3*2
***
***
2*3
**
**
**
The two expressions are not really equivalent, though we may be used to deem them such: the former may mean we distribute 3 by 2 dimensions.
The latter we distribute 2 by 3 dimensions.
Division (related to the Greek
antanairesis and its various spells) means once again to distribute a number N of items along as many Dimensions as number D prescribes:
N\D
The operation has the same intention of a multiplication, but is more ambiguous.
N/D
does that mean
(1) overall/items=dimensions to allocate
or
(2) overall/dimensions to allocate=items?
These operations are implicitly creating dimensions to allocate.
At this point, if you see the thing in this perspective, you can envision dozens of new mathematical operations (of which the "standard" division and multiplication are just one instance, I have no idea whatsoever why the one preferred), depending on how the starting setting "decides" to
create and
allocate such dimensions.
If you consider X as the amount of elements, Y as the amount of Dimensions, and R as the rounds you repeat the process, for each round you could have different ways to calculate the current X and Y:
(1) You derive the next X (elements) from the current Y (dimensions) amount
taking in only the first entry of the whole Y process
taking in only the last produced entry of the whole Y process
taking in the sum of all the previous entries of the whole Y process
taking in only 1
----------------------------------------------
(2) You derive the next X (elements) from the current X (elements) amount
taking in only the first entry of the whole X process
taking in only the last produced entry of the whole X process
taking in the sum of all the previous entries of the whole X process
taking in only 1
----------------------------------------------
(3) You derive the next Y (dimensions) from the current Y (dimensions) amount
taking in only the first entry of the whole Y process
taking in only the last produced entry of the whole Y process
taking in the sum of all the previous entries of the whole Y process
taking in only 1
----------------------------------------------
(4) You derive the next Y (dimensions) from the current X (elements) amount
taking in only the first entry of the whole X process
taking in only the last produced entry of the whole X process
taking in the sum of all the previous entries of the whole X process
taking in only 1
Please keep in mind that a division is no nuisance: it is the first mathematical operation that the Biblical demiurge used. And, indeed, it did not divide, but it... multiplicated!
m(i/y)t(h)osis