Numbers and the Making of Us: Counting and the Course of Human Cultures
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- Author：Caleb Everett
- ISBN：0674237811
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Summary
"A fascinating book。"
--James Ryerson， New York Times Book Review
A Smithsonian Best Science Book of the Year
Winner of the PROSE Award for Best Book in Language & Linguistics
Carved into our past and woven into our present， numbers shape our perceptions of the world far more than we think。 In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture， Caleb Everett draws on new discoveries in psychology， anthropology， and linguistics to reveal the many things made possible by numbers， from the concept of time to writing， agriculture， and commerce。
Numbers are a tool， like the wheel， developed and refined over millennia。 They allow us to grasp quantities precisely， but recent research confirms that they are not innate--and without numbers， we could not fully grasp quantities greater than three。 Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians。
"This is bold， heady stuff。。。 The breadth of research Everett covers is impressive， and allows him to develop a narrative that is both global and compelling。。。 Numbers is eye-opening， even eye-popping。"
--New Scientist
"A powerful and convincing case for Everett's main thesis: that numbers are neither natural nor innate to humans。"
--Wall Street Journal
--James Ryerson， New York Times Book Review
A Smithsonian Best Science Book of the Year
Winner of the PROSE Award for Best Book in Language & Linguistics
Carved into our past and woven into our present， numbers shape our perceptions of the world far more than we think。 In this sweeping account of how the invention of numbers sparked a revolution in human thought and culture， Caleb Everett draws on new discoveries in psychology， anthropology， and linguistics to reveal the many things made possible by numbers， from the concept of time to writing， agriculture， and commerce。
Numbers are a tool， like the wheel， developed and refined over millennia。 They allow us to grasp quantities precisely， but recent research confirms that they are not innate--and without numbers， we could not fully grasp quantities greater than three。 Everett considers the number systems that have developed in different societies as he shares insights from his fascinating work with indigenous Amazonians。
"This is bold， heady stuff。。。 The breadth of research Everett covers is impressive， and allows him to develop a narrative that is both global and compelling。。。 Numbers is eye-opening， even eye-popping。"
--New Scientist
"A powerful and convincing case for Everett's main thesis: that numbers are neither natural nor innate to humans。"
--Wall Street Journal
Reviews
Hadjer Kouidri
，
يأخذنا كيليب افريت في رحلة الى عالم الاعداد。。 رحلة توثق علاقتنا الشديدة بالاعداد。。حيث يوضع لنا ان اصابعنا هي ارقامنا الاولى ومنذ وجودنا داخل ارحام امهاتنا ونحن نستشعر الكميات من خلالها。。 في اللغات البدائية خمسة هي اليد وستة هي اليد +واحد。يقدم لنا الكتاب معلومات وفيرة حول الاعدادالاعداد عندما نقولها。。。 الارقام عندما نكتبها。ترتبط الاعداد المعقدة بالمجتمعات الزراعية。هناك عقل عددي فطري يميز بين الكميات。。 ولكن البشر هم الذين اخترعوا الارقام 。ساعدت الارقام في بناء الاهرامات。。 كما ساعدت الارقام في حساب يأخذنا كيليب افريت في رحلة الى عالم الاعداد。。 رحلة توثق علاقتنا الشديدة بالاعداد。。حيث يوضع لنا ان اصابعنا هي ارقامنا الاولى ومنذ وجودنا داخل ارحام امهاتنا ونحن نستشعر الكميات من خلالها。。 في اللغات البدائية خمسة هي اليد وستة هي اليد +واحد。يقدم لنا الكتاب معلومات وفيرة حول الاعدادالاعداد عندما نقولها。。。 الارقام عندما نكتبها。ترتبط الاعداد المعقدة بالمجتمعات الزراعية。هناك عقل عددي فطري يميز بين الكميات。。 ولكن البشر هم الذين اخترعوا الارقام 。ساعدت الارقام في بناء الاهرامات。。 كما ساعدت الارقام في حساب دورة القمر ومدارات الكواكب。نظام العصي llllll هو منطق الحروف الرومانية。ضمير المتكلم l في اللغة الانجليزية هو عصا واحدة او المتكلم الواحد。ارتبطت الارقام بالروحيات。。。ذلك بالببيولوجيا。。 اننا نفضل التعداد العشري لانه لدينا عشرة اصابع。كتاب جميل جدا。。 。。。more
Lizzie
，
I read about this in the New Yorker and decided to pick it up and read the whole thing！As always with a book this specific by an academic author， there are definitely parts that are just too in the weeds to enjoy。 But overall， I liked most of us。 I especially enjoyed the chapter on cultures who don't have numbers， and hmthr one on how babies perceive numbers！ From an equity perspective， he wasn't too bad。 It could have been better， but he did make a point to be clear that societies without numbe I read about this in the New Yorker and decided to pick it up and read the whole thing！As always with a book this specific by an academic author， there are definitely parts that are just too in the weeds to enjoy。 But overall， I liked most of us。 I especially enjoyed the chapter on cultures who don't have numbers， and hmthr one on how babies perceive numbers！ From an equity perspective， he wasn't too bad。 It could have been better， but he did make a point to be clear that societies without numbers （mostly indigenous to the Amazon and Australia at this point in time） are not "primitive"。 He was very clear in rejecting anti-indigenous narratives as well。 It was very Western civilization focused。 I wanted more on the South and Central American societies use of numbers。 It's a survey book so he mentions lots of cultures but doesn't have time to go into all of them。 Ultimately， I learned some cool new facts about numbers！ 。。。more
