Call number
Collection
Publication
New York City : Palgrave Macmillan, [2015]
Pages
x; 234
Description
"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. "--… (more)
Media reviews
As a child, he wanted to devote his life to traveling the world in search of an answer to the origin of numbers. In this book, he lives out part of that childhood dream. A brief discussion of the cumbersome Roman system, which lacked a zero, demonstrates the power of the zero, which makes our
Show More
number system so efficient. Aczel rejects the theory that it was a European or Arabic invention but rather posits that it developed in eastern Asia. To him, the concepts of both infinity and of nothingness seem embedded in Buddhism, Hinduism and Jainism. To get to zero, he takes readers through a short but sometimes bewildering course in Eastern philosophy that requires close attention. On learning that in the 1930s, a French archaeologist had discovered in Cambodia a stele inscribed with a date that utilized a dot for a zero in the seventh century, Aczel set out to find the stone tablet. Because the Khmer Rouge had destroyed so many of Cambodia’s cultural artifacts, his search was long, complicated and arduous and involves a slew of characters, helpful and otherwise. Aczel is nothing if not persistent, and in the end, he found the carving and photographed it. What happened afterward as he struggled to preserve this earliest known evidence of the use of zero is a story in itself. Show Less
Language
Original language
English
Original publication date
2015-01-06
Physical description
x, 234 p.; 8.3 inches
ISBN
9781137279842
Similar in this library
Library's review
Amir Aczel’s Finding Zero is interesting but very narrowly focused. Rather than a general history of numerals or even the importance of the zero, it is a look at his search for the oldest known instance of zero in the Old World. (He does acknowledge the greater age of the Mayan zero, but
The book begins with a purely personal account of Aczel’s developing childhood interest in math and numerals, and a brief reminder of the importance of zero for enabling the compact and efficient place-value notation (in which the same numeral “5” can be used to stand for “5”, “50”, or “500” depending on how many zeroes accompany it, rather than requiring separate symbols for the different values). From there, it moves to a detailed account of his quest to find a Cambodian stone with the oldest known zero.
It’s important to note that this was not a new discovery. The stone, designated K-217, was an important historical artifact, but the finding had been made and published decades previously; there were no photos, which Aczel thought was important, so he set off to find the stone. Many travelogue-style details of hotel and flight arrangements later, he locates it and arranges for it to be placed in the Cambodian national museum.
The weakest part of the book for me was Aczel’s fixation on Eastern philosophical principles relating to the development of the zero in Asia (rather than Europe or Arabia). He goes into considerable detail about details of Buddhist thought, especially the notion of the void as distinct from existence and non-existence and differing notions of what constitutes truth, and argues that somehow these lead to the development of the mathematical zero. He doesn’t address how the Mayans, with very different religious beliefs, also developed the zero if this association was so important, nor does he develop this connection with more than his own belief and several acquaintances of his agreeing that it sounds reasonable.
Show More
considers that since it never spread beyond its culture of origin and thus did not impact the development of mathematics outside of Mexico it was less important to the overall history of mathematics than the Eurasian zero.)The book begins with a purely personal account of Aczel’s developing childhood interest in math and numerals, and a brief reminder of the importance of zero for enabling the compact and efficient place-value notation (in which the same numeral “5” can be used to stand for “5”, “50”, or “500” depending on how many zeroes accompany it, rather than requiring separate symbols for the different values). From there, it moves to a detailed account of his quest to find a Cambodian stone with the oldest known zero.
It’s important to note that this was not a new discovery. The stone, designated K-217, was an important historical artifact, but the finding had been made and published decades previously; there were no photos, which Aczel thought was important, so he set off to find the stone. Many travelogue-style details of hotel and flight arrangements later, he locates it and arranges for it to be placed in the Cambodian national museum.
The weakest part of the book for me was Aczel’s fixation on Eastern philosophical principles relating to the development of the zero in Asia (rather than Europe or Arabia). He goes into considerable detail about details of Buddhist thought, especially the notion of the void as distinct from existence and non-existence and differing notions of what constitutes truth, and argues that somehow these lead to the development of the mathematical zero. He doesn’t address how the Mayans, with very different religious beliefs, also developed the zero if this association was so important, nor does he develop this connection with more than his own belief and several acquaintances of his agreeing that it sounds reasonable.
Show Less
User reviews
LibraryThing member bragan
Mathematican Amir D. Aczel, pursuing a lifelong fascination with the origins of both the so-called "Arabic numerals" and the concept of number itself, travels to India to look at ancient inscriptions that include numbers, and to Cambodia in search of a lost artifact said to feature the earliest
Unfortunately, I found this book really disappointing. There are a few interesting tidbits of math and history, but far too much of it is taken up by the author's thoughts about Eastern philosophy and mysticism, which he admires to the point, apparently, of believing its "non-Western logic" is a good approach to curing cancer. He also believes that the zero was invented in the East because it resonated with the Buddhist concept of the void. Which is an interesting thought, and may well even be true, but Aczel doesn't support the idea in any particularly coherent or scholarly way. He just... believes it.
