The triangle numbers sold me. Just have to come up with a use for it, uh, discover the intrinsic beauty of the universe.
Looking at degrees of freedom doesnt really help. A point is picked on a line by constraining it along 1 dimension, and a line on a plane can be picked the same way. So a -1D object should be pickable in a point by constraining on 1 dimension. But a point doesn't have any dimensions.
Maybe take a cue from imaginary numbers? i is orthogonal to the regular number line. Can't go beyond -1D though, to keep the triangle numbers intact.
Is it some kind of identity operation or metadata? Based on the table, every dimensional object has one -1D nega-line.
If it's a line, it could plausibly be time (thanks, Einstein!). Some kind of update history/version control.
What happens when you combine dimensional objects? A 0D point and another 0D point defines either a point (if theyre the same) or a 1D line. Even if you define the points in higher dimensional space, they simplify to a line.
A point combined with a line, either the point is on the line, along the line segment, or creates a 2D plane.
Line and a line can define up to a 3D space.
The table for that is:
___-1D__| 0D | 1D | 2D
-1D
0D_____| 1D | 2D | 3D
1D_____| 2D | 3D |
2D_____| 3D |
Does this mean a line + plane can be used to stake out a 4D hyperplane?
Filling it in for -1D, adding a -1D object to anything doesn't change its dimensionality.
And each object only has one -1D component (from the OG triangle table).
So far nothing against the -1D being a history of the object on a universal timeline. That works when combining objects too - a point with its own -1D history combined with a line with its -1D history makes a new line or plane with a -1D shared history.
But looking at it from the perspective of information theory + minimal encodings is probably going to ** all that up.
A line is easily definable, with just a length, or with 2 points in a 2D space etc. But it can hold an infinity of points that take infinite storage space to keep track of.
Looking at degrees of freedom doesnt really help. A point is picked on a line by constraining it along 1 dimension, and a line on a plane can be picked the same way. So a -1D object should be pickable in a point by constraining on 1 dimension. But a point doesn't have any dimensions.
Maybe take a cue from imaginary numbers? i is orthogonal to the regular number line. Can't go beyond -1D though, to keep the triangle numbers intact.
Is it some kind of identity operation or metadata? Based on the table, every dimensional object has one -1D nega-line.
If it's a line, it could plausibly be time (thanks, Einstein!). Some kind of update history/version control.
What happens when you combine dimensional objects? A 0D point and another 0D point defines either a point (if theyre the same) or a 1D line. Even if you define the points in higher dimensional space, they simplify to a line.
A point combined with a line, either the point is on the line, along the line segment, or creates a 2D plane.
Line and a line can define up to a 3D space.
The table for that is:
___-1D__| 0D | 1D | 2D
-1D
0D_____| 1D | 2D | 3D
1D_____| 2D | 3D |
2D_____| 3D |
Does this mean a line + plane can be used to stake out a 4D hyperplane?
Filling it in for -1D, adding a -1D object to anything doesn't change its dimensionality.
And each object only has one -1D component (from the OG triangle table).
So far nothing against the -1D being a history of the object on a universal timeline. That works when combining objects too - a point with its own -1D history combined with a line with its -1D history makes a new line or plane with a -1D shared history.
But looking at it from the perspective of information theory + minimal encodings is probably going to ** all that up.
A line is easily definable, with just a length, or with 2 points in a 2D space etc. But it can hold an infinity of points that take infinite storage space to keep track of.