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Tuesday, May 08, 2007

Non Euclidean Geometry

Rodrigo Vilanova asked,

"Please confirm that non-Euclidean geometries are in fact Fractal geometries."

While I have an answer for that, I don't think it's very funny, so I'm not going to put it in the show. However, I thought that you, the enterprising Lovecraft fan, might be interested in my guess at how Non-Euclidean Geometry works. So, here goes:



Well, yes and no. You see, Fractal geometry is an expedient to explain repeating complex patterns in nature by reducing them to simple repeating formulas, and as far as that goes, yeah.

The problem is that non-Euclidean geometry is based on a whole different number system. A basic ruleset for Euclidean geometry is that the shortest distance between two points is a straight line. Based on that, you can tell the distance between two points, you can define an object as a series of points, and you can map out the world. Unfortunately, in non-Euclidean geometry, there is no shortest distance between two points. Not a straight line, not a Bezier curve, not even a definable parabola.

Imagine that you treated the distance between two points as a four-dimensional value, where it is not only based on the length, depth, and breadth of the points, but also based on where they are at a given time. This assumes that all points move in a constant, but unpredictable manner. Now, despite the fact that distance is a four-dimensional value, it is still a single value (for the undefinable determinant of time).

But it gets worse. Now, instead of a four-dimensional line, you make it an n-dimensional line (where n can be a freaking huge number). There's almost no way of knowing from one moment to the next where a point is going to be, using your static form of math.

Now, add to that the fact that these almost undefinable values are just the simple functions used as a foundation for the more complicated fractal, and you add an order of magnitude more difficult than you had before, just to figure out the distance between two points.

Hope that helps clear up the issue.

7:37 PM

5 Comments:

At 10:04 AM, Blogger ][Shogun][ said...

Hi there... first of all, and like every freaking TV or Internet show fan says, I LOVE THE SHOW... IM YOUR BIGGEST FAN. But really... the show is very cool and i would love to see the Cthulhu DVD released and I was just wondering if you're needing another spanish translator i'm from Argentina and currently studying to become one (translator of course, i've been argentine since i can remember)

Thanks in advance for taking the time to read this. Keep up the good work.

][Shogun][ A.K.A. Gonzalo

 
At 10:29 PM, Blogger ][Shogun][ said...

Now... about THIS post... I GOT IT... i mean... im Latin, Male and 21... every single odd of getting this was against me AND I GOT IT... you rule Cthulhu... although you are a sock pupet (yes i know... that really says a lot about my mental health... but i just HAD to say it)

Greetings

 
At 6:43 AM, Blogger Michael said...

Your explanation is basically the extension of three dimensional Euclidian Geometry into the four dimension of Space-Time. This was first developed my Einstein in 1904 to explain relativity. A very good book covering this topic is Geometry, Relativity and the Forth Dimension by Rudolf v. B. Rucker. With a full understanding of four-dimensional space-time you can walk through wall (or rather pass them) and stepping from star to star would be relatively easy :) We actually do not live in a Euclidian Geometry of Three Dimensions but in a very Non-Euclidian Geometry of Four-Dimensional Space-Time. Euclid being a limited human could not perceive the true geometry of the world but the old ones have no problem with this.

Yours in Yog-Soggoth

 
At 7:52 PM, Blogger BrandG said...

Awwww. . . I'm pretty sure using real book-learning is against the rules. :)

 
At 11:04 AM, Blogger MC said...

Your blog has won the Homer Simpson Transmundanity Award at Culture Kills this week.

Congratulations Brandon.

 

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