He also grossly overestimates how interesting the details of his life and his travels are. (Here's a hint for people writing books of this nature: unless you've got a good story to tell about it, or are including some vivid description that gives readers a good feel for the setting, we really don't need to know the names of all the hotels you stayed at, or what you had for lunch, or what route you took to get to the museum. Really.) And he's trying way too hard to paint this as some kind of exciting Indiana Jones-style adventure with himself as the protagonist, even at times when, as far as I can tell, he mostly just seems to be noodling around at tourist sites.
Basically, this book was just really not at all what I was expecting or hoping for.
Show More
known use of the zero (or at least the earliest known use outside the Americas).Unfortunately, I found this book really disappointing. There are a few interesting tidbits of math and history, but far too much of it is taken up by the author's thoughts about Eastern philosophy and mysticism, which he admires to the point, apparently, of believing its "non-Western logic" is a good approach to curing cancer. He also believes that the zero was invented in the East because it resonated with the Buddhist concept of the void. Which is an interesting thought, and may well even be true, but Aczel doesn't support the idea in any particularly coherent or scholarly way. He just... believes it.
He also grossly overestimates how interesting the details of his life and his travels are. (Here's a hint for people writing books of this nature: unless you've got a good story to tell about it, or are including some vivid description that gives readers a good feel for the setting, we really don't need to know the names of all the hotels you stayed at, or what you had for lunch, or what route you took to get to the museum. Really.) And he's trying way too hard to paint this as some kind of exciting Indiana Jones-style adventure with himself as the protagonist, even at times when, as far as I can tell, he mostly just seems to be noodling around at tourist sites.
Basically, this book was just really not at all what I was expecting or hoping for.
Show Less
LibraryThing member lbeaumont
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
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?
Show More
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?
Show Less
LibraryThing member Larxol
Finding Zero recounts author Amir Aczel’s discovery, more accurately rediscovery, of a Cambodian stele inscribed in the year 683 with text including a dot used as a place-holding zero in a number we would write today as “605”. He makes the case that this is the oldest surviving use of a
In order to make a book of it, the author has produced a sort of memoir or diary about how he went about his research. But even to fill up this slim volume, he has to include details such as the aircraft used by Air Asia, their lack of meal service, and the revelation that he had to pass through immigration on arrival in Cambodia.
Anyone interested in the mathematics of the story would be better off with the magazine article. The book version is a sort of blog, and might have been better suited to social, rather than printed, media.
Show More
modern zero, although his argument involves stipulations that result in ignoring Mayan and Sumerian precedents. Whether you agree with his argument or not, the material would add up to a reasonable magazine article. In fact, Aczel published such an article in the Smithsonian’s Discover magazine in May, 2013, where it generated some debate.In order to make a book of it, the author has produced a sort of memoir or diary about how he went about his research. But even to fill up this slim volume, he has to include details such as the aircraft used by Air Asia, their lack of meal service, and the revelation that he had to pass through immigration on arrival in Cambodia.
Anyone interested in the mathematics of the story would be better off with the magazine article. The book version is a sort of blog, and might have been better suited to social, rather than printed, media.
Show Less
LibraryThing member elenchus
Part popular mathematics, part memoir / travelogue, the lion's share of Finding Zero is devoted to the latter. The discussion of math concepts is intriguing but brief, related to concept of number; the balance of the book describes Aczel's travels as he tracks down anthropological evidence for the
I benefited more from Devlin's Man of Numbers, though his concern lies with the pragmatic influence of the Arabic zero and a placeholder number system on arithmetic and commerce. I'd hoped Aczel's slant would provide a useful supplement to Devlin's account, but it doesn't.
//
Principal concepts:
• Zero (number) central to conception of negative numbers
• Zero (numeral) key to efficient notation & arithmetic: calculation of decimals / fractions of currency or other measure; placeholder function allowing numerals to cycle as numbers increase, important for higher orders of magnitude; binary code.
• Quantity expressed historically as substantives (nouns) rather than as numbers, and numerals are unnecessary in such an approach: eight Vasu, six flavours, five senses, four Veda, two eyes; and that number systems often contain numbers deriving from these earlier terms. In antiquity, Khmer knew only numbers 1, 2, 3, 4, 5, 10, 20 and then multiples of 20. In French, 80 is quatre vingt, or four twenties. [213 - 215]
• Mayan zero devised earlier but (a) did not involve a positional element in the Mayan number system, and (b) did not influence other number systems (no trade or travel) [79]
• Cantor's preliminary link of zero's origin in India or Babylon [74]; George Coedes discovery of earliest zero on steles in Cambodia (catalogued as K-127) and Indonesia, two centuries before Arab Caliphate and definitely separate from European or Arabian influence.
• Speculatively links concept of zero (sunya) to Buddhist / Hindu / Jain tradition of emptiness (sunyata) and infinite (105, 140).
