nullary
posted on 11 Nov 2019Nullary is a base-less numeric encoding. Unlike unary, which requires O(n)
symbols to encode the number n
, nullary encoding still requires just O(log(n))
symbols.
Nullary is the foundation of real numerology.
Nullary is a variant of the ‘xenotation’ described by Nick Land in his essays The Tic Xenotation and TX2.
why not use the xenotation
Tic Xenotation has an unnecessary base case.
Xenotation
----------
: -> 2
xy -> x * y
(x) -> the x'th prime
Nullary fixes this with a natural base case.
Nullary
-------
-> 1
xy -> x * y
(x) -> the x'th prime
canonical form
The expressions ()(())
and (())()
encode the same value.
The number of ways to encode a value is a key property of numbers.
Nevertheless, it is useful to have a canonical encoding. The canonical encoding is defined to be the one which places the largest factors first. This means (())()
is the canonical form of ()(())
. Another way to express this is to say that the canonical form is the first item in a lexical sort if '(' < ')'
.
forecast
Mr Land mentions an extension to identify 0 and 1:
((-P)): -> 0
(-P): -> 1
: -> 2
The idea is that ‘(-P)
’ is an operator that unwraps an expression. In this case, it is applied to ‘:
’. This formulation is unsatisfactory for a number of reasons…
For now, work some examples to get familiar with nullary. How do you encode your favorite number?
(()())(())()