Thursday, 10 January 2008

Judging by appearances - String Theory

In the recent issue of the New Scientist (january 5th, 2008) I have found an article on an new development in string theory, String theory may predict our universe after all, by Anil Ananthaswamy. The news is that instead of the `traditional' string theory landscape of Universes, with maybe 10^500 possible universes, differentiated by 10 dimensional manifolds, there may be a way to arrive at our Universe, via some kind of path through the landscape. An evolution through the landscape if you will.
The idea is quite interesting, it offers a new way of explaining our own Universe, other than anthropic principle of pure luck. So I read the article, and also adhered to my usual advice: I followed the sources, in this case a paper by Philip Candelas, Xenia de la Ossa, Yang-Hui He, Balazs Szendroi, titled Triadophilia: A Special Corner in the Landscape. I looked at both and come out with quite a lot of observations.

However, before I present them, a word of warning: I do not have any special knowledge of string theory beyond the popular books and papers. I would not recognize a string-theoretic equation. I have met most of the terms used in the discussion below for the first time. I am a perfect amateur here.
But - does it make me totally unqualified to judge the matter by appearances? I let you decide...


My problems started with the following paragraph in the New Scientist article, describing what Candelas and coworkers did:
The group placed all of the known Calabi-Yau manifolds on a diagram, plotting their topological complexity - for instance, how twisted and contorted the manifold is - against their "Euler number", which mathematicians use to dictate how the extra dimensions can be compacted.

The plot turned out to have the shape of a cone (see Diagram).

When I turned to the original paper I found a diagram that was similar, yet significantly different.

It is not the question of colour. It is, for example, how the axes are labelled. In case of New Scientist the vertical axis is a mysterious `complexity of manifolds'. In the original paper it is also rather mysterious quantity h^11+h^21. But knowing this makes the mysterious cone shape very simple of origin: The oblique axes bound the region where h^11 and h^21 are greater than zero.

The next problem is the visual suggestion that all interesting things happen at the bottom triangle, strengthened by the arrow in NS picture. Well, this is what the authors argue, that's true. But we should be really cautious to let us be guided away from the top of the triangle. The facts that points representing manifolds are getting sparser as one moves up is not a property of string theory (I think) but rather reflects our limited knowledge of the manifolds. as Candelas et al. write, the diagram represents only manifolds from Kreuzer-Skarke list. There are no informations on all the 10^500 (?) manifolds allowed by String Theory.

The question becomes: can such editing of the original research, undoubtedly aimed at improving understanding and making `the story' more colourful, be considered fair? Does the triangular shape comes from simple mathematical condition and not from profound discovery? Or am I oversensitive, and all journalist media, including blogs (such as mine) have to exaggerate...

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