This text specifies Ax, a cellular automaton for general purpose computation.
It is a work of mathematics in the public domain.
0 A noun is either an atom or a cell. An atom is any natural number.
1 A cell is an ordered pair of two nouns.
2 n refers to any atom. a, b, c, and d refer to nouns.
3 `Ξ` means to perform a rewrite as defined by this specification.
4 `→` shows the steps of such a reduction. All must be completed.
5 `?` means the reduction is undefined.
6 `:=` indicates a noun is the referent of a symbol.
7 `+` refers to the operation on the natural numbers, whose identity is 0.
8 `~` requires that n so defined be in the range (n1..n2), inclusive.
9 [a b c] → [a [b c]]
10 Symbols have no other semantics.
11 The lemmas are reduced in ordinary arithmetic; c and d refer to atoms.
This work would be impossible without the monumental efforts of Curtis Guy
Yarvin. In turn, his work is cannot be imagined without that of three
Johns: von Neumann, Conway, and McCarthy. I will thank John Nash also,
for personal reasons.
I would like to thank Josh Lauffer, my moshav in the Kabbalah, who instilled
a lifelong interest in the inherent properties of natural numbers.
Humble gratitude and love is due to any and all who have been kind to me,
during one of my manic episodes in which I was convinced that alien
intelligence was teaching me things. Whether I have succeed in my quest to
write a Kabbalistic computer is for the judgement of my peers to infer.
A special shout-out to Al, to whom much credit must incur, indeed.