THINKING ANIMALS 168 



predisposed in some manner to arithmetic. I say "in 

 some manner," and by that I do not wish to prejudge any 

 particular view of the argument ; and above all I do not 

 make of this predisposition or mathematical permeability, 

 a criterion of intelligence. I do not forget either the 

 mentally deficient or the prodigies among child calculators, 

 etc. But likewise I cannot forget another thing : that all 

 organisms are already throughout permeated with mathe- 

 matics, and that the more we descend the scale, from man 

 down to the most " simple " biological fact, the more 

 nearly we approach to physics, which is nothing but 

 mathematics. 



I have not the space here to digress on the intermediate 

 gradations. Besides, I have already done so, in part at 

 least, elsewhere. But I wish to recall the curious coinci- 

 dence that the mathematical achievements of the Elberfeld 

 horses were much more brilliant and much more prodigious 

 than those of the dogs which have up to now been experi- 

 mented on. And horses in the phylo-genetic line are more 

 ancient than dogs : they are lower in the zoologic scale. 

 Much lower still, i.e., among the Arthropoda, occur many 

 other mathematical wonders. I only mention in a cursory 

 way the logarithmic spiral of the spider's web, the precise 

 curves realized without instruments of any kind by the 

 Coleoptera and Hymenoptera in cutting leaves, the 

 stereometry of the aphides. Then, as it were, at the 

 bottom of the scale (if one may still speak of a descent and 

 a bottom) the marvellous plancton niters of the Appendi- 

 culata ; the geometrical spots of the Amoebae ; the cases 

 of perfect forms of so many other Protozoa ; and, finally, 

 think of the constructive technic of the static organs, or of 

 those of movement either in man or animals or plants ; 

 think of the complex mathematics of the mitosi, or of any 

 cell proceeding to its own indirect division. 



It seems to me clear that the mathematical faculty 

 assuming always, let it be understood, that it may give rise 

 to more or less conscious phenomena in the biological 

 subject may be amongst the most natural of imaginable 

 causes, and that even the smallest amount of conscious- 

 ness may help this existing capacity in the animal to 

 express itself. That we are concerned with an expression 

 by raps or not, does not seem to me as important as a 



