badger us! Kant himself put it, after his fashion: 'The laws of nature are 
the laws of our own minds.' Why? It is not the contents of the mind itself 
that we can cognise, but only its structure. But Kant has not gone to this 
length. He would have been extremely shocked if it had ever struck him 
that the final term in his sorites was 'Reason itself is the only reality.' On 
further examination, even this ultimate truth turns out to be meaningless. 
It is like the well known circular definition of an obscene book, which is: 
one that arouses certain ideas in the mind of the kind of person in whom 
such ideas are excited by that kind of book. 
     23. I notice that my excellent chairman is endeavouring to stifle a 
yawn and to convert it into a smile, and he will forgive me for saying that 
I find the effect somewhat sinister. But he has every right to be 
supercilious about it. These are indeed 'old, fond paradoxes to amuse 
wives in ale-houses.' Since philosophy began, it has always been a 
favourite game to prove your axioms absurd. 
     You will all naturally be very annoyed with me for indulging in these 
fatuous pastimes, especially as I started out with a pledge that I would 
deal with these subjects from the hard-headed scientific point of view. 
Forgive me if I have toyed with these shining gossamers of the thought-
web! I have only been trying to break it to you gently. I proceed to brush 
away with a sweep of my lily-white hand all this tenuous, filmy stuff, 
'such stuff as dreams are made of.' We will get down to modern science. 
     24. For general reading there is no better introduction than The Bases 
of Modern Science, by my old and valued friend the late J. W. N. 
Sullivan. I do not want to detain you too long with quotations from this 
admirable book. I would much rather you got it and read it yourself; you 
could hardly make better use of your time. But let us spend a few 
moments on his remarks about the question of geometry. 
     Our conceptions of space as a subjective entity has been completely 
upset by the discovery that the equations of Newton based on Euclidean 
Geometry are inadequate to explain the phenomena of gravitation. It is 
instinctive to us to think of a straight line; it is somehow axiomatic. But 
we learn that this does not exist in the objective universe. We have to use 
another geometry, Riemann's Geometry, which is one of the curved 
geometries. (There are, of course, as many systems of geometry as there 
are absurd axioms to build them on. Three lines make one ellipse: any 
nonsense you like: you can proceed to construct a geometry which is 
correct so long as it is coherent. And there is nothing right or wrong about 
the result: the only question is: which is the most convenient system for 
the purpose of describing phenomena? We found the idea of Gravitation 
awkward: we went to Riemann.) 
     This means that the phenomena are not taking place against a 
background of a flat surface; the surface itself is curved. What we have 
thought of as a straight line does not exist at all. And this is almost 
impossible to conceive; at least it is quite impossible for myself to 
visualise. The nearest one gets to it is by trying to imagine that you are a 
reflection on a polished door-knob.