Maths or strings?

Published on Monday, December 14, 2015

On December 12, the publishing house fri tanke with its CEO Christer Sturmark organized, together with the Royal Swedish Academy of Sciences, the so called "Pi symposium". This 2015 edition of a series of events got the title "Nyfikenhet & Förundran" ("Curiosity & Wonder").

The event was held in Stockholm and was completely sold out. About 1600 people of all ages gathered at Cirkus arena to listen to a debate between Max Tegmark and Ulf Danielsson, and to Björn Ulvaeus, former member of the pop group ABBA and now active in the Swedish Humanist Association, interviewing Richard Dawkins. Dawkins was of course the star of the afternoon and, later, a long queue of fans formed to get their books signed by him.

The interview was interesting but Ulvaeus rarely had follow-up questions and thus did not press Dawkins on any issue. There was thus little news for those that have followed the writings and sayings of Dawkins for a while. For me the real thing to remember - besides, yes, getting Dawkins signature in some books and shaking the "prophets" hands - was the first part of the afternoon, the discussion between Tegmark and Danielsson.

Sturmark introduced the debate - which lasted for about three quarters of an hour - by heralding that we would see and experience "Star Wars battle - episode 42".

Well, yes, the debaters had opposing views about some profound question but they are both scientists. Therefore there was no basic difference between their world views that might have led to a heated debate. No, the debate was learned, very friendly, and with a lot of joking about each others statements. And most of the jokes concerned the topics of this advanced discussion and were thus on a rather high level. Hence the audience was at times amused but got a thought provoking debate that was well in line with the title of the event. 

So what were these two theoretical physicists discussing about? Was it the mass of the Higgs boson? Or the 100 year anniversary of general relativity? No, not really, but closely related to that. The discussion went deeper and concerned what is "behind" particles and space. And within the discussion the question of "what is science" was automatically touched upon.

In brief and possibly a bit exaggerated: Danielsson holds that "everything is strings" while Tegmark thinks that in the end "there is only mathematics". Does that sound strange? Yes, for sure, but the debaters managed to put up an interesting discussion that was - mostly - understandable.

As a nuclear physicist with a background in particle physics, Danielssons view is immediately more appealing to me. But Tegmarks arguments were thought provoking and seem not easy to dismiss.

Let me try to briefly discuss what I perceived as Tegmarks and Danielssons points. It might very well be, though, that I do not understand Tegmark and the "mathematical universe hypothesis" or that I misrepresent his views. Then the blame is of course only on me. Maybe I should really read up and dig into Tegmarks book, watch this video, and read his paper, and this rather critical book review and blog post.

Lets start here with the very way the debate on stage started. Danielsson was pressed by the question whether string theory is science - since there are still no testable predictions and hence no way to falsify string theory - and how long it would be reasonable to wait for string theory to provide some testable prediction before one would out it aside and follow other tracks to solve the problem at hand (see here for a critical point of view on occasion of the 40th anniversary of string theory).

Danielsson admitted that the string theory still is not just there yet. But he claims it is the best candidate we have. The problem at hand is that we have two very nice theories that, sort of, do not want to talk to each other. The problem is to put theory of gravity (general relativity) and quantum theory in a common theoretical framework. As long as there is no other (good) candidate, Danielsson holds, string theory is what we have to follow. It is our best shot at solving this problem.

When I listened to that I could not help my thoughts following Tegmarks provoking questions. Assume string theory will never manage to produce a testable prediction. Assume that it will remain a mathematical construction. When would you give up? Is there a risk that science sort of splits an eventually produces a priesthood that calculates and calculates in order to try to solve a problems that cannot be solved this way? What if gravity and particles can never we united?

I guess the answer to this would be that science/scientists and the scientific method itself should eventually either (1) put string theory on track (provide a falsifiable prediction that might kill the theory), (2) produce a better alternative, or (3) dissolve the problem by finding some evidence that the two theories cannot be joined. Unless none of this happens it is the best we can do to follow the best shot.

Ok, so back from this diversion and over to Tegmark who thinks that strings (or anything else for that matter) is the real thing, but maths and numbers. This speculative thought that "our external physical reality is a mathematical structure" is called mathematical universe hypothesis(MUH).

Tegmark exemplifies this with the electron which is 1, 1/2 and 1. That is all there is. It is just numbers. It does not matter that we happen to call the first "1" the electric charge of the electron, the "1/2" its spin and the last "1" its "electron-ness" (the lepton number). He also held up his fingers to indicate the three dimensions of (Newtonian) space. The number is three and we happen to call it dimensions. But the word is not important. The number is and cannot be done without.

So what is it then that is at the very basis of what is, what is it that this universe - or any other universe - builds upon. Strings or some other kind of matter? Or mathematical structure?

One can wonder if one could conceive of a universe without matter. Or, on the hand, whether a universe without maths is possible. 

Personally I have a hard time to handle the idea that an abstraction, an idea, logical relations, something immaterial, is at the very basis of this universe or any other universe. I perceive mathematics as a tool, something that helps us to deal with the strangeness of the physical world. Maybe we, our brains, construct maths (by evolution) as a means to bring order into what we perceive as chaos. While the chaos (nature), of course, does not bother whether any-body understands it, our brains construct logic and maths as means to do so, to survive in the first place, and we then, falsely, believe that maths is so fantastic that is has an existence all by itself. This Pythagorean, non-materialist view of the universe as purely mathematical structure seems to turn the problem upside down. What is first? Matter that eventually produces mathematics, or maths that is the origin of matter?

Maybe one may conceive - not for my mind but maybe for someone else - a universe without material objects and even without any measurable structure. Without much any features at all in fact. You could then try to argue that maths is gone. There is nothing there to be counted. There are no spins and no charges and no one, two, three, many strings. Maybe there is nothing at all. But wait, you say, there is space time and space time has dimensions! So numbers are still there! True. But for a certain number to be there, and that we then call the number of dimensions, there first has to be anything to count. Hence you would argue that the hen (spacetime) needs to be there to produce the egg (some number).  

Although it might just be that I simply do not really grasp what MUH is, I rather prefer the thought that matter produces brains that construct ways to deal with the physical universe and that maths thus is a product of matter, than the other way round.

Therefore, at the end I still agree with Danielsson. Mathematics is a tool and not the thing itself. Or, to use a bit of Kant; "das Ding an sich" is matter and not logics and abstractions. It may even seem that Tegmarks view is a scientific - or rather philosophical - way to re-create an abstract, non-material god as the origin of everything. You just don't call it god, you call it maths instead. Maybe MUH is like scientism upon science itself.

Ok, with this we are back at religion and, besides science, a key topic of the afternoon. So lets at least very briefly go back to Dawkins who might have said the quote of the day. It went something like this: "I am fine with religion. If only people wouldn't that religion seriously!". Of course much has been asked by Ulvaeus and said by Dawkins, but, as I wrote above, it seemed there was little that a bit of googling would not reveal.

The event - which, hopefully, will eventually be available on youtube - was ended with an all too short discussion led by Sturmark and with Dawkins, Tegmark, Danielsson and Ulvaeus on stage. The last question posed by Sturmark was which problem everyone really would like to see solved. There was not discussion about it and everyone agreed. It is what David Chalmers called the hard problem; consciousness.

About the Author: Stephan Pomp was born in 1968 and Dipl. Phys. from the University of Erlangen-Nuremberg, Germany, PhD in experimental nuclear physics in 1999. Professor in Applied Nuclear Physics at Uppsala University. Engaged in Society Science and Popular Education. He is also a die hard atheist and a member of the Swedish Humanists. Website:

MM Editor on behalf of Stephan Pomp

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