Nada Khaled
，
يُضاف إلى قائمة أفضل كتب الرياضيات التي قرأتها❤️
ماهي
，
كتاب جيد، أثار لديّ أسئلة أكثر من الإجابات التي قدمها。。 بالرغم من التكرار والتأكيد على نفس الأفكار المحددة في كل فصل تقريبا。هناك الكثير من الافتراضات والتصورات الشخصية التي يفسر بها الكاتب، وغيره من الباحثين المذكورين، نتائج التجارب العملية والبيانات التي حصلوا عليها。لذلك بدا أن تاريخ الأعداد وبدايتها مثل أحجية تنقصها الكثير من القطع، ويحاول الباحثون إيجاد هذه القطع بتفسيرات معاصرة، من بينها أن أسلافنا اخترعوا الأعداد لتتبع التقويم أو تسجيل الكميات أو لأن أحدهم -بشكل ما - لاحظ التطابق العددي بين كتاب جيد، أثار لديّ أسئلة أكثر من الإجابات التي قدمها。。 بالرغم من التكرار والتأكيد على نفس الأفكار المحددة في كل فصل تقريبا。هناك الكثير من الافتراضات والتصورات الشخصية التي يفسر بها الكاتب، وغيره من الباحثين المذكورين، نتائج التجارب العملية والبيانات التي حصلوا عليها。لذلك بدا أن تاريخ الأعداد وبدايتها مثل أحجية تنقصها الكثير من القطع، ويحاول الباحثون إيجاد هذه القطع بتفسيرات معاصرة، من بينها أن أسلافنا اخترعوا الأعداد لتتبع التقويم أو تسجيل الكميات أو لأن أحدهم -بشكل ما - لاحظ التطابق العددي بين أصابع العد والكميات المنفصلة！ 。。。more
Jorge Martínez
，
Después de un inicio algo lento e intrascendente， el autor va adentrándose de manera fascinante en aspectos lingüísticos， psicológicos， neurológicos y culturales del origen e impacto de los números en el desarrollo de la historia humana。
Ahmed Mimon Ash-Shazlie
，
الكتاب غني بالأفكار التي قد تكون جديدة وتدفع لإعادة النظر في بعض مسلماتنا عن دور الأعداد في حياتنا。لغة الكتاب جزلة والترجمة جيدة。
Claire
，
This sounds like something that my friend Oğuz would probably be extremely interested in， particularly on the human history standpoint。 It talks about the Rosetta Stone and other stuff of interest such as that。 If you are interested in cultural anthropology， or honestly， linguistics， this is seriously your cup of tea， even if you microwave your water like the tea salespeople say you're not supposed to。Seek the index for the anthropomorphic history topics that seize your interest！ There is more t This sounds like something that my friend Oğuz would probably be extremely interested in， particularly on the human history standpoint。 It talks about the Rosetta Stone and other stuff of interest such as that。 If you are interested in cultural anthropology， or honestly， linguistics， this is seriously your cup of tea， even if you microwave your water like the tea salespeople say you're not supposed to。Seek the index for the anthropomorphic history topics that seize your interest！ There is more than algebra。Such as the Ainu！I originally got this book since I thought there really did have to be something rational behind such a small book on such an emormous topic。 I was so puzzled by that。 Why could that be？Well， as it turns out， Everett has created a piece that incorporates all these matters in this tiny space。Have you ever microwaved your water？ 。。。more
The Inquisitive Biologist
，
Very readable， this book makes a strong case for numeracy not being innate， but a culturally invented tool that changed the course of human history。 See my full review at https://inquisitivebiologist。com/2018。。。 Very readable， this book makes a strong case for numeracy not being innate， but a culturally invented tool that changed the course of human history。 See my full review at https://inquisitivebiologist。com/2018。。。 。。。more
Lia
，
About two years ago I got lucky enough to attend a talk by the famous linguist Dan Everett at my University in Potsdam。 During his presentation he mentioned that the Pirahã （the people whose language and culture he became famous for studying） don’t use numbers。 They don’t count and when they differentiate quantities， they use words similar to „a few“ and „a lot“。 He then told us about his son’s book， which is about numbers and language and different cultures。 Three things that interest me very m About two years ago I got lucky enough to attend a talk by the famous linguist Dan Everett at my University in Potsdam。 During his presentation he mentioned that the Pirahã （the people whose language and culture he became famous for studying） don’t use numbers。 