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Numbers and the Making of Us: Counting and the Course of Human Cultures
Carved into our past, woven into our present, numbers shape our perceptions of the world and of ourselves much more than we commonly think. Numbers and the Making of Us is a sweeping account of how numbers radically enhanced our species' cognitive capabilities and sparked a revolution in human culture. Caleb Everett brings new insights in psychology, anthropology, primatology, linguistics, and other disciplines to bear in explaining the myriad human behaviors and modes of thought numbers have made possible, from enabling us to conceptualize time in new ways to facilitating the development of writing, agriculture, and other advances of civilization.
Number concepts are a human invention--a tool, much like the wheel, developed and refined over millennia. Numbers allow us to grasp quantities precisely, but they are not innate. Recent research confirms that most specific quantities are not perceived in the absence of a number system. In fact, without the use of numbers, we cannot precisely grasp quantities greater than three; our minds can only estimate beyond this surprisingly minuscule limit.
Everett examines the various types of numbers that have developed in different societies, showing how most number systems derived from anatomical factors such as the number of fingers on each hand. He details fascinating work with indigenous Amazonians who demonstrate that, unlike language, numbers are not a universal human endowment. Yet without numbers, the world as we know it would not exist.
Number concepts are a human invention--a tool, much like the wheel, developed and refined over millennia. Numbers allow us to grasp quantities precisely, but they are not innate. Recent research confirms that most specific quantities are not perceived in the absence of a number system. In fact, without the use of numbers, we cannot precisely grasp quantities greater than three; our minds can only estimate beyond this surprisingly minuscule limit.
Everett examines the various types of numbers that have developed in different societies, showing how most number systems derived from anatomical factors such as the number of fingers on each hand. He details fascinating work with indigenous Amazonians who demonstrate that, unlike language, numbers are not a universal human endowment. Yet without numbers, the world as we know it would not exist.
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First published January 1, 2017
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Displaying 1 - 28 of 28 reviews
August 20, 2021
-Las expectativas son algo muy peligroso, tanto las de los autores como las de los lectores.-
Género. Ensayo.
Lo que nos cuenta. El libro Los números nos hicieron como somos (publicación original: Numbers and the Making of Us, 2017) trata, en palabras del propio autor, de retratar desde una perspectiva principalmente antropológica (pero no la única) cómo los números, entendidos como representación simbólica y verbal de cantidades, supusieron una transformación radical de la condición humana.
¿Quiere saber más de este libro, sin spoilers? Visite:
https://librosdeolethros.blogspot.com...
Género. Ensayo.
Lo que nos cuenta. El libro Los números nos hicieron como somos (publicación original: Numbers and the Making of Us, 2017) trata, en palabras del propio autor, de retratar desde una perspectiva principalmente antropológica (pero no la única) cómo los números, entendidos como representación simbólica y verbal de cantidades, supusieron una transformación radical de la condición humana.
¿Quiere saber más de este libro, sin spoilers? Visite:
https://librosdeolethros.blogspot.com...
July 6, 2017
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.)
(And, as some might expect, I wish he were more aware of philosophy of math, especially the work of Kitcher and Chihara.)
December 8, 2020
يُضاف إلى قائمة أفضل كتب الرياضيات التي قرأتها❤️
August 17, 2017
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.
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.
January 27, 2023
منذ بداية تدقيق الرضيع على ايديه، ولعبه بها، وادراك التناظر بين اليدين، والمقارنة مع كميات أخرى؛ تبدأ علاقتنا بالأعداد وتتزايد مع تقدم العمر. إذ نحسب أعمارنا، والسلع التي نشتريها، والرواتب التي نتقاضاها، ونصادف الأعداد في كل معرفة نحاول تعلمها، فالرياضيات هي أم العلوم الأخرى لا يمكن تعلم شيء إلا في ضوئها.
"لقد أمسكنا بأيدينا الأشياء الموجودة حولنا، وذلك بصورة مجازية وحرفية أيضًا. وقد شكلنا هذه التطابقات المجردة للكميات، وضعنا منها أعدادًا حقيقية للغاية، لكنها غير طبيعية على الإطلاق. لقد بنينا الأعداد، ونظرًا إلى تأثيرها التحويلي، فمن الإنصاف أن نقول إنَّ الأعداد قد بنتنا أيضًا."
يبحث الكتاب في الأعداد وعلاقتها مع تطور الإنسان وتطور الثقافة والاختراع، والأعداد من حيث هي التمثيل الرمزي للكميّات، وهذه الكميات هي كل شيء يرد بالطبيعة، سواء كان منتظم مثل عدد ارجل العنكبوت، أو دورات تكاثر بعض الحيوانات. لكن التمثيل الرمزي لهذه الكميات لا توجد بصورة مستقلة عن الابتكار البشري لها. التوصل لأنظمة العد وتدوينها أدى لانفجار ادراكي ما زال مستمرا لليوم مع كل تقدم في المعرفة الحسابية والرياضية.
