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"Est impossibile? Certum est."
--TERTULLIAN.


Leithen told me this story one evening in early September as we sat
beside the pony track which gropes its way from Glenvalin up the Correi
na Sidhe. I had arrived that afternoon from the south, while he had
been taking an off-day from a week's stalking, so we had walked up the
glen together after tea to get the news of the forest. A rifle was out
on the Correi na Sidhe beat, and a thin spire of smoke had risen from
the top of Sgurr Dearg to show that a stag had been killed at the
burnhead. The lumpish hill pony with its deer-saddle had gone up the
Correi in a gillie's charge while we followed at leisure, picking our
way among the loose granite rocks and the patches of wet bogland. The
track climbed high on one of the ridges of Sgurr Dearg, till it hung
over a caldron of green glen with the Alt-na-Sidhe churning in its linn
a thousand feet below. It was a breathless evening, I remember, with a
pale-blue sky just clearing from the haze of the day. West-wind
weather may make the North, even in September, no bad imitation of the
Tropics, and I sincerely pitied the man who all these stifling hours
had been toiling on the screes of Sgurr Dearg. By-and-by we sat down
on a bank of heather, and idly watched the trough swimming at our feet.
The clatter of the pony's hoofs grew fainter, the drone of bees had
gone, even the midges seemed to have forgotten their calling. No place
on earth can be so deathly still as a deer-forest early in the season
before the stags have begun roaring, for there are no sheep with their
homely noises, and only the rare croak of a raven breaks the silence.
The hillside was far from sheer-one could have walked down with a
little care-but something in the shape of the hollow and the remote
gleam of white water gave it an extraordinary depth and space. There
was a shimmer left from the day's heat, which invested bracken and rock
and scree with a curious airy unreality. One could almost have
believed that the eye had tricked the mind, that all was mirage, that
five yards from the path the solid earth fell away into nothingness. I
have a bad head, and instinctively I drew farther back into the
heather. Leithen's eyes were looking vacantly before him.

"Did you ever know Hollond?" he asked.

Then he laughed shortly. "I don't know why I asked that, but somehow
this place reminded me of Hollond. That glimmering hollow looks as if
it were the beginning of eternity. It must be eerie to live with the
feeling always on one."

Leithen seemed disinclined for further exercise. He lit a pipe and
smoked quietly for a little. "Odd that you didn't know Hollond. You
must have heard his name. I thought you amused yourself with
metaphysics."

Then I remembered. There had been an erratic genius who had written
some articles in Mind on that dreary subject, the mathematical
conception of infinity. Men had praised them to me, but I confess I
never quite understood their argument. "Wasn't he some sort of
mathematical professor?" I asked.

"He was, and, in his own way, a tremendous swell. He wrote a book on
Number which has translations in every European language. He is dead
now, and the Royal Society founded a medal in his honour. But I wasn't
thinking of that side of him."

It was the time and place for a story, for the pony would not be back
for an hour. So I asked Leithen about the other side of Hollond which
was recalled to him by Correi na Sidhe. He seemed a little unwilling
to speak...

"I wonder if you will understand it. You ought to, of course, better
than me, for you know something of philosophy. But it took me a long
time to get the hang of it, and I can't give you any kind of
explanation. He was my fag at Eton, and when I began to get on at the
Bar I was able to advise him on one or two private matters, so that he
rather fancied my legal ability. He came to me with his story because
he had to tell someone, and he wouldn't trust a colleague. He said he
didn't want a scientist to know, for scientists were either pledged to
their own theories and wouldn't understand, or, if they understood,
would get ahead of him in his researches. He wanted a lawyer, he said,
who was accustomed to weighing evidence. That was good sense, for
evidence must always be judged by the same laws, and I suppose in the
long-run the most abstruse business comes down to a fairly simple
deduction from certain data. Anyhow, that was the way he used to talk,
and I listened to him, for I liked the man, and had an enormous respect
for his brains. At Eton he sluiced down all the mathematics they could
give him, and he was an astonishing swell at Cambridge. He was a
simple fellow, too, and talked no more jargon than he could help. I
used to climb with him in the Alps now and then, and you would never
have guessed that he had any thoughts beyond getting up steep rocks.

"It was at Chamonix, I remember, that I first got a hint of the matter
that was filling his mind. We had been taking an off-day, and were
sitting in the hotel garden, watching the Aiguilles getting purple in
the twilight. Chamonix always makes me choke a little-it is so crushed
in by those great snow masses. I said something about it--said I liked
the open spaces like the Gornegrat or the Bel Alp better. He asked me
why: if it was the difference of the air, or merely the wider horizon?
I said it was the sense of not being crowded, of living in an empty
world. He repeated the word 'empty' and laughed.

"'By "empty" you mean,' he said, 'where things don't knock up against
you?'

I told him No. I mean just empty, void, nothing but blank aether.

"You don't knock up against things here, and the air is as good as you
want. It can't be the lack of ordinary emptiness you feel."

"I agreed that the word needed explaining. 'I suppose it is mental
restlessness,' I said. 'I like to feel that for a tremendous distance
there is nothing round me. Why, I don't know. Some men are built the
other way and have a terror of space.'

"He said that that was better. 'It is a personal fancy, and depends on
your KNOWING that there is nothing between you and the top of the Dent
Blanche. And you know because your eyes tell you there is nothing.
Even if you were blind, you might have a sort of sense about adjacent
matter. Blind men often have it. But in any case, whether got from
instinct or sight, the KNOWLEDGE is what matters.'

"Hollond was embarking on a Socratic dialogue in which I could see
little point. I told him so, and he laughed. "'I am not sure that I am
very clear myself. But yes--there IS a point. Supposing you knew-not
by sight or by instinct, but by sheer intellectual knowledge, as I know
the truth of a mathematical proposition--that what we call empty space
was full, crammed. Not with lumps of what we call matter like hills
and houses, but with things as real--as real to the mind. Would you
still feel crowded?'

