Is it possible for us to really understand tetraspace?

[sup2069]

I was watching a re-run of X-files last night. It was about a woman that could persuade you to do whatever she likes simply by putting thoughts into your mind and deceiving you. I was wondering if it was possible for us to see tetra space in our minds and comprehend it, if a tetronian placed his/her images in our heads?

Let?s say we were telepathic and we placed our understandings of realmspace and 3 dimensional object interactions into Fred's mind. Would he understand?

[Jay]

It hard to understand the difference between what the mind is capable of forming and what the eye can see. It may be possible, but I don't think we would understand what we were seeing if it happened to one of us.

[alkaline]

the mind is exceedingly complex, and memories are basically neural connections, neuron states, and many other chemical states within the brain. I don't know that these kinds of things can be directly manipulated. But that's getting into neuro-science...

[Keiji]

if a tetronian put their memory into our minds, we would know everything that they did, but the problem is how to get a 4d object into a 3d one.

[alkaline]

memory in the brain isn't like memory in the computer. Computer memory is simple bits. To give a human brain a new memory, you would actually have to rearrange neurons, their connections, the strengths of the connections between them, etc in order to give a person a particular memory. Plus, you'd have to know what was already in those neurons, and how to connect everything properly so that the person would have access to those memories that you implanted. Our brains are built around the third dimension, so you'd have to implant all the basics of the fourth dimension and everything else so the person could even understand what the memories meant in the first place. I'd say this is near an unsolvable problem.

[Keiji]

it's like saying that a circle is a circular object

[alkaline]

i don't understand - what is like saying that?

[Keiji]

any definition is based on another one. if trionians have no definitions that tetronians have, then it is impossible for tetronians to give trionians any of their definitions.

[alkaline]

if the tetronian gives the trionian a set of axioms that the trionian can accept, then the tetronian can give the trionian everything that follows from those axioms, as long as the trionian can make the logical leaps. So, the trionian would only need the foundations in order to begin learning.

[Keiji]

and trionians won't necaserily have tetronian foundations.

[alkaline]

well if we're here discussing 4d physics right now and we can figure out how certain things work in the fourth dimension, i argue that we have enough basics in order to understand the fourth dimension. It just takes a bit of work in order to make the understanding intuitive.

[Keiji]

what i meant was, trionians don't neccacerily have the foundations that a tetronian would have from birth, ie that that is needed to speak, read, write etc.

[alkaline]

true - but it takes a while for a trionian baby to learn the basics of working with a three-dimensional world. I'm not so sure three dimensions are truly fundamental to the brain.

[RQ]

surely the 4th dimension can be imagined just as we would picture the 3rd dimension on a piece of paper as 3 lines, two perpendicular to each other but the 3rd at most just perpendicular to only one of them, but if the 3 lines are pictured as being perpendicular to each other at different angles of perpspective instead of trying to picture them all perpendicular to each other at a fixed angle we can overall picture space from a 2-Dimensional point-of-view. Now since we aren't that limited and can visualize 3 dimensions all perpendicular to each other at the same time at a fixed angle, we just add a 4th line and picture it as perpendicular to the other 3 at different rotational angles (or at least two different angled perspectives).

[alkaline]

sounds good. so you have you done it yet? :-)

[RQ]

Yes, of course.

[sup2069]

how?

[RQ]

You just draw the 4 lines and picture each two of them perpendicular to each other, but from different perspectives

[Jay]

It's possible to draw a tesseract on a piece of paper as RQ just said. I think it's just impossible for one of us to lok at it and see the tesseract.

The illusion of a cube edge is created because we've seen one before and can interpret it from the drawing. I don't think anyone has seen a tesseract before. Even if you did, to see all 4 lines that meet at the edge, you would need the ability to see realms, not just planes.

[sup2069]

It's possible to draw a tesseract on a piece of paper as RQ just said. I think it's just impossible for one of us to lok at it and see the tesseract.

The illusion of a cube edge is created because we've seen one before and can interpret it from the drawing. I don't think anyone has seen a tesseract before. Even if you did, to see all 4 lines that meet at the edge, you would need the ability to see realms, not just planes.

Correct, remember that post where Alkaline was talking about seeing in the 4rth dimension? You would need 4th dimension rods in your eyes and your eye would have to be extruded ana or kata into the fourth dimension. Its like fred would need 3d cone rods in his eyes and thus, his eye ball would have to take on Z length inorder to see in planes, not linear.

[Jay]

You're right. And you know whar else, it may even be impossible to draw a 4d cube on a piece of paper.

Think about it. All Fred's writing is linear. However, maybe he could darken one part of the line. This would make the other part seem a little farther back, and give the illusion of a second dimension. However, there is no way for him to draw something that would hint at a third dimension. It's impossible for him to draw a cube.

Bob's writing is planar. But when drawing a cube he can place certain lines at non right-angles to each other, and give the illusion of a third dimension. But like Fred, he can't draw something that would hint at a higher dimension than himself.

So Emily would be able to write in 3d and draw something that had the illusion of 4d. But the method that she used would be impossible to duplicate in 3d, and we wouldn't be able to see it anyway. To Fred, the drawing of a cube just looks like a jumbled mess of lines. So to Bob, the drawing of a tesseract would seem a jumbled mess of planes.

