Metaphysics is only allowed as an attempt to verbalize and articulate one's intuitions and non-verbal (visual or too abstract for concrete words) insights.
Otherwise it is just an meaningless abuse of an abstract terminology especially invented for this purpose.
There is an example
A spiral is a metaphysical symbol.
A spiral-shaped process continually builds upon what it already have done (learned). It is just capture of a growth/build-up pattern.
This very notion has been captured in Logic (implication), Math (inductive proofs) CS (inductive/recursive definitions) and even AI (intelligent agents are constantly updating its inner map (representation) of environment (observable reality).
Viewed from above a spiral-shaped process is either converges or diverges.
From math we know, that diverging processes are hopeless.
A spiral-shaped process could be
- Inductive (generalizing - an expanding spiral, it diverges).
- Deductive (specializing - contracting spiral, it converges)
Viewed (imagined) from either side it is advancing (the notion of exploration of an unknown, of creating a map of an environment).
Knowing when to stop (and backtrack) is a crucial part, otherwise it will never terminate.
All the insects and animals have this hard-wired.
The base case (for a converging, deductive process) or a heuristic (for diverging, inductive process) is needed for a diverging process, to stop it.
This is the main difference between an endless loop and a spiral.
Loop does not advance in any direction, It is just a useless petition. A waste of energy.
Mother Nature uses emotions (signals) to prevent organisms to get stuck in an endless loop (a deadlock). Robots still cannot escape loops.
Spiral is an breadth-first (or a depth-first) process which advances in some direction and a base-case (or a heuristic) which serves as a terminating condition.
Recursive process is a capture of this natural pattern. So are logical Deduction and Induction.
Most of functions which implement AI searching/back-tracking algorithms such like
A* are recursive for these very reasons.
Process are spirals. Not merely loop. Spiral is an universal shape (even symbolic, imaginary one). That is why spirals are everywhere in the outer space. There the process could be literally seen.
It from bit
One is a magic number
1 * 1 = 1, and
sqrt(1) = 1.
sqrt, by the way, is what should I multiply by itself to get x, or simply what is the length of a side of a square with area x.
If the length of the size is one
unit then the area of a square is also one
unit. Magic. But this is the definition of a
square - a unit lenght with a unit height.
One is a number of its own type (or class)
Everything else is a multiple of 1.
Zero is a number of its own class (emptiness, nothing,
1 - 1, an empty set)
Two is a magic number, it is
One more than One.
It is the first compound natural number. Pair of ones. One AND another One. A composition. A thing of its own type. Non-atomic.
Adding one to one is the same as taking one more than one time
1 + 1 = 1 * 2 - the same notion (fusion), different operations
In nature it has a symmetric shape.
x - x
How many times
How many times something is present is a fundamental question.
One time. Something just Is. The base case of multiplication.
One and One means something is present
2 times, one more than once.
One and its copy is here. Now it is a product. Product of
One and One
This is exactly the notion of
AND - simultaneous presence (no time, just location). This is what a product type is.
Emptiness means that something (which is supposed to be here) is presented
1 - 1 times. Nothing is there.
Definition of N
Each number is a
successor of another number OR
Zero, successor of
Nothing, of emptiness, of void.
Successor function is based on the notion of one more
+1, a copy, a clone.
Zero is the universal base case - nothing left
One is a
successor of void, of nothing. Everything [wik:/WhatIs what is] is one. A closure, a distinct process. Sub-process. A "spiral" so to speak.
All the numbers from
2 to infinity are compounds.
Some of them are Primes. (not multiplies of anything prior to them)
1 are not even Primes, because they are not compounds.
Binary notation is God's notation (Leibniz) - everything else comes from it - something and nothing, existence and void, signal and noise.
An intelligent observer (who updates his own internal representation of environment) who could distinguish something from nothing, existence from void, a signal from lack of it could, in principle, observe everything.
This is why information is measured in
log base 2. (how many times should I observe).
Russel - self-reference is of its own kind (type of a reference). Russel used types to solve (avoid) paradoxes.