codes · craft · the Pattern seam

Every Cell Costs the Same

Two codes for the same twenty-six letters, invented within about a decade of each other. One was built by counting how often each letter turns up in English. The other was built out of arithmetic, by a blind student at a school in Paris, and does not appear to have counted anything. Measure them side by side and braille looks careless: it spends seventeen per cent more dots than its own patterns need, and nearly twice what its own cell could manage, while Morse lands within a few per cent of the best it could do. That measurement is correct and the conclusion drawn from it is wrong, and finding out why is the whole of this page.

every figure recomputed from the corpus · offline checks 55/55 · a live check runs in your browser as you read · translation by liblouis, the reference implementation

Two rulers

Type something. The same text is priced three ways at once: in braille dots, in braille cells, and in the time International Morse would take to key it. Then press the switch marked reassign for dots, which rebuilds the braille alphabet the way a Morse engineer would have, giving the commonest English letters the emptiest cells. Watch which number moves.

The dot count falls by about . The cell count does not move by one, and it cannot. A braille cell is a fixed rectangle of six dot positions, and the rectangle takes the same paper whether one position is raised or all six are. That is not an approximation, it is what the standard says in as many words. ISO 17049, the international standard for braille on signage and equipment, puts it at clause 3.1:

“A braille cell requires the space of all six nominal dots. Vacant dots shall not be neglected because they are a part of the braille pattern.”

ISO 17049:2013, clause 3.1

So the dots the rearrangement saves buy nothing you could measure with a ruler laid on the page. Morse is the other way round. Its cost is time on a wire, a dash takes three times as long as a dot, and every element you can drop is time you get back forever. There the rearrangement is worth having, and somebody had already done it.

The arithmetic nobody teaches

Braille is usually met as an alphabet in dots: one arbitrary pattern per letter, learned by rote. It is not arbitrary at all. Step through it.

The first ten letters, a to j, are built from the top four dot positions only, 1 2 4 5, and never touch the bottom row. Add dot 3 to each of those ten and you have k to t, in order, no exceptions. Add dots 3 and 6 and you have u v x y z. All three of those statements are tested rather than asserted; the verifier reads the alphabet out of liblouis and checks each one, and they come back .

The series is not short. English cannot see the rest of it

The third step above stops at five letters, and w is left sitting somewhere it does not belong. Both of those are artefacts of looking at a French system through a twenty-six letter alphabet. Braille's own scheme runs in séries of ten, and the third one is full:

So w is not stray at all. It is the tenth and last member of a perfectly regular fourth series, and its pattern, , is exactly j plus dot 6. What English braille inherited is one letter out of that entire series and half of the one before it, which is why the rule appears to break.

Why w is at the end rather than in alphabetical order is documented, and it is not the story usually told. The letter was not in ordinary French use at the time; a word that wanted one was written with a double v. The Paris institution's own historian, Edgard Guilbeau, writing in 1907, records that “le W fut ajouté sur la demande de l'Anglais Hayter, ce qui permit d'appliquer l'alphabet à la langue anglaise”: W was added at the request of the Englishman Hayter, which made it possible to apply the alphabet to English. Henry Hayter was a pupil of Braille's and the son of an English diplomat. And the reason it went on the end instead of into the sequence, as the French Ministry of Culture's own inventory dossier reconstructs it, was so that the system would not have to be partly rebuilt, so that people who had already learned it would not have to memorise changes, and so that the braille books that already existed would not have to be transcribed again.

That is a backward compatibility argument, made in a Paris classroom in the 1830s, by a man in his twenties who had been blind since he was three, and it is the reason the letter w is where it is on every braille page in the English language.

What each code costs

Now price them. Braille's cost is counted in raised dots, Morse's in the dot-length time unit that International Morse is defined in: a dot is one unit, a dash three, the gap inside a character one, the gap between characters three. For each code, the table gives what it actually costs on a real text, and what the very same set of patterns would have cost if they had been handed out to the letters in the best possible order, commonest letter to cheapest pattern.

Braille runs about above the best arrangement of its own twenty-six patterns, and about above the best twenty-six it could have picked from the sixty-three the cell allows. International Morse runs about above the best arrangement of its own. If dots and dot-times were the same kind of thing, that would be a rout.

Does the code know the language it encodes?

A blunter test. Rank the letters by how often they appear, rank them again by what they cost, and see whether the two rankings have anything to do with each other. If a code was tuned to a language, the correlation should be strongly negative: common letters, cheap codes.

Spearman rank correlation against letter frequency in Moby-Dick, with a two-sided permutation test over shuffles of the cost vector, fixed seed, so the p-values reproduce exactly. The floor of a test with that many shuffles is 1/(n+1), and a p below it is reported as below it rather than as zero.

