Meet a Mathematical Inventor!

The Hélice a Calcul and its quirky creator, Jean-Antoine Lafay

The Hélice a Calcul

Click photo to enlarge

Lafay's other inventions

    But Lafay was not satisfied in making one device, as were Otis King or Fuller. He was a prolific inventor of calculation aids. His other inventions were all in the form of tables – variously called “Tableaux Graphiques”, “Tables” and “barèmes”. These go from a simple 100 X 100 table of multiplication to complex tables for calculating logarithms, trigonometric functions, and specialized calculations for various professions. the “Graphical tables” were sold inside a “Pochette curseur”, which I’d love to see – it seems from the description to have been some sort of

An enigmatic inventor

    So much for Lafay’s products; but as I said before, the man himself turns out to be a very interesting fellow.
    As to his biography, we can find (praise Google) that he was born on October 8, 1887 to a middle class family (his father was a lawyer) in Montbrison, near Lyon; and he continued to live in the vicinity the rest of his life. He was married in 1914, had two children, and worked as a chemist. He died on February 24, 1964 in Saint-Chamond.
    The Hélice a Calcul was made in three models, a pocketable No. 1 and the larger No. 2 (the one I have) and No. 2Bis. He patented the idea in 1930, and was selling them for years out of his home, first in Saint-Chamond and then in Neuville-sur-Saône. He also went to great effort to advertise the Hélice and all his other inventions, and a first look at the materials (a copy of which I received when I bought the unit) leaves a strong impression of a man with unshakable confidence in his role as a mathematician and inventor. The home address he gives invariably starts with A. Lafay, mathematician.

Meet the real Jean-Antoine Lafay

    So I decided to learn some more, and set out to read every word in the dozens of pages of instructions and brochures I’d received. Given the somewhat rusty state of my French, it took an effort – but it was well worth it. Hidden among the technical instructions and marketing copy were gems of personal narrative and opinionated rants, which expose a lot about the man’s thinking, methods and uneven career as an inventor. Here is my translation of some pertinent passages (originals can be found in the brochure and instructions).

“[I was working on] a great table that, in 100 tabbed pages, would have directly given the products of the first 20,000 numbers by the 100 first ones, in less time than it would take to feed the data into a large calculating machine ... at a price very small compared to the machine’s. But in order to complete it I’d need the certainty of having at least 100 underwriters; only three have committed support. I therefore had to abandon this project, having already suffered too many losses with my other inventions”.

 “To help small merchants and accountants to make invoices containing tax calculations, I’ve produced on quality paper a few hundred copies of series of tables for fiscal calculations; it was a fiasco [I suspect that he uses Fiasco as a bitter word play on Fiscaux, fiscal –NZ]. The tables were rapidly made obsolete by changes in the taxes, and despite costly advertising and personal visits I could not convince more than a score of clients, admittedly enthusiastic but too few to allow me to continue to serve them, despite their insistent requests.”

He then launches into this poetic diatribe:

“Oh, routine! What wrong do you not do, firstly to your devotees who, to avoid a little effort of adapting to innovative tools and processes, which would render them remarkable service, are unwilling to budge from their old deplorable habits,... and then to these poor Don Quixotes who, in believing they might overcome them, only bruise themselves against your incredible force of inertia? And yet, poor fool that I am, with the present brochure I resume a battle that I should have abandoned, moved again by the illusion that I may end up victorious.”

Get it? In my long career as an internal change agent in a large company, I have had to combat that inertia many times; I can feel for poor Jean-Antoine.

And it isn’t only the prospective customers... he had even worse experiences with professors of mathematics. Here are a few snippets from a page-long tirade:

 “[I’ve managed to secure] a list of some 3,000 members of the association of mathematics professors. I’ve sent 800 of them my diverse documents, including that about factoring numbers; I got only one confirmation of receipt. Does the execrable routine strike even among professors?”

“When I approached mathematics professors, they caused me great disappointment. ... their almost universal response was negative, formulated roughly thus: ‘the goal of our teaching is to develop the spirit and intelligence of our students, and your purely utilitarian mathematics are of no use for that; they are even harmful’.”

A few professors were more accommodating, apparently:

“Among those who had most encouraged and helped me I can mention M. Joseph Pérès, Dean of the Faculty of Sciences of Paris; MM. Jacob and Zadou-Naïsky, both associate professors of Physics, without whose support it would have been impossible for me to pursue my labors; and dear brother Antoine, of the Lazarist academy at Lyon, who ... had introduced me so warmly to the many mathematics students under his tutelage that these had entirely dispossessed me of the Hélices and Pochettes I had brought them, forcing me each time to make a second trip to content them all.”

The cold reception by most professors notwithstanding, Lafay continues to reach out:

“May I again ask Messieurs the professors of mathematics to get acquainted with this new method, then to authorize its use by their students, for whom the decomposition of numbers into their prime factors ...  is purely a headache with no intellectual benefit whatsoever?”

 “I cannot continue [to send unsolicited materials], with so little result from spontaneous mailings, which are too expensive for my poor purse, but I will send for free my entire collection of instructions and tables to such professors as would ask me to do so.”

“Unfortunately for the author, whose time is very limited, [the graphic tables] are extremely time-consuming to devise, and it would take him several years before he can publish the collection on which he is working. He would, in the meantime, receive with thanks critiques and advice that would help him make good this lengthy work. He apologizes for the poor legibility of the first tables; they were trial pieces, he will redo them.”

And he also comes clean about his qualifications:

“I take no part in teaching ... I am but a simple autodidacte, and only with great effort was I able to acquire the mathematical knowledge necessary for solving the problems I had to handle in my subsequent endeavors.”    

So now we know: Jean-Antoine Lafay was, indeed, an amateur. Working outside the educational and academic establishment, with but rare encouragement and few paying customers, he waged the battle of the lone inventor with tenacity and courage. I’ve met a number of his kind in my life, some more admirable than others, but all alike in their conviction that their idea is a great improvement on what everyone else is doing, if only they would open their eyes to see.

To Lafay’s credit, his ideas may not have revolutionized science, or made him rich, but they do express great ingenuity. He successfully produced a long-scale slide rule at an amazingly low price point; his bizarre notations, scale arrangements, and “tableaux graphiques” are truly original, and full of interesting features. It is a pity he wasn’t born in the age of the Internet: he would have made a fine startup founder!

More info:
    Here are the Hélice a calcul patent and instructions.

    And here, Lafay's brochure describing his inventions (and tribulations).

    A web page with more information and photos of Lafay's products at the site
    of the surveyors' museum in the commune of Anse, in the region where he lived.