• Most intriguing here is the tradition of tetralemma (in the Greek, catuskoti in Sanskrit): Nagarjuna's logic of true / not true / both / neither. Western mathematical tradition as epitomised in Law of the Excluded Middle, allowing only true or not true, no middle ground [55]. (Note distinction between false & not true.)
• Alex Grothendieck's concept of topos, and critique of set theory. "Technically, our strict, either-or logic is necessitated by our reliance on the theory of sets as a basis for mathematics. This gives us the concept of set membership, which is unforgiving: an element is either a member of a set, or it is not; it cannot be both, or neither. What Grothendieck ... did was to free mathematics from the reliance on set theory and set membership. He employed something called category theory, in which there is no need for sets or membership laws." [58-60] Fred Linton's exploration of tetralemma in frame of Western mathematics, using topos and category theory. [57]
Show More
earliest appearance of zero, the numeral. Even his "search" is given short shrift, in that he largely leaves unaddressed his research into how zero was used throughout history, how math functioned without a zero, substitutes in other number systems (e.g. an empty depression in a counting board; use of multiples as with large denomination coins or in Roman numerals). Instead, Aczel describes journeys to India, Cambodia, Thailand, Laos, Viet Nam in search of artifacts which are of interest chiefly insofar as they are documentation of these historical concepts.I benefited more from Devlin's Man of Numbers, though his concern lies with the pragmatic influence of the Arabic zero and a placeholder number system on arithmetic and commerce. I'd hoped Aczel's slant would provide a useful supplement to Devlin's account, but it doesn't.
//
Principal concepts:
• Zero (number) central to conception of negative numbers
• Zero (numeral) key to efficient notation & arithmetic: calculation of decimals / fractions of currency or other measure; placeholder function allowing numerals to cycle as numbers increase, important for higher orders of magnitude; binary code.
• Quantity expressed historically as substantives (nouns) rather than as numbers, and numerals are unnecessary in such an approach: eight Vasu, six flavours, five senses, four Veda, two eyes; and that number systems often contain numbers deriving from these earlier terms. In antiquity, Khmer knew only numbers 1, 2, 3, 4, 5, 10, 20 and then multiples of 20. In French, 80 is quatre vingt, or four twenties. [213 - 215]
• Mayan zero devised earlier but (a) did not involve a positional element in the Mayan number system, and (b) did not influence other number systems (no trade or travel) [79]
• Cantor's preliminary link of zero's origin in India or Babylon [74]; George Coedes discovery of earliest zero on steles in Cambodia (catalogued as K-127) and Indonesia, two centuries before Arab Caliphate and definitely separate from European or Arabian influence.
• Speculatively links concept of zero (sunya) to Buddhist / Hindu / Jain tradition of emptiness (sunyata) and infinite (105, 140).
• Most intriguing here is the tradition of tetralemma (in the Greek, catuskoti in Sanskrit): Nagarjuna's logic of true / not true / both / neither. Western mathematical tradition as epitomised in Law of the Excluded Middle, allowing only true or not true, no middle ground [55]. (Note distinction between false & not true.)
• Alex Grothendieck's concept of topos, and critique of set theory. "Technically, our strict, either-or logic is necessitated by our reliance on the theory of sets as a basis for mathematics. This gives us the concept of set membership, which is unforgiving: an element is either a member of a set, or it is not; it cannot be both, or neither. What Grothendieck ... did was to free mathematics from the reliance on set theory and set membership. He employed something called category theory, in which there is no need for sets or membership laws." [58-60] Fred Linton's exploration of tetralemma in frame of Western mathematics, using topos and category theory. [57]
Show Less
LibraryThing member Meredy
Six-word review: The drive to seek, find, know.
Extended review:
(An Early Reviewer review)
This is not a book about mathematics. It's the story of a quest, of a man on a mission to satisfy a personal desire as much as to solve a great mystery of the past.
An all-consuming question about the history of
That the odyssey is a personal one is made plain by the structure of the book. It begins and ends with the author's connection to the man who set him on his course, a man whose own history lies in the shadows but whose enthusiasm for the ideas behind the numbers that are so familiar to us excited and inspired a young boy. In the course of his search for the ancient roots of mathematical understanding, the author sees links to religion and philosophy and especially to Buddhism, with its core concept of emptiness--shunyata. Here he refers to a passage in Zen master Thich Nhat Hanh's writing about the Buddhist idea of the void:
As I concentrated on these notions, I came to believe that I could even read the quoted verses above as saying: existence = 1, nonexistence = -1, and emptiness = 0. Emptiness was the door from nonexistence to existence, in the same way that zero was the conduit [sic] from positive to negative numbers, one set being a perfect geometrical reflection of the other along the number line. (page 106)
If this is mathematics, it's also mysticism; and the overlapping and merging of arbitrarily separated disciplines is one of the themes of this book.
