Non-Euclidean

[Cacodaemoniacal]

Have you ever seen one of those cards with blurry words--done in such a way as to make you think your eyes are malfunctioning--usually with a drunk or coffee joke inside. Something optical using spatial distortion or interference patterns would be cool.

http://www.wolfram.demon.co.uk/interference_pattern.jpg

http://www.nawama.ac.th/offline/offline/Mahidolwittayanusorn/Disk2/content_02/www.physicsclassroom.com/mmedia/waves/ipd.gif

http://cord.org/step_online/st1-10/st110eii.htm

[mcglothlin.13]

The sailors walked on R'lyeh because that's how Lovecraft wrote it. Therefore, it's plausible to believe that the sailors could in fact interact with these creatures and places even if they follow none of our physical laws and have an adverse effect on our minds and bodies as a result.

Let me get this straight: It's plausible to believe something because someone (perhaps someone qualified) wrote it.  That is completely implausible!

EDIT: The sailors aren't just Euclidean. You and I aren't just Euclidean either. The lines and curves of our bodies intersect and rebound and run every which way. Our geometries are very complex.

I never claimed they were just Euclidean.  But regardless, my main point was to claim that the geometry of R'lyeh could not be too alien; otherwise humans could not interact with it.  For if humans cannot interact with an idea (in any way!), how can that idea "hint" at anything?  Ideas must connect with our mind--in some way--even in order to "defy the imagination's ability to even conjure them up".

[Kaelestes]

Let me get this straight: It's plausible to believe something because someone (perhaps someone qualified) wrote it.  That is completely implausible!

In the context of an interpretation of a fictional text, yes, I'd say it's very plausible to believe something the author wrote down as an element of the story.  It's also very plausible to believe that my personal interpretations of the hazier elements of that story are as they may have been intended by that author, based on what we all know about him. These complex ideas are all a stretch of the imagination, and I move that, insofar as the imagination is concerned, anything goes. I don’t need to be able to create a clear picture in my head of what’s being described in order to appreciate it or to even imagine that characters were able to interact with it in some fashion. In fact, that’s the whole point of Lovecraft.  He was primarily interested in defying our ability to collate what he was describing, taking the text beyond our creative limits and creating a new kind of horror that was frightening not because of what you could see, but because of what you couldn't. I think Genus Unknown put it very well: "[It's] something literally unimaginable, something impossible, something that can't exist but just goes on existing in Lovecraft's world anyway." That's how I interpret non-Euclidean as it pertains to this story. I fully believe, as I know many others do, that being able to fully quantify what Lovecraft wrote, or simplifying things by saying they just looked weird, would take away from the mystery and the art of it. I apologize if I offended you in my previous post on this thread, but that’s my opinion as it currently stands and I'm not particularly interested in starting an argument over it; I just disagree with your take on the subject.

[lorddoomicus]

Maybe I could write a raytracer that uses some kind of non-linear dynamics or chaos system to make up strange looking worlds ... mmmmm... got me thinking now ...

- Derrik

Is that some kind of a graphics generator?

A raytracer generates an image by tracing the path of light through pixels in an image plane and simulating the effects of its encounters with virtual objects.

Povray and Bryce are the two raytracers I play around with.

- Derrik

[mcglothlin.13]

In the context of an interpretation of a fictional text, yes, I'd say it's very plausible to believe something the author wrote down as an element of the story. It's also very plausible to believe that my personal interpretations of the hazier elements of that story are as they may have been intended by that author, based on what we all know about him. These complex ideas are all a stretch of the imagination, and I move that, insofar as the imagination is concerned, anything goes.

You misunderstand me.  I'm not claiming that an author can't write whatever imaginative material he wants to or that such ideas can't stretch the imagination.  I'm just scrutinizing the details of one particular idea.  Doing so is not somehow contrary to such literature.  S. T. Joshi does this all of the time in his books on Lovecraft.

In fact, that’s the whole point of Lovecraft.  He was primarily interested in defying our ability to collate what he was describing, taking the text beyond our creative limits and creating a new kind of horror that was frightening not because of what you could see, but because of what you couldn't.

