telligible and real, though not with our common reality.'

"I found all this very puzzling and he had to repeat it several times
before I got a glimpse of what he was talking about.

"'I've wondered for a long time he went on 'but now quite suddenly, I
have begun to know.' He stopped and asked me abruptly if I knew much
about mathematics.

"'It's a pity,' he said,'but the main point is not technical, though I
wish you could appreciate the beauty of some of my proofs. Then he
began to tell me about his last six months' work. I should have
mentioned that he was a brilliant physicist besides other things. All
Hollond's tastes were on the borderlands of sciences, where mathematics
fades into metaphysics and physics merges in the abstrusest kind of
mathematics. Well, it seems he had been working for years at the
ultimate problem of matter, and especially of that rarefied matter we
call aether or space. I forget what his view was-atoms or molecules or
electric waves. If he ever told me I have forgotten, but I'm not
certain that I ever knew. However, the point was that these ultimate
constituents were dynamic and mobile, not a mere passive medium but a
medium in constant movement and change. He claimed to have
discovered--by ordinary inductive experiment--that the constituents of
aether possessed certain functions, and moved in certain figures
obedient to certain mathematical laws. Space, I gathered, was
perpetually 'forming fours' in some fancy way.

"Here he left his physics and became the mathematician. Among his
mathematical discoveries had been certain curves or figures or
something whose behaviour involved a new dimension. I gathered that
this wasn't the ordinary Fourth Dimension that people talk of, but that
fourth-dimensional inwardness or involution was part of it. The
explanation lay in the pile of manuscripts he left with me, but though
I tried honestly I couldn't get the hang of it. My mathematics stopped
with desperate finality just as he got into his subject.

"His point was that the constituents of Space moved according to these
new mathematical figures of his. They were always changing, but the
principles of their change were as fixed as the law of gravitation.
Therefore, if you once grasped these principles you knew the contents
of the void. What do you make of that?"

I said that it seemed to me a reasonable enough argument, but that it
got one very little way forward. "A man," I said, "