Some claim the “Universe is mathematical”. Their logic is flawed. I show why.
Max Tegmark, a MIT physics professor, wrote “Our Mathematical Universe”. I present here an abstract I concocted of an interview he just gave to La Recherche. Followed by my own incisive comments. However absurd Tegmark may sound, I changed nothing to the substance of what he said:
La Recherche (France; Special Issue on Reality, July-August 2014): Max, you said “Reality is only mathematical”. What do you mean?
Tegmark: The idea that the universe is a mathematical object is very old. It goes all the way back to Euclid and other Greek scientists. Everywhere around us, atoms, particles are all defined by numbers. Spacetime has only mathematical properties.
La Recherche: Everything is math, according to you?
Tegmark: Think about your best friend. Her great smile, her sense of humor. All this can be described by equations. Mathematics explain why tomatoes are red and bananas yellow. Brout, Englert, Higgs predicted a boson giving mass to all other particles. Its discovery in 2012 at CERN in Geneva led to the 2013 Nobel Prize in Physics!
Tyranosopher [unamused]: Notice, Max Tegmark, that the “Nobel” thoroughly excites you. You brandish it, as if it were a deep reality about the universe. But, in truth, the Nobel is strictly nothing for the universe. It’s just a banana offered by a few self-interested apes to other self-fascinated apes. The Nobel has more to do with the nature of apish society, rather than that of the universe. In other words, we ask you about the nature of the universe, and you answer with the Authority Principle among Hominidae. You may as well quote the Qur’an.
Tegmark [unphazed]: There are an enormous number of things that equations do not explain. Consciousness, for example. But I think we will make it. We are just limited by our imagination and our creativity.
La Recherche: According to you, there is no reason that part of the world escape mathematics?
Max Tegmark: None whatsoever. All properties are mathematical! We potentially can understand everything!
La Recherche: As a Platonic mathematician, you consider mathematical concepts are independent of all and any conscious act?
MT: I am an extreme Platonist, as I think that not only mathematical structures are real, but they are all what reality is.
Relativity and Quantum Physics confirmed that reality is always very different from what one believes. Very strange and very different from our intuition. Schrodinger’s equation, the fundamental equation of Quantum Mechanics, shows that a particle can be in several places at the same time. Thus one does not try to describe the motion of this particle, but the probability of its presence in such and such a place.
But, a century later, physicists are still in deep disagreement about what it all means. I think this interpretation keeps dividing people, because they refuse to admit what goes against their intuition.
Tyranosopher: Notice, Max Tegmark, that you presented as a fact (“a particle can be in several places at the same time”) something you admit later is only an “interpretation”. That’s dishonest: an “interpretation” is not a “fact”.
Tegmark [livid]: The strength of mathematics comes from the fact that they have no inhibition. Strangeness does not stop them.
Tyranosopher: Indeed, that’s why, as a trained mathematician, I am very insolent.
La Recherche: Max Tegmark, is it your mathematical approach that makes you defend another controversial idea, that of multiple universes?
Max Tegmark: I really believe that human beings never think big enough. We underestimate our capability to understand the world through mathematics, but also our capacity to apprehend its dimensions. To understand that we live on a planet with a diameter of a bit more than 12,000 kilometers was a first, enormous, step. That this planet is infinitesimal in this galaxy, itself one out of billions, was another enormous step. The idea of multiverses is more of the same. We discover again, and more, that what we understand is only a speck of something much larger. That much larger thing is the Multiverses, of types I, II, III, and IV.
Tyranosopher: La Recherche’s Interview then proceeds further, but let me unleash a fundamental critique here.
I am a deadly enemy of the Multiverse, as I believe that it rests on an ERROR of interpretation of Quantum Physics (the one Tegmark presented as a fact above, before admitting that it was, well, only an interpretation). The fact that it is another desperate scaffolding erected to save the Big bang theory does not make it better.
Now for the notion that the universe being full of math. This is understood to mean that the universe is full of equations. Equations were invented in the Sixteenth Century. Many, if not most, equate mathematics with the art of equating.
What’s an equation? It’s something that says that two things independently defined, one on the left side of the equal sign, the other on the right side, are equal. Great. What could be simpler: what is different is actually the same!
Notice this, though: before you can equate, you must define what you are equating. On both sides.
An equation equates concepts independently defined. Ultimately, definitions are not mathematical (see on the Nature of Mathematics, to follow soon). At best, definition is metamathematical. Our metamathematical universe? End of Mr. Tegmark’s naivety.
When we get down to it, it’s more our philosophical universe, before it’s our mathematical universe: no definitions, no equations.
How can a physicist make such a gross logical mistake? Are they not supposed to be smart? (OK, it’s smart to sell lots of books).
What allows to make that logical mistake? Education, or lack thereof. Many a mathematician will make the same mistake too. The problem is that neither conventional mathematicians, nor, a fortiori, physicists, are trained logicians. They just play some in the media.
Who needs a multiverse? It seems the universe of science is already too large for many physicists to understand.