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Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers
The story of how we got our numbers told through one mathematician s journey to find zero
The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. "Finding Zero" is an adventure-filled saga of Amir Aczel s lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride.
The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero the keystone of our entire system of numbers on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves who finally reveal where our numbers come from."
The invention of numerals is perhaps the greatest abstraction the human mind has ever created. Virtually everything in our lives is digital, numerical, or quantified. The story of how and where we got these numerals, which we so depend on, has for thousands of years been shrouded in mystery. "Finding Zero" is an adventure-filled saga of Amir Aczel s lifelong obsession: to find the original sources of our numerals. Aczel has doggedly crisscrossed the ancient world, scouring dusty, moldy texts, cross examining so-called scholars who offered wildly differing sets of facts, and ultimately penetrating deep into a Cambodian jungle to find a definitive proof. Here, he takes the reader along for the ride.
The history begins with the early Babylonian cuneiform numbers, followed by the later Greek and Roman letter numerals. Then Aczel asks the key question: where do the numbers we use today, the so-called Hindu-Arabic numerals, come from? It is this search that leads him to explore uncharted territory, to go on a grand quest into India, Thailand, Laos, Vietnam, and ultimately into the wilds of Cambodia. There he is blown away to find the earliest zero the keystone of our entire system of numbers on a crumbling, vine-covered wall of a seventh-century temple adorned with eaten-away erotic sculptures. While on this odyssey, Aczel meets a host of fascinating characters: academics in search of truth, jungle trekkers looking for adventure, surprisingly honest politicians, shameless smugglers, and treacherous archaeological thieves who finally reveal where our numbers come from."
6 pages, Audio CD
First published January 6, 2015
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About the author
Amir D. Aczel
46 books152 followersAmir Aczel was an Israeli-born American author of popular science and mathematics books. He was a lecturer in mathematics and history of mathematics.
He studied at the University of California, Berkeley. Getting graduating with a BA in mathematics in 1975, received a Master of Science in 1976 and several years later accomplished his Ph.D. in Statistics from the University of Oregon. He died in Nîmes, France in 2015.
He studied at the University of California, Berkeley. Getting graduating with a BA in mathematics in 1975, received a Master of Science in 1976 and several years later accomplished his Ph.D. in Statistics from the University of Oregon. He died in Nîmes, France in 2015.
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April 19, 2020
Everything Is Not Everything
One of the enduring but fruitless debates in the philosophy of mathematics is whether or not numbers exist apart from human thought about them. This little book provides a pleasing alternative to these abstruse arguments by suggesting that numbers and the mathematics which use numbers as its raw material are a remarkable genre of religious poetry devoted to the concept of the ‘void’. The oldest form of this poetry seems to arise in the Buddhist cultures of Southeast Asia, at the latest in about the sixth century CE, and in any case well before equivalent discoveries in Europe.
The critical insight of these religious meditations is the necessity of the (at least metaphorical) existence of the Shunyata, nothingness - what modern mathematicians would come to call the empty set, or more colloquially: zero. The form of logic that led to the discovery of zero is not only fascinating in itself, but it also remains relevant for addressing one of the most persistent of modern mathematical problems: the so-called Russell Paradox. According to set theory, the set of all sets both does and does not contain itself. Clearly there is a fly deep in the mathematical ointment. But there does seem to be a solution - in the wonderfully laconic explanation by a Buddhist monk: “Everything is not everything.” Zero might just be “the womb of all the other numbers.” It just doesn’t get more poetic than that.*
Aczel tells a personal tale of historical research, philosophical exploration, and at times somewhat trying travel in an enjoyable, unpretentious, and wonderfully informative style. His asides alone - from the linguistic remnants of the old French system of base 20 counting, to the ‘topos’ of Alexander Grothendieck, a leading mathematician of the 20th century - are worth the price of admission. But his central point “that the number system we use today developed in the East because of religious, spiritual, philosophical, and mystical reasons—not for the practical concerns of trade and industry as in the West,” is a remarkable and enlightening observation... and suitably poetic.
* Interestingly the great Leibniz seems to have a similar but independent conception. According to Laplace, as quoted by Dantzig: “Leibnitz saw in his binary arithmetic the image of Creation ... He imagined that Unity represented God, and Zero the void; that the Supreme Being drew all beings from the void, just as unity and zero express all numbers in his system of numeration.“ See: https://www.goodreads.com/review/show...
Postscript: for a remarkably similar source of scientific insight in religious poetry see: https://www.goodreads.com/review/show...
One of the enduring but fruitless debates in the philosophy of mathematics is whether or not numbers exist apart from human thought about them. This little book provides a pleasing alternative to these abstruse arguments by suggesting that numbers and the mathematics which use numbers as its raw material are a remarkable genre of religious poetry devoted to the concept of the ‘void’. The oldest form of this poetry seems to arise in the Buddhist cultures of Southeast Asia, at the latest in about the sixth century CE, and in any case well before equivalent discoveries in Europe.
The critical insight of these religious meditations is the necessity of the (at least metaphorical) existence of the Shunyata, nothingness - what modern mathematicians would come to call the empty set, or more colloquially: zero. The form of logic that led to the discovery of zero is not only fascinating in itself, but it also remains relevant for addressing one of the most persistent of modern mathematical problems: the so-called Russell Paradox. According to set theory, the set of all sets both does and does not contain itself. Clearly there is a fly deep in the mathematical ointment. But there does seem to be a solution - in the wonderfully laconic explanation by a Buddhist monk: “Everything is not everything.” Zero might just be “the womb of all the other numbers.” It just doesn’t get more poetic than that.*
Aczel tells a personal tale of historical research, philosophical exploration, and at times somewhat trying travel in an enjoyable, unpretentious, and wonderfully informative style. His asides alone - from the linguistic remnants of the old French system of base 20 counting, to the ‘topos’ of Alexander Grothendieck, a leading mathematician of the 20th century - are worth the price of admission. But his central point “that the number system we use today developed in the East because of religious, spiritual, philosophical, and mystical reasons—not for the practical concerns of trade and industry as in the West,” is a remarkable and enlightening observation... and suitably poetic.
* Interestingly the great Leibniz seems to have a similar but independent conception. According to Laplace, as quoted by Dantzig: “Leibnitz saw in his binary arithmetic the image of Creation ... He imagined that Unity represented God, and Zero the void; that the Supreme Being drew all beings from the void, just as unity and zero express all numbers in his system of numeration.“ See: https://www.goodreads.com/review/show...
Postscript: for a remarkably similar source of scientific insight in religious poetry see: https://www.goodreads.com/review/show...
May 7, 2016
Amir D. Aczel's Finding Zero presents the reader with a number of challenges:
1. Poor style
2. Parochial travelogue
3. Disturbing juxtaposition of `East' and `West'
4. Dated attitude to Hindu and Jain erotic art...as well as the suggestive art of Angkor Wat
5. Fascinating history of the search for Zero
The last of these, and the main reason for reading the book, is in fact not a challenge at all, but for those interested in the history of mathematics and the origin of one of the most important discoveries in human history a pure pleasure. However, readers are required to wade through a considerable amount embarrassment to get there.
Firstly, there is the style. It isn't simply that the sentences are inelegant, but immature and stilted. Mr. Aczel was in serious need of editorial aid in this respect.
As a travelogue, the reader is treated to a series of shockingly naïve attitudes to travel in the `East' where the author is frequently shocked by the sex trade/sex slavery, pickpockets, corrupt officials, and the general shocking customs of the countries he find himself in.
Beyond this there is the vulgar attempt to correct Western arrogance about the history of science in general and the origin of Zero in particular--most of these references are very dated. Nor does the author go into the problematic designation of the scientific method originated in the 17th Century in Europe and the methodologies used in the `East' so as to formalize the process by which conclusions are arrived at. Aczel simply offers a criticism of Western arrogance with no details and comparisons that analyse the methodologies being contrasted. There is some woolly discussion about `Eastern' and `Western' logic but this doesn't really help the reader come to terms with the differences because the differences in the methodologies and ideologies are unclearly stated.