They don’t count and when they differentiate quantities， they use words similar to „a few“ and „a lot“。 He then told us about his son’s book， which is about numbers and language and different cultures。 Three things that interest me very much， which is why I was very happy that an acquaintance actually owns the book and was willing to lend it to me。While reading this book， I got to learn fascinating things that I will certainly use as pretentious fun facts whenever the opportunity arises。 I found the book easy to read and think it should be quite accessible to most readers （it is not purely academic， it gives you more of an overview of what is known about how counting and numbers emerged among humans， cognitive aspects， linguistic aspects and so on）。To give you an idea of what this book is about， I have collected a few quotes with ideas or observations that I find fascinating: For speakers of Aymara and several other languages， the future does not lie in front of the speaker。 In fact， for the Aymara the future lies behind the speaker， while the past is located metaphorically in front of the speaker。 （p。 12） In an incredibly comprehensive survey of 1，066 languages， linguist Matthew Dryer recently found that 98 of them are like Karitâna and lack a grammatical means of marking nouns as being plural。 （p。 90） Everett states that we can always exactly recognize whether something consists of 1， 2 and 3 objects of any kind， while， as soon as there are 4 or more things， we can only estimate the number。 As a final example of the way in which smaller numbers are treated distinctly in human language， consider Roman numerals。 These numbers evolved based on a tally system based on linear marks。 In Roman numerals， smaller quantities are represented simply via lines: I （1）， II （2）， and III （3）。 Yet larger quantities are treated differently， because， unlike a series of three lines， larger series are cognitively unwieldy: IV is easier to discriminate than IIIIIIIII。 The latter series of lines is difficult to precisely quantify， when contrasted to， I， II， or III， which can be immediately subitized。 （p。 107） Number words also serve as references to simple realizations。 We may not be innately pre-equipped to make those realizations， but some humans do make them， and other humans can acquire them through linguistic means。 As noted in the Prologue， what makes our species so special is not so much that we are great art inventing， but that we are exceptional at inheriting and sharing inventions because of our linguistic nature。 （p。 195） 。。。more
Ilib4kids
，
*** From anthology point of view**Chapter 6， Quantity in the minds of Young Childrensuccessor principle p160， typically acquires at age 4Cardinal Principle。We are borne with two senses: Exact number sense only recognize 1， 2， or 3; and Approximate number sense。 Numbers humans invented give us tools to precisely differentiate them。 We made numbers， and numbers also made us。 Human body serves as the foundation for numeral systems。 All share a common bias。 They are all based somehow on ten or some *** From anthology point of view**Chapter 6， Quantity in the minds of Young Childrensuccessor principle p160， typically acquires at age 4Cardinal Principle。We are borne with two senses: Exact number sense only recognize 1， 2， or 3; and Approximate number sense。 Numbers humans invented give us tools to precisely differentiate them。 We made numbers， and numbers also made us。 Human body serves as the foundation for numeral systems。 All share a common bias。 They are all based somehow on ten or some other multiple of five。 Our minds needed our bodies， in particular our fingers and hands， to keep track of quantities。 Numbers reflect a strong bias toward our construal of quantities through individuated units of our biology， principally our fingers。 The prominence of the decimal base is clearly due to human biology rather than， as in sometimes assumed， some inherent roundedness or efficacy of grouping things into 10。 There higher numbers are based on multiplication rather addition （for example， 12 = 10 + 2， 22 = 2 * 10 + 2）Successor principle: Successor is one larger than predecessor Cardinal principle: when you count a number of objects， the number of items in total is the last word spoken as you count them。 For example， if there are five apples on a table: 'One' - 'Two' - 'Three' - 'Four' - 'Five'。Vocabulary:A base is a building block for other numbers。 The term can also refer to the value raised to specific powers in a written numeral system。 Mayan system of numerals was based on twenty。binary （ base 2）; ternary （Base 3）; quaternary （base 4）; quinary （base 5）; senary （base 6）; Octonary （Base 8）; nonary （Base 9）; duodecimal （base 12）; base vigesimal （base twenty， score）; sexagesimal （base 60）The trial number is a grammatical number referring to three item。 