Braille's dot count carries no relationship to English letter frequency that this test can distinguish from chance. What it is strongly related to is position in the alphabet, , which is what you would expect of a code that counts A, B, C rather than E, T, A. Both Morse codes are the opposite, and the original American one, the one Vail actually built, is the more tightly tuned of the two.

And the story about the type case is not sourced

The tuning is usually credited to Alfred Vail, with a specific and vivid anecdote: that he walked into a Morristown printer's shop and counted the letters in the type cases, finding twelve thousand e's and two hundred z's, and handed the shortest codes to the commonest letters. The numbers are quoted everywhere. They could not be traced here to any nineteenth century source.

What does exist is one passage, on page 28 of Early History of the Electro-Magnetic Telegraph, the 1914 volume of Vail's papers assembled by his son. It is a letter dated 5 December 1913 from a correspondent, reporting what a clergyman had said that Alfred Vail had told him:

“He said that it came to him like a flash one day when he was in the New York Observer office and he sat down and wrote it out, then upon his return to Morristown he went to the office of the Democratic Banner and ascertained which letters were most used, to which he applied the simplest characters.”

C. V. Smith to J. C. Vail, 5 December 1913, printed in Early History of the Electro-Magnetic Telegraph, 1914, p. 28

That is third hand, written seventy-five years after the events it describes, about a conversation with a man who had died in 1859, in a book whose purpose was to press a priority claim for Vail against Morse. It says he went to a newspaper office and found out which letters were most used. It does not mention a type case, and the famous counts are an accretion on top of it. Alfred Vail's own letters and journals, which make up the rest of that volume, do not contain the story at all.

Which is why the measurement above matters more than the anecdote. Whatever happened in Morristown, the code itself testifies: American Morse assigns its cheapest characters to English's commonest letters closely enough that a rank correlation comes out at , and the arrangement sits within a few per cent of the best one available to it. Something counted. The evidence for that is the code, not the story.

The ruler is the thing at stake

Here is the move that makes the measurement mean the opposite of what it looks like. Morse pays for what it sends. A dot is a unit of time, a dash is three, and shaving elements off the common letters shortens every message forever. Braille pays for what it occupies. The cell is a fixed footprint by definition, so a one-dot letter and a six-dot letter cost identical paper, identical page, identical volume on a shelf, and identical distance for a finger to travel.

Which means the is real and worthless. Reassigning braille's letters for dot economy would save no space at all, and it would cost something enormous, because the arithmetic is doing three jobs at once.

One decade, three jobs

Take the first ten patterns again. Put a single indicator cell in front of them and they are the ten digits: a is 1, b is 2, on to j as 0. Now slide the same ten patterns down one row inside the cell, so dot 1 becomes dot 2, dot 2 becomes dot 3, dot 4 becomes dot 5, dot 5 becomes dot 6, and they are the punctuation.

That is the payoff, and it is why the cheap patterns are not where a dot-counter would have put them. Only patterns confined to the top four dots can be slid downward at all, because dots 3 and 6 are already at the bottom and have nowhere to fall. There are exactly such patterns out of sixty-three. Braille's first decade occupies ten of them, and the ten shadows those ten cast are disjoint from the ten they occupy, which they have to be or a letter and a comma would be the same cell. Twenty patterns, spent once, buy thirty symbols.

Hand those ten slots to the ten commonest English letters instead, by dot count, and the first thing you lose is the digits, because the cheapest patterns include dot 3 and dot 6 alone and neither can be lowered. Then you lose the punctuation. Then you lose the fact that a child can derive twenty-six letters from ten. The saving, still, is zero millimetres.

Where braille does economise, and it is not subtle

None of this means braille is indifferent to size. It is obsessive about size. It simply economises at the level that costs it something, which is cells, and it does it with contractions rather than with dots. Contracted braille, “grade 2”, gives whole words and common letter groups their own cells. the is one cell. knowledge is one cell, the letter k standing alone. Run real books through the reference translator and the saving is this:

Roughly a quarter of the page, on English prose, and rather more than that in French, where the abrégé is more aggressive. It is worth noticing which English text resists contraction most: this site's own writing, at , because contractions are tuned to the common vocabulary of ordinary prose and we spend our days on words like amphidromic and Spearman.

What a book weighs

A braille page holds forty cells to a line and twenty-five lines, a thousand cells, and there is no way to put more on it, because the cell size is set by the finger and the page size by the hand. So:

This is the reason the contraction system exists and the reason the argument about it was never academic. On Moby-Dick the contractions are the difference between braille pages and , which at the standard of 160 pages to a bound volume is fewer volumes of paper, weight, shelf and cost, per book, forever.

