The Nothing that Is: A Natural History of Zero - Robert M. Kaplan, Ellen Kaplan This is a book that, a few years ago, made the perfect gift for my father, who has told me that he's read it several times. And so it's the perfect book to try and polish off while I'm visiting. (Because he'll miss it if I try to sneak off with it.) (My father does this too when visiting me. We both have more books than we can keep track of.)However it was also a book which I didn't give myself enough time to read. While the book is not entirely made up of them, every now and then there would be - I have no better way to describe it - story problems. No no, don't run away in horror if you are somewhat math-phobic - you don't have to actually solve anything, and could actually just hop over those bits. But in and around those story problems were also ideas that really made me want to sit back, rethink the statements, and actually read parts over again. This is also the point at which I wanted footnotes - but I'll rant on that in a bit. But the main point here is that Kaplan is telling the history of something I'd never put much thought into, and made me rethink the way math was taught to me. Looking back I really with we'd had history of math along with math itself, but I can see why that rarely happens - there is only so much class time to get through everything.One of the things that's still causing me amazement is the idea that when the Greeks memorized complicated mathematical computations they were doing them mentally with words - because there weren't numerals in the sense we knew them, numbers to them were represented by words. (Remember the old fashioned written checks? That line where you'd write the entire amount out in word form? Think of that. Now think of using that format with all forms of mathematics.) That's a vast amount to juggle in your memory, especially if you include the fact that they also didn't use zero as a placeholder for the larger numbers.Also the book made me realize how many mathematicians from other cultures I never was introduced to, and curious to read more of their histories.I should add here that this book would have easily rated four stars (Kaplan tells history in a delightful way) if not for the citation issue. It was also a problem in that I was reading the book in paper and stopping to go online to read cites every time I was interested in one wasn't easily done - if I'd read this in ebook form with cites it wouldn't have been an issue.Citations and SourcesIn a book like this citations are a big deal - well, for me-the-reader that is, and for anyone using this as part of a paper or secondary research material. The book gives you a url to check (and seems somewhat long in this day of "we can create shortened urls") which then refers you to this page: Oxford University Press, The Nothing That Is, which provides another link to the PDF of the citations (and a link to a quiz). Which makes me wonder - were the citations not ready at the time of publication? Did Kaplan just want them in a form he could easily update? Did the publisher quibble at the length of the citations? (The book is only 225 pages, so I doubt the later.) Is a PDF really the best format for this? (That PDF of footnotes is 170 pages long - and yes, I'll read them all. I'd rather have them with the rest of the text though.) It's kinda irritating to have to check this document just to see if there's a citation somewhere, because the book gives no indication whether or not there'll be a cite, footnote, or anything. (To be fair, it's not the first to use this style of endnotes. It's just divorcing them from the paper text that seems a bit odd to me.)Easily accessible footnotes are a somewhat critical point when the author is citing multiple ancient sources in his text, and notes that there are multiple ancients who disagree on which culture came up with the concept of zero (apparently Greek, Hindu, Syrian, Chaldean - all were working on various aspects of sciences that were in the neighborhood of the idea of zero.) In this kind of situation it's helpful to know what translation an author used (whether the same translator was used for multiple sources, or whether the author translated texts himself, etc.), how easily the text is to refer to (ex, I can find it on Amazon vs. it's long out of print), etc. People who write about math are usually very adamant about exact citations - and that's not a gross generalization when these are the same folk that love their proofs.Here's a specific example that happens multiple times in the book, p. 97:"Even for those immune to superstition, zero as a number 'donnant ombre et encombre,' as a fifteenth-century French writer put it: a