This leads into the last problem with the book--its attitude to erotic and suggestive ancient art/reliefs on temples of India and Cambodia. This was very difficult to read in the early 21st Century where everyone, wishing it or not, is exposed to some of the most extreme forms of sexuality as a matter of course on the Web.
There are many other instances in which this book would be a challenge for the typical thoughtful reader, but there is little reason in beating the point into the ground.
The only incentive for reading this book is the quest for the Eurasian origins of Zero [the earliest discovery of Zero, the author maintains, was Mayan but this was locked away in Meso-America and because of this did not impact Eurasia]. For this reason alone aficionados of mathematical history may wish to give this book a quick look, if you can go beyond its flaws.
Rating: 3 out of 5 stars
Recommended for buffs of mathematical history with a high tolerance for the above mentioned flaws.
Note:
This review was edited by the reviewer because of a threat of legal action from the author. The reason for the threat were twofold.
1. The reviewer referred to the author as Israeli and they, the author, claimed to be a Naturalized American. Mr Aczel was referred to as an Israeli because that was the nationality given on their Wikipedia page. The nationality of the author on the Wikipedia page, as of writing, was removed. Therefore, this has been removed from the review with apologies for the honest mistake.
2. The reviewer felt there was some unconscious glee taken by the author in an Anti-American sentiment the reviewer felt was presented by some actor[s] in the travelogue. This, as well, has been removed because going through a court battle on this issue seems not the most productive use of this reviewer's time and energy...and a misreading may have occurred on the part of the reviewer. It is unclear whether or not this occurred, but the author was adamant it had...hence the removal of the offending observation.
1. Poor style
2. Parochial travelogue
3. Disturbing juxtaposition of `East' and `West'
4. Dated attitude to Hindu and Jain erotic art...as well as the suggestive art of Angkor Wat
5. Fascinating history of the search for Zero
The last of these, and the main reason for reading the book, is in fact not a challenge at all, but for those interested in the history of mathematics and the origin of one of the most important discoveries in human history a pure pleasure. However, readers are required to wade through a considerable amount embarrassment to get there.
Firstly, there is the style. It isn't simply that the sentences are inelegant, but immature and stilted. Mr. Aczel was in serious need of editorial aid in this respect.
As a travelogue, the reader is treated to a series of shockingly naïve attitudes to travel in the `East' where the author is frequently shocked by the sex trade/sex slavery, pickpockets, corrupt officials, and the general shocking customs of the countries he find himself in.
Beyond this there is the vulgar attempt to correct Western arrogance about the history of science in general and the origin of Zero in particular--most of these references are very dated. Nor does the author go into the problematic designation of the scientific method originated in the 17th Century in Europe and the methodologies used in the `East' so as to formalize the process by which conclusions are arrived at. Aczel simply offers a criticism of Western arrogance with no details and comparisons that analyse the methodologies being contrasted. There is some woolly discussion about `Eastern' and `Western' logic but this doesn't really help the reader come to terms with the differences because the differences in the methodologies and ideologies are unclearly stated.
This leads into the last problem with the book--its attitude to erotic and suggestive ancient art/reliefs on temples of India and Cambodia. This was very difficult to read in the early 21st Century where everyone, wishing it or not, is exposed to some of the most extreme forms of sexuality as a matter of course on the Web.
There are many other instances in which this book would be a challenge for the typical thoughtful reader, but there is little reason in beating the point into the ground.
The only incentive for reading this book is the quest for the Eurasian origins of Zero [the earliest discovery of Zero, the author maintains, was Mayan but this was locked away in Meso-America and because of this did not impact Eurasia]. For this reason alone aficionados of mathematical history may wish to give this book a quick look, if you can go beyond its flaws.
Rating: 3 out of 5 stars
Recommended for buffs of mathematical history with a high tolerance for the above mentioned flaws.
Note:
This review was edited by the reviewer because of a threat of legal action from the author. The reason for the threat were twofold.
1. The reviewer referred to the author as Israeli and they, the author, claimed to be a Naturalized American. Mr Aczel was referred to as an Israeli because that was the nationality given on their Wikipedia page. The nationality of the author on the Wikipedia page, as of writing, was removed. Therefore, this has been removed from the review with apologies for the honest mistake.
2. The reviewer felt there was some unconscious glee taken by the author in an Anti-American sentiment the reviewer felt was presented by some actor[s] in the travelogue. This, as well, has been removed because going through a court battle on this issue seems not the most productive use of this reviewer's time and energy...and a misreading may have occurred on the part of the reviewer. It is unclear whether or not this occurred, but the author was adamant it had...hence the removal of the offending observation.
June 2, 2015
This book was comprised of rather stilted prose. I was hoping for an intriguing math book, and I do enjoy a good travel book, but I didn't fully get either. It was a solidly mediocre travel and math book. Another reviewer made a comparison of an off-brand Indiana Jones of math, and I very much got that vibe. I did enjoy the author's opening, describing how he was drawn into math at a young age.
July 29, 2015
I liked the math and history divulged in this book but wasn't too jazzed about the author's personal narrative and adventures. It's not that they were uninteresting but rather, detracted from the greater story of numbers and math.
March 27, 2015
This ponderous, self-indulgent, and anaesthetisingly dull book starts with a banal retelling Aczel's childhood before getting progressively less interesting. I am a fool for having read it.
February 7, 2015
There's nothing publishers like more than authors talking about themselves, because they think it connects them to their audience. I must admit, when it's, say, a physicist talking about their feelings about their latest discoveries, or how they travelled to yet another conference in a gorgeous location at taxpayers' expense, it makes me want to throw the book away. However there are some writers who have a genuinely interesting story to tell, and that's definitely the case with Amir Aczel's Finding Zero, a sort of 'India Jones does maths'.
There are two particularly excellent bits - the opening section, which describes the young Amir's introduction to mathematics in his highly unusual upbringing often on a cruise ship (his father was the captain), where one of the stewards (who had a sideline in smuggling) looked after him, and as a mathematician, enticed the boy into the wonders and history of mathematics. Then, later on, the latter half of the book is an attempt to find the oldest known example of zero, which disappeared many years ago, a quest that has as many ups and down as any Hollywood tale.
Although I do love the personal storytelling part, I would have liked a bit more mathematical content, but when we do get it, there's some interesting stuff about the different early number systems and the origin on the characters we use to represent numerals, which see to have come from India, but the route and the exact sources are still not clearly known.
I do have a couple of problems with the book. The big issue is that Aczel indulges in the same kind of woffly linking of Eastern philosophy and religion to scientific contents as the unfortunate Tao of Physics. The technique is to find something in ancient writing that bears a vague resemblance to modern science or maths and suggest that the ancients understood something that they clearly didn't. (This is nothing new - in medieval times it was common to think that ancient civilisations had much exotic knowledge that has since been lost.) This will put some readers off - but if you can get past it, there is much that is worth reading.
The other problem is that in trying to fight back against the early 20th century tendency to play down anything that came from the East, Aczel goes too far the other way, commenting, for instance, 'The three religions [Hinduism, Buddhism and Jainism] together give us concepts that did not arrive in the West until much later, in the late middle Ages. These concepts are zero, infinity and finite but extremely large numbers.' My issue with that is that infinity was discussed in the West since the Ancient Greeks (Aristotle, for instance, spent some considerable time on it) and you can't do better on finite but large numbers than Archimedes' magnificent Sand Reckoner, where he calculates how many games of sand it would take to fill the universe. (To his credit, when I mentioned this to Aczel he broadly agrees with the criticism.)
What is impressive, though, is the central core of the book, the search for zero. It's not only a case of hunting for the oldest known written zero, Aczel makes a convincing argument that there is something about the Eastern religions, particularly Buddhism, that make it easier to conceive the concept of emptiness, or the void, as a worthwhile concept. It doesn't seem unreasonable that this viewpoint was behind the development of that incredibly useful mathematical widget, the zero.
So, a bit of a mixed bag, but well worth overcoming a negative reaction (should you have one) to waffly Eastern philosophy bits to get to the valuable insights into the early history of mathematics.
