Actually, dimensions are represented like this:
1-D – 42
2-D – (42,0)
3-D – (42,0,0)
4-D – (42,0,0,0)
For coordinates or databases (and a coordinate system is a database), Peter Brooks‘s illustration is correct.
If there is no movement in the additional dimensions, you must have a placeholder value for “default”. Usually we use 0 for that.
afaik, relational databases are always 2-dimensional. This is why additional dimensions are represented as attributes.
a “datacube” is multidimensional. But relational is 2D.
Dimensions in a flat file database, interestingly, while represented on a 2D grid, can also simply mean attributes.
That’s what you were talking about – and I started to but then started thinking about dimensions of the database structure itself and NOT the purpose of a database which is to contain multiple dimensions in a compact way.
1, 2, 3, 4
Make a 4D Universe in a database. It’s 4 dimensions. Dimension is attribute.
Your intuition about 0th there actually led to an amazing leap forward in early studies of …. oh I think it was electromagnetism.
I’ll find the reference but it was one of those amazing bits of deduction that led to the notion of an ‘engine” of sorts at 0 in 3D space.
Ok, I found the clipping from a PDF of an old book that I used part of for my FB background picture and for this little video thing.
It was part of my studying of infinitessimals…. ugh. I’ll find it eventually. But there’s a guy whose reasoning was similar to yours Chris Hamberg and where he took it changed how we viewed reality.
From that book, it was the drawing of a 3D corner with rotations.
Your reasoning about 0 being something and doing something is similar to Hamilton wondering about 0, coordinates and “what happens there?”
Once he reasoned “rotations”, it opened things up.
[no, the LaTex is a lazy copy/paste from me]
Right, but what happens that turns one dimension into the next dimension?
Oh, it’s an amazingly simple answer that nobody thought about until Hamilton, at least mathematically.
It’s rotation. That’s how you get from 0D to 1D to 2D.
It forms the basis of quaternions. Without it, you couldn’t do 3D scaling on your video games .
In 0 dimensions though, you have rotation. If 0D rotates over time, it forms 1D. 1D rotating over time forms 2D.
The mindfuck of it all is “in what direction is it rotating?”
It’s rotating in the next dimension away from itself.