Again, I claim, Lovecraft wasn't trying to completely defy our ability to collate what he was describing.  If that was the case whatever he described would be completely incoherent--just babble!  Good writers, including Lovecraft, want to communicate ideas to their readers--not leave them utterly confused!  Lovecraft communicates his ideas very well; and, as you've noted, he was very sparse yet evocative in his language.

I apologize if I offended you in my previous post on this thread, but that’s my opinion as it currently stands and I'm not particularly interested in starting an argument over it; I just disagree with your take on the subject.

I have no idea what you're apologizing for.  It always amazes me on forums and blogs that when you challenge someone one on what they've written they either get defensive or apologetic.  You can obviously hold any opinion you want.  But opinions come cheap!  Feel free to disagree with me all you want.  My response was not meant to start an argument.

[Cacodaemoniacal]

Let me get this straight: It's plausible to believe something because someone (perhaps someone qualified) wrote it.  That is completely implausible!

Isn't that how the brain works?
http://en.wikipedia.org/wiki/Appeal_to_authority
People interact with all sorts of things at the level of belief because we cannot be an expert in everything. Plus, that's what Urban Myths are all about and they seem to be sort of successful at what they do. Lovecraft is good at hacking that mechanism.

Mr. Joe Hypothetical Schmo believes Mr. Smarty Appearing McSmartington because Mr. McSmartington is able to persuade Mr. Schmo that he has access to info or authority that Mr. Schmo lacks. Just as Mr. Schmo may not accept Mr. Humble McHumbleton's word--despite his 500 Phds because he doesn't "seem" expert-like.    

It's like: The Grizzled Captain, a hard bitten man with over 20 years on the open sea, scanned the horizon and sighed contentedly. vs: Paris Hilton, her first time on a big ship, looked the horizon and said "I feel scared, we should go back!" As a non-sailor, I'd probably think we were actually pretty safe. Little knowing, of course, that Paris has spent the last 10 years of her life researching oceanic currents with respect to weather system analysis; while the captain was listening to his iPod.

I never claimed they were just Euclidean.  But regardless, my main point was to claim that the geometry of R'lyeh could not be too alien; otherwise humans could not interact with it.  For if humans cannot interact with an idea (in any way!), how can that idea "hint" at anything?  Ideas must connect with our mind--in some way--even in order to "defy the imagination's ability to even conjure them up".

You've read The Unnamable? Joel Manton agrees with you.

Are you saying it doesn't work for you? Does it stand out when you read it in a discordant way? People seem to vary in how much they'll go along with an author or ignore things that bother them because they like the rest so much. A huge amount of people just LOVE the DaVinci Code and sometimes the way computers are used on TV makes me want to hurl a shoe.

Granted he's not telling us to "develop meaningful synergies in order to actualize our potential" but he uses what are essentially buzzwords. Gibbous moon, Cyclopaen, etc.

Plus, rather than it's so alien they can't interact with it, it's just that it's so alien that they can't fully wrap their heads around it. It doesn't interact well with their sensory systems.

[fubarinpittsburgh]

When building an addition to your home do not ask the general contractor for Non-Euclidean architecture. So far I have had three plumbers go mad and my electrician covered himself with gasoline and ran into the woods on fire.

And the people at Home Depot are starting to get suspicious about all the missing day laborers.

[mcglothlin.13]

I never claimed they were just Euclidean.  But regardless, my main point was to claim that the geometry of R'lyeh could not be too alien; otherwise humans could not interact with it.  For if humans cannot interact with an idea (in any way!), how can that idea "hint" at anything?  Ideas must connect with our mind--in some way--even in order to "defy the imagination's ability to even conjure them up".

Are you saying it doesn't work for you? Does it stand out when you read it in a discordant way?

No, that's not what I'm saying.

People seem to vary in how much they'll go along with an author or ignore things that bother them because they like the rest so much. A huge amount of people just LOVE the DaVinci Code and sometimes the way computers are used on TV makes me want to hurl a shoe.

Granted he's not telling us to "develop meaningful synergies in order to actualize our potential" but he uses what are essentially buzzwords. Gibbous moon, Cyclopaen, etc.

Plus, rather than it's so alien they can't interact with it, it's just that it's so alien that they can't fully wrap their heads around it. It doesn't interact well with their sensory systems.