The finger is not a small eye

Everything above follows from one physical fact, which is that touch resolves space far more coarsely than vision does, and the braille cell is sized to what a fingertip can actually resolve in a single contact. That coarseness has a consequence you can compute directly from the alphabet: braille letters sit very close together in dot space. Hover or tap a letter to see every other letter that is one dot away from it.

On average each letter of the alphabet has others exactly one dot away from it, and . A code with that little separation would be a poor choice for a noisy channel. It is a fine choice for a finger, which does not suffer random dropouts, and it is what the arithmetic costs: the decades put related letters near each other on purpose.

The cell is sized to that. The measurements below are from the two standards that actually govern it, and the acuity figures from the psychophysics literature. They are different measures on different stimuli and are not interchangeable, which is why they are in separate rows rather than a single column.

Two things fall out of that table. The gap between cells, 6.2 mm, is much larger than the gap inside one, 2.34 mm, which is what makes a cell read as a single object under a finger rather than as six loose dots. And a sighted eighty-year-old's threshold on Legge's dot chart, 2.44 mm, has just passed braille's within-cell spacing of 2.34 mm, while the blind readers in the same study showed no age decline at all across ages eighteen to seventy-four. Reading braille is not a matter of having unusually good fingers. It is a matter of having used them.

The same mistake, made for sixty years

Everything above is one error repeated: measuring a code with the ruler of a different problem. That error has a history, and it is not a small one.

What Barbier actually made

The story everybody knows is that a French artillery officer invented a dot code so soldiers could read orders at night without a lamp, that Napoleon commissioned it, and that a blind boy simplified it. Most of that appears not to be true. Philippa Campsie's 2021 study of Charles Barbier in Disability Studies Quarterly reports that the method which reached Louis Braille was never intended for the military but was designed for blind people; that Barbier did not demonstrate it at the Paris institution; that it was not used there in a phonetic version; and that Barbier and Braille met only in 1833, after Braille had already published his own system. The plainest fact against the Napoleon story is a service record: Barbier was made captain on 18 May 1792 and resigned two days later, thirteen years before Austerlitz.

Honesty about this source: the article is behind an anti-bot wall that returned 403 here, so it was read at abstract level plus Campsie's own account of the research and two independent institutional summaries, not in full. The myth is entrenched enough to appear inside otherwise careful institutional documents, sometimes contradicting their own history sections, and this page names that rather than pretending the literature is tidy.

What is not in doubt is the shape of what Barbier made and what Braille did to it. The Paris institution's historian, Guilbeau, describes Braille's alphabet as derived from Barbier's system “avec réduction du signe générateur de douze points à six”: with the generating sign reduced from twelve dots to six. Barbier's cell was two columns of up to six dots, twice the height of a fingertip's comfortable reach, and it encoded coordinates into a table rather than letters. Whether that table was five by five or six by six depends on which of the twelve different writings in Barbier's 1815 Essai you mean, and the sources genuinely disagree. Halving the cell is the whole invention: it is what makes a character something a finger takes in at once instead of something it has to travel down.

The dashes, and the book burning

Braille's first edition, in 1829, still contained horizontal strokes alongside the dots, inherited from Barbier. The 1837 second edition removed them, and Braille says why in his own preface: “Le système de musique a été refait en entier, afin d'obvier aux inconvénients du trait horizontal qui entre dans plusieurs signes de l'ancien système.” The music system was rebuilt entirely to get rid of the drawbacks of the horizontal stroke. A dash is not a dot: it needs its own width, and it breaks the one property the code has, which is that every character occupies the same box.

In 1840 Pierre-Armand Dufau became director of the Paris institution. He had decided to standardise on a smaller embossed Roman type bought from Philadelphia, and, in Guilbeau's words, “pour faire prévaloir son nouveau type, il détruisit les anciens livres, les 36 de Guillié et les 47 de Pignier”: to make his new type prevail, he destroyed the old books, Guillié's thirty-six and Pignier's forty-seven. The standard modern biography records that he forbade braille outright. Guilbeau records what happened next, which is the part worth keeping:

“Mais, si les tout jeunes enfants arrivaient à lire assez aisément le nouveau type, les aveugles âgés ne le lisaient pas du tout ; aussi l'usage du Braille fit-il de rapides progrès : les enfants se l'apprenaient hors des classes…”

Edgard Guilbeau, Histoire de l'Institution nationale des jeunes aveugles, 1907, p. 72

The very young could read the new type reasonably well; the older blind could not read it at all; so braille made rapid progress, and the children taught it to each other outside class. Dufau's assistant Joseph Guadet argued him round, and at the opening of the new building in February 1844 braille was demonstrated and restored. In his 1853 prize-giving speech Dufau referred to “l'habile et excellent Louis Braille.”

