## Monday, November 1, 2010

### A mathematician of the purest kind

Shrink points out this comment from Simon Cheung posted on 26 October 2010 to Physics Today and Spacetime as Fractal Geometry on About.com.

What are the experts thinking of the new proposal by El Naschie for the wave collapse? It is neat but I have one problem. It is too neat and too simple to be true. I do not believe that nature is that simple. OK I know all these philosophers that marvel at creation being the most simple of simple things. Whoever believes that, with the exception of Leibniz will be canonized. Here is El Naschie’s solution of the state vector reduction. The particle is a Cantor point. It has the dimension zero and the golden mean. The zero is the Menger-Urysohn topological dimension. The golden mean is the Hausdorff dimension. In other words a quantum particle is a fractal particle. Now comes the big thing. The quantum wave or the Bohm Einstein guiding wave or the probability wave and all mean the same thing, is the empty set. The empty fractal set has a dimension minus one and the golden mean squared. The minus one is the classical Menger-Urysohn topological dimension. The golden mean squared is the corresponding Hausdorff dimension. We all know that the empty set is the neighbourhood of the zero set. Said in a less sophisticated language, the empty set is the surface of the zero set. Following this logic the wave function is simply the surface of the quantum particle. They are part and parcel of each other. Now imagine you are taking measurements. At a minimum you will enter into the empty set to catch the zero set. That way the empty set becomes non-empty follow El Naschie’s logic which I must say is sound although it sounds a bit weird. Since the empty set is no longer empty and at best becomes a zero set, then the wave set is converted into a particle set. Hey presto! There is no more wave. I see it but I cannot believe it. I believe that is what Cantor said when he thought of his discovery about the cardinality of the continuum and that the number of points in a Cantor set are equal to the number of points in a continuous line or for that matter an area cube or a hyper cube. I am a mathematician of the purest kind so I can swallow this stuff but what is the feeling of the hard-nosed physicists? Awaiting eagerly your views.

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