Mobile Robots: Inspiration to Implementation by Anita Flynn and Joseph Jones (review)

Today, as we see the direction of scientific research change directions with the societal consequences of the end of the cold war, one is prompted to ask about the cultural context of Cantor or Mobius [1]. A discussion of the idea of progress, the Industrial Revolution and other theories of history would seem apropos in a discussion of nineteenth-century mathematics. Ironically, Maor's book treats mathematics as almost "outside " culture, rather than discussing the idea of infinite as embedded in a cultural context in which art, science, and technology are all elemental. Written in the early 1980s, the book highlights the exciting developments that had occurred in art and mathematics in the previous decade. The book privileges the work of Escher (all the color plates are of Escher's work-do no other artists deserve similar attention ?) and there is no discussion of the impact of computers on geometry or number theory. Fractals are relegated to a footnote, Penrose and quasicrystals are barely mentioned in the discussion of the tiling of the plane, the discussion of cosmology makes no mention of inflationing universe or missing matter, and the impact of virtual reality and hypermedia on ideas of the structure of infinite spaces is not even addressed. The fact that these omissions now appear as shortcomings is testimony to the prevalance of new ideas linking art and mathematics. In spite of this, Maor's book is to be highly recommended for its clear exposition and fresh views on the way that the human mind makes sense of the world through the use of number and mathematical relations. Reference 1. For more on the cultural context of Mobius, see Fauvel, Flood and Wilson, eds., Mobius and His Band: Mathematics and Astronomy in Nineteenth Century Germany (Oxford: Oxford Univ. Press, 1993). LES CHEVEUX DE LA RtALITt byJacques Mandelbrojt. Supplement to AlliageNo. 10, Editions ANAIS, Nice, France, 1991. 100 pages. 90 Francs. ISSN 1144-5645. Reviewed by MicheL MendesFrance, U.F. R Mathimatiques etInformatique, Unioersiu de Bordeaux1, 351 Coursde La Liberation, 33405 Talence Cedex, France. Jacques Mandelbrojt's delightful book is quite unique in that the author is both a painter and a theoretical physicist . Les Cheveuxde La Rialite (The Hair of Reality) discusses what brings art and science together and what distinguishes these fields from each other. Upon opening the book and glancing through it, readers may be surprised to discover that Mandelbrojt, although a scientist, is in no way a dry, dogmatic or rigid structuralist with regard to art. I would define his approach to art, both in his writing and in the drawings that illustrate the book, as close to expressionism. His sketches, for the most part, suggest bushes, trees and landscapes that remind the viewer of haikus. A few brush strokes and all is said, revealing the rich yet subtle perfume of lavender, thyme or laurel , the mystery of the tortured olive trees, the deep silence of the Provence countryside and its intolerable heat. Mandelbrojt insists that painting is movement. Painters never cease to move-even when their motions, like Einstein's thought experiments, may only be occurring in the brain. They see what is not seen; they make their way into reality but do not go beyond it. Computer images now allow us to travel through thick forests with no difficulty, to explore small details that can be blown up in order to reveal new ones. Painters do all of this mentally. Their perceptions penetrate the bark of trees, the surface of turf, the complex world of insects. Colours are also movement. One colour calls specifically for another. This causal necessity implies successionhence , time, and time is movement. Shapes playa similar role: shapes and colours resemble the letters ofa complex alphabet. Abstract painting is the list of available words made up of these letters, while figurative artists construct sentences with these words. The relationship between abstract and figurative painting is not unlike the relationship between mathematics and physics. From the great variety of mathematical concepts, the physicist chooses those that will best describe how he perceives reality. Does science influence art? Mandelbrojt argues that scientists and artists both feed on the same intuitions, which, when translated into their...