THE VALUE OF SCIENCE 5*9 



This is possible, but I shall observe first that this little humanness 

 which would remain in the non-Euclideans would suffice not only to 

 make possible the translation of a little of their language, but to make 

 possible the translation of all their language. 



Now, that there must be a minimum is what I concede; suppose 

 there exists I know not what fluid which penetrates between the 

 molecules of our matter, without having any action on it and without 

 being subject to any action coming from it. Suppose beings sensible 

 to the influence of this fluid and insensible to that of our matter. 

 It is clear that the science of these beings would differ absolutely from 

 ours and that it would be idle to seek an ' invariant ' common to these 

 two sciences. Or again, if these beings rejected our logic and did not 

 admit, for instance, the principle of contradiction. 



But truly I think it without interest to examine such hypotheses. 



And then, if we do not push whimsicality so far, if we introduce 

 only fictitious beings having senses analogous to ours and sensible to 

 the same impressions, and moreover admitting the principles of our 

 logic, we shall then be able to conclude that their language, however 

 different from ours it may be, would always be capable of translation. 

 Now the possibility of translation implies the existence of an invariant. 

 To translate is precisely to disengage this invariant. Thus, to decipher 

 a cryptogram is to seek what in this document remains invariant, when 

 the letters are permuted. 



What now is the nature of this invariant it is easy to understand, 

 and a word will suffice us. The invariant laws are the relations 

 between the crude facts, while the relations between the i scientific 

 facts ' remain always dependent on certain conventions. 



{To be concluded) 



vol. lxx. — 34 



