H.P. Lovecraft, Mathematician. Exotic Spheres May Reveal The Lair of Yog Sothoth.

“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...

Very cool!
He would have been someone I'd like to sit down and talk with! I read that he didn't have any formal education, and didn't quite graduate high school, right? And that many of his ideas were from night terrors that he had? I guess he was self-taught?

Love your thread! Have a house full of Lovecraft fans and look forward to sharing it with them. Have read most of his books over many years time but just recently read the Necronomicon. I found it very interesting and found that parts of it correspond to magical lore from several different ancient civilizations. It wouldn't shock me if the Old Ones turned out to be interdimentional beings: isn't that what a lot of people presume God and Satan to be- not to mention aliens?

This sort of stuff just blows my mind.

I wish I could think of more to add at the moment but my interests tend to lay more in the Zero Point Field (that I stumbled upon whilst doing HS physics) rather than 4th dimensional mathematics (hard to wrap my head around this). Maybe I should look closer at the latter!

In any case, well done OP! Food for the mind and soul

SnF

Peace & Respect,

-AS-

Ph'nglui mglw'nafh Cthulhu R'lyeh wgah'nagl fhtagn!!!!

Nice read Love Craft's stories are truly creepy

but not as creepy as this plush Cthulhu
[atsimg]http://files.abovetopsecret.com/images/member/bbd27b123759.jpg[/atsimg]

That is very Frightening.

Thank you all for coming by. It is, indeed, frightening.

It gives a whole new meaning to the term, 'Mathophobe'.

Here's a little something to lighten the mood...

Hey There Cthulhu...

That's some interesting stuff you put together I like it. S&F(first time I have got to say that). Ben a fan of Lovecraft since I was in grade school. "At the Mountains of Madness" was creepy to read at 11.

reply to post by Cthulhu33


Thank you. I am honored.

I also got a very early start in the 80s. I was just discussing with a friend how we seemed to be the only ones, when we were kids who knew who Cthulhu was. Now it is so popular but so far in the best way possible.

Thanks for coming to see the thread.

I am certain you will be amongst the first to be eaten when He returns.

You know the one that really creeped me out was
The Goat With A Thousand Young
Shub-Niggurath

[atsimg]http://files.abovetopsecret.com/images/member/e87a3e396994.jpg[/atsimg]

more so then cthulhu

reply to post by ELahrairah


Yes, for sure. The Black Goat of the Wood.

The Woods seem like just the kind of highly differentiated space the he might find odd trajectories and angles to slip in and out of.

Gibbering to his young in the hidden gloaming.

reply to post by Frater210


I never thought of the woods in the same way
after reading that story.

Originally posted by Frater210

I am certain you will be amongst the first to be eaten when He returns.

It is better to be eaten first and be spared the unknowable horrors that are to come.

reply to post by Exuberant1


Truly. Best to be consumed by the great one rather than be hurled down strange gulfs of hyperbolic geometry at the End of Time.

This just brought me even nearer to insanity.

It is stated in Dr. Richard Elwes' paper, linked above that the fractal called the Julia set has a shape such that, "Its outline is continuous, but nowhere smooth".
I went to check out the Julia Set on Wikipedia and found this 3D rendering of the mathematical function...

Here's your Mountains of Madness right here. In spades...


I am going to go and rock back and forth in the corner for a while...back soon.

en.wikipedia.org...

Lovecraft was on the bookshelves when I was a child and will certainly get a revival in this household.

Fabulous post. I will certainly read the links later today as I have to dash.

I suspect I will be at a total disadvantage at this because I got to a point with maths where my brain simply would not work once we got to algebra. It was not that I was not interested, it was more that an access road had been totally walled up, no matter how hard I tried to get round it. I wonder if any others here have loved the stories but failed the maths.

reply to post by Frater210

I see yor 3d julia set and raise you two 3d fractal animations to the order of infinity..

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

this quote reminded me of these optical illusion models where our brain processes the information in a different way than what it really is. now that is just a matter of our perspective. whether it is even possible for the human mind to comprehend the 4th dimension truly or not im pretty sure i cant personally wrap my head around this anyway lol

Nice thread, thantk you. I think Lovecraft is an amazing writer. He has a hidden depth to his work and sometimes I think there is more fact than fiction there...

reply to post by Frater210


Yes, this is very interesting.
H P Lowecraft, have by many been said to be a genius.

I don't know what they mean with Found in the 7'th Dimension.
How do you specify where the extra dimension are?

There are some info at Looking for extra dimensions.
The Advanced version if you like more calculations...
At The Official String Theory web site.