“My mother was a Frenchwoman, and my father an Essex bargeman,” he said abruptly.  “Hence my name—­Racine and Mudge.  My father died before I ever saw him.  My mother inherited money from her Bordeaux relations, and when she died soon after, I was left alone with wealth and a strange freedom.  I had no guardian, trustees, sisters, brothers, or any connection in the world to look after me.  I grew up, therefore, utterly without education.  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.”