This much was to my advantage; I learned none of
that deceitful rubbish taught in schools, and so had nothing to unlearn
when I awakened to my true love--mathematics, higher mathematics and
higher geometry. These, however, I seemed to know instinctively. It was
like the memory of what I had deeply studied before; the principles
were in my blood, and I simply raced through the ordinary stages, and
beyond, and then did the same with geometry. Afterwards, when I read
the books on these subjects, I understood how swift and undeviating
the knowledge had come back to me. It was simply memory. It was simply
_re-collecting_ the memories of what I had known before in a previous
existence and required no books to teach me." In his growing excitement, Mr. Mudge attempted to drag the chair
forward a little nearer to his listener, and then smiled faintly as he
resigned himself instantly again to its immovability, and plunged anew
into the recital of his singular "disease." "The audacious speculations of Bolyai, the amazing theories of
Gauss--that through a point more than one line could be drawn parallel
to a given line; the possibility that the angles of a triangle are
together _greater_ than two right angles, if drawn upon immense
curvatures-the breathless intuitions of Beltrami and Lobatchewsky--all
these I hurried through, and emerged, panting but unsatisfied, upon the
verge of my--my new world, my Higher Space possibilities--in a word, my
disease! "How I got there," he resumed after a brief pause, during which he
appeared to be listening intently for an approaching sound, "is more
than I can put intelligibly into words. I can only hope to leave your
mind with an intuitive comprehension of the possibility of what I say. "Here, however, came a change. At this point I was no longer absorbing
the fruits of studies I had made before; it was the beginning of
new efforts to learn for the first time, and I had to go slowly and
laboriously through terrible work. Here I sought for the theories and
speculations of others. But books were few and far between, and with
the exception of one man--a 'dreamer,' the world called him--whose
audacity and piercing intuition amazed and delighted me beyond
description, I found no one to guide or help. "You, of course, Dr. Silence, understand something of what I am
driving at with these stammering words, though you cannot perhaps yet
guess what depths of pain my new knowledge brought me to, nor why an
acquaintance with a new development of space should prove a source of
misery and terror." Mr. Racine Mudge, remembering that the chair would not move, did the
next best thing he could in his desire to draw nearer to the attentive
man facing him, and sat forward upon the very edge of the cushions,
crossing his legs and gesticulating with both hands as though he saw
into this region of new space he was attempting to describe, and
might any moment tumble into it bodily from the edge of the chair and
disappear from view. John Silence, separated from him by three paces,
sat with his eyes fixed upon the thin white face opposite, noting every
word and every gesture with deep attention. "This room we now sit in, Dr. Silence, has one side open to space--to
Higher Space. A closed box only _seems_ closed. There is a way in and
out of a soap bubble without breaking the skin." "You tell me no new thing," the doctor interposed gently. "Hence, if Higher Space exists and our world borders upon it and lies
partially in it, it follows necessarily that we see only portions
of all objects. We never see their true and complete shape. We see
their three measurements, but not their fourth. The new direction is
concealed from us, and when I hold this book and move my hand all round
it I have not really made a complete circuit. We only perceive those
portions of any object which exist in our three dimensions; the rest
escapes us. But, once we learn to see in Higher Space, and objects will
appear as they actually are. Only they will thus be hardly recognisable! "Now, you may begin to grasp something of what I am coming to." "I am beginning to understand something of what you must have
suffered," observed the doctor soothingly, "for I have made similar
experiments myself, and only stopped just in time----"

"You are the one man in all the world who can hear and understand,
_and_ sympathise," exclaimed Mr. Mudge, grasping his hand and holding
it tightly while he spoke. The nailed chair prevented further
excitability. "Well," he resumed, after a moment's pause, "I procured the implements
and the coloured blocks for practical experiment, and I followed the
instructions carefully till I had arrived at a working conception of
four-dimensional space. The tessaract, the figure whose boundaries are
cubes, I knew by heart. That is to say, I knew it and saw it mentally,
for my eye, of course, could never take in a new measurement, or my
hands and feet handle it. "So, at least, I thought," he added, making a wry face. "I had reached
the stage, you see, when I could _imagine_ in a new dimension. I was
able to conceive the shape of that new figure which is intrinsically
different to all we know--the shape of the tessaract. I could perceive
in four dimensions. When, therefore, I looked at a cube I could see
all its sides at once. Its top was not foreshortened, nor its farther
side and base invisible. I saw the whole thing out flat, so to speak. And this tessaract was bounded by cubes! Moreover, I also saw its
content--its insides." "You were not yourself able to enter this new world," interrupted Dr. Silence. "Not then. I was only able to conceive intuitively what it was like
and how exactly it must look. Later, when I slipped in there and
saw objects in their entirety, unlimited by the paucity of our poor
three measurements, I very nearly lost my life. For, you see, space
does not stop at a single new dimension, a fourth. It extends in all
possible new ones, and we must conceive it as containing any number of
new dimensions. In other words, there is no space at all, but only a
spiritual condition. But, meanwhile, I had come to grasp the strange
fact that the objects in our normal world appear to us only partially." Mr. Mudge moved farther forward till he was balanced dangerously on
the very edge of the chair. "From this starting point," he resumed,
"I began my studies and experiments, and continued them for years. I had money, and I was without friends. I lived in solitude and
experimented. My intellect, of course, had little part in the work,
for intellectually it was all unthinkable. Never was the limitation of
mere reason more plainly demonstrated. It was mystically, intuitively,
spiritually that I began to advance. And what I learnt, and knew, and
did is all impossible to put into language, since it all describes
experiences transcending the experiences of men.