A date this page will not repeat: braille is very widely said to have been officially adopted in France in 1854, two years after Braille's death. No primary decree or institutional minute naming that date could be found, Guilbeau's 1907 institutional history records no such event, and the French Ministry of Culture's own inventory dossier says 1852. What is documented is gradual displacement across the later 1840s and a favourable declaration by the 1878 Paris international congress.

The war of the dots, and the experiment at the top of this page

In America the argument ran another sixty years and it ran the same way. The three founding schools adopted embossed Roman letters in the early 1830s; Samuel Gridley Howe at Perkins refined them in 1835 into Boston Line Type, an angular Roman alphabet with no capitals, compressed to fit more on a page. Robert Irwin, who was blind and was a principal in the fight that followed, put the reason for that choice plainly in his 1955 memoir:

“Their virtue as compared with arbitrary codes seemed to be that they could be read by sight by the seeing teachers with no special instruction.”

Robert B. Irwin, As I Saw It, American Foundation for the Blind, 1955

That is the whole error in one sentence, and it is the same error as counting dots. An alphabet was chosen for legibility to the eye of the person not reading it. Irwin is writing in 1955 as a partisan of the winning side, so read it as his verdict rather than as a quotation from the 1830s, but it is a blind educator's verdict on how the decision got made.

Then the dot systems fought each other. William Bell Wait's New York Point (1868) turned the cell on its side: two dots high, one to four dots wide, variable width, expressly to reduce bulk. And in 1878 Joel W. Smith at Perkins proposed Modified Braille, later called American Braille, which kept the standard three-by-two cell and reassigned the characters by English letter frequency.

Which is to say: the switch at the top of this page is not a thought experiment. It was a real system, it was built by a blind man who taught at Perkins, it was printed by the American Printing House for the Blind from 1893, and it competed for forty years. It lost. When the Uniform Type Committee finally settled the question after stopwatch tests on hundreds of readers across several states, and after extending the tests to Halifax where British braille was in use, English Braille was chosen, and the reasons recorded were superior punctuation, reading speed, and the sheer quantity of material already in print. Dot economy is not among them.

How bitter it got is best left to the losing side's own title page. Wait's faction published a pamphlet in 1916 called:

“New aspects of the uniform type folly: an analysis of the scheme to destroy New York Point, American Braille, Roman Line and Moon Type, together with their vast accumulated resources of every kind, secure the adoption of British Braille, and create a type trust under the control of an international committee composed of only English-speaking members, with headquarters in a foreign country.”

Library of Congress, LCCN 16014649

The American Association of Workers for the Blind adopted Revised Braille Grade 1½ in 1917, a British braille cut down to forty-four contractions. In 1932 delegates met the British Braille Committee in London and signed the agreement that produced Standard English Braille grade 2 across the English-speaking world. It had taken a hundred and three years from Braille's first edition.

Checking this against the world

A pipeline that translates books and counts cells can be internally consistent and still be measuring nothing. Three outside checks, two of which it passes and one of which it fails in an informative way.

The contraction saving. Durre's 1996 study in the Journal of Visual Impairment & Blindness reports that the widely believed 31% space saving for grade 2 is wrong and the real reduction is about 20%. For French, Laroche and colleagues (2017) cite estimates of about 40% from Lewi-Dumont and 25% to 30% from Fontaine. This page measures on English literary prose and on French, which sits above Durre and inside Fontaine's band. Both of those are abstract level readings; the full texts are paywalled and were not read here.

Volumes of a novel. NLS Specification 800 caps a bound braille volume at 160 interpoint pages. At laid-out pages, this page's Moby-Dick would bind as volumes. A 1960 braille edition of Moby-Dick is listed at seven volumes, though only in an auction record, so treat the agreement as encouraging rather than as a result.

Volumes of a Bible, which it gets wrong. The same pipeline puts the King James Bible at pages, or about volumes. Real embossed braille Bibles run to thirty-seven volumes (Lutheran Braille Workers) or around forty. The estimate is roughly a third low, and the reason is visible the moment you state it: a Bible is not set as running prose. Verse numbers, running heads, poetry layout and book divisions all cost cells that a translator handed a plain text stream never sees. The novel figure is close because a novel really is running prose. That is the boundary of what this measurement can say, found by walking off it.

One more honest gap. There is a canonical paper on whether Morse code is efficient, E. N. Gilbert's “How Good is Morse Code?” (Information and Control, 1969), which reports a mean time per letter and a comparison with optimal codes. It is paywalled and was not read here, so none of its figures are compared with these. And on the number of contractions in grade 2: the entries listed in section 10 of the 2024 Rules of Unified English Braille count to 182, but the rulebook itself states no total, and the figures of 180 and 189 that circulate are not in it.

The check