There are two particularly excellent bits - the opening section, which describes the young Amir's introduction to mathematics in his highly unusual upbringing often on a cruise ship (his father was the captain), where one of the stewards (who had a sideline in smuggling) looked after him, and as a mathematician, enticed the boy into the wonders and history of mathematics. Then, later on, the latter half of the book is an attempt to find the oldest known example of zero, which disappeared many years ago, a quest that has as many ups and down as any Hollywood tale.
Although I do love the personal storytelling part, I would have liked a bit more mathematical content, but when we do get it, there's some interesting stuff about the different early number systems and the origin on the characters we use to represent numerals, which see to have come from India, but the route and the exact sources are still not clearly known.
I do have a couple of problems with the book. The big issue is that Aczel indulges in the same kind of woffly linking of Eastern philosophy and religion to scientific contents as the unfortunate Tao of Physics. The technique is to find something in ancient writing that bears a vague resemblance to modern science or maths and suggest that the ancients understood something that they clearly didn't. (This is nothing new - in medieval times it was common to think that ancient civilisations had much exotic knowledge that has since been lost.) This will put some readers off - but if you can get past it, there is much that is worth reading.
The other problem is that in trying to fight back against the early 20th century tendency to play down anything that came from the East, Aczel goes too far the other way, commenting, for instance, 'The three religions [Hinduism, Buddhism and Jainism] together give us concepts that did not arrive in the West until much later, in the late middle Ages. These concepts are zero, infinity and finite but extremely large numbers.' My issue with that is that infinity was discussed in the West since the Ancient Greeks (Aristotle, for instance, spent some considerable time on it) and you can't do better on finite but large numbers than Archimedes' magnificent Sand Reckoner, where he calculates how many games of sand it would take to fill the universe. (To his credit, when I mentioned this to Aczel he broadly agrees with the criticism.)
What is impressive, though, is the central core of the book, the search for zero. It's not only a case of hunting for the oldest known written zero, Aczel makes a convincing argument that there is something about the Eastern religions, particularly Buddhism, that make it easier to conceive the concept of emptiness, or the void, as a worthwhile concept. It doesn't seem unreasonable that this viewpoint was behind the development of that incredibly useful mathematical widget, the zero.
So, a bit of a mixed bag, but well worth overcoming a negative reaction (should you have one) to waffly Eastern philosophy bits to get to the valuable insights into the early history of mathematics.
March 4, 2017
Another reviewer hit the nail on the head when he described this book as "self-indulgent." That word encapsulates "Finding Zero" perfectly. A full 80% of this book is probably superfluous and has no bearing on the supposed point: the number zero. We learn where the author spent his layovers on long trips to Southeast Asia, which hotels he stayed in, what he ordered for lunch, and his sister's medical history, none of which has anything to do with numbers or zero. My wife and I were listening to the audio version in the car on a road trip, and we kept turning to each other and laughing at the frequent flagrant violations of good, tight writing. At one point I remarked to her that this manuscript wouldn't have been accepted as even a rough draft in my high school English classes -- it's all over the place, and the whole point of good writing is that the writer is taking us somewhere. Aczel, unfortunately, takes us everywhere, which ends up taking us nowhere.
Although I did find certain elements of "Finding Zero" to be interesting -- the philosophical underpinnings of zero, for instance -- I found Aczel's conclusions to be rather shoddy. For example, his whole quest to rediscover the oldest known zero was intended to prove that the zero originated in "the East" rather than "the West." Yet Aczel himself conceded several times in passing that the Mayans independently invented the concept of zero, possibly before the Hindu-Buddhist origination of the number. Yet the Mayan zero was apparently not as remarkable as the Hindu-Buddhist one, since Aczel single-mindedly hunted down the latter while ignoring the former. Why isn't the Mayan discovery of zero as great as the Hindu-Buddhist discovery?
I could go on and on, like Aczel, but I won't, unlike Aczel. In short, Aczel found a way to make a very interesting concept almost unreadable. I'm only giving it two stars instead of one because the brief examinations of the theory of numbers -- and zero in particular -- were quite interesting.
Although I did find certain elements of "Finding Zero" to be interesting -- the philosophical underpinnings of zero, for instance -- I found Aczel's conclusions to be rather shoddy. For example, his whole quest to rediscover the oldest known zero was intended to prove that the zero originated in "the East" rather than "the West." Yet Aczel himself conceded several times in passing that the Mayans independently invented the concept of zero, possibly before the Hindu-Buddhist origination of the number. Yet the Mayan zero was apparently not as remarkable as the Hindu-Buddhist one, since Aczel single-mindedly hunted down the latter while ignoring the former. Why isn't the Mayan discovery of zero as great as the Hindu-Buddhist discovery?
I could go on and on, like Aczel, but I won't, unlike Aczel. In short, Aczel found a way to make a very interesting concept almost unreadable. I'm only giving it two stars instead of one because the brief examinations of the theory of numbers -- and zero in particular -- were quite interesting.
Read
December 7, 2019Gobbled this book up, such a rich story of Aczel’s own fascination with numbers, and a wonderfully lucid explanation of why zero matters. The childhood stuff is great, and the ending, very moving.
January 17, 2015
Finding Zero is an interesting story very poorly written. The author is on a mission to find the first zero used with the so-called Arabic numerals, the familiar 0 though 9 used by most of the world. Some archaeologists have claimed that zero was a European invention; others claim Arabia as the source; others India. The author researches the claims and then goes on a search to rediscover the proof of the first Old World zero. Along the way we learn about the importance zero to modern calculations and some philosophy of mathematics, along with ties to eastern religion and the author's odd association between zero and sex.
Bottom line, if you're very interested in the subject, the book's worth reading, but I found it very hard to slog through the author's terrible prose.
Bottom line, if you're very interested in the subject, the book's worth reading, but I found it very hard to slog through the author's terrible prose.
November 6, 2018
Picked this up on a whim and I'm so glad I did. Some other readers complained that Amir would get off topic in describing his adventures, but I just loved it. I tend to have trouble remembering details unless they're embedded in narrative, and so I found Amir's storytelling to be so much more engaging and memorable than your usual mathematics nonfiction- I retained much more than usual. Amir's connection to numbers, math, and his hunt for the first zero gave new meaning to numbers for me and I look forward to reading his other books.
January 21, 2016
This book contains a little bit of interesting info about number systems. It contains a great deal of information about the author's travels which have nothing to do with mathematics or numbers. This book includes a significant amount of writing about eastern philosophy mumbo-jumbo along with much wild speculation misleadingly presented as well-reasoned fact about the role of eastern philosophy in the development of the concept of zero and infinity.
September 16, 2020
The origins of our numbers, of our decimal place value system, of our numerals, is certainly an interesting topic! After all, we take for granted that we write numbers the way we do today—most of us learned Roman numerals as kids and quickly realize they are clunky and formidable as we try to write the year we were born (although anyone born after 2000 has a much easier time of it now!). But Amir Aczel was curious about the origins of our number system, and in particular its linchpin of zero. Finding Zero is his very personal story of searching for evidence that the earliest known use of what became our zero symbol was in what is now Cambodia.
Aczel opens the book by describing his childhood aboard the cruise ship his father captained across the Mediterranean. Here, his father’s steward fostered a love of mathematics. Now, as a professor of mathematics in the United States, Aczel still dreamed of the origins of our numbers. Eventually he took a trip to India, which was basically the birthplace of the Arabic numerals we use today, to visit some of the oldest known examples of zero. Finally, he discovered the work of Georges Cœdès, an anthropologist who had previously noted the presence of a 0-like symbol in a Khmer inscription on a stele. The actual artifact, however, went missing during the Khmer Rouge’s destruction of Cambodia’s cultural history. Aczel’s story climaxes with his trip to Cambodia to find this artifact—if it still exists.
