





“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



Professor Elwes:

Thomas Hull ( I think):

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



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,, posits just this very idea,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,Now, with the bolded text above in mind, consider this quote from H.P. Lovecraft's,...And this quote from Professor Elwes' article...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...So I hope that that cranks up the ‘eldritch horror’ for you, ATS. Be sure to visit the links for the full story. plus.maths.org... -2513Wonderful Video on Geometry and Dimensions: www.dimensions-math.org...