hyperdimensional space

[TheLivingMartyr]

i'm sorry, i didn't know which specific subcatergory to put this in, there was no geometry section.

 

According to mathematics you can draw a line. this is 1 dimensional. you can then draw another line at 90^o to this; this occupies 2 dimensions: a square. you can then draw a third line which obviously cannot be at 90^o to both of these, but represents it. this is 3 dimensional space: a cube. so far, this can all be realised in a physcial situation, as you can take for example 12 pieces of uncooked spaghetti and put them into a cube. all the intersections will be at 90^o. now once again, according to modern mathematics, you can draw a fourth line, which connects 2 cubes, and this is supposed to be in 4 dimensions: a tesseract. this is where my logical, physics orientated brain, stops and says "hang on, surely, this 4th dimension thing is all void if i can't be physically realised". I am sure you all know what a tesseract looks like, so i wont explain it, but i would argue that it does not occupy 4 dimensions! the 4th set of lines are diagonal: that is not at 90^o to the others. i try to accept this fourth mathematical dimension and move on, but then realise, "oh dear, if you can just draw another line, then you can have infinite dimensions". so what i am saying is, what is achieved by "making up" more dimensions when they do not exist physically? There are 3 spacial dimensions that we exist in, and they are all at 90^o to each other. in our universe, for a fourth dimension to be achieved, it would have to be drawn at a non-right angle to the others, therefore making it not another dimension at all, just a line occupying 2 dimensions.

 

i would like to hear people's views on this, and maybe someone more understanding of maths can explain my fault

[ajb]

so what i am saying is, what is achieved by "making up" more dimensions when they do not exist physically?

 

1) Mathematically it is interesting and can give a better understanding of the 3-dim space.

2) Higher dimensional spaces are needed in physics. For example 6 dimensional spaces are needed in classical mechanics.

[Gozonji]

It's also important in mathematics. Our physical understanding of reality is the vector space R³. The vector space R⁴ is then the "fourth spatial dimension". This helps us in calculating systems of equations, digital encryption, even calculations in probability. MAthematically it's absolute necessary.

 

Oh, also, the model of the tesseract you've seen, the cube-inside-a-cube thing, that's not what they REALLY look like. It's a 3-D representation of a 4-D object, much like a picture of a cube is a 2-D representation of a 3-D object. The line representing the third dimension is diagonal because we don't have that third spatial dimension on a sheet of paper. Similarly, the diagonal lines of the tesseract are supposed to be 90^o to each of the other lines.