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?
Formulation Before Revelation of Mathematization
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.
Patrice Ayme’
Tags: Definitions, Equations, Mathematics, Metamathematics, Multiverse, Tegmark, Universe
Patrice Ayme's Thoughts 
August 14, 2014 at 11:40 pm |
First, what the Schrodinger equation actually states is that energy is conserved at the quantum level. It also states that what we call the Lagrangian applies, from which it follows that the virial theorem applies at the quantum level.
As stated, an equation is effectively a sentence. It says A is equal to B; nothing more. To state that mathematics defines the universe is simply wrong. To say it describes the Universe is far better. The fact is, one can come up with a number of mathematical theories that observation shows are simply wrong. Unfortunately, at the quantum level there is a requirement to interpret your observations, which has led to problems.
LikeLike
August 15, 2014 at 7:08 am |
Agreed. Some of the problems are purely semantic (yet drastic). Physicists say more than they know, sometimes (concept of particle or photon being the number one exhibit), and sometimes not enough (we have evidence that the world is made of particles, yes, but also many-slits “states”, so to speak… Yet these states that I christened as many slits states are not the “collapsed”, or final, states spanning the Hilbert spaces themselves. That’s a subtlety which seems to escape completely the multiversists, and at the core of their error.
I think Tegmark, when he said the Schrodinger equation (truly found in De Broglie thesis, BTW) says particles are everywhere is alluding to simply the fact “”””particles””” behavior is described by waves during fundamental processes.
In general, mathematics describes rules (“theorems”), under certain conditions (“axioms”). Depending upon the domain selected, that can be more or less valuable. I view all math resting irreducibly on the concept of infinity as false. “Irreducibly” being the important word.
PA
LikeLike
August 15, 2014 at 2:18 am |
mathematics itself is evolving, so i doubt you can use the 21st century maths to define/represent the reality of 25th (or 100th) century.
though, mathematics can be used to understand(logically) anything after the fact. If it couldn’t be done, they will invent new math 🙂 The cycle goes on. What are we talking about again ?
LikeLike
August 15, 2014 at 7:59 am |
Yes, math evolves. That’s a good point. Yet, one way it evolves is by discovering gaps in preceding logic. See Euclid. “Logic” means making a discourse out of it. Fundamentally, thus, philosophy, with more details. We have met the “Mathematical Universe”, and it’s a big blah blah blah…
LikeLike
August 15, 2014 at 8:14 am |
I think when people start talking about facts they enter into a state of hubris blinding themselves to the possibility that they may be wrong. Much of what the individual senses is nature is a matter of perception, which differs from individual to individual. I follow Heraclitus in considering the only truth worthy of knowing to be common patterns that repeat. I accept that these patterns that are common are only true when all the variables are similar, but might change if any variable changes significantly, for instance the moon does not teleport but an electron does. I can only say that it is probable that a pattern will repeat, like the metaphorical white swans, but I am humble in accepting the possibility of a change to the pattern, a black swan. Nothing can be said to be fact, nor can anything be deterministic, nature is too random and there are too many variables.
I consider that as common patterns repeat; that there can be ten roses. ten stars, ten galaxies, there can be many universes too. It is hubristic to say with so much certainty that there is only one universe, it denies the pattern of nature that loves diversity, multiples and repetitions. When I write about nature I incorporate everything, be it one universe, or many; I reject universe, I think nature is a better description of the reality we exist in.
Some of the ancient philosophers describes everything in nature as of one core pure material, some name “the boundless”, it is out of this principle material all things arise. These same philosophers such as Pythagoras describe this primal material as having both an unlimited and a limited state. The limited state is that part of nature that we see, where it is possible to apply mathematics, but scientists miss the other face of nature, the unlimited, which has an impact on the limited face of nature, but this unlimited is beyond the measure of mathematics.
Since the limited side of nature is expressed as patterns, mathematics is the language of these patterns, and it is a good method to describe these patterns in numbers.
LikeLike
August 15, 2014 at 10:22 am |
Dear Alex:
I roughly agree with most of what you say. However, here are a few questions:
1) Why do you say electrons “teleport”?
2) One of my gripes with conventional math is the notion of “infinity”. I view the initial proof of Euclid as false (call me more modest than other mathematicians!). Modern logic has several dozens of kinds of infinities. So they assuredly considered the “unlimited state”.
The argument you found that, if one sees one universe, there should be more than one is explicitly used by Tegmark (although I did not report it). Universes are like cockroaches. However, the problem is one has never seen a different version of a fundamental physical law.
PA
LikeLike
August 15, 2014 at 10:54 am |
1. I think it would be clearer to say that information teleports between two electrons rather than the electrons teleporting, though I am open-minded to that too. Experiments have shown information can teleport between two electrons in a state of entanglement.
2. Raw chaos is infinite since it has no direction, form or pattern due to its random nature.
LikeLike
August 15, 2014 at 11:15 am |
Quantum states can be somewhat “teleported”, indeed. But what Tegmark pretended, that a particle can be in two places at the same time, is bad sci-fi (although I considered it a bit myself, somewhat, long ago, before rejecting the idea as too much too soon).
Chaos is now a science, and a complicated, not to say chaotic, one. Creating “random” is hard. Two of the Fields Medals just attributed (the Iranian and the Franco-Brazilian) made progress in the field…
PA
LikeLike
August 16, 2014 at 4:52 pm |
Silly ideas sell better: Tegmark is stupid from greed, probably
LikeLike
August 16, 2014 at 11:48 pm |
Tegmark’s business model is good: even I bought his book. However I got quickly bored, and read just a handful of pages.
LikeLike