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 form 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, 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.”