Often when a writer includes personal anecdotes, it’s relatable and interesting. I can’t say the same for this book. I was so interested in hearing Aczel talk about the properties of zero and why it’s important, but I could have done without the discussion of his childhood, etc. While it’s ultimately his choice how he decides to tell this story, it isn’t satisfying to me, and it’s quite self-aggrandizing. Aczel seems to see himself as a mathematical Indiana Jones on an epic quest to find the first 0. This is less about his discovery and more about his discovery. I would be much more tolerant of that if the writing were better—to be clear, I don’t think Aczel is doing anything wrong by writing this in a memoir form. I applaud him for trying to make the history of mathematics into an intense, exciting quest. Similarly, this book sheds light on the bias of Western mathematicians, the way we have shunned or dismissed the contributions of Asian—particularly south Asian—mathematics. Aczel does his best to explain how the inscription fits into what was a vibrant, advanced culture; similarly, he asserts the importance of making sure that the inscription survives and remains in Cambodia. These are laudable attitudes.
But honestly, there are better books about zero. Although 20 years old now, Charles Seife’s Zero: The Biography of a Dangerous Idea remains my favourite book about this number. Seife certainly doesn’t go into the same level of detail that Aczel devotes to tracking the origin of the 0 symbol, that’s true. He basically attributes it to India and leaves it at that. Nevertheless, Seife’s book is so rich in history and ideas—and very well-written.
Moreover, it’s worth noting that in the years since this book was published, the Bahkshali manuscript has been carbon dated. Aczel mentions this manuscript in his book—it contains some of the suspected earliest examples of a 0 symbol in India. At the time he wrote the book, no one had been allowed to extract samples from the manuscript to date it for fear of irreparably damaging the fragile artifact. I guess that changed, and the results are in: pars of the manuscript pre-date, by several centuries, the inscription Aczel rediscovered in Cambodia. So Finding Zero is also somewhat out of date in this respect.
This is not a bad book, but it also isn’t one I would recommend. The mathematics are explored elsewhere in more detailed and interesting ways. And as much as I applaud Aczel’s adventurous spirit, I didn’t enjoy the way he told the story of his quest for the 0 symbol. I had hoped for a lot more here.
Originally posted on Kara.Reviews, where you can easily browse all my reviews and subscribe to my newsletter.
Aczel opens the book by describing his childhood aboard the cruise ship his father captained across the Mediterranean. Here, his father’s steward fostered a love of mathematics. Now, as a professor of mathematics in the United States, Aczel still dreamed of the origins of our numbers. Eventually he took a trip to India, which was basically the birthplace of the Arabic numerals we use today, to visit some of the oldest known examples of zero. Finally, he discovered the work of Georges Cœdès, an anthropologist who had previously noted the presence of a 0-like symbol in a Khmer inscription on a stele. The actual artifact, however, went missing during the Khmer Rouge’s destruction of Cambodia’s cultural history. Aczel’s story climaxes with his trip to Cambodia to find this artifact—if it still exists.
Often when a writer includes personal anecdotes, it’s relatable and interesting. I can’t say the same for this book. I was so interested in hearing Aczel talk about the properties of zero and why it’s important, but I could have done without the discussion of his childhood, etc. While it’s ultimately his choice how he decides to tell this story, it isn’t satisfying to me, and it’s quite self-aggrandizing. Aczel seems to see himself as a mathematical Indiana Jones on an epic quest to find the first 0. This is less about his discovery and more about his discovery. I would be much more tolerant of that if the writing were better—to be clear, I don’t think Aczel is doing anything wrong by writing this in a memoir form. I applaud him for trying to make the history of mathematics into an intense, exciting quest. Similarly, this book sheds light on the bias of Western mathematicians, the way we have shunned or dismissed the contributions of Asian—particularly south Asian—mathematics. Aczel does his best to explain how the inscription fits into what was a vibrant, advanced culture; similarly, he asserts the importance of making sure that the inscription survives and remains in Cambodia. These are laudable attitudes.
But honestly, there are better books about zero. Although 20 years old now, Charles Seife’s Zero: The Biography of a Dangerous Idea remains my favourite book about this number. Seife certainly doesn’t go into the same level of detail that Aczel devotes to tracking the origin of the 0 symbol, that’s true. He basically attributes it to India and leaves it at that. Nevertheless, Seife’s book is so rich in history and ideas—and very well-written.
Moreover, it’s worth noting that in the years since this book was published, the Bahkshali manuscript has been carbon dated. Aczel mentions this manuscript in his book—it contains some of the suspected earliest examples of a 0 symbol in India. At the time he wrote the book, no one had been allowed to extract samples from the manuscript to date it for fear of irreparably damaging the fragile artifact. I guess that changed, and the results are in: pars of the manuscript pre-date, by several centuries, the inscription Aczel rediscovered in Cambodia. So Finding Zero is also somewhat out of date in this respect.
This is not a bad book, but it also isn’t one I would recommend. The mathematics are explored elsewhere in more detailed and interesting ways. And as much as I applaud Aczel’s adventurous spirit, I didn’t enjoy the way he told the story of his quest for the 0 symbol. I had hoped for a lot more here.
Originally posted on Kara.Reviews, where you can easily browse all my reviews and subscribe to my newsletter.
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December 19, 2020Interesting ~ I enjoy numbers.
December 4, 2016
This is not really a book about math, as an abstract topic of human thought. However, it is a book about math, in the sense of the human custom and tradition of thinking about numbers and logic. Not just in the sense that it involves the author's personal quest to find the first-ever known use of the numeral zero (in the Old World), but also in the sense that it involves people who, like mathematicians, way overthink things.
This isn't to say that it isn't fun reading, or even of intrinsic interest. The idea of having a symbol, a numeral, that represents the absence of anything, is not nearly as intuitive as having numerals for the positive values. However, having a numeral for zero is more or less necessary in order to have a positional numbering system, where the same numeral 5 could be used to mean five, or fifty, or five hundred, depending on how many zeroes you put after it. It's easy for us to think of this as an obvious step, but the example of Roman numerals shows that it is not, and you don't want to try to do multiplication or division with Roman numerals. It's not too much of a stretch to say that you must have a numeral 0 before you can have all of modern science and the technology that goes with it.
Thus, when Amir Aczel decides to become obsessed with finding K-127, an artifact of the ancient Khmer civilization that is the oldest known instance of a use of a numeral for zero (not counting the Mayans, whose use of a zero cannot have been the basis for our use of it for obvious reasons), it is not too hard to see how he could find the topic intriguing. However, Aczel shows us the kind of mindset that makes a person decide to get into math, not just as a way to balance your checkbook or calculate the tip at a restaurant, but as a way of filling your mental life. He thinks about numbers, a lot. He is delighted that the arbitrary number given to this artifact by it's discoverers, 127, is a prime. My God, it's even a Merseinne prime (look it up). He thinks that kind of thing is really cool. Well, it is, but really the fun part of this book is not the actual content, it's how excited and passionate Aczel is about it.
Reading this book is a lot like taking a course in a topic you're not that into, but the teacher is so excited about it that their excitement kind of rubs off on you. I like the idea that there exists (or existed, he is recently deceased) a person who was so excited about the concept of zero that he travels around the planet looking for evidence of where and when it developed. He becomes convinced that the discovery (invention?) of the concept of zero is related to the Buddhist and Hindu concept of "sunyata", often translated into English as "emptiness". He does a lot of talking to people about Eastern philosophy and religion and how its history differs from Western philosophy and religion. He looks around a lot of old temples in southeast Asia. He talks to many different bureaucrats, and despite the fact that the Khmer Rouge trashed a lot of ancient Cambodian artifacts, he finds the one he is looking for, and rescues it from oblivion.
If you find a person's obsession with something that doesn't really, at this point in the game, matter (we have the concept of zero, and don't need this particular artifact to remember it) to be just pointless, then this book may not be for you. I, however, think you have to spend your life in pursuit of something, and obsessing over a piece of mathematical and cultural history, in a way that leads you into many different countries and conversations with a lot of different and interesting people, is a pretty good use of it.
