In which mathematical structure are we living?

Some thoughts on the nature of reality

Published on July 21, 2014

Mark Tegmark suggests that the ultimate reality of the Universe is Math. Specifically, it’s a mathematical structure. The Universe is existing just like a mathematical theorem is existing: no more, no less.

What is Math?

When we think about math, we see some boring equations. Actually those equations are not “math”, they are just the “mathematical language”. To many people, the mathematical language is special, quite magical and separate from other sciences. But the math language is just a normal language: it is not more fundamentally powerful that any other common language. The main property of the math language is its conciseness: each symbol has a precise meaning, so that you can build complex sentences within only a little space. It would be possible to write “Principia Mathematica”, the 2000 pages book from Russell, in plain English, but well it would explode in size and being, finally, not humanly readable nor writable. But when saying “The Universe is Math”, we are not referring to the math language but to a mathematical structure. There are very simple mathematical structures: for example a group or a ring. Those two structures are too simple to generate the whole reality, but some presumably would be able to.

Digging the reality

To me, arguing that the Universe, at its very bottom, is a mathematical structure is quite natural: after all, when searching for the essence of reality, the physicist will look at each property of the universe and say: this property can be deduced from these others, so I can drop it as being non primitive. Doing that, we are removing, layer by layer, properties that are non primitives. Assuming that there is a finite number of properties, at the end all that remains will be a hand-full of properties, coming “bare”, without baggage as Max Tegmark puts it, that is to say without context. And what is an object consisting of a bunch of properties without baggage? A mathematical structure, of course!

It’s facinating to see that when looking down to the infinite small, thing get more and more simple. At our scale, the vocabulary necessary to describe the reality surrounding us is astoundingly big: think about all the biology, politics, economics, weather and the associated theories, but also about films, novels and even sentiments, behaviours around here… All those require an enormous amout of vocabulary to describe them. But when it comes to describe the infinitely small, this vocabulary narrows down. It narrows down to actually only a handful of particles. In the same way, when looking up into the infinitely big, thinks also simplifies. This corroborate the idea that, at the very bottom, the laws of nature are very simple and, so to say, mathematical. Life seems to lie in a sweet spot of complexity generated by the mathematical structure. The same thing happens for cellular automata, where the interresting things happen in the “chaotic” fringe between order and anarchy.

Who chose?

We experience only a small part of this mathematical structure: it is actually a multiverse. The multiverse according to Tegmark has 4 layers. The multiverse solves two big questions:

Indeed, let’s imagine that you’re a great physicist. You invent a new theory, that explains very well the reality surrounding us (for example, you come up with a “E=mc²”). What more, every experiment tend to confirm it. However, there will always be someone that will come and tell you “Nice equation! It seems to describe very well the reality. But why this one in particular? Who chose??”. The multiverse solves this problem (“Who chose?”) by removing it: nobody chose since all possible reality do exist. Then why do we experiment this one in particular? Because we are conscious into it! Although all states of particles do exist in parallel universes according to the multiverse interpretation of quantum physics, this special state of mind called consciousness makes me experience only the world surrounding it.

The mathematical structure we live in, yet undeciphered, does not have to evolve. There is no notion of change nor time: it is called the “block universe”. Again, our reality exists statically just like a mathematical theorem exists. What makes a mathematical theorem exist? The simple fact that it is non-contradictory. We experience the world around us as physical because we are a part of this mathematical structure interacting with other parts of the same structure. Furthermore, this mathematical structure generates all the space, all the time, of all parallel universes. It is all, at once, with no evolution. We experience one particular universe within the multiverse because of the consciousness.

We chose!

Most people have a hierarchical vision of the reality: each layer of reality is based on the underlying one. For example, psychology is based on neurology, which is in turn based on biology, chemistry and ultimately particle physics and quantum mechanics. But in fact, with the multiverse hypothesis, the opposite is also true: the laws of quantum mechanics are influenced, at least partially, by psychology. Indeed, to be able to develop such a thing as consciousness, the base laws of our universe within the multiverse should be able to allow it. Some of the fundamental parameters of our universe, such as the speed of light and the Planck’s constant, seem indeed very finely tuned so to allow our existence. For example, if one of those constants would be 1 millionth greater or smaller, the atoms would not stick together, no chemistry would exists, and even less Humans able to study it. The special structure called consciousness exists in one branch of one of the parralel Universes (at least), and we are experiencing the world through this structure. Then it is not surprising that the physic laws and constants are “so that” we can be alive and conscious in the Universe we observe: first of all not only those laws and constants do exist in the multiverse but all of them, and secondly we are the consciousness structure in one of them. This is called the anthropic principle: to justify a fact in our universe by saying that if it was any different, we wouldn’t be there to discuss it.