Yes, your last line is getting at what I'm saying.  I'm trying to figure out and spell out how Lovecraft can use evocative language that implies to us something that is unpicturable, incoherent, weird and disturbing; yet, Lovecraft does this in a way, I claim, is coherent and logical.  It's not enough to say that Lovecraft blows our mind away or writes stuff that we "can't fully wrap [our] heads around".  If that was simply the case, or all there was to his writing, then what he wrote would be just babble--but it's not!  Lovecraft's prose are incredibly coherent.  In fact, I think that's one of the many reasons he has had a lasting influence: he knew how to evoke implausibility in a very plausible way; he knew how to evoke chaos in very logical formats.  

I think this was my main point about the adjective "non-Euclidean".  It's actually not a very bizarre concept, though there are incredibly bizarre and unpicturable implications in non-Euclidean geometries.  Regardless of his actual familiarity with such geometries, Lovecraft knew that many of us commonly associate "Euclidean" with our everyday normal experience.  By appealing to "non-Euclidean" as a concept, he knows that this somehow implies a negation of our normal experience.  And as many theorists in horror literature attest (e.g. Noel Carroll, The Philosophy of Horror), feelings of horror are many times connected to things that are contrary to what we consider to be "normal".

[Cacodaemoniacal]

I think that's one of the many reasons he has had a lasting influence: he knew how to evoke implausibility in a very plausible way; he knew how to evoke chaos in very logical formats.  

At his best, his hints are very potent (Of course, we get to fill in the blanks with our scariest images or thoughts). He uses the music of the words--how they sound--to reinforce the idea he's trying to avoid describing. By it's sound and rhythm Gibbous evokes something more than a phase of the moon.

I think there's the rational part of the mind; and then there's the rest of the brain--our pre-verbal reptile  brain--that is working very hard to keep us from being eaten by lions or what not. I think the implication of a thing acts like seeing something out of the corner of your eye that might be a threat.

[fishy]

As always i am dragging in Stephen King`s  book "Danse Macabre". When speaking of Shirley Jacksons book "The Haunting of Hill House" he make several references to Lovecraft and about human perception. The quotes are as follows:

Stephen King "One thing we know about Hill House is that it is all wrong. It is like stepping into the mind of a madman, it is not long before you weird out yourself.

From the book:

No human eye can isolate the unhappy coincidence of line and place which suggests evil in the face of a house, yet somehow a maniac juxtaposition, a badly turned angle, some chance meeting of root and sky, turned Hill House into a place of despair...
It had an unbelievable faulty design which left it chillingly wrong in all its dimensions, so that walls seemed always in one direction longer than the eye could endure, and in another direction a fraction less than the barest tolerable length

Stephen King "We see a horror story developing here that Lovecraft would have embraced enthusiastically, had he lived long enough to read it.It might have taught the Old Providence Spook a thing or two. HPL was struck by the horror of wrong geometry; he wrote frequently of non-Euclidian angles that tortured the eye and hurt the mind, and suggested other dimensions where the sum of a triangle might equal more or less than 180 degrees. Contemplating such things, he suggested, might be enough in itself to drive a man crazy. Nor was he far wrong; we know from various psychological experiments that when you tamper with a man or womans perspective on the physical world, you tamper with what may be the fulcrum of the human mind."

Hope you found it interesting

[sciguy98]

As a former math major (yeah, I washed out, Calc III made my head hurt too much, lol) I have a few thoughts on this.

I would first of all like to say that the actual math and science of spacial topography and non-Euclidean space hasn't changed much since Einstein.  Relativity was introduced in 1905 and Call of Cthulhu was written in 1928, so any college book on the subject Lovecraft would have on hand would contain much of what I'm about to relate.

The thing with Euclid are his postulates on parallelism.  There are non-Euclidean maths, such as hyperbolic, that have been previously mentioned.  The trouble comes when we apply this to space.  Humans are Euclidean, space, as far as we can measure it is Euclidean.  Parallel lines never intersect and the angle measures of a triangle always sum to 180 degrees and a number of other things we learn in High School geometry.  We've picked out distant stars, measured their distances from us and from each other and space appears to be, over all, extremely flat.  In order for a space to have non-Euclidean angles and forms, this would have to be false.  I think that Lovecraft referred to spacial curvature, and what it does to straight lines.

