360 Murray Eden 



estimates made on a molecular level. In the terminology of communication 

 theory, the redundancy of the source m.ay be extremely high. An examination 

 of the literature indicates that there is some support for this view. Studies of 

 properties of monozygotic twins have special relevance to this point. It may 

 be noted in passing that the existence of twins or high multiplets derived from 

 a single germ cell is in itself strong evidence of the presence of at least a small 

 amount of redundancy in the germ cell (4). Monozygotic twins presumably 

 arise from an identical genetic background and they develop into mature 

 organisms that can be compared with regard to certain of their properties. 



As long ago as 1876 Galton (5) studied what he called 'The History of 

 Twins as a Criterion of the Relative Power of Nature and Nurture'. Newman, 

 in a long series of pubhcations begun in 1912 (6) has studied both human twins 

 and armadillo quadruplets. The nine-banded armadillo is exceptional in that 

 the female gives birth to monozygotic quadruplets. The scales or scutes on 

 the back of an armadillo are regular and easily counted, even in the fetus. 

 Newman prepared a fairly large statistical study on these quadruplets and he 

 found a correlation coefficient for fifty-six sets of male quadruplets of 0.93 and 

 for fifty-nine sets of females of 0.91. Still there was no identity in the scute counts. 



Work of a similar character has been done by Hancock (7) on mono- 

 zygotic calf twins, and by Went (8) on genetically identical seedlings. The 

 conclusion that may be reached on the basis of studies such as these is that 

 even when embryonic growth starts from genetically isomorphic cells, by the 

 time the organism has developed to maturity there is, it is true, a great similarity 

 in the large, but at the cellular level there is very httle similarity. 



This would suggest that, aside from the genetic signals or instructions, 

 there are certain statistical variables or environmental factors operating that 

 permit the development of an organism to an ultimately recognizable form 

 but require a good deal less information than would be required if every element 

 in the structure of the organism had to be specified with microscopic exactitude. 



An attempt to construct a theoretical model was made by Turing (9), 

 who in 1952 posed the following problem. Given a group of identical cells 

 arranged in some symmetrical configuration, e.g. a ring or a sphere; assume 

 that each cell contains the same concentrations of certain chemical substrates 

 and that the laws of diffusion and other classical physical laws hold. How 

 can one devise a procedure whereby this homogeneous collection of cells 

 could develop and differentiate so as to produce asymmetric or periodic forms? 



Turing proposed accomplishing this in a way that does not do too much 

 violence to biological understanding. He postulated certain hypothetical 

 chemical reactions involving substrate, inteiTnediates and enzymes, and built 

 into this set of hypothetical reactions appropriate reaction rate constants so 

 that the resulting reaction system would exhibit a special property: namely, 

 that statistical fluctuations in the concentrations of chemical components 

 in various cells would increase in amplitude so as to produce an instability 

 and result in an asymmetric form or a form exhibiting periodicity. By use of 

 a specific example he showed how a ring of cells might grow into something 

 more or less petal-shaped with three or four lobes or petals. In another example 

 he developed a mottled pattern on a two-dimensional surface. 



The model described below is entirely mathematical; physical or chemical 



