Non-Euclidean

[sciguy98]

Saying that space is flat means that all of Euclid's axioms test as correct, and that your high school geometry works in the real world.  The known universe, as far as we can tell, is flat.  It has no global curve.  Mind you that space is boundless and we may just happen to be a flatter part of the universe, so space's overall topology may not be flat.

In our universe, as far as we can see, parallel lines stay parallel.  Circles have static arcs, triangle angle measures sum to 180 degrees, and straight lines always apear straight.  In curved space, some or all of these suddenly become false.

[lorddoomicus]

In our universe, as far as we can see, parallel lines stay parallel.  Circles have static arcs, triangle angle measures sum to 180 degrees, and straight lines always apear straight.  In curved space, some or all of these suddenly become false.

Actually, there is a lot a curvature in the Universe.  That comes to you complements of General relativity.  It's how gravity works.  For a couple of good examples, do a google search on gravitational lenses and black holes.

- Derrik

[mcglothlin.13]

In our universe, as far as we can see, parallel lines stay parallel.  Circles have static arcs, triangle angle measures sum to 180 degrees, and straight lines always apear straight.  In curved space, some or all of these suddenly become false.

Actually, there is a lot a curvature in the Universe.  That comes to you complements of General relativity.  It's how gravity works.  For a couple of good examples, do a google search on gravitational lenses and black holes.

- Derrik

Thanks Derrick.  I thought this was the case.  Therefore, I'm doubly confused why sciguy98 is making the claims that he is.

[sciguy98]

In our universe, as far as we can see, parallel lines stay parallel.  Circles have static arcs, triangle angle measures sum to 180 degrees, and straight lines always apear straight.  In curved space, some or all of these suddenly become false.

Actually, there is a lot a curvature in the Universe.  That comes to you complements of General relativity.  It's how gravity works.  For a couple of good examples, do a google search on gravitational lenses and black holes.

- Derrik

Thanks Derrick.  I thought this was the case.  Therefore, I'm doubly confused why sciguy98 is making the claims that he is.

I addressed this a few posts up:

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...

On a local scale, anything with mass curves space.  I'm curving space by sitting in my office chair right now.  And I thought about bringing up gravitational lensing, but felt it wasn't really relevant to the topic.  When I say that overall, or globally, that space is flat, I mean that in the absence of any massive object, there is no detectable space curvature.

EDIT:  I'm tired of trying to explain it, as I appear to be doing a poor job of it (and I admit that I don't myself understand it 100%) so I'm going to step away from this discussion for a while and leave a link to an excellent wiki article on the subject: http://en.wikipedia.org/wiki/Shape_of_the_Universe

[Cacodaemoniacal]

I thought you did a good job explaining it. I for one appreciated a scholarly voice. What you said jibed with my vague memories of  It's a fairly complex subject no? It's an interesting topic on its own, then you throw in how Lovecraft used it and why he chose it etc. and it's doubly interesting.

[Chris Lackey]

What a great thread! Uh... that's it. I wish I had more to say.

[Chrizzie Frizzie]

I came across this: http://obob.com/wowser/warp1.htm

It's a 3D engine that visualizes a world that follows very strange rules. Try it out. It seems ok to start with, like its just a fishbowl effect. Then you try to find that door that you came in through... I can DEFINITELY see how madness could ensue if I encountered this space in reality.

[Chrizzie Frizzie]

Huh... found this. Cool!
http://www.jstor.org/pss/1575193

reading this literary article, seems like "non-euclidian" geometry was part of a very popular trend at that time to explore scientific boundaries through art. Apparently, "the fourth dimension" was the more popular idea, as "non-euclidian" was not as strong in its suggestiveness. Artists that DID like "non-eculidian" included russian poets, founder of Dadaism and later the Surrealists. The concepts represented "a new freedom from the tyranny of established laws"

Seems to me that the question isn't whether Lovecraft was familiar with the mathematics of it, but rather to what degree his use of "non-Euclidian" was intended to be linked to that strong contemporary movement (the way he was commenting on various philosophies in the silver key) or whether he was just going for "alien"

[Chrizzie Frizzie]

We all agree that he's trying to instill a sense of alien architecture. Was he also saying something about the literary concept?

• Was he saying that too much Freedom is ultimately alien to us and will drive us mad?
  
• Was he saying that Freedom is not a concept that we can understand with our human morals, as in total Freedom we are faced with an inhuman universe?

Before you say I read too much into it, remember that he was very intellectually hungry, very interested in both science and art. If there WAS an artistic movement at that time around "non-euclidian" concepts, then id bet money he was familiar with them. He wrote primarily for himself and his peers, so he expected his readers to be familiar with the same concepts he was familiar with...

[MaryAnn]

The process of using your mind to consider something carefully..

[mcglothlin.13]

The process of using your mind to consider something carefully..

That's deep.

[jason10mm]

I've always imagined it as a combination of acute and obtuse angles that, when taken to the extreme like in R'lyeh ends up looking like Superman's Fortress of Solitude from the films (all crystaline structures at odd angles to each other) combined with some M.C. Escher style perspective twists. The "Inception" movie might be a good example of how it could work, or that PS3/PSP game that came out a few years back. Sure, in our reality, stairs that appear to connect from one perpective might be seperated by a large gap, but in non-Euclidean geometry they somehow WOULD connect, while at the same time from another perspective they are seperated and a boat could sail through the gap.

One thing to consider is that HPL is writing without the benefit of all the visual special effects we have become accustomed to. Fantastic model landscapes, mind warping CGI, etc, all that stuff was extremely primitive or just plain non-existant in his time. So he had to probably draw inspiration from static paintings or from his own imagination, and the vocabulary he had to use needed to compensate for that lack. Today I could talk about a sword of light and everyone would imagine a lightsaber, but HPL didn't have that benefit, so he ended up being overly descriptive trying to get his point across.

[osyrisdiamond]

THe Reanimator is at it again!

I believe helps to visualize things. Non-Euclidean Level Design (Portal 2 Version)

[Cacodaemoniacal]

HPL didn't have that benefit, so he ended up being overly descriptive trying to get his point across.

I think at his best, every word counts, even if there are a lot of them.

What amazes me is his grasp of physics.

[old book]

Poe wrote some essay about cosmology, among other things, that made some surprisingly good points, I thought. Lovecraft was no dull blade either.