Space can have 4 "shapes".  The first is flat.  There's no need for me to explain this, as we live in a flat space.

Second is positive curve, or spherical space.  In this universe, there is no parallelism.  Two lines that start out parallel will eventually cross.  Twice.  This is like the surface of the earth in that we think its a straight line, but from another angle we realize that the line is curved, following the curvature of the earth.  If R'lyeh has this attribute, a door frame would look truly bizarre.  Each angle would be a right angle, and looking at individual parts of the frame would have it appear straight, but the overall look would be mishapen and bent.  It's practically impossible to picture and would be unsettling to see.

Third is negative curve, or hyperbolic space.  In this version, there are instead infinite "parallel" lines.  This would be like space on a saddle, where suddenly a triangle's angles would sum to less than 180 degrees.  Our door frame would be bizarre yet again.  This time, we have our apparent right angles and straight lines, but this time it would seem really small and buckling inward but allow the sailors easy passage through, despite it appearing to be too small.  We'd have an instance of things being bigger on the inside than they are on the outside, so to speak.  this may be less obviously upsetting, but likely more confounding.

Fourth is the one I'll likely have a hard time explaining, Torical space.  Combining the effects of spherical and hyperbolic space, we add in another oddity: recurrance.  We're experiencing space superimposed on the inside of a torus (or donut), so a large enough object will loop in around on itself.  Now we have our door, all right angles, all straight lines, warped oddly, bigger on the inside than on the outside, and we can see the backs of our own heads through it, because we're peering toward the center of the curvature.  Or perhaps the door is made from a single board stretched along the curve in such a way to have 3 "copies".  We're nailing the board to itself and forming a square from a single striahg tboard and not actually breaking any rules.

I may be giving Lovecraft a lot of credit that he may not seserve by assuming that this was along his line of thinking, but this is how I persoanlly rationalized R'lyeh when I read The Call of Cthulhu.

Thanks for reading~

[Barrucadu]

R'lyeh has suddenly become far more weird in my head now. Thanks for explaining.

[Cacodaemoniacal]

Imagination Exercise

• if something comes from a non-Euclidean universe into a Euclidean universe, does it have to immediately become Euclidean in order to move/operate/exist?
  Does it get flattened or straightened in awkward ways?
  Does it transform the Euclidean universe instead?

Maybe Cthulhu is pressing into this world like a bubble of "other reality." The stars being right is when the time/space fabric is thinnest.

Scarier than him wanting to take over this reality, is him just trying to get from point A to point B by taking a shortcut through our universe, and utterly destroying it in the process...and not even noticing.

[sciguy98]

Imagination Exercise

• if something comes from a non-Euclidean universe into a Euclidean universe, does it have to immediately become Euclidean in order to move/operate/exist?
  Does it get flattened or straightened in awkward ways?
  Does it transform the Euclidean universe instead?

Maybe Cthulhu is pressing into this world like a bubble of "other reality." The stars being right is when the time/space fabric is thinnest.

Scarier than him wanting to take over this reality, is him just trying to get from point A to point B by taking a shortcut through our universe, and utterly destroying it in the process...and not even noticing.

I'm not sure how to respond to this without being too abstract, but I'll give it a go!

Above, I stated that space is flat overall.  Globally, this is correct, however local space can curve in strange ways.  Gravity is the way we usually see this happen, but good work by Mr. Alcubierre shows us that we don't need gravity to give space a bit more topography.  I think that an island, like R'lyeh, could have odd bends and warps in its space that would completely impossible to detect at a distance, or even close up (as long as nothing is moving).

I guess the point I'm trying (and failing) to express is that our universe is capable of following and breaking Euclid's laws at the same time.  Objects exist in space, but objects are noy made of space, if that makes any sense.  You can toss cube through a curved space and at no point does it cease to be a cube.  I guess I'm trying to say that a being cannot be non-Euclidean and the spatial curve or lack thereof shouldn't really effect the physics of anything.

I really hope that made some logical sense ^^;;

[mcglothlin.13]

I'm not trying to turn this into an academic enterprise, but there's a lot that you (sciguy98) are saying that assumes so much.  For instance, what do you mean that "space is flat overall"?  Are we talking three dimensions or what?  I'm not a mathematician.  Please explain.