The Third Row

For half a century, American schools for the blind fought over which of two alphabets wasted less paper. The figures thrown at the question ran from 51.75 per cent to three hundred, and not one of the men throwing them ever wrote down the geometry he was holding still. So the numbers cannot be compared with each other, and none of them has ever been checked. Here is the check. Type something and watch both codes emboss at the same scale.

What they were actually arguing about

Louis Braille’s cell is two dots wide and three tall. Every character occupies it, whether the character is e or z. In 1868 William Bell Wait, a teacher at the New York Institute for the Education of the Blind, decided that was waste. He built a cell two dots tall and one to four columns wide, and he made the width follow how often a letter turns up. He was explicit that this was the whole idea:

Let it ever be remembered, however, that comparative recurrence of letters is the primary and only consideration that can properly deterrnine the size and position of the type bodies or base forms… and a system constructed in any other way, as is the Braille and all its English and American imitations, will inevitably be unscientific in design and wasteful of money and time in practice. William B. Wait, Key to the New York Point System, 1908, foreword. (deterrnine is the scan’s optical reading of determine.)

Ten years after Wait, Joel W. Smith, a blind piano-tuning teacher at Perkins, applied the same principle inside the shape Wait had rejected. He kept braille’s cell and reshuffled which letter sat in which pattern, so that the commonest letters got the fewest dots. That was American Braille. Three codes, then, and each optimises a different quantity: Braille’s optimises neither, Wait’s optimises width, Smith’s optimises dots.

Each one can be scored against the best that its own geometry allows, which is a thing that can be computed exactly and never was.

The number that has been repeated for a hundred and seventeen years

In 1909 the Catholic Encyclopedia printed a figure, and it is the only figure from the whole dispute that states the conditions it was measured under:

Thus, in printing a font of 520 letters in each system on a perfectly uniform scale, the letter-, word-, and line-spaces being the same in each system, any Braille code (where the alphabet only is used, and no contractions or punctuation marks) requires 51.75 per cent more space than the New York Point. Joseph Stadelman, “Education of the Blind”, Catholic Encyclopedia, vol. 5, 1909. Stadelman was not a bystander: the same article records that he founded a society to publish in New York Point, and he is on the speakers’ list for that side at the New York hearings held two months earlier.

It reproduces. Take the bounding box of a braille character, two columns by three rows, and the bounding box of a New York Point character, its own width by two rows. Weight by English letter frequency. Count nothing else.

So the arithmetic is sound, and the figure is a real measurement of a real thing. The trouble is what the thing is. A page of braille is mostly not braille. The published standard puts adjacent dots inside a cell 0.092 inches apart and adjacent cells 0.245 inches apart, so 0.153 of every 0.245 is the space between characters; lines sit 0.400 inches apart around a cell 0.184 inches tall, so 0.216 of every 0.400 is the space between lines. Count the letters alone and you have priced under a third of the paper.

Put the spacing back and the number moves. How far it moves depends on choices nobody in 1909 wrote down, so here are three models, each stating its own:

Wait’s demonstration, and the two rulers in it

At the New York Board of Education hearing of 24 March 1909, Wait produced physical specimens. He had had the Gettysburg Address written out on a New York Point tablet, and the same text written at the Overbrook school on an American Braille slate, and he measured them:

The same has been done upon the New York Point tablet which I have shown you, with capitals and with full spelling. It occupies 108 square inches. The same piece done at the Overbrook School in American Braille takes 437 square inches or upwards of three hundred per cent more space than is required to do the same writing in New York Point. William B. Wait, hearing of 24 March 1909, printed in New York Point or Braille: Which Tactile Print for New York City?

The address is a text anyone can count. Encoding it in both codes, with capitals and full spelling exactly as he says, gives the character counts each specimen must have held, and his own square inches then give away the size of the dots he was comparing.

There is a tell inside his own testimony, and it needs no arithmetic at all. In the same hearing Wait gave three figures for the same pair of codes: 75 per cent, from a blackboard demonstration at sixteen times scale; 125 per cent, from machine-written specimens; and upwards of 300 per cent, from these stylus-written ones. One comparison cannot be all three unless something is moving between them. Seven years later he would accuse the Uniform Type Committee of exactly this, of having “clandestinely introduced” an expanded scale into its test sheets, inflating them by 16 per cent. He was probably right about them. He was certainly doing more of it himself.

