Math is an unfixed reference. It is an series of frequencies that triggers an action script. The action script then may render random entities related to it. The visual cortex renders random mathematical entities after prompted by the action script (the action script is triggered by a series of frequencies that make the sound of the word Math, which activated its associated memory neurons.) Random mathematical entities, when rendered by the visual cortex, have spatial properties.
Allow me to share my opinion.
conway, the descrepancy seems to be a confusion caused by the placement of runes.
You see expressions like this 2 x 3
A more accurate way to look at it, would be like an inventory in a videogame… 2 x3
Mathematical operators, change what a number represents.
When a number doesn’t have any runes next to it, it is a naked number, the 2.
2 indicates a volume of substance. 2 apples, 2 atoms. 1 indicates 1 atom. 0 indicates no substance no space no atoms.
When the negative - rune is next to it, it looks like -2. Now it is not a naked number. Instead it indicates a number with an operation attached next to it. -2 does not indicate a volume of substance, it indicates an operation, and what is to be done with the operation.
So, 2 x3
2 is the naked number, 2 is the volume of substance.
x3 is not a volume of substance, but an operation to be performed. x3 says to add the number left of it, and to repeat this operation, 2 times.
The hidden number is the “scale”. We assume the scale to be abstract and a 1 unit value…the scale remains coherent and relative to the expression. If we put it as 2m x3, the scale would be whatever m is, for example m could refer to a meter. And since 2m means multiplied, after the equation is done, we multiply the abstraction (1 unit) by a meter.
The thing I talked about earlier was volume mode, or unit mode of mathematics.
However, spatial mode is an entirely different phase of mathematics.
In spatial mode, the 2 in 2 x 3 does not refer to a volume, but a zero-point in space.
Essentially, the 2 refers to a location, not a volume.
Therein lies the confusion.
Mathematics has two modes, volume mode (real numbers are only positive)
and spatial mode (negative numbers and zero are real numbers.)
In spatial mode, objects can be scaled using negative numbers, to still fill a volume of space.
The 2x2 matrix [0,1,2,2] refers to a finite plane, the 2x3 matrix [0,0,0,2,2,2] refers to a finite cube.
The size of the distance between points indicates its real volume, which is absolute. It’s position is relative, and therefore the 2x3
matrix is expanded to [0,0,0,2,2,2,3,1,5] in order to denote it’s location (relative to the origin.)