Philosophy Now Forum

(1 --> 1) --> 2
(1 --> 2) --> 3
(1 --> 3) --> 4
Etc. As an expanding circle or spiral.

Or as evidenced by a number line where the point projects as a quantifiable line.
(0 --> 0) = 1.
(1 ---> 0) = (1/2, 2)
****where the line projecting to another 0d point results in the line divided in half as two lines.
(2 ---> 0) = (1/4, 4)
****where each line as projecting to another 0d point results in each line simultaneously halved and doubled.

A line resulting in a fraction results in each line, as individual lines, multiplied. Multiplication and division occur simultaneously in spatial phenomenon.

unicycle
bicycle
tricycle

recycle

-Imp

Are you perhaps thinking of the successor function S(), which plays an important part in the development of the natural number line? For the whole numbers, S() evaluates to a number which is 1 greater than the number given in the argument:

S(0) = 0 + 1 = 1
S(1) = 1 + 1 = 2
S(2) = 2 + 1 = 3
....

This is the protocol which allows us to develop the natural number line to infinity. It is certainly iterative, and I suppose one could describe it as "circular" or even "helical" in character, because with each iteration it recommences at a point 1 higher than the previous point.

alan1000 wrote: ↑Sat May 30, 2020 11:11 am ...

He is talking about ALL numbers (or integers anyway)

Which can be defined recursively (cycles).

If you have infinite memory, this recursor produces "all integers". It doesn't halt, but that's another matter. This is the Kolmogorov complexity of the Integers.

alan1000 wrote: ↑Sat May 30, 2020 11:11 am Are you perhaps thinking of the successor function S(), which plays an important part in the development of the natural number line? For the whole numbers, S() evaluates to a number which is 1 greater than the number given in the argument:

S(0) = 0 + 1 = 1
S(1) = 1 + 1 = 2
S(2) = 2 + 1 = 3
....

This is the protocol which allows us to develop the natural number line to infinity. It is certainly iterative, and I suppose one could describe it as "circular" or even "helical" in character, because with each iteration it recommences at a point 1 higher than the previous point.

No, I am thinking about the formation of numbers through the most basic method of counting, which is the line.

The line starts with point 0. This point zero projects to form the most basic quantifiable form: the line as 1 unit and -1 unit respectively (considering the line relativistically projects in both directions as one direction. The projection of 1 is the projection of -1 considering the line is relative in directions).

As the point projects again -2 and 2 results where -1/2 and 1/2 occurs simultaneously (this is considering 2 lines necessitates each line as 1/2 the original line).

The sequence continues as the line projects to another point as 3 and -3 and 1/3 and -1/3. For each projection of the point comes a projection of another line thus resulting in the number line as the projection of a point 0. All numbers, as x=x, originate with the projection of point 0 to another point 0 as (0 --> 0) and (0 <-- 0) as (0<-->0) or (0=0). The number line originates with 0.