"'No,' I said, 'I don't think so. It is only what we call matter that
signifies. It would be just as well not to feel crowded by the other
thing, for there would be no escape from it. But what are you getting
at? Do you mean atoms or electric currents or what?'

"He said he wasn't thinking about that sort of thing, and began to talk
of another subject.

"Next night, when we were pigging it at the Geant cabane, he started
again on the same tack. He asked me how I accounted for the fact that
animals could find their way back over great tracts of unknown country.
I said I supposed it was the homing instinct.

"'Rubbish, man,' he said. 'That's only another name for the puzzle,
not an explanation. There must be some reason for it. They must KNOW
something that we cannot understand. Tie a cat in a bag and take it
fifty miles by train and it will make its way home. That cat has some
clue that we haven't.'

"I was tired and sleepy, and told him that I did not care a rush about
the psychology of cats. But he was not to be snubbed, and went on
talking.

"'How if Space is really full of things we cannot see and as yet do not
know? How if all animals and some savages have a cell in their brain
or a nerve which responds to the invisible world? How if all Space be
full of these landmarks, not material in our sense, but quite real? A
dog barks at nothing, a wild beast makes an aimless circuit. Why?
Perhaps because Space is made up of corridors and alleys, ways to
travel and things to shun? For all we know, to a greater intelligence
than ours the top of Mont Blanc may be as crowded as Piccadilly Circus.'

"But at that point I fell asleep and left Hollond to repeat his
questions to a guide who knew no English and a snoring porter.

"Six months later, one foggy January afternoon, Hollond rang me up at
the Temple and proposed to come to see me that night after dinner. I
thought he wanted to talk Alpine shop, but he turned up in Duke Street
about nine with a kit-bag full of papers. He was an odd fellow to look
at--a yellowish face with the skin stretched tight on the cheek-bones,
clean-shaven, a sharp chin which he kept poking forward, and deep-set,
greyish eyes. He was a hard fellow, too, always in pretty good
condition, which was remarkable considering how he slaved for nine
months out of the twelve. He had a quiet, slow-spoken manner, but that
night I saw that he was considerably excited.

"He said that he had come to me because we were old friends. He
proposed to tell me a tremendous secret. 'I must get another mind to
work on it or I'll go crazy. I don't want a scientist. I want a plain
man.'

"Then he fixed me with a look like a tragic actor's. 'Do you remember
that talk we had in August at Chamonix--about Space? I daresay you
thought I was playing the fool. So I was in a sense, but I was feeling
my way towards something which has been in my mind for ten years. Now
I have got it, and you must hear about it. You may take my word that
it's a pretty startling discovery.'

"I lit a pipe and told him to go ahead, warning him that I knew about
as much science as the dustman.

"I am bound to say that it took me a long time to understand what he
meant. He began by saying that everybody thought of Space as an 'empty
homogeneous medium.' 'Never mind at present what the ultimate
constituents of that medium are. We take it as a finished product, and
we think of it as mere extension, something without any quality at all.
That is the view of civilised man. You will find all the philosophers
taking it for granted. Yes, but every living thing does not take that
view. An animal, for instance. It feels a kind of quality in Space.
It can find its way over new country, because it perceives certain
landmarks, not necessarily material, but perceptible, or if you like
intelligible. Take an Australian savage. He has the same power, and,
I believe, for the same reason. He is conscious of intelligible
landmarks.'

"'You mean what people call a sense of direction,' I put in.

"'Yes, but what in Heaven's name is a sense of direction? The phrase
explains nothing. However incoherent the mind of the animal or the
savage may be, it is there somewhere, working on some data. I've been
all through the psychological and anthropological side of the business,
and after you eliminate the clues from sight and hearing and smell and
half-conscious memory there remains a solid lump of the inexplicable.'

"Hollond's eye had kindled, and he sat doubled up in his chair,
dominating me with a finger.

"'Here, then is a power which man is civilising himself out of. Call
it anything you like, but you must admit that it is a power. Don't you
see that it is a perception of another kind of reality that we are
leaving behind us? ', Well, you know the way nature works. The wheel
comes full circle, and what we think we have lost we regain in a higher
form. So for a long time I have been wondering whether the civilised
mind could not recreate for itself this lost gift, the gift of seeing
the quality of Space. I mean that I wondered whether the scientific
modern brain could not get to the stage of realising that Space is not
an empty homogeneous medium, but full of intricate differences,
intelligible 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, "might know the
contents of Space and the laws of their arrangement and yet be unable
to see anything more than his fellows. It is a purely academic
knowledge. His mind knows it as the result of many deductions, but his
senses perceive nothing."

Leithen laughed. "Just what I said to Hollond. He asked the opinion
of my legal mind. I said I could not pronounce on his argument but
that I could point out that he had established no trait d'union between
the intellect which understood and the senses which perceived. It was
like a blind man with immense knowledge but no eyes, and therefore no
peg to hang his knowledge on and make it useful. He had not explained
his savage or his cat. 'Hang it, man,' I said, 'before you can
appreciate the existence of your Spacial forms you have to go through
elaborate experiments and deductions. You can't be doing that every
minute. Therefore you don't get any nearer to the USE of the sense you
say that man once possessed, though you can explain it a bit.'"

"What did he say?" I asked.

"The funny thing was that he never seemed to see my difficulty. When I
kept bringing him back to it he shied off with a new wild theory of
perception. He argued that the mind can live in a world of realities
without any sensuous stimulus to connect them with the world of our
ordinary life. Of course that wasn't my point. I supposed that this
world of S
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