This isn't to say that it isn't fun reading, or even of intrinsic interest. The idea of having a symbol, a numeral, that represents the absence of anything, is not nearly as intuitive as having numerals for the positive values. However, having a numeral for zero is more or less necessary in order to have a positional numbering system, where the same numeral 5 could be used to mean five, or fifty, or five hundred, depending on how many zeroes you put after it. It's easy for us to think of this as an obvious step, but the example of Roman numerals shows that it is not, and you don't want to try to do multiplication or division with Roman numerals. It's not too much of a stretch to say that you must have a numeral 0 before you can have all of modern science and the technology that goes with it.
Thus, when Amir Aczel decides to become obsessed with finding K-127, an artifact of the ancient Khmer civilization that is the oldest known instance of a use of a numeral for zero (not counting the Mayans, whose use of a zero cannot have been the basis for our use of it for obvious reasons), it is not too hard to see how he could find the topic intriguing. However, Aczel shows us the kind of mindset that makes a person decide to get into math, not just as a way to balance your checkbook or calculate the tip at a restaurant, but as a way of filling your mental life. He thinks about numbers, a lot. He is delighted that the arbitrary number given to this artifact by it's discoverers, 127, is a prime. My God, it's even a Merseinne prime (look it up). He thinks that kind of thing is really cool. Well, it is, but really the fun part of this book is not the actual content, it's how excited and passionate Aczel is about it.
Reading this book is a lot like taking a course in a topic you're not that into, but the teacher is so excited about it that their excitement kind of rubs off on you. I like the idea that there exists (or existed, he is recently deceased) a person who was so excited about the concept of zero that he travels around the planet looking for evidence of where and when it developed. He becomes convinced that the discovery (invention?) of the concept of zero is related to the Buddhist and Hindu concept of "sunyata", often translated into English as "emptiness". He does a lot of talking to people about Eastern philosophy and religion and how its history differs from Western philosophy and religion. He looks around a lot of old temples in southeast Asia. He talks to many different bureaucrats, and despite the fact that the Khmer Rouge trashed a lot of ancient Cambodian artifacts, he finds the one he is looking for, and rescues it from oblivion.
If you find a person's obsession with something that doesn't really, at this point in the game, matter (we have the concept of zero, and don't need this particular artifact to remember it) to be just pointless, then this book may not be for you. I, however, think you have to spend your life in pursuit of something, and obsessing over a piece of mathematical and cultural history, in a way that leads you into many different countries and conversations with a lot of different and interesting people, is a pretty good use of it.
November 2, 2015
The early parts of this book, in which the author discusses his early introduction to mathematics really grabbed me. And I found his central argument that the concept of zero was essentially an outgrowth of eastern philosophy and religion intriguing. But sometimes I felt that point was stretched a bit.
It wasn't exactly a travel narrative, and not exactly a mathematics book, either. Non mathematicians won't find it very intimidating. But there were moments of drama that seemed a bit exaggerated, and I never really felt that the central artifact being sought was ever truly lost.
A particularly interesting section was the one that described the life and work of George Cœdès. But overall, I got the feeling that the author got to travel a lot (his grant was mentioned several times in the main text) and really needed to write something up about it.
It wasn't exactly a travel narrative, and not exactly a mathematics book, either. Non mathematicians won't find it very intimidating. But there were moments of drama that seemed a bit exaggerated, and I never really felt that the central artifact being sought was ever truly lost.
A particularly interesting section was the one that described the life and work of George Cœdès. But overall, I got the feeling that the author got to travel a lot (his grant was mentioned several times in the main text) and really needed to write something up about it.
January 26, 2020
The parts of the book that actually talked about the mathematical history were interesting.
But the rest—a memoir / travelogue—wasn’t great. The writing is stilted, at times literally repeating previous sentences from other sections. And there were cultural attitudes that were problematically interwoven with the history, and which unfortunately made all the claims made (even the ones that were more in the realm of mathematics) suspect. I assume the author was trying to make the story more relatable / engaging for his readers, but it needed a strong editorial hand to help shape the final form.
But the rest—a memoir / travelogue—wasn’t great. The writing is stilted, at times literally repeating previous sentences from other sections. And there were cultural attitudes that were problematically interwoven with the history, and which unfortunately made all the claims made (even the ones that were more in the realm of mathematics) suspect. I assume the author was trying to make the story more relatable / engaging for his readers, but it needed a strong editorial hand to help shape the final form.
November 8, 2014
I am not a math person but the writing was interesting and I learned as I read. Since I teach history I thought, "I will read it through quickly and pass it on to one of our math teachers". To my surprise , once I got into the book I had to find out what happened next. After 2 days of trying to walk away from it, I finished it. Thoroughly enjoyed it.
January 7, 2024
I was slightly disappointed by this book. I had hoped to read a book about mathematics and the history of the number 0. This book tells the story of the authors search for one of the first written zeros. Still an interesting story, but there was a lot of personal narrative that I personally wouldn't have needed.
November 16, 2017
The book has brought me to a new level of understanding and appreciation for our decimal number system. It is a fascinating book.
February 7, 2024
This is a story about a man's personal quest to find a stone tablet with the earliest known inscription of the number zero. But, as soon as he finds it, he brags to the closest person within earshot, and they end up taking credit for the re-discovery. This makes him so butthurt that he wrote this entire book overemphasizing just how important the object, the journey, and his life is. Though it was an easy read, I can't say I'd recommend this to anyone.
August 16, 2024
Fascinating look at the origins of the number 0. Also the rediscovery of the first known written zero on a Cambodian stele from the 7th century and its restoration to its proper place in the Cambodian Museum.
January 5, 2019
One of the best books I've ever read. When I finished I thought I was going to have to read it again because I couldn't find a new title that I wasn't afraid would be a total let down after this one.
February 4, 2025
Not smart enough for the math but the adventure was interesting!
September 12, 2020
You know those book reviews that tend to read more like someone's blog? The ones that are full of personal details that seem relevant to a certain degree to the subject matter of a particular book or author but ultimately loses sight of the fact that they are supposedly writing a review? Well, this book, "Finding Zero," by Amir D. Aczel is very similar to reading one of those. The book cover and its inside jacket description all tell you about what the book is about but ultimately what you get is something else entirely.
Evidently, this book is about discovering the origins of the concept of zero. So, in a way it's actually a book about nothing. Frankly, this is exactly what I felt that I got, not much at all, or rather more specifically, a whole lot about nothing. Overall, I found the writing here stilted and bumbling and contained little substance. It is far more chatty and conversational than I would have anticipated for such a subject as this. For me, it comes across more like raw unedited journal entries than a clear and concise work. Admittedly, it's full of passion for the subject matter but ultimately provides far more content on hotel stays, taxi rides, food, and some rather narrow views about the social conditions found in certain underdeveloped countries. But what about Zero, Amir?
Yes, the book does contain some brief historical background on the subject, as well as a few theories about its origins and, of course, math. The author is a mathematics professor, after all. Only, in my opinion, he should stick to his day job and leave off writing books if this is the kind of work he puts out.
After eventually slogging through this man's miserable effort at researching the subject of zero, I made a quick lookup on the internet and found that the Wikipedia page for this subject has a far more comprehensive amount of information there than this book could ever hope to. It also has far more impressive notes and sources (one of which is actually the author himself!). Whereas, as sources for his book Amir tended to interview random stray tourists and other assorted novices of unrelated fields, like art dealers, (oftentimes more than once). Ultimately, by this lackadaisical manner of researching, the author completely lost all my trust and I essentially ended up questioning nearly everything he states as a fact in this book.
However, the biggest problem for me was the narrative itself. I patiently sat through all of his memoirs and childhood stories of his family and friends in the beginning of the book because eventually he connects it all to his passion for numbers. It's not that gripping or terribly interesting but it's relevant. Only, this book never really progresses beyond this informal approach. He strays so far from the main subject of zero in this quest of his that I became increasingly frustrated with the book's focus. I mean, I've absolutely no interest in how he got a palatial hotel room I India for the price of a standard hotel room in the States. Yes, very nice. Everyone likes and appreciates a deal, including William Shatner, but really? Does it have a place here in this book about discovering the origins of the concept of zero?