[alkaline]

ok here's the deal with drawing things from higher dimensions. In planespace, if they use lines for their drawings, they can only see the front "face" of the object drawn. They don't know what the rear of the object is shaped like, because lines hide what is behind them. However, if they use points, they can show all the vertices of a shape. They can use darker colors for closer points and lighter colors for farther points, giving an impression of its shape. This is hard to do with circles - the more points you use, the more like a circle the shape looks, but the more complicated it is and the more points in the front hide the ones in the rear. The big problem with points though is that you can't show how they are connected to each other - They are just a random set of dots with it not being obvious how they are related.

Enter realmspace. We can draw points like bionians, but we can also draw lines that don't hide each other. Thus, we can show the connectedness of shapes. Circles are easy to depict. Spheres are difficult though - the more lines we draw to make a sphere, the more the rear of the sphere is covered by the lines in the front. But, the situation is better than in planespace - we can show more of the shape than bionians can of the circle. It's quite difficult to show the shape of a sphere with dots. When we use planes for drawing, it is like using lines in planespace - we only see the front of the shape.

Then there is tetraspace. They can draw with points, lines, and planes. When they draw with planes, the planes don't cover each other up, they only cross in linear intersections. The drawings of theirs that don't cover the rear of the object (using planes) look fuller to them than our drawings of shapes that don't cover the rear (using lines): their planar-surface drawings use 2 of 4 dimensions, verses our linear drawings which use 1 of 3. Tetronians can still draw in lines though, as we can draw in points - but lines are more useful to them than points are to us, because they give an overall shape (through their connectedness) instead of a set of random-looking points. Thus, tetronians can make useful drawings out of either lines or planes. They can make either line drawings or plane-drawings of glomes.

Our line drawings of 3-dimensional objects are distorted because of the projection onto a plane. They are not what the real shape is. Line drawings of tetronian shapes on tetronian paper are also distorted versions of the real tetronian shapes. Line drawings of tetronian shapes on planar paper are even more distorted, but you can still draw them. All of the hypercube applets on the internet show tesseracts projected onto a plane, thus showing that drawing these shapes is possible, even if they are hard to understand.

Bob can draw lines at various angles, and although the shape may not hint at a 4-dimensional shape to you, maybe to a tetronian used to dealing with distorted drawings of shapes within his own space, would recognize the shape. Thus, to the tetronian, Bob has drawn something that hinted at the fourth dimension.

[sup2069]

Our line drawings of 3-dimensional objects are distorted because of the projection onto a plane.

What if we used 3d holograms to generate images? Instead of using a 2d piece of paper. I am interested in seeing what a computer drawin image of the fourth dimenson, floating in the air by a 3d image.

Wouldn't it be similar to Emily's 3d paper?

[alkaline]

There's a java applet on the internet that you can use 3d glasses to see the shape pop out at you:

http://dogfeathers.com/java/hyprcube.html

It shows a tesseract.

Maybe someday, someone will create a hologram that shows a drawing from the 4th dimension.

[RQ]

I really agree with Jay that we may be able to draw a somewhat representation of a 4th dimension, but never really be able to see or understand it the way we understand drawing a cube, square, line, or point. And that Fred would never come close to imagining the third dimension the way we do. So motion in the 4th dimension should still be motion in one dimension with no forces acting on it afterwards.

[Simeon]

Perhaps the ability to see in 4 dimensions is already built into our brains, waiting for the chance to be used. So that we would only need a tetronian to give us a 4-d stereoscope and a few 3-D stereo photos of 4-D objects. Just as we can put two star photos into a stereoscope (or wear special spectacles) and at once it ups us to the third D, a true effect, since we can see which stars are closer than others. As to whether 4-D vision is impossible without actually experiencing life in it, I believe (not sure) that some people colour-blind from birth can dream in colour.

Simeon

[Jay]

My only reservations on the drawings of tesseracts that I see is that they are so far from the real thing that they are nearly useless. I imagine little Fred trying to draw a cube on his linear paper. It's nearly impossible.

We can easily draw a cube on planar paper, by drawing two squares and connecting all their vertices with equal lines. How can this be done in a 2d world, where they write on lines of paper, not sheets? To draw a cube, you need to be able to draw lines that connected at angles to each other. You can't do that on a line. Even if you put Fred on the plane of the paper, and he saw the cube drawing, it would seem a jumbled mess.

Emily would easily be able to draw a tesseract on her swock (3d paper), by drawing 2 cubes and connecting all their vertices with equal lines. But on planar paper?

Also, let's say that the drawing is oriented on the x and y axes. The illusion of depth is created from lookign at from the z-axis. As said above: Fred, looking at it while on the y or x axis, cannot make sense of it. A real drawing of a tesseract cannot be drawn on a plane, just as a cube can't be portrayed on a line. Even if we were in the realm of the swock, we would see an incoherent jumbling of planes.

Parts of it that need to be seen to create the illusion of depth would seem inside the drawing to us. Some of the lines of a cube drawing (one made my connecting all 4 vertices of the squares) would seem inside the structure to Fred.

[RQ]

Fred can just imagine it as we do only that from his perspective he would have to try a little harder, and wouldn't be able to see or at least understand it the way we do.

[Jay]

I disagree. If you look at a drawing of a cube from Fred's perspective, you just see a line. Maybe one part of it is receding away into dimness.

If we saw a REAL drawing of a tesseract, it would just look like a giant plane, with one part receding. There's no way you can infer an (n+1) object that's represented on an (n-1) object.

[RQ]

Just as we realize the shape of a cube drawn on the 2D surface of a piece of paper, can Fred realize the shape of a square drawn in 2D although he might only see lines. Now whether he understands the picture of a cube on his paper is up to him, but he will be able to see it.