The Language of a Universe

Part 4.9 gives a universe's note, the sound of its pulse. This part reads what its pulse writes. The data layer is written once, as the Pulsecore fills (Part 3.15), and that writing is a text. Read with the methods linguists and information theorists use on any text, it can be asked the questions they ask: what its alphabet is, what its words are, whether it follows the laws every language follows, and whether it says anything beyond what its rule says on its own.

Alphabet and Silence

A pulser flips every pulse, so read directly its letter would change each moment. Read against the clock, its phase set against the pulse's own parity, it holds still: a 0 or a 1 for the whole life. Between the pulsers lies the null, ∅, the Pre-Pulse Field that has never pulsed. The null is the silence between words. A Universe Word is a run of pulsers between two silences along a row of the torus, counted when it is written: on a pulse with births or folds, a run that was not there the pulse before. The first word of all is 0 → 1 → 0, the Prime Pulse.

No dictionary has to be invented for this text. A text without spaces has its words found by compression, the way Lempel–Ziv coding (Ziv & Lempel, 1977; 1978) and byte-pair encoding (Gage, 1994; Sennrich, Haddow & Birch, 2016) do. A universe writes its own spaces.

The Law Every Language Follows

In every human language a few words are used very often and most words rarely, in a fixed proportion: the word ranked r appears about 1/r^s as often as the commonest, with s close to 1 (Zipf, 1949).

Rank–Frequency Law G

n_r = n₁ / r^s

Dimensional analysis:
Where (from the book): n_r [∅], n₁ [∅], r [∅], s [∅]
[∅]
[∅] ÷ [∅]^([∅]) = [∅] ÷ [∅] = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓

The word ranked r is written 1/r^s as often as the commonest

Where:

• n_r [∅] — how many times the word of rank r was written
• n₁ [∅] — how many times the commonest word was written
• r [∅] — the word's rank, 1 for the commonest
• s [∅] — the slope, about 1 in human languages

➢ Fitted on the log of count against the log of rank over the words written at least twice.

A slope near 1 does not prove a language. George Miller showed that a monkey typing at random, with letters and a space bar, also gives a rank–frequency slope (Miller, 1957), and Mandelbrot had found its form from the cost of coding (Mandelbrot, 1953). For two letters and a silence that falls with chance p, the monkey's slope is fixed by p alone.

Monkey Exponent G

s_m = 1 + ln(1 / (1 − p)) / ln(2)

Dimensional analysis:
Where (from the book): s_m [∅], p [∅]
[∅]
[∅] + ln([∅] ÷ ([∅] - [∅])) ÷ [∅] = [∅] + ln([∅] ÷ [∅]) ÷ [∅] = [∅] + ln([∅]) ÷ [∅] = [∅] + [∅] ÷ [∅] = [∅] + [∅] = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓

The slope random typing gives, from two letters and the share of silence

Where:

• s_m [∅] — the rank–frequency slope of random typing
• p [∅] — the share of the text that is silence

➢ Miller's random-typing result for an alphabet of two letters (Miller, 1957; Mandelbrot, 1953): words of n letters are 2ⁿ in kind and each is written with chance ((1 − p)/2)ⁿ · p, so the slope is ln(2/(1 − p)) / ln 2. With little silence the monkey's slope sits just above 1.

So the slope is read against two controls: the monkey's formula for the universe's own share of silence, and the universe's own text shuffled symbol by symbol.

Predictability

A language is predictable: each word narrows the next. Shannon measured it for English by how uncertain the next letter is given the letters before it (Shannon, 1951), and program code proves more predictable still than English (Hindle et al., 2012).

Next-Symbol Uncertainty G

h_n = ℋ_n − ℋ_k

Dimensional analysis:
Where (from the book): h_n [∅], ℋ_n [∅], ℋ_k [∅]
[∅]
[∅] - [∅] = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓

How uncertain the next symbol is, given the symbols before it

Where:

• h_n [∅] — the uncertainty of the next symbol given the n − 1 before it, in bits
• ℋ_n [∅] — the entropy of the blocks of n symbols, in bits (Shannon, 1948)
• ℋ_k [∅] — the entropy of the blocks of k = n − 1 symbols

➢ Read on the drive, the written field, row by row, with the silence as a third symbol; n up to 8.

Structure Over Chance G

S = 1 − h_n / h_s

Dimensional analysis:
Where (from the book): S [∅], h_n [∅], h_s [∅]
[∅]
[∅] - [∅] ÷ [∅] = [∅] - [∅] = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓

How much more predictable the text is than itself shuffled

Where:

• S [∅] — the share of the uncertainty the text's order removes
• h_n [∅] — the next-symbol uncertainty of the drive
• h_s [∅] — the same, for the drive shuffled

➢ 0 for a text with no order beyond its letter counts, 1 for a text that is wholly predictable.

