3d in 2d, 4d in 3d

[DenijsD]

Rather than mathematical I was just thinking of a more pratical approach of getting to know the 4th D.

We are able to draw 3d object on a piece of paper (Or computer screen), by drawing the 3rd dimension, in an angle different to the other 2 (<> 90 degrees), making it look like a 3d object.

Now if you were to imagine a 4d object, would it be possible to extend a 3b object (rather than drawing it in 2d) i.e. your mobile, and add the (imaginable) 4th dimension by drawing or attaching an object in an angle <> 90 degrees, helping us to visualise the 4th D.

Writing this I think: Would a 2d creature be able to visualise a 3d object drawn in his 2d world by one of us, probably not, he'll just see a spaghetti of lines making no sense whatsoever

[bo198214]

Writing this I think: Would a 2d creature be able to visualise a 3d object drawn in his 2d world by one of us, probably not, he'll just see a spaghetti of lines making no sense whatsoever

Your are not the first thinking about this. Indeed there is a bunch of programs out there that project/draw a 4d cube (keyword tesseract) into our 3 dimensions, and also other 4d geometrical shapes. You can (4d-)rotate and look from different angles and perhaps with time from the spaghetti lines develops a feeling for 4d ...

Take a look at tetraspace and you will find vast set of references. And by the way this approach is quite mathematical by nature.

[DenijsD]

And by the way this approach is quite mathematical by nature.

It is, isn't it :-)
I do think however, that maths is not the right way to figure out this problem (no no, i know, it isn't a problem), as maths as we know it are based on things around us and do not give an explenation for things we can't see (i.e. infinity) (mathemetisians will probably disagree, but they are wrong!! ;-))

So we have to leave all that behind and think differently to figure this out. We have to make new rules that don't fit in our universe. I don't know how yet, though :-)

[bo198214]

as maths as we know it are based on things around us and do not give an explenation for things we can't see (i.e. infinity) (mathemetisians will probably disagree, but they are wrong!! ;-))

Yes, indeed I absolutely disagree. Mathematics may be *inspired* by things around us (so physics had major impact on some mathematical research). But it *especially* explains things we cant see, for example infinity! It explores what is *thinkable* (i.e. not contradictive) mostly disregarding what apparently exist.

{pathos off}

[DenijsD]

Yes, indeed I absolutely disagree

:-)
Let's not start that discussion; I just knew you'd bite :-).

Infinity, however, is a nice subject. It might be explained in a mathimatical way, still we don't know whether it exists. Yet, it has to because every ending is a beginning. And if that is true then beyond the limitations of the 4th dimensions are the possibilities of the fifth and so on. So does that mean that there is an infinit number of dimensions?

Is that is so, that means that we probably are very primitive :wink:

[bo198214]

So does that mean that there is an infinit number of dimensions?

There is even an infinite number of infinite numbers (of dimensions)

Is that is so, that means that we probably are very primitive :wink:

Absolutely!

[moonlord]

You can approach higher dimensions with pure maths, but it's pretty tedious and difficult to cope with.

we don't know whether it exists

I personally think there is nothing infinite in our world (reffered as "realm" here around).

[jinydu]

Of course it is possible to study infinite-dimensional spaces mathematically. For a simple example, consider the set of all one-variable polynomials with real coefficients. Clearly, this forms an infinite-dimensional space, since (if x is the variable), a basis for the space is {1, x, x^2, x^3, ...}

In fact, infinite-dimensional spaces show up often in quantum mechanics. Often, you find that a Hamiltonian has infinitely many linearly independent eigenfunctions. Thus, a superposition of the eigenfunctions requires infinitely many coordinates to be specified.

A lot of the ideas that work in finite-dimensional vector spaces continue to function in infinite-dimensional vector spaces. For instance, it is still possible to talk about subspaces, linear independence and orthogonality (so long as you have defined a suitable inner product).