It's not the discoveries but the passion that is the subject of this account; not the numbers but the zeal. An individual commits himself to a goal, and an ineffable something in him impels him to persevere and not give up. His hunger for the answer draws him on; his persistence and unflagging excitement infuse his tale, and that's what draws us on as readers.
If his ascription of supernatural significance to such things as the label number of the sought-after archeological artifact ventures over into woo woo territory, well, that might be one of the reasons for a moderate rating. That his approach and his narrative are not strictly rational simply confirms that this is not a book about math.
Extended review:
(An Early Reviewer review)
This is not a book about mathematics. It's the story of a quest, of a man on a mission to satisfy a personal desire as much as to solve a great mystery of the past.
An all-consuming question about the history of
Show More
human intelligence and abstract thought drives the author's lifelong search. His goal is to locate the birthplace of the concept of number and especially of the number zero. For Aczel, this is not some bodiless mental pursuit but a thrilling intellectual and geographical quest for a historical moment of invention that stands alone among peak human achievements. That the odyssey is a personal one is made plain by the structure of the book. It begins and ends with the author's connection to the man who set him on his course, a man whose own history lies in the shadows but whose enthusiasm for the ideas behind the numbers that are so familiar to us excited and inspired a young boy. In the course of his search for the ancient roots of mathematical understanding, the author sees links to religion and philosophy and especially to Buddhism, with its core concept of emptiness--shunyata. Here he refers to a passage in Zen master Thich Nhat Hanh's writing about the Buddhist idea of the void:
As I concentrated on these notions, I came to believe that I could even read the quoted verses above as saying: existence = 1, nonexistence = -1, and emptiness = 0. Emptiness was the door from nonexistence to existence, in the same way that zero was the conduit [sic] from positive to negative numbers, one set being a perfect geometrical reflection of the other along the number line. (page 106)
If this is mathematics, it's also mysticism; and the overlapping and merging of arbitrarily separated disciplines is one of the themes of this book.
It's not the discoveries but the passion that is the subject of this account; not the numbers but the zeal. An individual commits himself to a goal, and an ineffable something in him impels him to persevere and not give up. His hunger for the answer draws him on; his persistence and unflagging excitement infuse his tale, and that's what draws us on as readers.
If his ascription of supernatural significance to such things as the label number of the sought-after archeological artifact ventures over into woo woo territory, well, that might be one of the reasons for a moderate rating. That his approach and his narrative are not strictly rational simply confirms that this is not a book about math.
Show Less
LibraryThing member drneutron
There's little question that the use of positional notation for numbers is one of the most useful human inventions. I mean, can you imagine trying to do calculus with Roman numerals? And in our modern mathematical notation, the most important idea is that of the zero - representing nothing!
Sometime in the early Renaissance, these concepts migrated to Europe through the Arabic world, initially through the work of Fibonacci. And the merchants and business people loved the efficiency of accounting using this new system.
What we don't know is who invented our numbers, especially introducing the concept of zero. Many think they came out of the East - India, or perhaps the Middle East - hence we call them Hindu-Arabic numerals. But the evidence for this is skimpy and the history of our numerals isn't known. Finding Zero is Aczel's memoir of his years-long search for that evidence. It's well-written, and an interesting story. I wish Aczel had given us more on ancient numbering systems and arithmetic - what was there was great, but more would have been better!
Recommended, even for the non-mathematically inclined. The level of expertise needed is absolutely minimal while still a fun story!
Show More
Sometime in the early Renaissance, these concepts migrated to Europe through the Arabic world, initially through the work of Fibonacci. And the merchants and business people loved the efficiency of accounting using this new system.
What we don't know is who invented our numbers, especially introducing the concept of zero. Many think they came out of the East - India, or perhaps the Middle East - hence we call them Hindu-Arabic numerals. But the evidence for this is skimpy and the history of our numerals isn't known. Finding Zero is Aczel's memoir of his years-long search for that evidence. It's well-written, and an interesting story. I wish Aczel had given us more on ancient numbering systems and arithmetic - what was there was great, but more would have been better!
Recommended, even for the non-mathematically inclined. The level of expertise needed is absolutely minimal while still a fun story!
Show Less
LibraryThing member John_Vaughan
I did not think I would enjoy this book, having always been a mathematics dummy, but I did - greatly. Not only did the author finally help to understand what 'Sets" are but I got closer to understanding "Primes" that I ever had before.
I have always believed that mankind is broadly split into two
I think that some of the rather negative reviews about this work are expressing the disappointment from the analytical viewpoint that is is not more of a tome of pure mathematics.
it is instead a travel and adventure book about math. And what adventures as the author wanders around the far east, seeking the grail of finding the first recorded zero.
Recommended if you enjoy armchair travels, history ... and even math.
I have always believed that mankind is broadly split into two
Show More
types of mind, either analytical or aesthetic and i was convinced that the twain could not meet, but only, like parallel lines in infinity ... Zero in fact. Dr. Aczel showed me the absolute value of zero and some of the impact on our culture in a very enjoyable read.I think that some of the rather negative reviews about this work are expressing the disappointment from the analytical viewpoint that is is not more of a tome of pure mathematics.
it is instead a travel and adventure book about math. And what adventures as the author wanders around the far east, seeking the grail of finding the first recorded zero.
