4D shapes.

[Holiday20310401]

Since I don't have very good spatial reasoning, there's so much I realise I can't perceive, how would you you go about creating a 4D shape, what laws must there be to follow, laws that would correlate to making a 3D shape.
I always try and end up making a 3D shape with 3D shapes surrounding it with vertices connecting to one another. I know it must be a false sense of how to go about making a 4D shape. I call this the honeycomb effect.

[Aedes]

I think what people don't talk about enough is that to say we're in a 3-dimensional space is NOT in actuality a statement about the space we're in. There's nothing sacred about a dimension.

Dimensions are the way in which we describe the space we're in. And it turns out that of the infinite axes you can draw in a 360 degree sphere (emanating out from a single point in the center), there are only THREE in which you can have a value along one axis but no value along the others.

So something can have a positive value in X, but be zero in both Y and Z. Etc, etc.

Thus, if we want to describe the spatial characteristics of something, or the location of something relative to something else, we need to independently specify the three entirely independent dimensions.

That's why we cannot talk of building something in a fourth spatial dimension -- there just isn't a fourth spatial direction that can be described independently of the other three. This doesn't take into account the time component of spacetime, but that's not the question you're asking -- you're asking about creating something that is 4 dimensional.

And if you take a piece of paper and DRAW a 3D shape, it's not actually a 3D shape -- it's 2D but it has perspective cues that make us think of a 3D shape. So whatever you draw, you're not going to make it any more than 2D, and until we can actually see in 4 spatial dimensions we're not going to be able to conceive of it as 4-dimensional.

[de_budding]

Ever seen the film Cube 2: hypercube? It's awesome. This is a hypercube, the tesseract... Image:Tesseract.gif - Wikipedia, the free encyclopedia there is a wikipedia article and a 4d shape applet as well. I never really new got the concept but I like the idea of 'em.

DAN.

[Zetetic11235]

Hyperdimentional space is simply a mathematical topic which has shown somewhat fruitful when applied to theoretical quantum physics such as string theory, the idea is simply this:for a single dimention, you have a single line, no up and down, just back and forth. for two dimensions, you have a plane, up down right and left. You get this plane by sliding the sinle line in the diretions orthoganal(perpendicular) to it, ieup and down infinitely. The same is true of 3 dimentional space, you move the plane orthogonally to itself in to get R^3 space(3 dimentional space), imagine taking a piece of paper and it leaving a trail in the shape of a box as you move it form left to right and then imagine that the paper is infinite in length and height. Now, you can continue ths rule mathematically to R^n dimentions(where n is any integer).
You can make a 3d "shadow" of a 4d object, just as you can make a 2d trace of a 3d object, but the 2d trace is somewhat useless without an experiential base for 3 dimentions. Such considerations are only mathematically understandable and applicable to physical models such as string theory; they are fruitful in calculating physical laws and their consequences, but you cannot experience them visually.

[urangutan]

Zetetic11235, I like that comment,'you can make a 3d "shadow" of a 4d object.' What we see beyond our skies, isn't that a 3d "shadow", making the universe a 4d shape. I don't believe half of what we can see is there and I don't mean the time factor effect of the speed of light.

Hypothetically this would imply that the universe we see is unfolding to expand beyond a diameter. The term unfolding would mean that at some point the view in our screen is not a direct view and may take several diversions from a direct line. Hence our vision out into the universe may be no different than the road from Chicago to LA, while the direct route would carve through the land.

I am not saying that the diameter is the boundary, simply that at the point we see from the west no longer travels east from there. I know also that a compass doesn't point in space but hypothetically, I hope you get my meaning.

[Zetetic11235]

Consider this: Our 3 dimensional relm can be thought of as a composite of an infinite number of infinitely thin 2 dimentional relm, and just as we pass through the "inside" of these two dimentional rels and would have a blob like look to us, so can a 4 dimentional object pass through each three dimentional subspace as a 3d partial entity or touch the "insides" of 3d objects. Not exactly scientific, but it is a pretty cool thought experiment.

[urangutan]

I don't think you can pass anything through a two dimensional realm as it doesn't have an inside, two opposisng magnets,ie; north to north, will connect provided the realm is between them. So would this make magnetism two dimentional or is it simply gravity that is.

[Zetetic11235]

What? You don't seem to have a great grasp of of magnetism, its a field force as is gravity, the have a spherical radius where the strength of the pull increases with the proximity of the affected object.

[edwardelrich]

For an object to be 4D, you would have to percieve things at a 360 degree angle.
What makes an object 3D is from the view is see it in. So a 4D veiw would be like a whole other dimension literally.

[socrato]

Originally Posted by Holiday20310401

Since I don't have very good spatial reasoning, there's so much I realise I can't perceive, how would you you go about creating a 4D shape, what laws must there be to follow, laws that would correlate to making a 3D shape.
I always try and end up making a 3D shape with 3D shapes surrounding it with vertices connecting to one another. I know it must be a false sense of how to go about making a 4D shape. I call this the honeycomb effect.

In my opinion if there was such thing as 4D or other higher dimensions we as humans wouldn't be capable of perceiving it.