9. 



J. D. COWAN, ed. 1973. SOME MATHEMATICAL QUESTIONS IN BIOLOGY. IV 

 Am. Mathemat. Soc, Providence. Lectures on Mathematics in the 

 Life Sciences. Vol.5. VI, 150 pp., 76 figs., 7 tabs., author and 

 subject indexes 



The Symposium on which this book is based was held in Phila- 

 delphia in December, 1971. The only lecture which is of direct 

 significance to developmental biologists is that by R. Thorn en- 

 titled "A global dynamical scheme for vertebrate embryology". 

 Although the paper is very condensed (it covers only 43 small 

 pages) and presupposes considerable mathematical knowledge, it 

 may be useful as a first introduction into Thorn's thinking, 

 particularly for those to whom his recent book (see review nr. 

 5) is inaccessible for linguistic reasons. In fact, the article 

 is in part a further elaboration of that portion of the book 

 that deals with embryos. 



Thorn starts from the topological theory of "catastrophes", 

 i.e. of those characteristic discontinuities which arise in the 

 solutions of systems of differential equations with macroscopic 

 parameters. He then applies this theory to the following pheno- 

 mena: amphibian and avian gastrulation and their homology, bi- 

 lateral symmetry in the mesoderm, notochord formation, forma- 

 tion of the axial system, closure of the neural tube, and heart 

 formation. In his concluding remarks the author anticipates the 

 objection that he uses finalistic reasoning as follows: "even 

 if you allow yourself all the facilities of teleological think- 

 ing, you are still very far from explaining development. For 

 embryology is full of enigmatic structures, of transient mor- 

 phologies, which do not seem to have the slightest biological 

 usefulness. Catastrophe theory may help in interpreting these 

 structures, as it describes the basic and universal constraints 

 of stability imposed on epigenetic mechanisms". 



10. 



C.H.WADDINGTON, ed. 1972. TOWARDS A THEORETICAL BIOLOGY. 4. 



Essays 



Edinburgh Univ. Press, Edinburgh. VI, 299 pp., 74 figs., 3 tabs., 



author and subject indexes. £ 5-50 



Participants: Arbib, Conrad, Cowan, Elsdale, Fowler, Goodwin, 

 Kauffman, Pattee, Thorn, Waddington, Wolpert, Zeeman 



This is the last of a series of volumes emerging from the 

 IUBS Symposia held in Bellagio, Italy in the years 1966 through 

 1969. The first three volumes were reviewed in Gen. Embryol. 

 Inf. Serv., Suppl.l_3, 1970, p. 12/13. The present volume contains 

 13 essays partly based on, and partly grown from the presenta- 

 tions given at the Symposium. 



The volume has more unity than the preceding ones, both as to 

 style and content. In an epilogue Waddington presents his per- 

 sonal interpretation of the particular types of question and 

 frameworks of thought that seemed to emerge towards the end of 

 the series of Symposia. The focal point is the confrontation of 

 microstates and macrostates of biological systems, and more par- 

 ticularly "the ways of handling simple macrostates without 

 having to break them down into an unmanageable plethora of vast- 

 ly complex microstates". Waddington points out that the "struc- 

 tures mediating global simplicity" may perhaps be clarified with 

 the help of the analogy of language, a procedure which is prom- 

 inent in several of the contributions. 



Most of the contributions deal either with morphogenesis or 



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