Why is it, that when we started to develop a formalism, through which we explain our most abstract thoughts, we chose the only formalism that seems to be the right one in describing the nature? The question has bothered me since the first day of university. Starting with the fundamental physics course, I was always amazed by the fact that we write equations, and they just happen to work! In a series of writings I am going to explore my original ideas (maybe be biased by the books I read) about the idea of mathematical universe. In the first post I will try to demonstrate what it means for the universe to be mathematical. Despite that what a mathematical universe would be in order to answer this question.

Any post that would ever be published on this blog (I hope the number is large after a year or so) is going to be short draft of my ideas, beside some which are a complete understanding of the problem and solution (which maybe become research papers themselves). The point of writing these is to get into a discussion with my thoughts in an ordered way.

## What is a Mathematical Universe?

Every day, physicists all around the world, use mathematics in their papers and research; they use a lot of different notations to describe different phenomena. Without considering the nature of mathematical formalisms as mathematicians do. This would lead us through a path, where we lose some important connections between the reality of mathematics. But aside from that, one would be amazed to see that the developments of mathematical formalisms that didn’t have anything to do with nature at first, are now being used over and over in new fields of science and specially in physics.

As an example consider Group Theory. The theory of objects called a group with a set of axioms that are defined; their relations; their generators; their operations. One could argue that it wasn’t obvious for many people that they are going to help us in describing elementary particles that are fundamental to our nature. Such examples provide us a hint, that maybe the mathematics that we are developing over time, simply cannot be what is now acceptable by nature.

Note that I am not suggesting that any piece of mathematics is going to be used as an equation or a rule describing a natural phenomena. What I was trying to say is rather deeper than that.

### Mathematics as a Tool, Approximation, and Reality

Some physicists would argue that the nature is apart from the mathematics that we develop. What does that mean? it means that whatever we are calling the *equations of nature* is just not what nature actually is. Therefore we only developed a mathematical structure so that we could talk about nature without it’s essence get in the way, leading to unavoidable complexities that our brains could not handle. The problem with such view, in my opinion, is that it lacks some logical compatibility.

The nature, as one would normally think of, is everything outside; things that we experience. From another point of view, this means that nature is *everything but us.* I think one of reasons that people would believe that mathematics is just a tool to describe complex behavior of nature. But this is simply false! we are, also, part of nature. The complexity of nature doesn’t only belong to the outside world, but also to us. To suggest that a natural system, such as human brain (which with it’s undeniable complexity is able to do much more than a rock) can develop a logical basis, mathematical formalism, deductions and more that are otherworldly, is a hard task. I would suggest that it is impossible!

Another physicist would tell us that mathematical models that we develop to describe nature are just better and better approximations of the reality, which we don’t know anything about. I would agree but why should an approximate model based on a logical model that doesn’t belong to this world make sense, and work? A physical model is non-theless predictive. If we measure the outcome we get the predictions right away! This is another example of how contradictory it sounds, to call mathematics tool or approximation.

### Mathematics as Reality

A third option, which I am trying to argue in favor of, is that mathematics, is reality. Well sure now the title “*Mathematical Universe*” makes more sense. This suggestion, which shall be proved later (probably by me or other people who are a fan of such option), is describing the reality as a mathematics. One of great people that I know who had such view is Plato, whom beliefs I would talk about in later published posts (probably the next). Accepting mathematical reality, shines on the fact that everything is an actual mathematical procedure, not that we have the complete equations or the write structure, but the descriptions that we are giving as approximations, are able to predict approximately because there’s simply a real mathematical procedure that is underneath the illusive nature that we preserve. A photon is an actual manifestation of a set of mathematical equations, rules and formalisms that is what it is to be a photon.

## Argument 1: Mathematics is the Best Descriptive Notion

We use language, in order to talk about concepts, that are abstract or real. There are notions like the natural languages, English, Arabic, Persian and more. I want to focus your attention on what do we do when we describe things. As an example how do we define a circle using English? One would suggest to say: *a round object, which roundness is unique throughout its **surface. *Fair enough, but now we have to define roundness, uniqueness, and surface. Say we accept the term *circle* as an axiom, the problem is now how to deal with real objects and validate them as circular or non-circular objects. I would talk more about how the natural language that we are going to use to describe the world around us, is insufficient, it cannot be exact, it would permit contradictory statements to exist and the most important of all, it cannot give us a good way to look for truth. Descriptions can vary from person to person without being able to check if the description is correct, or to compare with others. This is a problem.

On the other hand a mathematician can describe a circle fully without the loss of generality. He can also provide a basis to determine if an object is circle or not (because the description is unique and completely sufficient). I has a basis of axioms, and a deductive system that is then able to make more statements about circles and circular objects without making false statements. This is why mathematics is so powerful.

Here now I raise the glory of mathematics even more, I suggest that not only circle, but for describing any real object (chair, human, cables, the sun) the most complete description would be a mathematical one. Sure we may not be able to deal with such complex object fully mathematically, but the nature of a human can be described using natural languages, biology, and chemistry, but after all they are descriptions that like the natural language itself, they are not as consistent as mathematics can be, also they cannot grow easily because they lack deductive reasoning. Note that I am not trying to say that chemists and biologists are wasting their time with a type of science that cannot be sure! These topics are hard and because they’re specially complex situations, one cannot deal with mathematics of them easily! What I am suggesting is that if we lived in an ideal world where we had much more intelligence in our genes (like a billion times more) then the best way to describe physical reality including, life forms, is to describe them through mathematics. Since only using that we can have the most precise and most useful description of anything.

Anyway this short post would be continued in later chapters with more descrptions on the main ideas that are discussed here.

Piece.