Recommended if you enjoy armchair travels, history ... and even math.
Show Less
LibraryThing member jwmccormack
Aczel is a talented writer of popular books on the history of science and mathematics. This book offers a brisk overview of the history of our understanding of "zero" couched in a memoir of his travels and intellectual journey. I'm not sure whether most readers will find his research travelogue
For this reviewer, the connections Aczel explores between religious thought and mathematics were the most interesting. The insights into emptiness of Buddhist philosopher Nagarjuna draw Aczel into the search for zero in Asia, unable to shake the thought that Western logical systems seem too rigid to have given birth to mathematical notions of either zero or infinity. It would seem that archaeological evidence bears out this hunch. Aczel isn't the first to explore connections between religion and mathematics, and his treatment of Indian religions leaves much to be desired. Still, his openness to insights beyond the Western scientific academy and his participation in the broader effort to integrate Western and non-Western logic and philosophy are commendable. (He seems at times unaware of mainstream efforts in philosophy, religious studies, anthropology, and history of science to do just that, but his contribution will nevertheless be worth it if his book finds a wide audience.)
Show More
compelling, though his depiction of a childhood aboard a Mediterranean cruise ship discussing math with his father's friend is Idyllic. For this reviewer, the connections Aczel explores between religious thought and mathematics were the most interesting. The insights into emptiness of Buddhist philosopher Nagarjuna draw Aczel into the search for zero in Asia, unable to shake the thought that Western logical systems seem too rigid to have given birth to mathematical notions of either zero or infinity. It would seem that archaeological evidence bears out this hunch. Aczel isn't the first to explore connections between religion and mathematics, and his treatment of Indian religions leaves much to be desired. Still, his openness to insights beyond the Western scientific academy and his participation in the broader effort to integrate Western and non-Western logic and philosophy are commendable. (He seems at times unaware of mainstream efforts in philosophy, religious studies, anthropology, and history of science to do just that, but his contribution will nevertheless be worth it if his book finds a wide audience.)
Show Less
LibraryThing member amyblue
I really enjoyed this author's Fermat's Last Theorem so I expected to love this book, but I didn't. The problem was, the author was trying to write a memoir, a travelogue and a history of mathematics at the same time...and failed at all three. Although his writing style is engaging, the book lacked
Show More
focus and I had to force myself to finish it. Show Less
LibraryThing member Micah
A fascinating memoir about Amir Aczel's search for the philosophical and numerical origins of zero spanning Mesoamerica, Europe, the Arabic Caliphate, India, and Southeast Asia.
LibraryThing member TheDivineOomba
I liked this book, but the story didn't keep my attention. I found the book to drag in the latter half - the spiritual aspect I found a bit dragging. I am not a big a fan of books about self discovery.
I was horrified at the archaeologist and their attempt at restoration. One thing - as a an
I was horrified at the archaeologist and their attempt at restoration. One thing - as a an
Show More
American, the discoveries of non-western cultures get overlooked - and we as a society, need to start thinking as part of a global society, rather than us vs them. Show Less
LibraryThing member SharronA
I requested this book through Library Thing's Early Review program because I remembered enjoying the author's earlier book, "Fermat's Last Theorem: Unlocking the Secret of an Ancient Mathematical Problem."
"Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers" was written in a
If you're really interested in a history of the concept of zero, try reading Charles Seife's "Zero: The Biography of a Dangerous Idea," a slim volume, engagingly written, and strictly about what its title suggests.
"Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers" was written in a
Show More
conversational style and incorporated much more than cut-and-dried mathematics. The personal vignettes were charming, and the historical details were interesting (if perhaps selected with a certain bias). But to this reader, the philosophical, religious, and even racist views expressed were a distraction from what I thought the story was about. So my rating of 3 stars is an average of the good parts and the not-so-good.If you're really interested in a history of the concept of zero, try reading Charles Seife's "Zero: The Biography of a Dangerous Idea," a slim volume, engagingly written, and strictly about what its title suggests.
Show Less
LibraryThing member InfoQuest
To begin with, I really did want to like this book. While somewhat math-phobic during my academic career, I've developed a casual interest in pop math and science bookssince finishing undergrad math requirements, and so on that account, I was curious about the source of our numbering system and the
After a couple chapters, though, my interest began to wane. I'm not sure who the expected audience of this story was, but surely just about anyone could be expected to understand the basic principles of, say, prime numbers that he lays out in the middle of a retelling of his childhood. While I think this is an attempt to make sure everyone's on the same page mathematically, in order to make the revolutionary quality of zero/zeroness more apparent, it feels clumsily done. If it were fiction, I'd call it random info-dumping and poor world-building.
