Monday, April 25, 2011

Amusing reviews of El Naschie's work

Thanks to the reader who provided these in the comments to the German Wikipedia article post on El Naschie. I am quoting him in full:

The Wikipedia links to an awesome Mathematical Reviews review of an El Naschie bogus paper. Since subscription is required to access it, here is the review's text for everyone to read:

MR1428296 (98b:83036)
El Naschie, M. S.(4-CAMB-A)

A note on quantum gravity and Cantorian spacetime. (English summary)
Chaos Solitons Fractals 8 (1997), no. 1, 131–133.
83C45 (83C99)

The author suggests that the use of Cantorian spacetime (not defined in this paper, but apparently to be found in other papers by the author; see, e.g., the collection edited by the author, O. E. Rössler and I. Prigogine [Quantum mechanics, diffusion and chaotic fractals, Pergamon, Oxford, 1995; MR1394491 (96m:81002)]), with a point-to-point notion of time, can effect a reconciliation between quantum mechanics and gravity.

This paper seems to the reviewer to contain no mathematics.

Reviewed by J. S. Joel

Also of relevance is:

Institution Information for 4-CAMB-A

Department of Applied Mathematics and Theoretical Physics (DAMTP)
University of Cambridge

Cambridge CB3 9EW

Another awesome review from El Naschie's pre-fractal-spacetime days:

MR1146758 (94d:58098)
El Naschie, M. S.(1-CRNL)

Peano dynamics as a model for turbulence and strange nonchaotic behaviour.
Acta Phys. Polon. A 80 (1991), no. 1, 3–13.
58F13 (76F20)

From the paper: "The starting point of this analysis is the generally accepted realization that fractals are the carries of complex strange behaviour. Second, we follow Yorke's conjecture that single Cantor sets are somehow the back bone of all strange behaviour. To that we add what is intuitively evident, namely that in one dimension the simplest fractal set is Cantor's middle-third set with dc=log2/log3. If we accept this, then we can claim that in four-dimensional phase space a strange set will typically have a Cantor-like fractal dimension dc≈4.''

There is plenty of wild speculation and misprints, but no rigorous arguments.

Reviewed by Christoph Bandt

Institution Information for 1-CRNL

Department of Mathematics
Cornell University

Ithaca, NY 14853

MR1103961 (92b:58147)
Kapitaniak, T.(PL-PLDZ-MC); El Naschie, M. S.(1-CRNL-A)

A note on randomness and strange behaviour.
Phys. Lett. A 154 (1991), no. 5-6, 249–253.
58F13 (82C03)

The problem the authors seem to be concerned with stems from their own misreading of the Poincaré map as a representational tool to distinguish strange chaotic attractors from strange nonchaotic ones. The authors present some numerical experiments to estimate Lyapunov exponents which should allow one to distinguish between both cases. However, they disregard an analysis of the Poincaré maps claiming that such maps do not contain the signature for chaotic and nonchaotic behavior. This confusion arises from the fact that a simple qualitative assessment of the Poincaré map, as the authors perform in their work, will of course not reveal differences between both types of attractors. However, they have chosen to cast the problem in terms absolutely equivalent to a proper assessment of the Poincaré map, simply reading the Poincaré map in a different fashion. Moreover, their bringing into the picture a deterministic system forced by random noise does nothing but introduce an additional perversion, for, once more, they assert based on qualitative considerations that the resulting behavior is similar to strange deterministic behavior. Both scenarios belong to entirely different realms which stem from different paradigms.

Reviewed by Ariel Fernández

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