The Rule's Grammar and a Universe's Own Words

The first time the game listened, it found something that has to be separated before any universe can be said to speak: the Cell Rule has a grammar of its own. Whatever data it fills, it writes the same short words, 01, 10, 101, 1010, the rings of each wave of births as it spreads. Structure in the drive therefore shows the rule at work, not yet a universe saying anything.

The test that separates them runs the rule twice more on a window of the universe's starting field: once as it was, and three times with its blocks shuffled at the grain of its own data, the same letters and the same texture with the arrangement destroyed. The words the scrambled copies write are the rule's Core Vocabulary, shared by every universe; a word the scrambles would have written at least three times and never did is the universe's own.

Speaking Condition G

S_own − S_scr > max(ε, σ)

Dimensional analysis:
Where (from the book): S_own [∅], S_scr [∅], ε [∅], σ [∅]
[∅] - [∅] > max([∅], [∅]) = [∅] > max([∅], [∅]) = [∅] > [∅] ✓ Valid PulseCore Verified ✓

A universe speaks when its own arrangement says more than the best of its scrambles, by more than their scatter

Where:

• S_own [∅] — the structure over chance the rule writes from the universe's own starting window
• S_scr [∅] — the best of the same from three scrambled copies
• ε [∅] — the least margin counted, 0.02, a named choice
• σ [∅] — the spread of the three scrambles, their own noise

➢ Three verdicts follow: speaking, when the condition holds; grammar only, when the text is ordered but the universe's arrangement adds nothing the scrambles lack; noise, when the text is no more ordered than its shuffle.

The Codebook

With words in hand, the game reads which words wrote the places where wells and starry bodies formed, and how much more often than their share of the text. This is how the genetic code was first read: by matching what went in to what came out (Nirenberg & Matthaei, 1961). It is a match, not a cause. Stars form by the physics of Chapter 2, not by words calling a routine, and wells close together share words because they share a place; a word that turns up under many wells far apart is the finding to look for.

Cognates

Linguists date the split of two languages by the share of their core words they still hold in common (Swadesh, 1952).

Cognate Share G

c = n_s / n_p

Dimensional analysis:
Where (from the book): c [∅], n_s [∅], n_p [∅]
[∅]
[∅] ÷ [∅] = [∅]
[∅] = [∅] ✓ Valid PulseCore Verified ✓

The share of a parent's own words its child still writes

Where:

• c [∅] — the cognate share
• n_s [∅] — how many of the parent's own words the child writes
• n_p [∅] — how many of the parent's own words were compared, at least five

➢ Read only on own words, never on the rule's core vocabulary, which every universe writes.

If a lineage's vocabulary and its note (Part 4.9) drift from one cause, the cognate share should fall generation by generation at a rate that tracks the Lineage Note's drift. That is a prediction the game can test as lineages grow.

The Game's Reading

A level-25 universe started from a draw in PulseCore 8.3 wrote for 636 pulses as its Pulsecore filled: 76,396 words, 57,032 of them distinct, with silence 0.8% of the text. Its rank–frequency slope was 1.07, close to the monkey's formula for that silence, 1.01, and above its own shuffled text, 0.83. Its drive was 52% more predictable than itself shuffled. And its own arrangement said no more than its scrambled copies: grammar only. The comparisons of Part 3.16 show where speech appears: in the children, whose Pulsecores hold their parents' written data.

The Language Block

At the end of each universe the game prints its Language Block, every line of it the universe's own:

• Universe and Written: its level and lineage; whether its data was inherited or drawn, and the Genesis Seed of a draw.
• Note: its note, the accent of Part 4.9; and its dimensions, fundamental and etheric (Part 4.8).
• Alphabet: silence, 0 and 1, and the first word, 0 → 1 → 0.
• Writing and Vocabulary: how long it wrote, how many words, and its most written words, each marked as the rule's or its own.
• Tests: its slope against the monkey and Miller's formula, its structure over chance, its own arrangement against its scrambles, its cognate share, and the verdict.
• Instruction Set: each routine its engine ran or skipped, with the law that skipped it, marked inherited, new or lost (Part 3.15).
• Codebook: the words that wrote its wells and its starry bodies.
• Fingerprint: a short hash of its sixteen most written words and their counts, with its parent's beside it.

Links to Binary Pulse Theory

• Chapter 1: the Binary Pulse, 0 → 1 → 0, the first word.
• Part 3.15: the drive the text is written on.
• Part 3.16: the inherited compiler, and the test that tells speech from grammar.
• Part 4.8: the fundamental and etheric harmonics a block lists.
• Part 4.9: the note, a universe's accent.