# Metaphysics

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

## Spiral-shaped process

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.

and `Zero`

is `x - x`

### How many times

How many times something is present is a fundamental question. `1`

means `One`

time. Something just Is. The base case of multiplication.

the setting `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 `Zero`

times. `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)

`0`

and `1`

are *not* even Primes, because they are *not* compounds.

### Binary

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).

### Self-reference

Russel - self-reference is *of its own kind* (*type* of a reference). Russel used types to solve (avoid) paradoxes.

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