Notes and literature cited
- Some universities, for example Edinburgh, still have chairs in natural philosophy.
- K. R. Popper: ‘The logic of scientific discovery’; 1977, London, Routledge.
- This example is due to J. Kirchner: ‘The Gaia hypotheses: are they testable? are they useful?’, in ‘Scientists on Gaia ’, (ed. S. H. Schneider and P. J. Boston); 1991, Cambridge, MA, MIT Press.
- R. Hoffmann, V. Minkin, and B. K. Carpenter: ‘Ockham’s razor and chemistry’, Hyle – Int. J. Philos. Chem., 1997, 3, 3–28; and Encyclopaedia Britannica, 1994.
- A. Goddard Lindh: ‘Did Popper solve Hume’s problem?’, Nature, 1993, 366, 105–106.
- U. Frisch: ‘Turbulence: the legacy of A. N. Kolmogorov’; 1995, Cambridge, Cambridge University Press.
- I. Newton: ‘Principia mathematica’, Book III: ‘The system of the world’, 1687, (trans. Andrew Motte, 1729).
- It is interesting to note the etymology of the word: it is derived from the Latin turba, meaning ‘crowd’.
- G. I. Taylor: ‘Statistical theory of turbulence: I-IV’, Proc. R. Soc. (London) A, 1935, 151, 421–478; A. N. Kolmogorov: ‘The local structure of turbulence in incompressible fluids at very high Reynolds number’, Dokl. Akad. Nauk., 1941, 30, 299–303. For a complete treatment, see Frisch’s book (Ref. 6) or A. S. Monin and A. M. Yaglom: ‘Statistical fluid mechanics’, Vols. I and II; 1971/1975, Cambridge, MA, MIT Press.
- A whole book would be needed to study the infatuation with fractals among both the scientific and non- scientific communities. Let me just recommend a quick look on the Internet: a search for the word ‘fractals’ using Yahoo yields 13 220 websites, most of them non- scientific! Note that my use of the term ‘fractals’ includes multifractal tools.
- K. R. Sreenivasan: ‘Fractals and multifractals in fluid turbulence’, Annu. Rev. Fluid Mech., 1991, 23, 539–600; in turn quoting Mandelbrot: ‘It [fractal geometry] fails to have a clean definition and unified tools.’
- In fact, most natural fractal objects are locally self similar (see Ref. 14).
- B. Mandelbrot: ‘The fractal geometry of nature’; 1982, New York, NY, W. H. Freeman.
- G. I. Barenblatt: ‘Scaling, self-similarity, and intermediate asymptotics’; 1996, Cambridge, Cambridge University Press.
- A. Tsinober: Review of ‘Turbulence: the legacy of A. N. Kolmogorov’ by U. Frisch, J. Fluid Mech., 1996, 317, 407–410.
- L. P. Kadanoff: ‘Fractals: where’s the physics?’, Phys. Today, 1986, 39, (2), 6–7.
- T. C. Halsey, et al. : ‘Fractal measures and their singularities: the characterization of strange sets’, Phys. Rev. A, 1986, 33, 1141–1151.
- B. Mandelbrot: ‘Multifractal measures, especially for the geophysicist’, Pure Appl. Geophys., 1989, 131, 5–42.
- Z. Werblowsky and G. Wigoder: ‘The Oxford dictionary of the Jewish religion’; 1997, Oxford, Oxford University Press.
- Talmud comes from the Hebrew word ‘Lamed’, which means ‘to learn’.
- For an introduction, see M. A. Ouaknin: ‘The burnt book: reading the Talmud’; 1995, Princeton, NJ, Princeton University Press; and E. Levinas: ‘Beyond the verse: Talmudic readings and lectures’; 1994, Bloomington, IN, Indiana University Press.
- Like Arabic, Hebrew is a consonantal language, which is why we write ‘PaRDeS’ to transliterate a four consonant word. The use of this acronym is linked to a metaphor on the coming of four rabbis into Paradise (another sense of PaRDeS) and the different ways in which they dealt with the questions they were asked (see Ouaknin’s book cited in Ref. 21 ).
- Sod is related to cabalistic knowledge. Cabbala has been another recent object of great infatuation, however the ‘New Age’ fascination for the esoteric has completely misinterpreted the cabalistic tradition. Indeed, to attain such levels of knowledge, many years of intense and rigorous analytical study of the Talmud and other texts are needed. This obsession with rigour and study has nothing in common with the numerous holistic versions that can be found on the ‘esoteric’ shelves of many bookshops. For a rigorous introduction for non-specialists, a category which includes the present author, see G. Scholem: ‘Major trends in Jewish mysticism’; 1995, Schocken Books. Note, however, that even among the Talmudists, the cabalistic approach is not always appreciated, because of its too frequent drifts towards ‘supermarket’ mysticism.
- ‘Strange attractors for chaotic dynamical systems, configurations of Ising spins at critical points, the regions of high vorticity in fully developed turbulence, percolating clusters and their backbones, and diffusion-limited aggregates’ are some relevant examples (see Ref. 17).
- M. E. Mcintyre: ‘Lucidity and science. III: Hypercredulity, quantum mechanics, and scientific truth’, Interdisc. Sci. Rev., 1998, 23, 29–70.
- C. Darwin: ‘The origin of species’; 1998, Oxford, Oxford Paperbacks.
- C. B. Frith and B. M. Beehler: ‘The birds of paradise’; 1998, Oxford, Oxford University Press.
- C. Darwin: ‘The descent of man and selection in relation to sex’; 1990, New York, NY, New York University Press.
- This is particularly true for the existence of sexual reproduction, which disadvantages the female individual but which is advantageous for the population. Interesting discussions may be found in two of Richard Dawkins’ books: ‘The selfish gene’ and ‘The extended phenotype’ (both 1989, Oxford, Oxford Paperbacks).
- Note, however, that we are perhaps falling into the ‘hypercredulity trap’ in thinking that the whole of Nature has a single law!
- C. B. Chavel: ‘The disputation at Barcelona’; 1983, New York, NY, Shilo Publishing House.
- M. E. Mcintyre: private communication, 1999.
- Y. B. Zeldovich, A. Ruzmaikin, and D. Sokoloff: ‘The almighty chance’, World Scientific Lecture Notes in Physics Vol. 20; 1990, Singapore, World Scientific.