Sometimes, rather than just prattling on about something completely irrelevant he charges ahead into the matter at hand and takes us absolutely nowhere. Literally! At one point he sets off in quest of a particularly intriguing and fabled archeological artifact but after hearing about his hotel room experience, taxi rides, etc. at great length along the way...he does NOT even find it! Why even bother telling us about the journey if you know that it ends up in failure? Naturally, I will allow that it could warrant a mention in a paragraph or two as an incidental anecdote but to stretch out this episode into a whole chapter is beyond reason and more than just being anticlimactic, it's downright maddening. At least it was for this particular reader.
Ultimately, the author does not adequately answer the question as to the origins of the concept of zero. He does try. He strongly suspects where it may lie, as well as discounts all other competing theories. He makes a fair and convincing case but does not conclusively prove anything by way of his reasoning. To be fair, based on the available evidence left to us I'm not sure anyone can.
To his credit, however, he does track down an ancient stone tablet that has the first instance of a zero being used. Only, it's not actually his discovery but rather a rediscovery of another man's work. (It was lost, or rather severely misplaced, during the upheaval of a cultural revolution in Cambodia.) For his rescuing of this artifact from obscurity, we can be thankful to him but the story behind it all could have been more mercifully summed up in a more relevant account, without all the excess chaff!
I won this book in a Goodreads giveaway in exchange for an honest review.
Evidently, this book is about discovering the origins of the concept of zero. So, in a way it's actually a book about nothing. Frankly, this is exactly what I felt that I got, not much at all, or rather more specifically, a whole lot about nothing. Overall, I found the writing here stilted and bumbling and contained little substance. It is far more chatty and conversational than I would have anticipated for such a subject as this. For me, it comes across more like raw unedited journal entries than a clear and concise work. Admittedly, it's full of passion for the subject matter but ultimately provides far more content on hotel stays, taxi rides, food, and some rather narrow views about the social conditions found in certain underdeveloped countries. But what about Zero, Amir?
Yes, the book does contain some brief historical background on the subject, as well as a few theories about its origins and, of course, math. The author is a mathematics professor, after all. Only, in my opinion, he should stick to his day job and leave off writing books if this is the kind of work he puts out.
After eventually slogging through this man's miserable effort at researching the subject of zero, I made a quick lookup on the internet and found that the Wikipedia page for this subject has a far more comprehensive amount of information there than this book could ever hope to. It also has far more impressive notes and sources (one of which is actually the author himself!). Whereas, as sources for his book Amir tended to interview random stray tourists and other assorted novices of unrelated fields, like art dealers, (oftentimes more than once). Ultimately, by this lackadaisical manner of researching, the author completely lost all my trust and I essentially ended up questioning nearly everything he states as a fact in this book.
However, the biggest problem for me was the narrative itself. I patiently sat through all of his memoirs and childhood stories of his family and friends in the beginning of the book because eventually he connects it all to his passion for numbers. It's not that gripping or terribly interesting but it's relevant. Only, this book never really progresses beyond this informal approach. He strays so far from the main subject of zero in this quest of his that I became increasingly frustrated with the book's focus. I mean, I've absolutely no interest in how he got a palatial hotel room I India for the price of a standard hotel room in the States. Yes, very nice. Everyone likes and appreciates a deal, including William Shatner, but really? Does it have a place here in this book about discovering the origins of the concept of zero?
Sometimes, rather than just prattling on about something completely irrelevant he charges ahead into the matter at hand and takes us absolutely nowhere. Literally! At one point he sets off in quest of a particularly intriguing and fabled archeological artifact but after hearing about his hotel room experience, taxi rides, etc. at great length along the way...he does NOT even find it! Why even bother telling us about the journey if you know that it ends up in failure? Naturally, I will allow that it could warrant a mention in a paragraph or two as an incidental anecdote but to stretch out this episode into a whole chapter is beyond reason and more than just being anticlimactic, it's downright maddening. At least it was for this particular reader.
Ultimately, the author does not adequately answer the question as to the origins of the concept of zero. He does try. He strongly suspects where it may lie, as well as discounts all other competing theories. He makes a fair and convincing case but does not conclusively prove anything by way of his reasoning. To be fair, based on the available evidence left to us I'm not sure anyone can.
To his credit, however, he does track down an ancient stone tablet that has the first instance of a zero being used. Only, it's not actually his discovery but rather a rediscovery of another man's work. (It was lost, or rather severely misplaced, during the upheaval of a cultural revolution in Cambodia.) For his rescuing of this artifact from obscurity, we can be thankful to him but the story behind it all could have been more mercifully summed up in a more relevant account, without all the excess chaff!
I won this book in a Goodreads giveaway in exchange for an honest review.
March 28, 2017
Seemed to me like it spent more time telling you how cool the author's life is than about math. Felt like a vanity book, there are better things to read if you're interested in math.
July 29, 2019
An archeological adventure mixed with mathematics. This book made mathematics interesting and (mostly) understandable for someone who never enjoyed or understood math. The quest to find the first zero was mixed with interesting historical anecdotes and the journey through south east Asia was visually descriptive. Very well written about a topic that is far more interesting than you would expect!
July 25, 2019
Numbers are mysterious. Indeed, the more we try to understand them, the more mysterious they become. Yet there is no doubt that without them, the world as we know it would be the poorer. This book attempts to explore some of the concepts and ideas relating to numbers, and present them in a more or less accessible format for the ordinary reader.
Aczel frames his narrative in a kind of personal autobiography relating to his lifelong fascination with numbers. This is the dominant narrative arc of the book, and it includes some of the fascinating aspects of what numbers are and can reveal about themselves. What the reader gets in these is a basic inkling of what has become known as Number Theory (one of the many sub-divisions of Mathematics) — relatively easy enough to stimulate interest, but also an area where some of the most difficult and mind-expanding abstractions can be explored by those talented and adept enough to do so.
The biographical element becomes particularly relevant in that it deals eventually with Aczel’s adventures relating to an engraving on a particular Cambodian artefact known as K-127 which, if located, would establish the earliest date for the appearance of the symbol 0 as a place-holder in the way we now write numbers. That date would be some 200 years earlier than the oldest Indian engraving of such a place-holder. This book provides the result of that search.
I feel that the term “place-holder” might need some clarification (apologies for those who don’t need it). In our decimal system we use only nine separate symbols (1,2,3,4,5,6,7,8,9) for counting; for larger numbers we need to introduce the idea of a number occupying a “place”. Starting from the right hand side of the number and moving backwards, the first place is meant to represent the “unit” position, the next position left of that is the “tens” position, then the third is the “hundreds”, and so on, each place towards the left increasing by a power of ten. For example, the number 4682 stands for: 4 thousands, plus 6 hundreds, plus 8 tens, plus 2 units. All this is well and good so long as we can use one of our nine symbols. What is missing here, however, is to cover the situation when a particular “position” does not contain any of our nine symbols — and this is where the use of the symbol 0 comes in: it is used to “hold the place”, meaning that the position it holds contains none of the nine regular symbols for counting.
But there is also another use for the 0 symbol, and that is in the so-called “number line” where it is used to indicate a “number” location half way between –1 and +1. Here the 0 is used more like a regular number, and is an important element relating more to analytical and coordinate geometry, which has no real connection to the idea of it being a place-holder. On another tack, the “number line” idea does bring the idea of “infinity” into the picture — and that is another question altogether for which there are many questions, but few answers so far…
Another element of this book, however, is dedicated to finding out the origins of numbers, and it is here that I find problems.
It is all very well to clearly identify scientifically the earliest western inscription using 0 as a place-marker (the Mayans had used a symbol for this way earlier); but in trying to identify this as the symbol from which all things numerical arose, Aczel brings in the concepts more readily accommodated in eastern philosophical discourses where the love of paradoxes to illustrate the limitations of rational thinking is paramount. There we will find such written statements as “Nothing is not nothing” and logical elements which eschew simple black and white distinctions (one example in evaluative thinking is that whereas in much western logic we might find statements such as: “[proposition] A is either true or not true”, eastern logic might posit instead: “A is EITHER true or not true, OR both true and not true, OR neither true nor not true.”). Epistemic concerns, yes; but what this might have to do with the origins of numbers eludes me.
