in the express powers of the brain is due to the wide and imperfect
education of the populace at the present moment."

"That is not the case," answered the old man sharply, when I had made
myself clear by repeating my remarks in a louder tone, for he was a
little deaf.

"That is not the case. The follies of which I speak are not particularly
to be discovered among the poorer classes who have passed through the
elementary schools. _These_" (it was to the schools that he was
alluding with a comprehensive pessimism) "may account for the gross
decline apparent in the public manners of our people, but not for faults
which are peculiar to the upper and middle classes. It is not in the
populace, but in those wealthier ranks that you will find the sort of
intellectual decay of which I spoke."

I asked him whether he thought the tricks it was now considered cultured
to play with mathematics came within the category of this intellectual
decay. The old gentleman answered me a little abruptly that he could not
judge what I was talking about.

"Why," said I, "do you believe that parallel straight lines
_converge_ or _diverge_?"

"Neither," said he, a little bewildered. "If they are parallel they
cannot by definition either diverge or converge."

"You are, then," said I, "an old-fashioned adherent of the theory of the
parabolic universe?" At which sensible reply of mine the old man
muttered rather ill-temperedly, and begged me to speak of something