in contrast to and 'plural' （four or more items）;'singular' （one item）， 'dual' （two items）， trial （three items）， quadral （four items）In linguistics， reduplication is a morphological process in which the root or stem of a word （or part of it） or even the whole word is repeated exactly or with a slight change。ontogeny: the development of an individual from a fertilized ovum to maturity， as contrasted with the development of a group or species。个体发育phylogeny: the development over time of a species， genus， or group， as contrasted with the development of an individual 种族发生史a school of fish， a pod of dolphinsA gaggle: refers to a group of geese that are not flying。A skein: refers to a group of geese that are flying。A flock of ducks。 。。。more
Aurora
，
Fascinating concepts。。。unfortunately I didn't find the writing engaging for the majority of the book， and at times it was even repetitive。 An interesting read--subject-wise--but not so much in other regards。 Fascinating concepts。。。unfortunately I didn't find the writing engaging for the majority of the book， and at times it was even repetitive。 An interesting read--subject-wise--but not so much in other regards。 。。。more
Eduardo Sauret
，
En 20 páginas pudo haber resumido lo que escribió en más de 200
Mishehu
，
A very interesting book。 Makes a few essential claims about the origins of numeracy （in certain seemingly hard-wired human -- and non-human -- instincts） and the impact of numeracy on the human species。 Book is well written and convincingly argued。 Less one star on account of some repetition in the writing， and because it's not clear to me that the book treads new ground。 But as brief surveys of fascinating topics go， this one was well worth my time。 I highly recommend it。 A very interesting book。 Makes a few essential claims about the origins of numeracy （in certain seemingly hard-wired human -- and non-human -- instincts） and the impact of numeracy on the human species。 Book is well written and convincingly argued。 Less one star on account of some repetition in the writing， and because it's not clear to me that the book treads new ground。 But as brief surveys of fascinating topics go， this one was well worth my time。 I highly recommend it。 。。。more
Rafelmenmell
，
La idea es interesante pero el desarrollo no， el libro es muy repetitivo; cada idea se expone al menos tres veces。 Salen los piraha lo que lo hace algo más agradable。
Debbie
，
This review has been hidden because it contains spoilers。 To view it， click here。 I thought this book was going to be a lot more interesting than it was。 It was very repetitious - points that could have been made in one paragraph were strung out into complete chapters。 There are basically six key points made in this book over 258 pages - in other words， there's a lot of filler。To save you the trouble of ploughing through those 258 pages， I'll summarise the book for you:1。 Humans are born with the innate ability to distinguish between quantities of 1， 2 & 32。 Humans are born w I thought this book was going to be a lot more interesting than it was。 It was very repetitious - points that could have been made in one paragraph were strung out into complete chapters。 There are basically six key points made in this book over 258 pages - in other words， there's a lot of filler。To save you the trouble of ploughing through those 258 pages， I'll summarise the book for you:1。 Humans are born with the innate ability to distinguish between quantities of 1， 2 & 32。 Humans are born with the innate ability to distinguish between smaller and larger quantities of items as long as the ratio exceeds 1:2， i。e。 even if we don't know numbers we can tell that a set of 16 items is larger than a set of 8， but not that a set of 12 items is larger than a set of 83。 Humans cannot comprehend the concept of discrete quantities higher than 3 without being brought up in a numerate culture - we need language to pass this knowledge on4。 Virtually all numerate cultures have number systems based on the number of fingers we have， e。g。 decimal systems5。 There is a big difference between being numerate and developing abstract mathematics6。 The development of elaborate number systems was a necessary precursor to the development of agriculture which in turn led to the development of large civilisations and god-centred religions 。。。more
Mills College Library
，
513。211 E933 2017
Victor Sonkin
，
