What is the 3rd dimension?

[CuriosOne]

On 10/15/2020 at 12:56 AM, studiot said:

Gosh you are a hard person to keep up with on ideas. I see you have started another thread this morning.

I seriously recommend you at least get to a sensible pause point with each one before moving on, we still have a long way to go in your calculus one.

Anyway swansont has answered your question but here is more on my comment.

Here is a brilliant experiment you can easily perform to gain insight.

You will need a cardboard box with all six sides intact.

Here is a quick blackboard sketch.

Rotations can be represented by complete circles.

Consider first one single space dimension.

There is nowhere for rotations to occur. You have to leave the dimension (employ another one) to even turn around. This is Fig 0.

Move up to two dimensions  _  I have modelled this as a plane in two dimensions in Fig 1
You can have a rotation about any point in the plane.

Draw this as a circle on one face of your box, as in Fig 2.
But any rotation is about an axis which has to be a line in a third dimension.
So if you extend a line through your point through the opposite side you have the z axis.
You can draw a circle round it though any plane parallel to the first side like the opposite side.

Now move up to 3 dimensions.
You have to pairs of sides you can draw rotation circles on to generate two more axes, making 3 in all.
As in Figs 3 and 4.
I have shown the conventional right handed rectangular xyz coordinate system.

Now comes the clever part  - your experiment.
Use the box to convince yourself that rotation on any plane at any angle has an axis within the 3D system.
You do not need to leave 3D and have a rotation axis pointing into a fourth or higher dimension.

This is what I mean when I say that 3D is complete for rotations.

Let us know how you get on with your box.

Still sort of confusing becuase all I see are 6 sides of 1 dimension ( 1 flat hyper plane of 6) and rotations look reflected on all 6 dimensions of the box. Its mind boggling...Atleast its how I perceive it to be.

[studiot]

10 hours ago, CuriosOne said:

Still sort of confusing becuase all I see are 6 sides of 1 dimension ( 1 flat hyper plane of 6) and rotations look reflected on all 6 dimensions of the box. Its mind boggling...Atleast its how I perceive it to be.

Well you really have got me there.

What on earth do you mean ?
6 dimensions of the box?

Edited October 17, 2020 by studiot

[MigL]

This is quite ridiculous ...

If you have a ruler ( a one dimensional line with numbers on it ) all you need is one number to specify any position on it.
If you have a sheet of graph paper ( 2 dimensional numbered grid lines ) you need two numbers to specify any position on it.

It is a simple mental jump to imagine a height above that sheet of graph paper with the same grid lines. That is the third dimension, and you now need three numbers to specify a location in that space above the sheet of graph paper.
And should you want to assign variables to a specified location, you can call them x, y, and z.

Dimensions are simply the directions you can move in a given space.
Back and forth, side to side, and up down for 3 dimensional space.

[Sensei]

On 10/17/2020 at 12:11 AM, CuriosOne said:

Still sort of confusing (..)

Download, install and play with some 3D software.

e.g. Blender, Lightwave, Maya etc (but majority of 3d apps have 30 day trials)..

 

[CuriosOne]

On 10/19/2020 at 3:15 AM, Sensei said:

Download, install and play with some 3D software.

e.g. Blender, Lightwave, Maya etc (but majority of 3d apps have 30 day trials)..

 

I've been using Maya for the past 10 years, I love 3d...

[Sensei]

1 minute ago, CuriosOne said:

I've been using Maya for the past 10 years, I love 3d...

...did not you just posted thread with title "what is the 3rd dimension?"..... ?
 

[CuriosOne]

12 minutes ago, Sensei said:

...did not you just posted thread with title "what is the 3rd dimension?"..... ?
 

Yes, but I use 3d to create 3d video games, 3d models, basically 3d "toys" and when I render the images it looks very similar to images I see in the real world..

 

The same is true for animations that uses the evolution of time to move.

For instance, how do numbers "know" left, right, up or down??

If you say computer software programs them, then that's more than obvious, but say we do math on plain "paper" and pencil, how then can the numbers do what they do in 3d space x,y,z??

 

I guess I'm asking what links "instructions to numbers in the phyiscal world without computers??

The universe has been here for billions of years before the thought of the computer processor..

Edited October 20, 2020 by CuriosOne

[cannongray]

The human brain is sharpened for three-dimensional space, but in our hypothetical scenario, even the brain itself will be five-dimensional. If you start with organic matter, amino acids are useful precisely because they form certain three-dimensional structures. Then all the tricks immediately become available, such as passing through locked doors, mirroring, etc. This is when the heart is on the right, and all L-amino acids change to D-. If there is a transparent sheet of text on the table, then turning it over will give you a mirrored text. And if the sheet is obliged to remain in the plane of the table, then this effect cannot be achieved in any way. Adding extra dimensions to 3D space is the same story. Specular reflection turns out to be a special case of rotation