# 42

42 is a Gödel numbering language, or set of languages, where the self-interpreter is represented by the number `42`

.

## Bootstrapping

Input the number 42 into 42, then input any other number to have it execute the corresponding 42 program.

## Properties

Not all numbers are necessarily cleanly executable as 42.

42 (when discovered) is necessarily Turing complete.

There may be many 42 languages to discover.

## Examples

### Self-interpreter

42

## Practical implementation

Even though this is a joke-language, where the joke is that a Turing complete language can bootstrap itself ex-nihilo from its Gödel number if the program represented by that number is a Turing complete language self-interpreter which contains a Gödel number mapping that ensures the value of its own code is 42 (similar to how Quines are constructed), it is nevertheless possible to implement.

### Suggested procedure

- Start with a bf self-interpreter
- Modify it so that it accepts Brainfoctal like Gödel numbers as input and converts to bf to execute
- Add bf code which maps the number 42 to the Brainfoctal value of itself + resulting interpreter

Trivial examples:

{mapped Gödel number} = 42 - {input program's Brainfoctal value} + {interpreter's Brainfoctal value}

{mapped Gödel number} = 42 if {input program's Brainfoctal value} == {interpreter's Brainfoctal value}, {interpreter's Brainfoctal value} if {input program's Brainfoctal value} == 42, else {input program's Brainfoctal value}

or some other more or less silly transform.

- Adjust by iteration / experimentation so that the resulting Gödel number is still 42

The result will be a bf program that executes 42 Gödel numbers. Feeding it `42`

executes an identical program in 42 that accepts and executes 42 programs (which will be Gödel encoded bf, in this implementation).

### Example

The implementation here is a 42 done in a slightly different way. It takes the base-9 digits of the source number as symbols of a language that consists of brainfuck plus an `eval`

that takes the number in the current cell and runs it as 42 code, such that the number 42 (written '46' in base 9) corresponds to the program `,e`

.

## Implications / Speculation verging on the mystical

There is possibly something profound hidden in this joke, that may explain how *anything* exists. Numbers can encode systems to self-interpret themselves and every other possible algorithm, because: *mathematics*... woo!

Alternatively, information theory may provide some insight into how the 6 bits `101010`

is *not* sufficient to store a self-interpreter for a Turing complete programming language...