Amir D. Aczel (1950–2015)

I really enjoyed this book. Now what are we going to call the numerals used in the West that seem to have evolved from several sources? Arabic-Indian-Cambodian? AIC? Who knows what other cultures may have had a hand in them? Africa south of the Mediterranean countries and their near neighbors, sunken Southeast Asia?

Aczel has two main issues that he is looking into, although at time I think that they get a bit in each other's way. One is the form of the letters, and the other is the concepts of zero and infinity. He has mostly limited himself to Eurasia, with a brief side trip to Egypt. He isn't interested in the Americas because the numerals that interest him developed independently, but he does mention that the Mayans had a numeral representing zero. Interesting in view of Aczel's argument that he thinks the concept of zero originated from south Asian religion and philosophy.

That wouldn't apply to the Mayan zero, but I don't know that we know enough about indigenous American religions to say if they had the same ideas, especially with the realization that South America was much more heavily populated and had a lot more cities than we supposed. The history of Africa, particularly outside of the Mediterranean rim, is also in need of a lot more study. Similar things often develop independently around the world in any case.

Aczel includes a lot of personal information, as he is recording his search for a lost artifact that was written about in the early 2oth century. Sometimes this can get tedious, as in a certain book where the author kept going off on unrelated tangents, and filling the reader in on personal trivia. Aczel led a very interesting life, and tells his story well, so I enjoyed this. Most of his tangents related to interesting fact about famous mathematicians that were interesting in their own right, or mathematical controversies such as the arguments about Set Theory, as well as other mathematical systems that used base 60 and base 20 instead of base 10.

His father, of Hungarian heritage, was a cruise ship captain of the S. S. Theodor Herzl, named for the Hungarian political theorist, and his steward, Laci, a Hungarian mathematics student who ran afoul of the Soviets, was one of the most influential people in Aczel's life, who served as an informal tutor and developed his interest in mathematics and numbers.

A Hungarian-French mathematician named George Cœdès (another Hungarian connection) was a language teacher who discovered that he had an uncanny ability to decipher ancient scripts, and spent much of his life in Cambodia. In the 1920s and 1930s, there was a bitter linguistic debate about whether the zero originated in eastern or western Eurasia. Cœdès published a paper in 1931 arguing that the oldest zero represented by a character was on a seventh-century Cambodian inscription. on a stone marked designated as K-127, Unfortunately, it had disappeared, and with the destruction wrought by the Khmer Rouge, possibly destroyed. Aczel made it his mission to find the stone, and declared that he would spend the rest of his life trying to find it if need be. I won't ruin the suspense.

This is where the distinction between representation and concept gets a little murky. Other people's had the concept of zero, without developing a character to represent it, so one might question its tie to philosophy. They often simply left a space to represent it, which probably worked well enough to represent 20 cows, but not 2,000 soldiers. Europe and Indian weren't the only thinkers in Eurasia. An Egyptologist, Alan Gardiner suggested that the nfr hieroglyph, found in the the eighteenth century BC/BCE represented zero, although under his requirements, Aczel might dismiss it as not leading to the zero used in Western nations today. The Cambodian zero in the inscription was a round depression in a stone, part of the number 605. The Indian zero was a circle, and it is easy to see how in writing, rather than chiseling, the two characters could be interchanged.

Aczel presents an eloquent, even moving, description of the importance of the representation, especially for dealing with large numbers. It permits the same ten digits to be used to represent numbers of any size. I felt very fortunate to be one of the heirs of this system.

One of my favorite chapters was Six, in which Aczel is explaining Indian philosophy in which something can simultaneously be one both true and untrue, as opposed to Aristotelian philosophy in which something is or is not. His example is that a cup of coffee with a very small amount of sugar in it could be said to be neither sweet or unsweet. A friend long ago pointed out that Aristotelian logic doesn't really allow for something becoming. It also highlights something that has always frustrated me about the English language: the difficulty of expressing neutrality or indifference. If someone asked me if I like so-and-so, and I say "no" they are likely to assume that I dislike them, and ask what I have against them, unless I explain that I have no strong feelings or use.a double negative: "I don't dislike them," or perhaps shrug my shoulders. Yes and no stand in opposition to each other.… (meer)