Aczel seems to be arguing that, since the earliest use of a 0 place-holder symbol seems to have originated in the East, then perhaps eastern mysticism, with its use of symbols and metaphors and logical paradoxes might provide some answers to the question of origins. If 0 = nothing, and nothing is not nothing, then perhaps everything comes from nothing, and so 0 might be considered as the origin of everything, including all numbers? Sadly, I can’t help feeling that such “answers” aren’t answers at all. I would suggest that the origin of numbers began with the first symbol used by humans to represent the number 1.
Aczel frames his narrative in a kind of personal autobiography relating to his lifelong fascination with numbers. This is the dominant narrative arc of the book, and it includes some of the fascinating aspects of what numbers are and can reveal about themselves. What the reader gets in these is a basic inkling of what has become known as Number Theory (one of the many sub-divisions of Mathematics) — relatively easy enough to stimulate interest, but also an area where some of the most difficult and mind-expanding abstractions can be explored by those talented and adept enough to do so.
The biographical element becomes particularly relevant in that it deals eventually with Aczel’s adventures relating to an engraving on a particular Cambodian artefact known as K-127 which, if located, would establish the earliest date for the appearance of the symbol 0 as a place-holder in the way we now write numbers. That date would be some 200 years earlier than the oldest Indian engraving of such a place-holder. This book provides the result of that search.
I feel that the term “place-holder” might need some clarification (apologies for those who don’t need it). In our decimal system we use only nine separate symbols (1,2,3,4,5,6,7,8,9) for counting; for larger numbers we need to introduce the idea of a number occupying a “place”. Starting from the right hand side of the number and moving backwards, the first place is meant to represent the “unit” position, the next position left of that is the “tens” position, then the third is the “hundreds”, and so on, each place towards the left increasing by a power of ten. For example, the number 4682 stands for: 4 thousands, plus 6 hundreds, plus 8 tens, plus 2 units. All this is well and good so long as we can use one of our nine symbols. What is missing here, however, is to cover the situation when a particular “position” does not contain any of our nine symbols — and this is where the use of the symbol 0 comes in: it is used to “hold the place”, meaning that the position it holds contains none of the nine regular symbols for counting.
But there is also another use for the 0 symbol, and that is in the so-called “number line” where it is used to indicate a “number” location half way between –1 and +1. Here the 0 is used more like a regular number, and is an important element relating more to analytical and coordinate geometry, which has no real connection to the idea of it being a place-holder. On another tack, the “number line” idea does bring the idea of “infinity” into the picture — and that is another question altogether for which there are many questions, but few answers so far…
Another element of this book, however, is dedicated to finding out the origins of numbers, and it is here that I find problems.
It is all very well to clearly identify scientifically the earliest western inscription using 0 as a place-marker (the Mayans had used a symbol for this way earlier); but in trying to identify this as the symbol from which all things numerical arose, Aczel brings in the concepts more readily accommodated in eastern philosophical discourses where the love of paradoxes to illustrate the limitations of rational thinking is paramount. There we will find such written statements as “Nothing is not nothing” and logical elements which eschew simple black and white distinctions (one example in evaluative thinking is that whereas in much western logic we might find statements such as: “[proposition] A is either true or not true”, eastern logic might posit instead: “A is EITHER true or not true, OR both true and not true, OR neither true nor not true.”). Epistemic concerns, yes; but what this might have to do with the origins of numbers eludes me.
Aczel seems to be arguing that, since the earliest use of a 0 place-holder symbol seems to have originated in the East, then perhaps eastern mysticism, with its use of symbols and metaphors and logical paradoxes might provide some answers to the question of origins. If 0 = nothing, and nothing is not nothing, then perhaps everything comes from nothing, and so 0 might be considered as the origin of everything, including all numbers? Sadly, I can’t help feeling that such “answers” aren’t answers at all. I would suggest that the origin of numbers began with the first symbol used by humans to represent the number 1.
November 6, 2014
Use of the numeral zero as a placeholder is a deceptively clever invention. The zero allows reuse of a small set of numerals to represent an infinitely large set of numbers. For example: 4, 40, 400, 404, 4400, 0.4, .04, .044 use only the numeral 4 and the zero placeholder to represent a wide range of numbers. Only nine numerals in addition to zero are required for a complete, compact, and unambiguous representation of all numbers. Similar representations become unwieldy with number systems lacking a zero, such as roman numerals.
Author Amir Aczel has been curious about numbers since his childhood. As the son of a Mediterranean cruise ship captain, he enjoyed unique opportunities to travel, visit exotic destinations, and explore mathematics guided by his father’s clever personal steward. Recently Aczel focused on a search for the origins of zero. This book takes us along on his adventure.
It is likely that Italian mathematician Fibonacci popularized today’s Hindu-Arabic numerals in Europe, as a result of the 1202 publication of his book Liber Abaci, The book of the Abacus. These numerals, including the zero, are often attributed to Arab and Indian origins, but details are unclear and disputed. The ancient Mayans understood the concept of zero as early as the first century BC, but because their culture remained isolated, this did not contribute to creation of the Hindu-Arabic numerals.
An ancient mathematical document, written on birch bark, was discovered in the 1800s near the village of Bakhshail, in present-day Pakistan. It contains a wealth of mathematical writings, including the use of zero. Its creation date is disputed, with estimates ranging from 200 BC to the twelfth century AD. British authorities have denied permission for samples to be taken for carbon dating.
Study of Eastern cultures provides intriguing clues to the origins of important mathematical concepts. The Buddhist concept of “emptiness” provides a solution to a puzzle known as the tetralemma. Meditation on the concept of emptiness may have led to the concept of zero. The idea of infinity is quite strong in Hinduism. Another Eastern religion, Jainism, was concerned with very large numbers. These three Eastern religious explored the mathematical concepts of zero, infinity, and exponentially large numbers long before they were known to the West. Also, ancient southeastern Asian temples are filled with symbols of sex and mathematics.
The earliest known zero in India was found in the city of Gwalior, famous for the Taj Mahal. An inscription there reliably dated as AD 876 records a land grant length of 270 hastas—an ancient measure of length. Inspired by his hunch that zero had earlier, Buddhist origins, Aczel continued his search. He learned that in 1931 French archaeologist Georges Cœdès published a paper describing an inscription on a stone he labeled K-127, found in the Trapang Prei temple of Cambodia. The stone was reliably dated as AD683, and it included the inscription written in Old Khmer language, translated as: “The çaka era has reached 605 on the fifth day of the waning moon…” If this could be confirmed it would establish a zero originating in the East nearly two centuries earlier than the Gwalior zero.
Pol Pot and the Khmer Rouge took over Cambodia and ransacked the country’s museums and collections of archeological artifacts beginning in 1975. Could K-127 have survived this desecration, and if it did, how could it be found?
Aczel describes the details of his adventures and the fascinating people he meets as he travels through Cambodia searching for K-127. He also explores related avenues of mathematical development along the way. The sometimes indulgent adventure story is fun, and can be enjoyed and understood without an advanced background in mathematics.
I am left wondering if the inscription itself is sufficient to establish the Eastern origins of zero as a placeholder. What foundations in numerical representation and thinking allowed the inscription to be read by others at the time it was written? What, if any, sequence of thought and developments connect the K-127 Khmer zero to today’s Hindu-Arabic numerals? Have Aczel’s findings and claims been examined and verified by other scholars? What alternative theories and unanswered questions deserve exploration?
Author Amir Aczel has been curious about numbers since his childhood. As the son of a Mediterranean cruise ship captain, he enjoyed unique opportunities to travel, visit exotic destinations, and explore mathematics guided by his father’s clever personal steward. Recently Aczel focused on a search for the origins of zero. This book takes us along on his adventure.
It is likely that Italian mathematician Fibonacci popularized today’s Hindu-Arabic numerals in Europe, as a result of the 1202 publication of his book Liber Abaci, The book of the Abacus. These numerals, including the zero, are often attributed to Arab and Indian origins, but details are unclear and disputed. The ancient Mayans understood the concept of zero as early as the first century BC, but because their culture remained isolated, this did not contribute to creation of the Hindu-Arabic numerals.
