Toward the end of March he began to pick up in his mathematics, though the other stndies bothered him increasingly. He was getting an intuitive knack for solving Riemannian equations, and astonished Professor Upham by his comprehension of fourth-dimensional and other problems which had floored all the rest of the class. One afternoon there was a discussion of possible freakish curvatures in space, and of theoretical points of approach or even contact between our part of the cosmos and various other regions as distant as the farthest stars or the transgalactic gulfs themselves — or even as fabulously remote as the tentatively conceivable cosmic units beyond the whole Einsteinian space-time continuum. Gilman's handling of this theme filled everyone with admiration, even though some of his hypothetical illustrations caused an increase in the always plentiful gossip about his nervous and solitary eccentricity. What made the students shake their heads was his sober theory that a man might — given mathematical knowledge admittedly beyond all likelihood of human acquirement — step deliberately from the earth to any other celestial body which might lie at one of an infinity of specifc points in the cosmic pattern.

Such a step, he said, would require only two stages; first, a passage out of the three-dimensional sphere we know, and second, a passage back to the three-dimensional sphere at another point, perhaps one of infinite remoteness. That this could be accomplished without loss of life was in many cases conceivable. Any being from any part of three-dimensional space could probably survive in the fourth dimension; and its survival of the second stage would depend upon what alien part of three-dimensional space it might select for its re-entry. Denizens of some planets might be able to live on certain others — even planets belonging to other galaxies, or to similar dimensional phases of other space-time continua — though of course there must be vast numbers of mutually uninhabitable even though mathematically juxtaposed bodies or zones of space.

It was also possible that the inhabitants of a given dimensional realm could survive entry to many unknown and incomprehensible realms of additional or indefinitely multiplied dimensions — be they within or outside the given space-time continuum — and that the converse would be likewise true. This was a matter for speculation, though one could be fairly certain that the type of mutation involved in a passage from any given dimensional plane to the next higher one would not be destructive of biological integrity as we understand it. Gilman could not be very clear about his reasons for this last assumption, but his haziness here was more than overbalanced by his clearness on other complex points. Professor Upham especially liked his demonstration of the kinship of higher mathematics to certain phases of magical lore transmitted down the ages from an ineffable antiquity — human or pre-human — whose knowledge of the cosmos and its laws was greater than ours.

Around 1 April Gilman worried cosiderably because his slow fever did not abate. He was also troubled by what some of his fellow lodgers said about his sleep-walking. It seened that he was often absent from his bed and that the creaking of his floor at certain hours of the night was remarked by the man in the room below. This fellow also spoke of hearing the tread of shod feet in the night; but Gilman was sure he must have been mistaken in this, since shoes as well as other apparel were always precisely in place in the morning. One could develop all sorts of aural delusions in this morbid old house — for did not Gilman himself, even in daylight, now feel certain that noises other than rat-scratching came from the black voids beyond the slanting wall and above the slanting ceiling? His pathologically sensitive ears began to listen for faint footfalls in the immemorially sealed loft overhead, and sometimes the illusion of such things was agonizingly realistic.

However, he knew that he had actually become a somnambulist; for twice at night his room had been found vacant, though with all his clothing in place. Of this he had been assured by Frank Elwood, the one fellow-student whose poverty forced him to room in this squalid and unpopular house. Elwood had been studying in the small hours and had come up for help on a differential equation, only to find Gilman absent. It had been rather presumptuous of him to open the unlocked door after knocking had failed to rouse a response, but he had needed the help very badly and thought that his host would not mind a gentle prodding awake. On neither occasion, though, had Gilman been there; and when told of the matter he wondered where he could have been wandering, barefoot and with only his night clothes on. He resolved to investigate the matter if reports of his sleep-walking continued, and thought of sprinkling flour on the floor of the corridor to see where his footsteps might lead. The door was the only conceivable egress, for there was no possible foothold outside the narrow window.

As April advanced, Gilman's fever-sharpened ears were disturbed by the whining prayers of a superstitious loom-fixer named Joe Mazurewicz who had a room on the ground floor. Mazurewicz had told long, rambling stories about the ghost of old Keziah and the furry sharp-fanged, nuzzling thing, and had said he was so badly haunted at times that only his silver crucifix — given him for the purpose by Father Iwanicki of St. Stanislaus' Church — could bring him relief. Now he was praying because the Witches' Sabbath was drawing near. May Eve was Walpurgis Night, when hell's blackest evil roamed the earth and all the slaves of Satan gathered for nameless rites and deeds. It was always a very bad lime in Arkham, even though the fine folks up in Miskatonic Avenue and High and Saltonstall Streets pretended to know nothing about it. There would be bad doings, and a child or two would probably be missing. Joe knew about such things, for his grandmother in the old country had heard tales from her grandmother. It was wise to pray and count one's beads at this season. For three months Keziah and Brown Jenkin had not been near Joe's room, nor near Paul Choynski's room, nor anywhere else — and it meant no good when they held off like that. They must be up to something.

Gilman dropped in at the doctor's office on the sixteenth of the month, and was surprised to find his temperature was not as high as he had feared. The physician questioned him sharply, and advised him to see a nerve specialist. On reflection, he was glad he had not consulted the still more inquisitive college doctor. Old Waldron, who had curtailed his activities before, would have made him take a rest — an impossible thing now that he was so close to great results in his equations. He was certainly near the boundary between the known universe and the fourth dimension, and who could say how much farther he might go?

But even as these thoughts came to him he wondered at the source of his strange confidence. Did all of this perilous sense of immininence come from the formulae on the sheets he covered day by day? The soft, stealthy, imaginary footsteps in the sealed loft above were unnerving. And now, too, there was a growing feeling that somebody was constantly persuading him to do something terrible which he could not do. How about the somnambulism? Where did he go sometimes in the night? And what was that faint suggestion of sound which once in a while seemed to trickle through the confusion of identifiable sounds even in broad daylight and full wakefulness? Its rhythm did not correspond to anything on earth, unless perhaps to the cadence of one or two unmentionable Sabbat-chants, and sometimes he feared it corresponded to certain attributes of the vague shrieking or roaring in those wholly alien abysses of dream.