Mathematical HyperObjects study

[virtualmeet]

Hi all,

String theory suggests that we live in 11D hyperspace but no one can actually say what that means and what an 11D Hyperobject looks like because our perception is "limited" to the 4D Hyperspace (3D space + 1D time). Mathematical programming can give us an introduction to the mysterious field of "string theory" that involve Hyperobjects and Hyperspace, because of two reasons :

1) HyperSpace can be fully described by mathematical equations, which mean that we can modelise HyperObjets and study their propreties.

2) Informatics give us the power to "simulate" our human perception of HyperObjects since we already know how our eyes act in our perception's process.

Here is a description of one program that go a bit more than others in the discovery of HyperObjects :

K3DSurf is a program to visualize and manipulate Multidimensional surfaces by using Mathematical equations. It's also a "Modeler" for POV-Ray in the area of parametric surfaces.

 

Features :

* 3D, 4D, 5D and 6D HyperObjects visualization.

* Full support of all functions (like C language).

* Support of mouse event in the drawing area(Left:Rotate, Right:scale and Midle: translate).

* Animation an Morph effect.

* Povscript and Mesh file generation. VRML2 and OBJ files also supported.

* More than 100 well known examples.

 

Official Site :

http://k3dsurf.sourceforge.net/

All your comments, bug reports are welcome.

Thanks

[UncleAl]

String theory suggests that we live in 11D hyperspace but no one can actually say what that means and what an 11D Hyperobject looks like because our perception is "limited" to the 4D Hyperspace (3D space + 1D time).

 

M-theory compactified dimensions are not percepitible at macroscopic scales,

 

http://www.mazepath.com/uncleal/eotvos.htm#b29

http://arxiv.org/abs/astro-ph/0508572

3 compactified dimensions, 10 nm diameter

 

"Extra" six dimensions loosely comprise one charge dimension, two isospin dimensions, and three color dimensions. Their physical meaning is debatable. Below compactified dimensions' radius gravity non-classically varies as 1/r^(2+n). At larger spans the anomaly exponentially decays as a Yukawa potential, [1 + (alpha)10^(-R/lambda)] where

 

"n" is the number of compactified dimensions;

"r" is centers of mass separation;

"alpha" is anomaly magnitude vs. Newtonian gravity, (n+1) or 2n (n-sphere or n-torus winding);

"R" is compactified dimension radius;

"lambda" is total anomaly radius, compactified dimension plus fringing.

 

http://www.stanford.edu/group/kgb/Research/gravity2.html

http://www.phys.lsu.edu/mog/mog15/node12.html

http://arxiv.org/abs/hep-ph/0303057

 

K3DSurf is a program to visualize and manipulate Multidimensional surfaces by using Mathematical equations.

Kewl! What happens if all the dimensions are not of the same size and shape? What happens if they are embedded in a non-Euclidean space?

[Tormod]

Great initiative, virtualmeet.

[virtualmeet]

Thanks for your explanations. It's abvious that we can never understand the signification behind extra dimensions but, and thanks to the mathematics, we can fully describe them and study their properties !!!

The difference between describing and understanding here is huge and has a lot of consequences.

To explain a little more what that means, suppose that a 2D human being (a mathematician), living in a flat land, decided one day to study hyperspace. This creature can never "build" a simple 3D sphere in his flat land BUT, like us , he can describe it mathematicaly with the same simple equations (even if he can't understand the Z axis) :

X = cos(u)*cos(v)

Y = cos(u)*sin(v)

Z = sin(u).

More interesting thing: he can make it move, scale, tweak and take a picture of it by projecting this sphere into his flat land...

In other words, the 2D being can, with his mind, modelise and study an hyperobject (3D sphere)...

 

Kewl! What happens if all the dimensions are not of the same size and shape? What happens if they are embedded in a non-Euclidean space?

Then we can simply apply some changes to our equations, but the principle still the same :-)

[virtualmeet]

Thanks Tormod, I'll try to do my best.

Great initiative, virtualmeet.

[Dark Mind]

Glad to have you here virtualmeet :shrug:. It looks like you've done some studying ;)...

 

Unfortunately you've left little room for discussion. Not really a problem right now, but in the future try to make it to where other members can participate more openly ;).

[virtualmeet]

Glad to have you here virtualmeet :shrug:. It looks like you've done some studying :eek:...

 

Thanks Dark Mind and yes, I've done some studying with K3DSurf and it turns to be quitte easy than expected ;) ...all we have to do is to think abstract

Unfortunately you've left little room for discussion. Not really a problem right now, but in the future try to make it to where other members can participate more openly ;).

I've just discovred this excellent website and I'm not yet aware of all it's features...perhaps next time ;)