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.