about the foundations of the reality of nature by creating models based on mathematics. The extreme result of this approach is when we believe that mathematics not only describes how nature works, but mathematics itself is what works. This is also an option, but let us not come to this conclusion just because we see no other way out. The method based on mathematics is not unsuitable for learning about reality, but can be dangerous. If we are not careful, if we use only mathematics as a basis, if we only want to use mathematics to get to know the reality, then mystical, contradictory to themselves, yet seemingly realistic models can emerge.

Of course, we can think that then we will try to improve our math and find a way out. Maybe, but there may be another way.

To really get to know nature is not enough to know how it works, we also need to know what is working. We also need to create a realistic model of nature. However, mathematics is not only an omnipotent tool for this task, but can be even a misleading method.

Currently, we can describe the behavior of elementary particles and space very accurately mathematically, but we do not really have a suitable model for what space is and what elementary particles are. To move forward in our knowledge, we need to find the reality of the model of elementary particles and space.

String theory is an attempt to find a model of elementary particles, but has not yet led to success. Why? Maybe it’s because we use mathematics primarily as a tool in setting up the model. As we are learning about space, the well-functioning mathematics of quantum theory and general relativity uses contradictory models. Our process of learning about nature has stalled, and we don’t know how to go on.

What can we do? Let’s use our imagination for the model and not start with math. Let mathematics be only a means of control, a judge of the possibility of the model, not the way of discovery. Let us first use our imagination to create a model of nature. If we already have a model, we check it with the math of reality, since the model of reality cannot contradict the math of reality.

What is mathematics unsuitable for in learning about nature? For the creation of a model. Our imagination is the best way to set up models. Let’s use it independently of math. Let us not be afraid to use our imagination to discover nature. In recognition of reality, the model, what we can create with our imagination, is an equal level of the operation described by mathematics. Mathematics is not omnipotent in describing reality. Imagination is the same level of recognition as mathematics.

Of course, our imagination also has limits. We cannot imagine the shape of four-dimensional objects. This is true. Nor is our imagination perfect and omnipotent. Nevertheless, it is a tool on a par with mathematics in learning about nature.

We can describe the operation of elementary particles and the behavior of space well with mathematics. Even so, we do not know what the elementary particle is and what space itself is. Let’s try to use our imagination to get to know nature.

What is the real model of elementary particles and space? Can we imagine a corresponding model of these without math?

The grid model, which has been discussed several times in the thoughts, is one of the efforts to further learn about nature, a model created by imagination to learn the basics of nature. Maybe it is a realistic model.