shadowy, obstructive number."Writers or scholars are vaguely referred to like this - if only once I'd think it might be someone nameless due to the age of the text. Without an immediate citation, I'm at sea. [If you look this up in the notes, this is referred to as "vdW 59; M 422." I'm still working out what vdW refers to - there's not a separate bibliography. The first reference to vdW in that PDF is from page 7 - but I don't see anything prior to that that could be a "acronymic reference" - feel free to help me out on this, anyone.]Source info, SHORT version: Book has an index, but no bibliography. If you want to know the texts used you must cull through the online citations - there's no stand-alone bibliography, all information is within the notes. If you use this text as a reference do make note that the paper version has cites online (your professor will thank you). I'm assuming that the ebook version has them included, since that would be logical.Mentioned in book, so interesting that it sent me googling (not in any order): Karl Lang-Kirnberg, Gerbert/Pope Sylvester II (Gerbert's aspices), Bhaskara, Diophantus, Heron, Pappus, Thymaridas, Plato's Timaeus, Petrus of Dacia, Adelard of Bath, psephos (counting stone), Al-Khowarizmi, Mahavira, Brahmagupta, James Ussher/Archibishop of Armagh, Ruth Benedict, Avicenna (autobiography of), Mancala or Kalaha (game), Manichaeism, Alexander de Villa Dei, John Sacrobosco, Filius Bonacci (Fibonacci), Nicolas Chuquet (Lyons 1484), Tally-stick, Counting board, Italy and double entry bookkeeping, Mattaus Schwartz and Jakob Fuller the Rich, Lucas Pacioli, Ulrich Wagner, Adam Riese, John Palegrave, Gregor Reisch, Nicole Oresme Bishop of Normandy, Michael Stifel, Pierre de Fermat, jeroboam, Kurt Godel, John Napier baron of Merchiston, Flann O'Brien and The Third Policeman, Gottfried Wilhelm Leibniz, Johann Bernoulli Normally I'd link all of those to wikipedia - but you can see how many there are. That all of these made me want to read more history? A positive thing.[An aside - I wasn't able to find anyone discussing these books of Kaplan in light of his other work. So I'm still unsure how I feel about this. Also assuming that Dr. Robert-Michael Kaplan is the same Kaplan who wrote the book I'm reviewing.]I was at first somewhat concerned with buying this book for my father because I noticed that Kaplan has written books on eyesight like Seeing Without Glasses. This immediately worried me that it might be along the lines of the Bates System of Eye Exercises which came out in the 1940s, but which was still kicking about in the 1970s, and apparently still around today. I have vision such that I can't see much of anything without glasses, so this sort of thing annoys me in that there are a large amount of eye conditions where the vision can't be improved. (Personal bias here: I was placed in contacts at an early age to reduce the speed at which my vision was worsening. It's somewhat inconclusive as to how much this helped or whether the amount my vision was worsening naturally slowed down - but since I now have peripheral vision with contacts I'm not complaining!) Most of us wearing glasses aren't going to be able to cure the problem with exercise. Why would it matter what other books Kaplan wrote? Well, perhaps this is my bias, but if someone was promoting something that's not proven by science in another field, I'd worry about the rigor of their research and theory in other fields. Perhaps somewhat unfair on my part to judge other books by the subject of another, but I'm skeptical that way.Quotes I enjoyed/pondered:p 31: "...The fact remains that Archimedes worked with number names rather than digits, and the largest of the Greek names was 'myriad,' for 10,000."p 37: "...Names belong to things, but zero belongs to nothing. It counts the totality of what isn't there. By this reasoning it must be everywhere with regard to this and that: with regard, for instance, to the number of humming-birds that that bowl with seven - or now six - apples. Then what does zero name? It looks like a smaller version of Gertrude Stein's Oakland, having no there there."p 38, where I miss an easy to look up citation while reading, as the Marlow reference makes me curious: "...Even an early edition of the Surya Siddhanta - the first important Indian book on astronomy - claimed the work to be some 2,163,500 years older than it has since been shown to be (though this revising wasn't made in time to excuse Christopher Marlowe, accused of atheism partly for pointing out that Indian texts predated Adam)."p 39: "...the fulfillment of every schoolboy's dream: the examiner prostrates himself before the youth and exclaims: 'You, not I, are the master