posted on Jul, 30 2004 @ 02:48 AM
I happened across this sweet little gem, which IMO is the best and most complete example of 'Dimensional Theory'. It covers it both in a
philosophical/logical method as well as a scientific/mathematic method, while still being totally understandable for just about anyone. With all the
theories about there being 3 to 6 to 10 to 100 or even infinite 'Dimensions of Reality', I have to say that this is the first time I've come across
such a convincing case for 'Infinite Dimensions' along with examples and methods which anyone can experiment with themselves after reading it.
For many of you who are familiar with this topic and/or similar ideas, (even the more uncommon type ideas), you will probable notice at various point
during the reading of this that some very cool and insightful revelations or clues are going to pop up. A lot of them however are left to the reader
to explore further as this guy is very good about keeping to the topic without getting distracted or making it too long or speculative. So I advise
everyone to really pay attention and read it all. It's not that long even though it may seem like it at first, but it goes fast.
A Study of Dimensions - by Bill Price
1. Understanding other dimensions
www.geocities.com...
2. Multi-dimensional Geometric Units
www.geocities.com...
3. Computing Components of Basic Units
www.geocities.com...
4. Distances Within Basic Units
www.geocities.com...
5. How Many Dimensions?
www.geocities.com...
Now, I will include just a little example of the kind of stuff that is being talked about in here for those who aren't sure what it's all about or
perhaps thinking that this is going to be something dull or confusing to bother even reading it.
One example that is used throughout this is a comparison kind of thing between the 2D, 3D & 4D 'Reality Views' to help visualize what is happening
and why. It's kinda cool so that's what I'll be providing here, partially anyway, for a kind of tasty treat to get ya started.
NOTE: For some reason the img code was off when I posted this so the links to the pics may not show up. Hopefully the problem will be fixed
soon and they'll show up then.
If not, no biggie, they aren't anything real special, just simple line-art. If you want to check the site for them yourself, most all of them are
from the first chapter link above. Most of the example can be understood just by reading the text for the most part also.
Let’s imagine a world of only two dimensions, something like a huge thick piece of paper (actually, of course, with no thickness at all)
inhabited by 2-dimensional men. Someone from our 3-dimensional world with the aid of a light bulb projects the image of a cube into the 2-dimensional
world, much to the surprise of our 2-dimensional friends. What they see is not a cube as we know it, but two squares, one within the other, with lines
connecting the corners of one to the other:
We could, for instance, picture it as a small room with the small square in the middle representing the far wall, the sides being the right and
left walls, the top part the ceiling and the bottom the floor. But what are 2-dimensional "men" able to make of it? All they understand is two
dimensions, no more and no less. All they see is one large 2-dimensional square enclosing a smaller square with the corners connected. And if they
were confronted with a figure like this or they would merely see two squares intermeshed with the corners connected, or perhaps two parallelograms
with corners connected: The idea of "depth" is inconceivable to him. He only understands length and width, two dimensions.
Just as the 2-dimensional man tried in vain to find a third line perpendicular to the cross in front of him - no matter which way he placed it,
it would not work - we, too, try in vain to imagine a fourth unique line perpendicular to the lines described by the three edges of a cube. But the
answer is a line entirely outside our 3-D world, just as the line extending up wards from the surface of the paper is entirely out of the paper.
He is inside of the same plane as the square. What he sees, then, is not actually a square at all! What he sees is a line segment - with "depth"! He
is fully aware of this "depth" and understands it without any problems, since it is a part of his daily experience. But he cannot actually see this
depth, this second dimension, because it is in the same direction as his eyesight. His eyes perceive a square not as we do: but as a line
segment:
Now let’s have some fun with our 2-dimensional friends. They would like very much to see a 3-D cube face-to-face, but have no way of doing so
unless we help them. The best we can do is to take a cube and to push it through their 2-D world for them to observe. What do they see? If we push it
through, keeping it parallel with the plane of their 2-D environment, they first see a square which suddenly appears out of nowhere. As we continue to
push it through, the square seems to remain motionless and unchanged. Then it disappears as suddenly and as mysteriously as it had
appeared.
Even more interesting is to pass a sphere through their world for them to observe. What would they see this time? First a dot appears, which
rapidly grows into a circle. The wider the circle becomes, the slower it grows. Having reached its maximum size, namely the diameter of the sphere
itself, the circle slowly diminishes, shrinking more rapidly until it suddenly disappears altogether.
By analogy we may conclude that a similar spectacle would unfold before our eyes should we desire to see a 4-D supercube or 4-D supersphere pass
through our space. In the case of a 4-D supercube, we would first see a cube appear out of thin air, hover a bit, and then instantaneously disappear.
It has just passed 4-dimensionally from one side of our 3-D world to the other, just as the cube passed through the plane. No motion was visible,
because the only moving that took place was in a direction not found in our world of three dimensions.
I found this next little concept very interesting!! I even made up a little example artwork which you will see below, to better visualize this
idea.
If we were able to warp our 2-D friend slightly and place him within the surface of a sphere, he would have nowhere to go but the surface of
the sphere itself. No matter which direction he chooses to go, he ends up in the same spot. Being enclosed within the sphere’s surface, he is doomed
to travel in endless circles, although he himself is not aware of any turning. Striking out in a direction which seems to him to be a straight line,
he invariably comes back to his original starting place and is completely baffled as to how this could be.
Similarly, if one of us were "warped" 4-dimensionally and placed within the 3-D surface of a supersphere, he would find himself in exactly the same
predicament as the 2-D man described above. Regardless of which direction he chooses to go, he finds himself mysteriously going in a circle. The space
in which he is situated seems to be infinite in all directions, but is actually finite. In fact, we would even be able to measure its volume down to
the last cubic inch. What to him seems to be an immeasurable expanse of space is in actuality a finite volume of space curved 4-dimensionally into
itself, like the curve surface of a balloon.
Here is a quickie 3D animation showing a first person perspective just doing a simple half circle view of a road and trees. The quality sux but
that isn't the point anyway, FYI. It's just showing an example of a 3D Reality View.
But, is it truly a 3D reality??? Here is what it really is, which is similar to the example of the 2D Man being trapped within a sphere, only he
doesn't realize it because it's set up in a way where 'Dimensional Space' actually folds back in on itself.
The illusion is that there is somewhere to go which reacts normal for those trapped inside, however, they never get anywhere because what they see as
a straight line is really curved and they will always come back to where they started regardless of their direction of escape.
This is the 'Sphere Egg Prison' from the outside and a cut-out section to show that the environment is really a 2D curved space mapped within the
interior of the egg.
The teaser stuff I provided above is just the tip of the iceburg of what is explaned and for the most part, it's just the simple fun stuff as
well. I recommend anyone interested in this topic, as well as the real technical side of the 'Proof', that they go read the entire thing using the
links above!!
There is also some other interesting things this guy has done as well, such as inventing his own completely functional language and some cool info on
Prime Number Patterns too.
Enjoy and let me know what ya think after reading it!!