“The Old Ones were, the Old Ones are, and the Old Ones shall be. Not in the spaces we know, but between them, They walk serene and primal, undimensioned and to us unseen …

"Yog Sothoth knows where They have trod earth’s fields, and where They still tread them, and why no one can behold Them as They tread… The wind gibbers with Their voices, and the earth mutters with Their consciousness…"

— H.P. Lovecraft, Through the Gates of the Silver Key

"According to the early 20th century horror writer H.P. Lovecraft, these higher dimensions do indeed exist, and are home to all manner of evil creatures. In Lovecraft's mythology, the most terrible of these beings goes by the name of Yog-Sothoth. Interestingly, on the rare occasions that Yog-Sothoth appears in the human realm, it takes the form of "a congeries of iridescent globes... stupendous in its malign suggestiveness".

Lovecraft had some interest in mathematics, and indeed used ideas such as hyperbolic geometry to lend extra strangeness to his stories. But he could not have known how fortunate was the decision to represent Yog-Sothoth in this manner.

Strange spheres really are the keys to higher dimensional worlds, and our understanding of them has increased greatly in recent years. Over the last 50 years a subject called differential topology has grown up, and revealed just how alien these places are.

Milnor had found the first exotic sphere, and he went on to find several more in other dimensions. In each case, the result was topologically spherical, but not differentially so. Another way to say the same thing is that the exotic spheres represent ways to impose unusual notions of distance and curvature on the ordinary sphere.

Three men were swept up by the flabby claws before anybody turned. God rest them, if there be any rest in the universe.

They were Donovan, Guerrera, and Angstrom. Parker slipped as the other three were plunging frenziedly over endless vistas of green-crusted rock to the boat, and Johansen swears he was swallowed up by an angle of masonry which shouldn’t have been there; an angle which was acute, but behaved as if it were obtuse.

It is now known that 4-dimensional space itself (or R4) comes in a variety of flavours. There is the usual flat space, but alongside it are the exotic R4s.Each of these is topologically identical to ordinary space, but not differentially so. Amazingly, as Clifford Taubes showed in 1987, there are actually infinitely many of these alternative realities. In this respect, the fourth dimension really is an infinitely stranger place than every other domain

Yet in all of these stories we see twin ideas concerning mathematics. On the one hand, math concepts are used to describe the indescribable, to attempt to convey, in as concrete a manner as possible, a sense of the alien and the unknown in the reader.

On the other hand, we see that mathematics is clearly one of the keys to understanding secrets of the universe, a universe which would drive one babbling mad if only a fraction of it were clearly comprehended.

After all, most of the population is terrified and intimidated by math, yet most people also recognize the power of mathematics. What better logical support is there for inspiring a mood of terror and the unknown?

H.P. Lovecraft: a Horror in Higher Dimensions
Author: Thomas Hull
Source: Math Horizons, Vol. 13, No. 3 (Feb. 2006), pp. 10-12

Originally posted by Frater210

Three men were swept up by the flabby claws before anybody turned. God rest them, if there be any rest in the universe.

They were Donovan, Guerrera, and Angstrom. Parker slipped as the other three were plunging frenziedly over endless vistas of green-crusted rock to the boat, and Johansen swears he was swallowed up by an angle of masonry which shouldn’t have been there; an angle which was acute, but behaved as if it were obtuse.

edit on 10-6-2011 by Frater210 because: Syntax