An ancient mathematical document, written on birch bark, was discovered in the 1800s near the village of Bakhshail, in present-day Pakistan. It contains a wealth of mathematical writings, including the use of zero. Its creation date is disputed, with estimates ranging from 200 BC to the twelfth century AD. British authorities have denied permission for samples to be taken for carbon dating.
Study of Eastern cultures provides intriguing clues to the origins of important mathematical concepts. The Buddhist concept of “emptiness” provides a solution to a puzzle known as the tetralemma. Meditation on the concept of emptiness may have led to the concept of zero. The idea of infinity is quite strong in Hinduism. Another Eastern religion, Jainism, was concerned with very large numbers. These three Eastern religious explored the mathematical concepts of zero, infinity, and exponentially large numbers long before they were known to the West. Also, ancient southeastern Asian temples are filled with symbols of sex and mathematics.
The earliest known zero in India was found in the city of Gwalior, famous for the Taj Mahal. An inscription there reliably dated as AD 876 records a land grant length of 270 hastas—an ancient measure of length. Inspired by his hunch that zero had earlier, Buddhist origins, Aczel continued his search. He learned that in 1931 French archaeologist Georges Cœdès published a paper describing an inscription on a stone he labeled K-127, found in the Trapang Prei temple of Cambodia. The stone was reliably dated as AD683, and it included the inscription written in Old Khmer language, translated as: “The çaka era has reached 605 on the fifth day of the waning moon…” If this could be confirmed it would establish a zero originating in the East nearly two centuries earlier than the Gwalior zero.
Pol Pot and the Khmer Rouge took over Cambodia and ransacked the country’s museums and collections of archeological artifacts beginning in 1975. Could K-127 have survived this desecration, and if it did, how could it be found?
Aczel describes the details of his adventures and the fascinating people he meets as he travels through Cambodia searching for K-127. He also explores related avenues of mathematical development along the way. The sometimes indulgent adventure story is fun, and can be enjoyed and understood without an advanced background in mathematics.
I am left wondering if the inscription itself is sufficient to establish the Eastern origins of zero as a placeholder. What foundations in numerical representation and thinking allowed the inscription to be read by others at the time it was written? What, if any, sequence of thought and developments connect the K-127 Khmer zero to today’s Hindu-Arabic numerals? Have Aczel’s findings and claims been examined and verified by other scholars? What alternative theories and unanswered questions deserve exploration?
January 29, 2015
shelfnotes.com
Dear Reader,
This book was so much more than I expected. I went in to it anticipating a somewhat dry (if layperson) look at numbers and how they came to be a part of our world. I expected chapters to be organized by history, or by theory. Instead, this book read much more like a memoir. It began with the author's adventures as a young boy as the son of a ship captain, and how he became interested in seeking out the source of our Arabic numerals. There were parts that were kind of slow and there were parts which I just wanted to get through, but by the end I was almost on the edge of my seat! Aczel isn't a great writer - you can tell he is more of a math-minded person than a literature one - but he really did capture my attention and got me joining him during his triumphs and missteps as he traveled the world seeking that elusive first zero. I will admit the book took some getting used to, and as I said there were certainly parts which had me questioning whether I wanted to go on, but I am so glad that I did. The story as a whole was really worth it. And, I learned so much more than I thought I would along the way!
Going back to Dr. Aczel being more of an academic, there were certain points of the book which frustrated me, mostly relating to him skimming over concepts which I either didn't fully grasp from his glazed-over explanations, or ideas or references which I would have liked him to delve into further. For instance, on page 24 he mentions Maxwell's equations in physics as a good example of the important role the zero can play in other fields outside of mathematics - but never actually tells me what those are. Granted, they could be well beyond my understanding, I get that. But I'd have loved at least a footnote that gave me further reading or some sort of basic idea of the concept. I don't like having to pull myself away from a book just to Wikipedia something to get the gist of it. Another thing he mentions a page earlier is that "the double-entry bookkeeping system used in accounting today was developed in Europe in the thirteenth century in part to avoid using negative numbers." Okay, but I am not an account, and that intrigued me - I wanted to know more. I think I am familiar with the idea, but I'd have loved an example. In yet another point in the book, he examines logic and looks at syllogisms, using shorthand "A" and "O" which I am guessing to mean "assumption" and "observation" but...I don't know, and that bothers me. It was just those little tidbits which I would have liked to have given to me, the lay reader. He is clearly not writing to the mathematician. (NB: This was an ARC, and explanatory text may have been added during the final editing stages - I'd love to see a finished copy to check.)
On the flip side, Aczel did a wonderful job of throwing in lots of little extras - from photos of his father and many of the other people he encountered there, to fascinating little histories that he scattered throughout the book which really made it the gem it turned out to be. Outside of his own quest, he shared those of fellow zero seekers, and short histories of many of the places he visited. While, for example, I had always been vaguely aware of the Khmer Rouge, I learned so much more about that awful era and what it did to Cambodia's history. It makes me eager to learn more - and I do so love books which can do that.
Yours,
Arianna
Dear Reader,
This book was so much more than I expected. I went in to it anticipating a somewhat dry (if layperson) look at numbers and how they came to be a part of our world. I expected chapters to be organized by history, or by theory. Instead, this book read much more like a memoir. It began with the author's adventures as a young boy as the son of a ship captain, and how he became interested in seeking out the source of our Arabic numerals. There were parts that were kind of slow and there were parts which I just wanted to get through, but by the end I was almost on the edge of my seat! Aczel isn't a great writer - you can tell he is more of a math-minded person than a literature one - but he really did capture my attention and got me joining him during his triumphs and missteps as he traveled the world seeking that elusive first zero. I will admit the book took some getting used to, and as I said there were certainly parts which had me questioning whether I wanted to go on, but I am so glad that I did. The story as a whole was really worth it. And, I learned so much more than I thought I would along the way!
Going back to Dr. Aczel being more of an academic, there were certain points of the book which frustrated me, mostly relating to him skimming over concepts which I either didn't fully grasp from his glazed-over explanations, or ideas or references which I would have liked him to delve into further. For instance, on page 24 he mentions Maxwell's equations in physics as a good example of the important role the zero can play in other fields outside of mathematics - but never actually tells me what those are. Granted, they could be well beyond my understanding, I get that. But I'd have loved at least a footnote that gave me further reading or some sort of basic idea of the concept. I don't like having to pull myself away from a book just to Wikipedia something to get the gist of it. Another thing he mentions a page earlier is that "the double-entry bookkeeping system used in accounting today was developed in Europe in the thirteenth century in part to avoid using negative numbers." Okay, but I am not an account, and that intrigued me - I wanted to know more. I think I am familiar with the idea, but I'd have loved an example. In yet another point in the book, he examines logic and looks at syllogisms, using shorthand "A" and "O" which I am guessing to mean "assumption" and "observation" but...I don't know, and that bothers me. It was just those little tidbits which I would have liked to have given to me, the lay reader. He is clearly not writing to the mathematician. (NB: This was an ARC, and explanatory text may have been added during the final editing stages - I'd love to see a finished copy to check.)
On the flip side, Aczel did a wonderful job of throwing in lots of little extras - from photos of his father and many of the other people he encountered there, to fascinating little histories that he scattered throughout the book which really made it the gem it turned out to be. Outside of his own quest, he shared those of fellow zero seekers, and short histories of many of the places he visited. While, for example, I had always been vaguely aware of the Khmer Rouge, I learned so much more about that awful era and what it did to Cambodia's history. It makes me eager to learn more - and I do so love books which can do that.
Yours,
Arianna
June 21, 2018
This was a really fun read: part history of math, part adventure story. Though Aczel's adventures may not have been death-defying like Indiana Jones, they have something of the same fun and adventurous spirit. Aczel's telling really makes the journey engaging, and it's neat that he was able to find the first known zero and restore such a neat artifact. He does a great job explaining why zero is so important for mathematics as well as why this particular archaeological discovery is so important.
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