What braille had instead of frequency

Wait called braille “unscientific in design”, and it is worth being exact about what the design actually was, because it was not nothing. Braille’s letters are not a list. The first ten use only the top four dots. The next ten are the first ten with dot 3 added. The next are the first ten with dots 3 and 6. A fourth series adds dot 6 alone, and in French it holds the accented letters. Twenty-six letters, generated by four rules, and the same ten shapes go on to serve as the digits and, dropped a row, as the punctuation.

That structure, and what it costs in dots, is the subject of an earlier layer here, Every Cell Costs the Same, which built its own corpus and its own implementation three weeks before this one. Three of its texts are three of ours. On every figure the two share, the two independent implementations agree to within four parts in a hundred thousand, the residue being 56 letters in 955,234 where the two normalisers treat ligatures and accented vowels differently. This page’s verifier checks that against the earlier layer’s committed data rather than assuming it.

Almost everyone is taught that Louis Braille left w out, because French does not use it, and that someone bolted it on afterwards. The first half is nearly right and the second half is wrong. The National Federation of the Blind’s introduction to the 1829 original is blunt about it:

Contrary to what many have been taught, Louis Braille did make room for the w; it is a ‘j’ with dot 6 added, and it belongs at the end of the fourth series. Edward T. Morman, introduction to The First Publication of the Braille Code, National Federation of the Blind.

The table above is the same claim arriving from the other direction, and it did not need the history. w is dots 2456, which is j plus dot 6, which is the tenth slot of the fourth series and not a third-decade slot at all. The arithmetic puts it where the document says it is. And the counterfactual is visible too: had w taken the third-decade slot its alphabetical position calls for, it would have displaced , which is presumably why it did not.

What actually decided it

Not paper. The Uniform Type Committee, five members, all of them blind, spent eight years testing readers in thirty-six states, and its own conclusion was that there was nothing in it:

the UNIFORM TYPE COMMITTEE, of the American Association of WORKERS for the Blind, after years of study and experiment, was convinced that the three punctographic systems — New York Point, American Braille, British Braille — are so nearly equal, so far as their general fitness to fulfill the purposes for which they were designed is concerned, as to make it impossible to demonstrate the absolute superiority of any one over that of the other two. Commission on Uniform Type to the British committee, 30 March 1916, reproduced in William B. Wait, New Aspects of the Uniform Type Folly, 1916. Wait is a hostile witness quoting an official circular; this study could not reach an independent copy.

The same letter concedes that the system they were about to choose cost more to emboss than either American one, and says plainly what the deciding argument was: “possession is nine points of the law”, and therefore “the problem is essentially a politico-economic one.” British Braille had the world’s books already printed in it.

There was a machine, too. Frank Hall built the first practical braille writer, and explained why it wrote braille:

At first it was thought by me to be of advantage to write New York ‘Point,’ but when I took into consideration that the letters of that system were not of uniform length, and that each Braille character occupied precisely the same amount of longitudinal space as any other character, I determined to attempt the easier task. Frank H. Hall, quoted in the 1909 New York Point brief. Wait’s gloss: Hall “abandoned it for the vertical Braille plan, simply because the mechanical problem involved in making a machine to write the latter was the easier of the two.”

The variable width that was supposed to save the paper is the same property that made the typewriter hard. And when it lost, New York Point was not the minority code. The 1910 census asked, and of 6,044 blind Americans who could read raised type, 3,460 read New York Point: more than twice the number reading American Braille.

Which leaves the third row. Everything New York Point actually gained, it gained by being two dots tall instead of three, and that is not a coding decision at all. It is a claim about a fingertip, and the committee tested it directly, by asking blind readers to call out the number of dots under the finger as fast as they could recognise them. Characters three dots tall were read faster, including in the parts of the country where New York Point was the system people had grown up on. Helen Keller had said the same thing in a letter to the Board of Education the year before, and she put it as a fact about her own hand rather than about paper:

It wears my reading finger more to travel over letters three dots wide and two high as they are in New York Point than over letters two dots wide and three high as they are in American Braille. Helen Keller to A. Emerson Palmer, read at the hearing of 24 March 1909.

The paper argument was worth about a third of a page, and it was won by the code that lost. The finger argument was worth the whole thing.