But anyway, the travel narrative part is moderately interesting, if a little more focused on the exoticism of "Eastern" thought and religion than seems reasonable. Claiming to have no working knowledge of Hinduism and Buddhism prior to searching for the origins of zero in India, the author nonetheless makes the rather interesting claim that zero was naturally an "Eastern" idea and an obvious product of Buddhism, which the all too literal-minded "West" just couldn't have developed. Now I won't make any counterclaims, exactly, but it seems unnecessary to use stereotypical East/West claims like this and I'd have liked a more in-depth and nuanced treatment of the philosophies of religions from both hemispheres, if such a claim were to be made central.
More bothersomely, the author also appears to overeager to defame another academic with whom he clashes over the care of the earliest record of zero he ultimately rediscovers--giving both her name and a photo. While it's possible that woman was really the malevolent, greedy, would-be history-destroyer he depicts, I really doubt it very much. Besides which, the "evidences" he presents for her wickedness don't hold water for me, personally, as they don't show her doing anything immoral or damaging to the item in question; if anything, she seemed surprisingly willing to collaborate and he far too quick to suspect the worst and insist on his own importance. Anything that smacks of a vendetta is really very off-putting in any personal writing, but it feels especially egregious in this instance, and it rather colored the rest of my reading.
While I'm still interested in the topic of the book and am glad to have more background knowledge on it, I don't think I'll keep this book. I also really wish he would have went more into the origins of the "Hindu-Arabic" numbers we use today, as both the subtitle and introductory materials implied, and hope to find an accessible work on that topic in the future.
Show More
use of zero. And when it seemed that the story was told travelogue-style, I was also intrigued, as concept-driven travel narrative (a la Bill Bryson or Tony Horwitz) is also a favorite non-fiction format of mine.After a couple chapters, though, my interest began to wane. I'm not sure who the expected audience of this story was, but surely just about anyone could be expected to understand the basic principles of, say, prime numbers that he lays out in the middle of a retelling of his childhood. While I think this is an attempt to make sure everyone's on the same page mathematically, in order to make the revolutionary quality of zero/zeroness more apparent, it feels clumsily done. If it were fiction, I'd call it random info-dumping and poor world-building.
But anyway, the travel narrative part is moderately interesting, if a little more focused on the exoticism of "Eastern" thought and religion than seems reasonable. Claiming to have no working knowledge of Hinduism and Buddhism prior to searching for the origins of zero in India, the author nonetheless makes the rather interesting claim that zero was naturally an "Eastern" idea and an obvious product of Buddhism, which the all too literal-minded "West" just couldn't have developed. Now I won't make any counterclaims, exactly, but it seems unnecessary to use stereotypical East/West claims like this and I'd have liked a more in-depth and nuanced treatment of the philosophies of religions from both hemispheres, if such a claim were to be made central.
More bothersomely, the author also appears to overeager to defame another academic with whom he clashes over the care of the earliest record of zero he ultimately rediscovers--giving both her name and a photo. While it's possible that woman was really the malevolent, greedy, would-be history-destroyer he depicts, I really doubt it very much. Besides which, the "evidences" he presents for her wickedness don't hold water for me, personally, as they don't show her doing anything immoral or damaging to the item in question; if anything, she seemed surprisingly willing to collaborate and he far too quick to suspect the worst and insist on his own importance. Anything that smacks of a vendetta is really very off-putting in any personal writing, but it feels especially egregious in this instance, and it rather colored the rest of my reading.
While I'm still interested in the topic of the book and am glad to have more background knowledge on it, I don't think I'll keep this book. I also really wish he would have went more into the origins of the "Hindu-Arabic" numbers we use today, as both the subtitle and introductory materials implied, and hope to find an accessible work on that topic in the future.
Show Less
LibraryThing member jjvors
Where did the number zero come from? Where did numbers in general come from? In Finding Zero: A Mathematician's Odyssey to Uncover the Origins of Numbers, author Amir D. Aczel traces his personal interest in number origins and how it led him to a mathematical career and then along an improbable
This is a satisfying book to anyone who enjoys history, mathematics, philosophy, or different cultures. I recommend it without reservation.
Show More
four year search to find the oldest example of the number zero. His search takes him from France to Israel to India to Thailand and Cambodia. He encounters smugglers, corrupt government officials, great mathematicians, historians, travelers and adventurers. Engaging and personal, Dr. Aczel makes what could be a dry, esoteric subject, into a great adventure of mystery, with unexpected turns. This is a satisfying book to anyone who enjoys history, mathematics, philosophy, or different cultures. I recommend it without reservation.