mathematician!' "p. 45: "...Or was it that the Indians, like the Greeks, tended to equate wisdom, knowledge and memory, so that important matters such as mathematics were written in the memorable form of verse."p 52: "...The counting board sprinkled with green sand and blue sand that Remigius of Auxerre described in 900 AD sounds like something one would dearly love to own - but since he says that figures were drawn on it with a pointer (radius), it belongs to the same tradition, which also produced the wax tablets that Horace's schoolboy hung over his arm, and the slates that long after screeched in village schoolrooms."p 66, about Adelard of Bath, returning from many travels: "...And he brought back with him precious manuscripts, the real treasures of the East: a treatise on alchemy thinly disguised as a text on mixing pigments (though it also contained a recipe for making toffee), works on how to build foundations under water and how rightly to spring vaulted structures. He wrote a book of his own on falconry, in the form of a dialogue with his nephew."Am I the only one who wonders if that recipe for toffee was any good, and who the researcher was that bumped into it years later?!!!p 68: "...One of our commonest words for zero, 'null,' comes from the medieval Latin nulla figura, 'no number,' and a Frenchman, writing in the fifteenth century, expressed the popular view well: 'Just as the rag doll wanted to be an eagle, the donkey a lion and the monkey a queen, the zero put on airs and pretended to be a digit.' "p 70: "...Think of the situation with words and with ideas. New words are always frisking about us like puppies - one month people go 'ballistic' and the next 'postal' - but few settle in companionably over the years and fewer still reach that venerable state where we can't imagine never having been able to whistle them up, there at our bidding. ......But the Republic of Numbers is vastly more conservative than those of language or ideas: Swiss in its reluctance to accept new members, Mafiesque in never letting them go, once sworn in. Think of irrational numbers, the guilty secret of the Pythagoreans, whose exposure shook Greek confidence to the core. Twenty-five hundred years later we can't do without them, though the sense in which they exist is debated still. And imaginaries? Mathematicians, who love high-wire acts, began thinking about the square roots of numbers as far back as Heron and Diophantus, but whenever these came up as solutions of equations they were called fictitious and the equations judged insoluble. Then in the Renaissance people began to calculate them, fictitious though they were."p 85, compulsive counting: "...Some have reached accommodation with their monster: Sir Francis Galton, cousin of Darwin and the father of Eugenics, counted everything in sight and even had gloves made up for him with pistons that drove ten separate counters, so that he could unobtrusively keep track of the percentage of beautiful women in Macedonian villages while tallying up the average price of goods in their shop windows. Others have just given themselves up, like the otherwise lumpish farm-hand Jedediah Buxton, who in the eighteenth century couldn't help calculating how many hair-breadths wide was every object in his path; and who, when taken to London as a treat to see the great Garrick in a play, announced at its end precisely how many words each actor had spoken, and how many steps they had taken in their dances."p 88, Mayans and zero: "...I mentioned that the gods of the underworld, the nine Lords of the Night, were ruled by the Death God - but I didn't tell you who this death-god was: he was Zero. His was the day of the Haab when time might stop. His was the end of each lesser and greater cycle, fearful pause. Now if a human were found who could take on Zero's personna - and if he could be put to a ritualistic death - then Death would die! And this, it seems, is just what the Maya did. They had a ritual ballgame between a player dressed as one of their hero twins, and one dressed as the God of Zero. The ball was an important hostage, such as a defeated king, who had been kept for many years and was now trussed up for the occasion. The two players skillfully passed and kicked and beat him to death, or killed him in the end by rolling him down a long flight of stairs; and it was the hero twin who always won by outwitting Zero. In other such games, the loser was sacrificed. But outwitting death wasn't enough. A human would be dressed in the regalia of the God of Zero, and then sacrificed by having his lower jaw torn off. As with most religions, the failure of ritual to achieve its aim didn't alter it, since even the barbarous live in hope."