G''Day. I was just trying to determine physically what this situation meant... Having a set of 4-dimensional linear equations that have a 2 parameter infinite family of solutions. Would it be correct in saying that a way to visualise this is to imagine a set of planes moving over time. So (3 spacial plus 1 temporal = 4 ) dimensions. Then the solution (if u consider time to be a leading variable) could be visualised as the intersection point that moves in time along with the planes??? What do you think?

In math, when you''re speaking of 4 dimensions, you''re usually speaking of spatial dimensions. In other words, no time. While our world is 3-Dimensional (spatialy), the math can work out for an infinite number of spatial dimensions.

thx 4 the reply, but it is still plausible to represent any of the dimensions as anything isn''t it? they could represent temperature, time, flavour(?)...i realise that if this were a geometrically problem then space would be the dimension involved, but i am just trying to mentally visualise the problem. i suppose the human brain finds it easier to represent things as objects moving through time, rather than having to visualise a 4-space problem.

I think that''s still a plane. For example, if w = 0, then you have a plane in the 3D coordinate system. For other values of w, you have to imagine what it may look like. Make a Google search, maybe you can find some pictures.

Cédric

I think it would be much more consistent to just think of the 4th (and any higher dimensions) as just another spatial dimension. Representing them with anonther characteristics like colour, taste, etc... is not uniform enough. I know it''s maybe hard to imagine, but don''t try to think of it in terms of something that exists in our world. Just try to _imagine_ 4 vectors perpendicular to each other. Don''t try to draw, construct or build them: just IMAGINE. It''s really not that hard.
From that point, going to n-dimesions isn''t really that difficult to work with.

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Click NOW!

lol

you cant imagine 4 vectors perpendicular to each other..
it justs to much for our little 3D brains to cope with

or if u think u can imagine it.. then do it.. draw it on a piece of paper.. AND...

THE NOBEL PRIZE AWAITS!

You can draw it.. You can project 4 dimensions on a 2 dimensional paper

http://www.mrl.nyu.edu/%7Eperlin/demox/Hyper.html

The Problem is that we only have 3 natural dimensions, which makes 4 dimensions hard to imagine (and I have to admit that I have problems too)

It is perfectly alright to visualize the situation as a plane moving through the time.

As you said, data dimensions can be visualized as just about anything. In fact, this is quite often done in scientific visualization. For example shape, color, size, etc. are commonly used.

i have problems with that webpage..

i dont see how u can possibly hope to display 4d image on a 2d screen..

its as pointless as drawing 3d on a 1d screen.. u lose ALL the detail

4d in a 3d hologram.. that i can beleave.. but not 3d on a 2d screen

quote:

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could be visualised as the intersection point that moves in time along with the planes???

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Well, it would be an intersection *line* that moves in time. Other than that, it seems correct.

If you are intersecting only linear sub-spaces of R^4, you can interpret the situation as intersecting projective sub-spaces of the 3 dimensional real projective (this can be seen as the reason why we use R^4 to make transformations). Your situation would be a set of planes intersecting in a line.