Reflections and Laterality

Leonurdo, zyxwvutsrqpo Vol. zyxwvutsrq 2,zyxwvutsrqpon pp. 301-313. Pergamon Press 1969. Printed in Great Britain BOOKS-LIVRES GUY 8. MBtraux, CorrespondingEditor Readers are invited to recommend books (within the scope of the journal) to be reviewed. Only books in English and French can be reviewed at this stage. Readers who would like to be added to Leonardo’spanel of reviewers should write to the Founder-Editor, indicating their particular interests and specialization . Nous serions reconnaissants 6 zyxwv nos lecteurs de bien vouloir nous indiquer les livres-conps dans I‘esprit de notre revue-qui pourraient faire I‘objet zy d’un compte-rendudans lesprochains numhos. Seuls les ouvrages re‘digds en anglais ou enfrancais peuvent &re pris en considtration pour le moment. Les lecteurs qui dhireraient figurer parmi les critiques de livres peuvent s’adresser au Fondateur-Directeur de Leonardo, en indiquant leurs inte‘rCts particuliers et leur specialisation. REFLECTIONS AND LATERALITY KennethR. Adams* Left and Right in Science and Life. Vilma Fritsch, Barrie and Rockliff, London, zyxwvuts 1968. 202 pp. zyxwvu 35s. (German edition, W. Kohlhammer GmbH, Stuttgart , 1964.) The AmbidextrousUniverse. Martin Gardner, Allen Lane, The Penguin Press, London, 1967. 272 pp. 42s. (U.S.A. edition, Basic Books, 1964.) Introduction A complete geometrical description of a left hand cannot be distinguished from a complete geometrical description of a right hand, unless the words ‘left’, ‘right’ or equivalent concepts, are built into the descriptions (cf. Figs. 1(a) and 1 (b)). For the relative positions(or internalrelations)of the parts of the hands are the same for left and right. It is when we try to superposethe two hands that we discover that the same description applies equally well to two objects which are not identical. Two objects, so related, are called enantiomorphs. Left and Right in Science and Life by Dr. Fritsch covers a wide range of topics: for example, the conservation of parity by fundamental particles, stereoisomers,the relation of the hermit crab to the right-handed shellitinhabits, left-and right-handedness in humans, and conventions concerning left and right in human culture and art. Martin Gardner’s The Ambidextrous Universehas a similar range but it concentrates on the physical and mathematical aspects of the subject. I refer to ‘the subject’ but neither author begins as I had hoped that they would by asking whether the concepts of left and right, or enantiomorphism, doconstitute anintelligiblefield of study. A book on the Hexagon, which included studies of molecular structures, the honeycomb, the Giant’s Causeway and hexagonal sociograms would raise doubts similar to those I experienced on reading these +19 Dartmouth Park Road, London, N.W.5, England. books. Although the concepts of left and right can be applied to most areas of experience, empirical statements which employ these concepts in one area of study often have no significant relationship with empirical statements employing the same concepts in another area of study. More seriously, I think that there are two logically independent concepts involved, which neither author has properly distinguished. The first of these concepts, enantiomorphism, is well known. It is the second, which I shall call laterality, that requires clarification. I describe an object as possessing laterality if criteria exist for distinguishing two of its opposed aspects as ‘left’ and ‘right’ sides. (In a more complete account, I would qualify this as determinate laterality, in order to distinguish it from the indeterminate laterality of an object with sides but no left and right. Failure to distinguish determinate and indeterminate laterality is the basis of the well-knownpro-semiticjoke about Hitler, Goebbels and the left-handed tea set.) We can imaginea universein which all the objects possessed laterality but there were no enantiomorphic pairs; and, conversely, we can imagine a universe in which no objects possessed laterality but every object had its enantiomorphic partner (cf. Fig. 2). As human beings, we naturally start, as I started thisreview,by talkingabout the human body. Our own bodies have laterality and their two sides are enantiomorphic with each other; in short, we are bilaterally symmetrical;yet bilateral symmetry would be entirely absent from both the universes imagined above. The same point can be expressed using logical symbols. Let L and B...