Georges Ifrah
I am torn about this month’s Library issue; I loved reading it, despite the many inaccuracies reported by third-party experts after its publication. The book in question is the “Histoire Universelle des Chiffres” (“From One to Zero: A Universal History of Numbers” in English) by Georges Ifrah, originally published in French, but also available in English and many other languages.
I read the second edition of this work back in 1994. The printed edition I own, shown in the cover picture of this article, is not the original one published by Robert Laffont, but a special edition for Club France Loisirs, a book-reading club I was a member of three decades ago.
So, as I said, my feelings about this book are mixed. Let me start with the positive aspects. To begin with, the work is, simply put, magnificent. This second edition is composed of two tomes, each around a thousand (!) pages long, printed in fine Bible paper.
Mr. Ifrah, a primary school math teacher, became entangled with the history of numbers after one of his pupils innocently asked one morning of 1974, “M’sieur, d’où viennent les chiffres? Qui est-ce qui a inventé le zéro?” (“Sir, where do numbers come from? Who invented the zero?”)
Embarrassment and perplexity ensued.
Mr. Ifrah reacted to his uneasy feeling by an obsessive quest to understand and catalog all the possible representations of numbers that Mankind had ever come up with. Mr. Ifrah literally quit his job and traveled, financed out of his own pocket, to Peru, Egypt, Iraq, India, China, Mexico, and wherever there was a hint of how people have represented numbers since the earliest times of humanity.
(Kids: there was no World Wide Web back then, and the early Internet was restricted to mostly university researchers and military agencies, groups Mr. Ifrah was not a member of.)
He published the first edition of his work in 1981, and a second one (the one I read 30 years ago) in 1994.
We find then, in the pages of this impressive book, the description of Inca quipus in chapter 6; the cuneiform base-60 numeric system of the Akkadian and the Sumerian, from chapters 8 to 13; Egyptian numerals in chapter 14; Greek and Roman numerals in chapter 16; Chinese numerals in chapter 21; the Maya system in chapter 22; and last but not least, a glorious homage to the major triumph of human ingenuity, the invention of Zero (a milestone shared by Indians and Babylonians), towards the end of the first part.
This history of numeric systems forms the first part of this “Histoire Universelle”. The second part contains a somewhat interesting (albeit incomplete, even by the standards of 1994) history of computing systems, from the history of Arab arithmetic to the creation of Boole’s binary algebra, to the creation of the modern digital computer.
This second part, around 400 pages long, is not as engaging as the first (at least in my opinion). If you are interested in a short yet more accurate description of the history of computers, I can recommend “A Brief History of Computing, Third Edition” instead, written by Gerard O’Regan and published by Springer in 2021.
But I digress. I would like to point out that Mr. Ifrah benefited from his fluent knowledge of Hebrew, Arab, English, and French to gather as much information as he could about the subject, and boy, there is a lot to read in these two tomes.
The popular and critical reaction to the publication of this book was phenomenal, with the English version even being named by the American Scientist’s as one of the “100 or so Books that shaped a Century of Science” in 1999. The book appeared in various bestseller lists on both sides of the Atlantic and elsewhere, and received rave reviews on TV shows and newspaper articles.
However, (and this is where the tone of this article changes), not everyone agreed on such an enthusiastic reception. In particular, experts of Sumerian, Akkadian, Egyptian, Mayan, Chinese, and Indian numerals somehow agreed in one thing: that the contents of the book are, to put it bluntly, and for the most part, wrong.
At the end of his 1995 review of the “Histoire Universelle des Chiffres”, James Ritter, historian of Mathematics at the Université de Paris Sorbonne, said:
Tout ceci rend, hélas, le livre inutilisable; quand les erreurs - de fait, d’interprétation, d’appréciation - sont tellement répandues, le lecteur non spécialiste ne peut distinguer ce qui est vrai de ce qui est possible et faux.
Translated to English:
Alas, all this renders the book unusable; when errors - of fact, interpretation, appreciation - are so widespread, the non-specialist reader cannot distinguish what is true from what is possible and false.
Ouch.
More damning still, Joseph Dauben, professor of history at the City University of New York, wrote in a two-part review of Ifrah’s magnum opus in 2002:
In 1995 a group of five experts in France agreed it was necessary to confront the popularity Ifrah’s work was being accorded and to point out explicitly his numerous misreadings, misinterpretations, and pure fabrications.
As I write these words, I am reading another work of speculative science (clearly, I love the genre): “Sapiens: A Brief History of Humankind”, a worldwide bestseller book by Yuval Noah Harari.
I am pretty sure you have heard about “Sapiens” and even seen it prominently featured on bookstores around the world. I also hope you have heard about the academic backlash that it has generated, exemplified in an article titled “The Dangerous Populist Science of Yuval Noah Harari” by Princeton psychology Ph.D. and journalist Darshana Narayanan.
We have been seduced by Harari because of the power not of his truth or scholarship but of his storytelling. As a scientist, I know how difficult it is to spin complex issues into appealing and accurate storytelling. I also know when science is being sacrificed to sensationalism. Yuval Harari is what I call a “science populist.” (Canadian clinical psychologist and YouTube guru Jordan Peterson is another example.) (…)
This may be surprising, but the factual validity of Yuval Harari’s work has received little evaluation from scholars or major publications. Harari’s own thesis advisor, Professor Steven Gunn from Oxford—who guided Harari’s research on “Renaissance Military Memoirs: War, History and Identity, 1450-1600”—has made a startling acknowledgement: that his ex-pupil has essentially managed to dodge the fact-checking process.
I cannot but to see parallels between Harari and Ifrah, both somehow privileging, as Ms. Narayanan said, storytelling to scholarship. In this sense, both “Sapiens” and the “Histoire Universelle des Chiffres” are as enjoyable to read as they are inaccurate.
(I sincerely do hope that the very publication you are reading right now does not fall into this description. Disclaimer: every effort is made, month after month, to make this text accurate and enjoyable, reviewing our sources as faithfully as possible. Despite our best efforts, every so often a mistake might slip through our keyboards. In case that happens, please excuse us, and let us know, so we can apply the correction as needed.)
Ms Narayanan is not alone in this opinion: for what is worth, both Charles Mann of The Wall Street Journal and Galen Strawson of The Guardian (from two newspapers who could not be at more opposite sides of the political spectrum) shared similar nuanced perspectives of “Sapiens”.
Can science and storytelling work together harmoniously? Can you find enjoyable examples of peer-reviewed scientific facts, told with engaging prose targeting a wider (not just academic) audience? Of course this is possible. Carl Sagan did it with “Cosmos”, just like Stephen W. Hawking with “A Brief History of Time”, and Roger Penrose’s “The Emperor’s New Mind”, to name just a few.
All the written works we have talked about so far in the “Library” section of “De Programmatica Ipsum” for the past five years are, in general, in the “must read” category. Having said that, can I recommend the reading of the “Histoire Universelle des Chiffres” by Georges Ifrah? Not really. Well, not as an academic reference, anyway.
However, if you want to enjoy a colorful description of the history of mathematics and the various ways humans have represented numbers throughout the ages, sprinkled with some academic facts here and there, be my guest. I am sure you are going to enjoy the colorful writing and the never ending series of analytic tables and illustrations, although, frankly, you will have a hard time distinguishing the wheat from the chaff.
Just like with Yuval Noah Harari, read Georges Ifrah’s words with proper care, and aware of their respective contexts. Be critical; or as IBM used to say, “think”. This is why I borrow Professor Dauben’s final statement at the end of his two-part review to end mine:
In other words, Caveat lector.
Cover photo by the author.