Show Less
LibraryThing member jlbrownn23
This book is a little hard to review. It is part memoir/travelogue - I normally dislike those, but found this one somewhat charming. I like the stories from his younger days, and he gave just the right amount of flavor and detail on his travels. It was also part philosophical, which I did not like
The math was interesting, but there wasn't a whole lot of it. There was some really basic number theory that I think most people could understand, and some set theory. I think there could have been a little more on just why zero was so odd & took so long to be "discovered". This is one of those things that SEEMS obvious until you start to think about why it might NOT be. It's obvious what the difference between 3 apples and 2 apples and 1 apple is, but it is not obvious that the absence of apples is the same thing as a quantity of apples. The one is concrete, and the other IS a bit philosophical, i.e., can something used to represent the presence of something also be used to denote its absence. Today the answer to that is obvious, but why did it take so long to figure out, and why does it have to be that way?
I was definitely more compelled by the final part of the book. I was getting close to the end of the book & starting to drag a little with the philosophical parts, when suddenly a engaging archaeological adventure started to unfold! I don't think it has any danger of getting made in to an Indiana Jones movie, but it pulled me in on a very human level. I could feel the authors anguish and was suddenly engrossed and rooting for him in a way I hadn't been until then. And the last chapter was actually touching, and to me set the perfect tone to end the book on.
My rating system is generally:
1 star = so bad I couldn't bear to finish and gave up.
2 stars = I finished, but wish it had been worse so I would have given up.
3 stars = I liked it, but would be hesitant to recommend it to anyone who didn't have a very specific interest in the topic.
4 stars = although there were some flaws, it was a very good book and I would recommend it to anyone with a general interest
5 stars = outstanding! I stayed up late reading it every night, if you have even a slight interest buy it and read it now.
Show More
as much. The crux of it was that eastern cultures are not as tied to true/false, black/white forms of logic, which is what enabled them to be able to conceive of the concept of zero when western cultures did not. It's a somewhat compelling argument, but it takes far too may turns in to hippyish fuzzy headed philosophy. Just because a guy with a beard in robe says weird stuff doesn't mean he has any idea what he is talking about. It's not a proof or evidence of anything, and felt out of place.The math was interesting, but there wasn't a whole lot of it. There was some really basic number theory that I think most people could understand, and some set theory. I think there could have been a little more on just why zero was so odd & took so long to be "discovered". This is one of those things that SEEMS obvious until you start to think about why it might NOT be. It's obvious what the difference between 3 apples and 2 apples and 1 apple is, but it is not obvious that the absence of apples is the same thing as a quantity of apples. The one is concrete, and the other IS a bit philosophical, i.e., can something used to represent the presence of something also be used to denote its absence. Today the answer to that is obvious, but why did it take so long to figure out, and why does it have to be that way?
I was definitely more compelled by the final part of the book. I was getting close to the end of the book & starting to drag a little with the philosophical parts, when suddenly a engaging archaeological adventure started to unfold! I don't think it has any danger of getting made in to an Indiana Jones movie, but it pulled me in on a very human level. I could feel the authors anguish and was suddenly engrossed and rooting for him in a way I hadn't been until then. And the last chapter was actually touching, and to me set the perfect tone to end the book on.
My rating system is generally:
1 star = so bad I couldn't bear to finish and gave up.
2 stars = I finished, but wish it had been worse so I would have given up.
3 stars = I liked it, but would be hesitant to recommend it to anyone who didn't have a very specific interest in the topic.
4 stars = although there were some flaws, it was a very good book and I would recommend it to anyone with a general interest
5 stars = outstanding! I stayed up late reading it every night, if you have even a slight interest buy it and read it now.
Show Less
LibraryThing member tim.taylor
As others have noted this book is partly a memoir and travelogue, and partly a review of the history of mathematics and its interrelation with religion. I found the latter theme most interesting. The concepts of zero and infinity, as they developed in both East and West, are for me the heart of
Show More
this book. Show Less
LibraryThing member jpporter
Amir D. Aczel gives us an excellent account of the development of our system of numbers, and the special function played by the number "0." Specifically, Aczel spent a substantial portion of his professional life searching for physical proof of the first use of "0" (as signifying "nothing", and as
Along the way, Aczel gives us an intriguing history of numbers, an interesting history of the search for zero, and a usually interesting account of his search and the people he encountered. Some parts of the book almost read like an adventure story, rather than a history, and it is easy to get quite caught up in the hunt for zero.
At the same time, Aczel does succumb to the temptation to make things a bit melodramatic, and some parts of the book are a bit over-long and/or repetitive. Whether some choice editing and excision would have helped the book is a moot point, however - what you see is what you get.
I am fascinated by math, and this book was a lot more interesting than I thought it would be. You don't have to know math to appreciate what the search is about, and discovering the ultimate conclusion of the search makes the book well worth reading.
Show More
a placeholder in large numbers - like 104 for 'one hundred and four').Along the way, Aczel gives us an intriguing history of numbers, an interesting history of the search for zero, and a usually interesting account of his search and the people he encountered. Some parts of the book almost read like an adventure story, rather than a history, and it is easy to get quite caught up in the hunt for zero.
At the same time, Aczel does succumb to the temptation to make things a bit melodramatic, and some parts of the book are a bit over-long and/or repetitive. Whether some choice editing and excision would have helped the book is a moot point, however - what you see is what you get.
