Imagining the tenth dimension

[martin]

Did anyone see this website?

http:(2slash)tenthdimension.com

It's a flash animation explaining the nature of dimensions from 1D to 10D.
I lack of any scientific background but found it very interesting.
They also made a book, which seems to be more speculative and philosophical than scientific.

 

[ark]

I am not yet in 10th dimension. I am in 4th. Still some way to go. Desperately working on finishing my paper on quantum fractals in n-dimensions, with illustrations mainly in 4d. Anyway, right now, this very minute, I am busy with one of the simplest 4d "cristals" - the hypercube, or tesseract". You can find many pictures on the net, but here comes one from my own "picture factory" (I am programming in Borland's Delphi):

It is not very difficult to understand the meaning of this picture. If you take two parallel flat squares, move them away in the direction perpendicular
to their planes, and connect their vertices - you get a cube. Each square has 4 vertices, so the cube has 4+4=8 vertices.

Now, repeat the same with cubes. Take two cubes, each with 8 vertices, move them apart in 4th dimension, and connect together the corresponding vertices (easier said than done :) ). You get hypercube. It has 8+8=16 vertices. Now look at the picture above: find two cubes there, and see that their vertices are connected. Good exercise in 3d visualization! So, this is a 2d representation of the four dimensional "not-so-sacred" polyhedron - the hypercube.

In my program I can rotate it in 4d, and I rotated it so that the projection looks "nice'.

The hypercube is also called the 8-cell. When you count carefully - you will be able to find 8 cubes altogether, though they will be somewhat distorted by two projections, first from 4d to 3d, and then from 3d to to 2d of the computer screen!

 

[ark]

And here is the quantum fractal generated by the tesseract. I am taking a section of the 3-sphere at the height x4=0.8 (x4 is the fourth coordinate) and project it onto the (x-y) plane.
The height of mauntains is the log of the probability that the quantum state will jump to the given point.

Of course the "true" fractal has an infinite depth (infinitely many details, and infinite zoom possibility). In the graph above I choose only a certain, rather low, level (lavel=3) of details.
To get more details I would need run my computer VERY long (hours, days, years, etc.) So, the 1 million dollar question is: how is Nature computing ALL THAT, in no time at all?

 

[CarpeDiem]

The height of mauntains is the log of the probability that the quantum state will jump to the given point.

Ark, and the "depth of abyss" is return to initial point? and is measured as depth -0,20 being min. point at XY plane?
Sorry, my wild imagination...

 

[domi]

So, the 1 million dollar question is: how is Nature computing ALL THAT, in no time at all?

All of creation is used for this? i.e. the computer and the computed are one?

 

[CarpeDiem]

computer computed and programmist - Godhead triad?

 

[Russ]

Welcome to the Tenth Dimension

In string theory, physicists tell us that the subatomic particles that make up our universe are created within ten spatial dimensions (plus an eleventh dimension of "time") by the vibrations of exquisitely small "superstrings". The average person has barely gotten used to the idea of there being four dimensions: how can we possibly imagine the tenth?

If you are a new visitor, start out by clicking on "Imagining the Ten Dimensions" in the Navigation section: you will see a set of animations, with narration and sound effects, which take you from the first to the tenth dimension. We would suggest watching them in order from zero to ten the first time... but hey, you're a creature with free will, so do whatever you'd like. The ideas in this animation come from chapter one of a new science/philosophy book called "Imagining the Tenth Dimension: a new way of thinking about time, space, and string theory".

Link - http://www(dot)tenthdimension.com/flash2.php
Click on "Imagining the ten dimensions" to see a flash animation.

I haven't read the book but I thought this might be of interest. It does sound interesting to me, but I haven't made much sense of it yet ;)

Not sure about that "you're a creature with free will" bit. But there might be some truth/sense in the website/book.

 

[Cyre2067]

Well, i must say its interesting, but in my opinion, doesn't add anything new to the overall ideal of multiple dimensions. The concept provided by the Cs of density is much more illuminating as far as philosophy goes, but this 10 dimension idea seems useful if one's primary area of interest is hopping dimensions/time in a sliders-esque fashion.

Now all you need is to be able to bend space time and create a singularity through which you can hop around.

 

[anart]

Russ, this is also covered here...

http://www.cassiopaea.org/forum/index.php?topic=2465

[Mod note: merged threads]

 

[Russ]

Ah, thanks Anart.
Nice cat btw :D

 

[Russ]

I made an animated gif of the hypercube, showing the 8 cells and the joining of the vertices:

 

[Russ]

Of course the "true" fractal has an infinite depth (infinitely many details, and infinite zoom possibility). In the graph above I choose only a certain, rather low, level (lavel=3) of details.
To get more details I would need run my computer VERY long (hours, days, years, etc.) So, the 1 million dollar question is: how is Nature computing ALL THAT, in no time at all?

What if it doesn't have to compute it, or its all been "pre-computed"? Is that a possibility?

 

[John Chang]

And here is the quantum fractal generated by the tesseract. I am taking a section of the 3-sphere at the height x4=0.8 (x4 is the fourth coordinate) and project it onto the (x-y) plane.
The height of mauntains is the log of the probability that the quantum state will jump to the given point.
http://www.signs-of-the-times.org/images/hypercube_a06x40.8l3.jpg
Of course the "true" fractal has an infinite depth (infinitely many details, and infinite zoom possibility). In the graph above I choose only a certain, rather low, level (lavel=3) of details.
To get more details I would need run my computer VERY long (hours, days, years, etc.) So, the 1 million dollar question is: how is Nature computing ALL THAT, in no time at all?

There has to be some lower bound, if the universe if digital. Planck length? Perhaps it's doing it in parallel, like a cellular automata machine?

 

[John G]

What if it doesn't have to compute it, or its all been "pre-computed"? Is that a possibility?

There has to be some lower bound, if the universe if digital. Planck length? Perhaps it's doing it in parallel, like a cellular automata machine?

Pre-computed still requires information to be stored somewhere and I'm not sure there's any more efficient information than what is out there in the lattice, there's certainly pre-existing lattice information about the future (as in the Cs). Planck length lattice sounds good though the wierd concept of exotic spacetime/duality would let the Planck length act as a maximum as well as a minimum. Lattice/Cellular Automata/Quantum Computer-like parallel processing could help with Hamiltonion Circuit travelling salesman-like problems that might show up. One though is kind of in many worlds at once until some "decoherence" event/cycle puts you in one world. Ark's quantum jumps to the best of my ability to understand them seem like a way to get non-linearities into quantum mechanics. From our third density view, non-linearities would certainly seem like quantum jumps but maybe from the Cs point of view even the non-linearities look "smooth". I think Ark wants to get a wave function out of his model so maybe that means there is some "smoothness" at higher dimensions?

 

[John Chang]

Here's another thought - how would we know how long it takes the universe to do the computations? For all we know, it's all being run on a 286 with floating point emulation :)

Or, without referring to anything external, is it possible for a program to know how fast it's executing? Hey, that sorta reminds me of Newton and his bucket...