“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
Is it possible that the bizarre realms of the Old Ones described in the works of H.P. Lovecraft may exist?
A new publication by mathematician Richard Elwes called,
Exotic Spheres, or why 4-dimensional space is a crazy place, posits just this very
idea,
"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.
Professor Elwes' article goes in to topology and differential topology to help describe how the realms described by Lovecraft could be a real
possibility. Elwes' article is most concerned with hyperspheres in the 4th dimension and their quality as judged by either Topology or Differential
Topology.
The difference between the two is that differential topology allows for the study of whether morphological (shape-changing) processes are continuous
or smooth. Continuous morphing processes involve no jumps, angles, tears or jerks while changing. The emphasis placed upon 'smooth' in differential
topology allows for 'not smooth' so it is possible, in other mathematically described dimensions, to have shapes that morph continuously but are not
smooth.
But this never occurs in dimensions 1,2 or 3 and this is where it gets interesting. In 1956 John Milnor discovered 'Exotic Spheres' in the 7th
dimension,
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.
Now, with the bolded text above in mind, consider this quote from H.P. Lovecraft's,
Call of Cthulhu...
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.
And this quote from Professor Elwes' article...
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
It is suggested that the reader of this thread, that has sufficient interest, go and read the article which I will link you to. It's a great read and
will put a smile on the face of any Lovecraft fan and give you a whirlwind tour of exotic mathematics at the same time.
I find it interesting after all of these years as a fan to find that Lovecraft was a serious mathematician and deeply interested in physics.
Mathematics can be found in many of his novels like, "At the Mountains of Madness," "Through the Gates of the Silver Key," and "Dreams in the Witch
House."
A wonderful article published by Thomas Hull goes into pretty fair detail concerning where mathematical references can be found in Lovecraft's work
and I will link to that as well.
Let's wrap up with something from Thomas Hull...
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
So I hope that that cranks up the ‘eldritch horror’ for you, ATS. Be sure to visit the links for the full story.
Professor Elwes:plus.maths.org...-2513
Thomas Hull ( I think):dl.dropbox.com...
Wonderful Video on Geometry and Dimensions:
www.dimensions-math.org...
edit on 10-6-2011 by Frater210 because: Syntax