I am fascinated by math, and this book was a lot more interesting than I thought it would be. You don't have to know math to appreciate what the search is about, and discovering the ultimate conclusion of the search makes the book well worth reading.
Show Less
LibraryThing member CA2Balloon
This was an Early Reviewers copy. The title intrigued me since I am fascinated by numbers and a history buff -- what more could I ask?
Other reviewers have thoroughly detailed the contents of the book much more competently than I could so I'll just say I found the book enjoyable.
The author managed
Other reviewers have thoroughly detailed the contents of the book much more competently than I could so I'll just say I found the book enjoyable.
The author managed
Show More
to hold my attention throughout the book although, as another reviewer noted, I found his disparagement of other researchers a bit off-putting. Show Less
LibraryThing member Anietzerck
I won this book as part of LibraryThing.com's Early Reviewers. Over all, I really enjoyed this book. I never had an opinion about the origin of the zero, but I've always known it came later and was one of the most significant mathematical creations. We are made to believe that our numbers,
Show More
including the zero, are an Arab creation, and Mr. Aczel sets out to correct our misconceptions regarding the first zero's origins. His curiosity regarding numbers started at a very young age, encouraged by a mathematician who worked on his father's boat as a child. It is amazing how much the interactions in our lives at childhood can set the path for later in life. This passion for numbers never died down, but instead stayed with him throughout his life and set him on the path to be a mathematician himself. Although, the writing style was very matter-of-fact in many places, lacking some descriptives that would have made the story flow a little easier, the adventure that Mr. Aczel had was, indeed, interesting. As a mathematician who has no archeological background, searching the world for this lost artifact, the odds seemed to be stacked against him. Through the right connections, and a lot of luck, everything works out in the end and the first known zero is rediscovered. (Until we find the next earliest zero.) If you are into math, or even history, you should give this a read. Show Less
LibraryThing member dds1981
I shouldn't look forward to books by Amir Aczel as much as I do, but I really enjoy them. The most miserable course I had in business school was Statistics and he was the lead editor of the text book. Problem was the instructor, not the book.
Finding Zero is a very personal memoir. Beginning with
Finding Zero is a very personal memoir. Beginning with
Show More
the very childlike wonder of Aczel being introduced to the mysteries of mathematics by the chief steward of the cruise ship on which his father was a captain, to the sense of adventure traveling through Laos and Cambodia to solve the mystery of the first zero, Aczel's voice is at once that of an adult and the age he was at each stage of his life. A quick read, a lot of fun. Highly recommended. Show Less
LibraryThing member LeesyLou
The author isn't obsessed with a conceptualization. He was eager to geographically identify the specific earliest plaque known to depict the actual number zero in use.
More a memoir, and a pleasantly compelling one, than a book about mathematics or history, this includes academic intrigue, ancient
More a memoir, and a pleasantly compelling one, than a book about mathematics or history, this includes academic intrigue, ancient
Show More
history, twentieth century smuggling and more. For those who enjoy historical oddities or memoirs, it's a pleasant, easy read. Perfect beach reading. Show Less
LibraryThing member LeesyLou
The author isn't obsessed with a conceptualization. He was eager to geographically identify the specific earliest plaque known to depict the actual number zero in use.
More a memoir, and a pleasantly compelling one, than a book about mathematics or history, this includes academic intrigue, ancient
More a memoir, and a pleasantly compelling one, than a book about mathematics or history, this includes academic intrigue, ancient
Show More
history, twentieth century smuggling and more. For those who enjoy historical oddities or memoirs, it's a pleasant, easy read. Perfect beach reading. Show Less
LibraryThing member kleos_aphthiton
Memoir meets travelogue meets mathematics and archaeology meets philosophy and religion. There was a lot in here that I enjoyed, particularly the segments of the book that dealt with Aczel's quest to find a particular important artifact, encountering many of the challenges that archaeologists and
Show More
other scholars face in the field -- bureaucracy, corruption, wartime destruction of antiquities, unscrupulous scholars out to steal your find. When he focused instead on his obsession with understanding the origin of the zero, delving into Eastern religions and philosophy, I got a bit frustrated at times with his perhaps-overstated claims about the differences between Eastern and Western minds, while also sympathetic to his desire to redress some of the wrongs Western societies have done in colonial and post-colonial times. Ultimately, I found the story of his personal quest at least to be satisfying. Show Less
LibraryThing member rbartholomew
I love the intersection of science/math and history and have read a dozen books in this genre. I thought this work feel short of the mark, as there is less historical rigor, less explanation of the under-pinning concepts, development, and hard facts bringing the reader from unknowing to
Show More
understanding. This is instead more of a mathematician's travel log of southeastern Asia. There is some philosophy, some mathematical discussion, some history and the author's odyssey to find what he was looking for is told with a story teller's gift of intrigue. Nonetheless, not my favorite in this genre, though I am willing to give Aczel's other books a try. Show Less