Physics and mathematics: boundaries and interactionsAn article in Discover Magazine sparked some new blogospherical discussions about the mathematical "body" of the Universe.

Platonic world of mathematical ideas

Max Tegmark: The mathematical universe

The article explains that Max Tegmark lives a double life - in one incarnation, he is the ultra-mainstream cosmologist that many of us know from his talks, in the other one, he is a mysterious philosopher. It is the other face that we look at.

Tegmark says that there is only mathematics and nothing else exists. The world is made out of maths. Is it true? Well, it is a philosophical question that can't really be "settled". I am used to say that the real world is isomorphic to a subset of mathematics. But is it the same thing?

In fact, I am only using the word "isomorphic" not to irritate too many people but in my real opinion, the "isomorphism" may be treated as "equality" from all physical points of view. It has the same properties and it is thus the same thing. The whole reality "is" the information and all relationships between pieces of reality "are" mathematical laws.

I don't think that you gain anything by assuming that the reality is "something else" than the appropriate mathematics. But I am sure that you lose a lot if you deny that the reality is the same thing as mathematics and should be studied mathematically.

I find Max Tegmark's propositions somewhat vague but at the philosophical level, he is not claiming anything else than the elementary philosophy that most theoretical physicists, with Einstein as a key example, have believed for quite some time. The real world is a mathematical structure. A subtle "additional" task for the scientists is to find out what subdiscipline of mathematics is most appropriate to match the Universe and what are the actual answers to more detailed physical questions. ;-)

Of course, I am only joking when I say that these detailed questions are a "subtle" addition. They're the bulk of the scientists' work and Max Tegmark's philosophy doesn't seem to offer them anything useful to advance.

While Tegmark's comments are vague but they have a sensible core, the comments by many Tegmark's critics are downright incoherent or wrong. For example, the blog post "Discover: Interview with Tegmark" ("the post") says that "just because we (i.e. human beings) don't know anything except maths without 'human baggage' it doesn't follow from this it is the only thing there can be."

OK, I have no idea how to interpret that comment so that it makes sense. Besides mathematics, humans know a lot of things

*with*'human baggage'. It is one of the main points of Tegmark that the reality "is not" this human baggage. The reality is a pure structure from which the 'human baggage' has been removed. Such a "purified" structure is mathematics, almost by definition. Tegmark surely doesn't claim that we know everything about mathematics - or that we have always known everything about mathematics. Quite on the contrary, he says that the true aspects of reality "live" somewhere in the Platonic world of mathematical ideas and wait to be found.

**Principle of finite imagination**

The post calls the principle behind her reasoning "the principle of finite imagination". The brain is finite and it is therefore able to understand "finite complexity" structures only. Some of the structures relevant for the real world can be too tough for the human brains.

Is it true? Well, it might be. If you sometimes read the loads of dopes on her or Peter Woit's blogs whose thinking collapses once they collide with a rather simple mathematical notion or with a number comparable to 10^{500} - error, beep! - you can see very easily that many (and probably most) human brains are painfully finite. But the limited realm of ideas that are accessible to average and lazy brains is surely not what Tegmark or your humble correspondent mean by the world of mathematics.

We clearly mean the idealized realm whose beauty and wisdom is only available to those who are both talented and patient enough to walk through these abstract valleys and to understand them.

Are (some of) the human brains able to understand all the necessary mathematics in principle? We don't know for sure. But it is exactly one of Tegmark's conjectures that we can. By "mathematics", he doesn't mean "anything impersonal". He means a collection of structures whose properties and relationships can be described by a finite amount of "scholarship". Such structures are therefore accessible to a sufficiently talented and hard-working human.

Moreover, the post seems to be making a childish, "materialist" mistake when the author equates the number of the neurons with the number of elements of a mathematical structure that can be grasped by the brain. However, people have pretty much understood the monster group whose order is close to the number of electrons in Jupiter [thanks, Mitchell]. They can study the landscape of stringy vacua or the landscape of DNA molecules, too. Mathematics is able to self-organize itself in such a way that large structures can be studied at a small piece of paper (or brain), after all.

I am convinced that circumstantial evidence - and the history of science and mathematics so far - indicate that the world is "finite enough" to be accessible by talented and hard-working brains. Most mysteries that looked inaccessible in the past are suddenly understood and quantified. This is no proof that we can extrapolate this success but it is certainly a strong indication that we should try and we should believe in our success.

I can't tell you about the timescale when new things should be discovered - only crackpots are ready to promise you timelines of future revolutions in science and to criticize the real world if it disagrees with their timelines. ;-) However, I can assure you that if we give up, the progress will slow down or come to a halt.

**Academic system**

The alternative physicists on the blogosphere write that Tegmark's comments are untrue; but everyone should be allowed to study whatever he wants; in particular, Tegmark should be allowed to study "the mathematical Universe" all the time.

My answers to all three questions are completely opposite.

The essence of Tegmark's framework is true because his comments are just an idiosyncratic edition of some basic philosophical assumptions of theoretical physics. People can study whatever they want but the researchers can (or should) only be paid by the society if their production has a certain value because of the "principle of finite money for scholarship".

While Tegmark's philosophical musings are essentially correct, they are not valuable or new enough to deserve a separate support. So I think that it is very correct that Tegmark is paid for his careful analyses of the WMAP data and similar stuff and not for his mostly vacuous philosophical musings about the mathematical universe. In non-scientific disciplines, there can be different criteria besides the "validity" and "potency" of scientific results but every discipline must have some criteria and no field of human activity can fund "any" people who are working on "anything they want". Only hardcore communist utopians think otherwise.

The opinions in the post represent a large portion of what I dislike about the excessively self-confident but insufficiently informed writers and self-centered pseudointellectuals. The author doesn't care a single bit whether Tegmark's - or her - ideas are valid, interesting, useful, or anything like that. What she cares about is her status as a "thinker" and she wants to create a similar "clique" of people who call themselves "thinkers" - for the taxpayers' money. She is rating other people's work in science not according to the content of the work but according to their readiness to form the "clique" with her.

I am sorry but the elimination of wrong (and worthless) ideas is the #1 principle of all of science. So if you are proposing to hire people regardless of the value of their work, and it seems that it is exactly what these people are doing all the time, then you are definitely not building a scientific community. You are building a pompous quasi-religious community of arrogant and stupid crackpots of the Lee Smolin type whose babbling is incoherent and who don't understand basics of "their field" but who like to dress up as intellectuals and to emit populist clichés that sound good to the complete ignorants among the laymen.

This should stop as soon as possible because it is getting out of control. The Academia is already overflooded by incoherent pseudointellectuals and pompous fools who only like to paint themselves as fantastic guys despite their breathtaking ignorance and inconsistency and who are building on the support of the most ignorant and stupid people in the world rather than the most well-informed ones. Sometimes they are doing so not only to feed themselves but even to actively undermine the work of their much better peers. This is definitely not a path to progress.

So I think that it's fine if Tegmark's musings are reserved for no-longer-scientific magazines such as the Discover Magazine and if hard science is both required and expected in the professional spheres.

More precisely, it would be great if we could return to this old regime.

And that's the memo.

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