An introduction into the world of numbers。 Though kind of schoolish and vague， it gave me at least one thought — very simple， but still: imagine you're given 16 stones， then they are removed and you are asked to put the exact same thing （number of stones） on the sand （or wherever）。 This is extremely easy if you can count; virtually impossible if you can't （and there are whole civilizations that can't）。 This is a startling thought。 Also， there's a division between 1-2-3 and everything else: 1-2-3 An introduction into the world of numbers。 Though kind of schoolish and vague， it gave me at least one thought — very simple， but still: imagine you're given 16 stones， then they are removed and you are asked to put the exact same thing （number of stones） on the sand （or wherever）。 This is extremely easy if you can count; virtually impossible if you can't （and there are whole civilizations that can't）。 This is a startling thought。 Also， there's a division between 1-2-3 and everything else: 1-2-3 objects/people etc。 are perceived immediately as such; for everything larger， you need to count。 （Criminology etc。） 。。。more
A。 J。
，
Very interesting premise and quite interesting rationale。 Evidence and speculation are clearly separated。 The concept of higher （than 3 or4） numbers sparking a cultural turn in the history of human evolution is quite provocative。 The author does a good （but not great） job explaining his thoughts。 At times it is repetitive and the redundancy gets laborious。 3。5 stars would be my preference over a full “hand。”
Jay Eckard
，
I thought at first that this book just didn't understand who its audience is。 And that's certainly true; it's too academic for a strictly popular audience and far too weak， methodologically， to appeal to an academic audience with its expectations of rigorous thinking。 But it took til almost the end of me reading the book for me to realize that this book's closest relatives are pseudo-history and pseudo-science books， like the works of Erich von Daniken or Anatoly Fomenko。 I'm not suggesting this I thought at first that this book just didn't understand who its audience is。 And that's certainly true; it's too academic for a strictly popular audience and far too weak， methodologically， to appeal to an academic audience with its expectations of rigorous thinking。 But it took til almost the end of me reading the book for me to realize that this book's closest relatives are pseudo-history and pseudo-science books， like the works of Erich von Daniken or Anatoly Fomenko。 I'm not suggesting this book is ipsa re pseudo-science， but Everett certainly adopts many of their habits。 Perhaps more generously， the author is so excited by his own research that he opens himself out to frequent methodological weakness。 With an editor at HUP this seems unlikely， but who knows？ Maybe that editor is actually taken with the tiresome youthful elan the author forces into the text， but I don't think many readers will be。Maybe buoyed up on that elan， Everett is willing and able， time after time， to jump to the most tenuous conclusions based on scant evidence。 There must be at least a dozen variations in the text of an argument that runs "the evidence weakly supports X， so we can safely assume X is a reasonable conclusion。" This trend builds too strongly on the weak foundations the author provides: thus in the last chapters， Everett tries to tie the existence of god（s） and large-scale religion to the invention of numbers。 Before that， though， are the theses that numbers allowed the existence of language， cities， and agriculture。 The author's overall premise is also curious: it boils down to "numbers helped us evolve into what we are now。" That's a fair enough idea， but it also begs a basic question: who would disagree with that？ Why build a string of weak arguments to support a theory no one wants to contradict？ For as much circumstantial evidence as is provided and as few solid answers are provided， this reading of this text is just too much work for too little a reward。 。。。more
Dan Ust
，
Good stuff on the history， neurobiology， and anthropology of numbers。 I especially liked the sections on anumeric peoples。 The flaw for me is it's often repetitious。 I'd give it 3。5 stars if that were possible。 （And， as some might expect， I wish he were more aware of philosophy of math， especially the work of Kitcher and Chihara。） Good stuff on the history， neurobiology， and anthropology of numbers。 I especially liked the sections on anumeric peoples。 The flaw for me is it's often repetitious。 I'd give it 3。5 stars if that were possible。 （And， as some might expect， I wish he were more aware of philosophy of math， especially the work of Kitcher and Chihara。） 。。。more
Megan
，
I really enjoyed this book at the juncture of written language and math。 It is fascinating how many languages have the hand at the basis of their number system。 The only thing I would have enjoyed more in this book is even more photos of the described objects。 And way more detail。 Except more detail would have bogged the book down。 Print。
Marko_cibej
，