يناقش الكتاب بهذه الفكرة الأساسية (الأعداد كتمثيل رمزي للكميات هي أدوات ادراكية اساسية ساهمت في بناء الانسان)، واعتمد اسلوبه على البحث في عدة اصعدة:
* علم الآثار: رصد المكتشفات الأثرية المنقوش عليها أنظمة عددية قديمة حول العالم ، وأنماط هذه الانظمة
* علم الانسان: رحلات ميدانية لاستكشاف بعض الشعوب والقبائل التي لا تتبع النظام العشري العالمي، واستكشاف لغاتها العددية وتأثيرها على ادراكهم
* اللسانيات: وظفها في أكثر من مكان، لتأكيد السمة النحوية المشتركة في بنية الدماغ البشري، رغم عدم استعمالها في بعض الثقافات
* النمو: استعرض دراسات طويلة المدى عن تطور الأطفال في قدرتهم على ادراك الكميات، وطرح أهمية التعلّم في تطوير هذه المهارات والنشأة في بيئة تحفز استخدام الحاسة العددية
*البيولوجيا التطورية: قدم لنا تتبع للادراك العددي لدى بعض الحيوانات، والتي تمتلك بالفعل قدرة على تمييز بعض الكميات بصورة تقريبية بما يتناسب مع بقائها في البرية، لكن ما يختلف فيه الإنسان هو وجود الأعداد المجردة الخارجية (المكتوبة) والألفاظ التي تطلق عليها في اللغة
الأعداد تجاوزت إطلاق كلمات معينة على كميات موجودة أمامنا إلى مجموعات عددية معقدة ومجردة، يظهر لنا في كل مرة انه يتم استخدامها فيما بعد لتطوير اختراع او برمجية او فهم لطبيعة الكون والحياة، فقد أدى إطلاق كلمات وكتابة رموز لكميات بسيطة إلى عالم حضاري مليء بالاكتشافات العلمية والاختراعات التقنية التي نعيش فيها الآن.
"لقد أمسكنا بأيدينا الأشياء الموجودة حولنا، وذلك بصورة مجازية وحرفية أيضًا. وقد شكلنا هذه التطابقات المجردة للكميات، وضعنا منها أعدادًا حقيقية للغاية، لكنها غير طبيعية على الإطلاق. لقد بنينا الأعداد، ونظرًا إلى تأثيرها التحويلي، فمن الإنصاف أن نقول إنَّ الأعداد قد بنتنا أيضًا."
يبحث الكتاب في الأعداد وعلاقتها مع تطور الإنسان وتطور الثقافة والاختراع، والأعداد من حيث هي التمثيل الرمزي للكميّات، وهذه الكميات هي كل شيء يرد بالطبيعة، سواء كان منتظم مثل عدد ارجل العنكبوت، أو دورات تكاثر بعض الحيوانات. لكن التمثيل الرمزي لهذه الكميات لا توجد بصورة مستقلة عن الابتكار البشري لها. التوصل لأنظمة العد وتدوينها أدى لانفجار ادراكي ما زال مستمرا لليوم مع كل تقدم في المعرفة الحسابية والرياضية.
يناقش الكتاب بهذه الفكرة الأساسية (الأعداد كتمثيل رمزي للكميات هي أدوات ادراكية اساسية ساهمت في بناء الانسان)، واعتمد اسلوبه على البحث في عدة اصعدة:
* علم الآثار: رصد المكتشفات الأثرية المنقوش عليها أنظمة عددية قديمة حول العالم ، وأنماط هذه الانظمة
* علم الانسان: رحلات ميدانية لاستكشاف بعض الشعوب والقبائل التي لا تتبع النظام العشري العالمي، واستكشاف لغاتها العددية وتأثيرها على ادراكهم
* اللسانيات: وظفها في أكثر من مكان، لتأكيد السمة النحوية المشتركة في بنية الدماغ البشري، رغم عدم استعمالها في بعض الثقافات
* النمو: استعرض دراسات طويلة المدى عن تطور الأطفال في قدرتهم على ادراك الكميات، وطرح أهمية التعلّم في تطوير هذه المهارات والنشأة في بيئة تحفز استخدام الحاسة العددية
*البيولوجيا التطورية: قدم لنا تتبع للادراك العددي لدى بعض الحيوانات، والتي تمتلك بالفعل قدرة على تمييز بعض الكميات بصورة تقريبية بما يتناسب مع بقائها في البرية، لكن ما يختلف فيه الإنسان هو وجود الأعداد المجردة الخارجية (المكتوبة) والألفاظ التي تطلق عليها في اللغة
الأعداد تجاوزت إطلاق كلمات معينة على كميات موجودة أمامنا إلى مجموعات عددية معقدة ومجردة، يظهر لنا في كل مرة انه يتم استخدامها فيما بعد لتطوير اختراع او برمجية او فهم لطبيعة الكون والحياة، فقد أدى إطلاق كلمات وكتابة رموز لكميات بسيطة إلى عالم حضاري مليء بالاكتشافات العلمية والاختراعات التقنية التي نعيش فيها الآن.
May 2, 2017
A poorly written book on an interesting topic.
I've always been interested in cognition, the limits of thought, concepts we can form and those that will remain for ever beyond us. Of course, I picked up this book as soon as I came across it. I won't say I'm completely disappointed—the actual research presented is interesting and convincing—but the presentation is pretty bad.
On the one hand, the style is academic: lots of end notes, carefully worded conclusions, absence of any ideas that are not directly supported by evidence. On the other hand, the level is basic: concepts that should be familiar to any follower of popular science are carefully explained with simple words, then repeated again and again and again until the reader loses count. And yes, lame number-based wordplay like that abounds.
All of that is annoying, but the real disappointment is the lack of an overarching idea, or rather its dimness. One does get the impression that numbers, as opposed to quantities, are a human invention, that they impacted the development of language, preceded the development of writing, and enabled human culture.
But the author leaves this conclusion and its shape for the reader to deduce and keeps any insights and leaps of understanding to himself. He sticks to careful, evidence-supported academic exposition and never strays from the straight and narrow. Essentially, his fault is a failure of nerve, which is a great pity.
I've always been interested in cognition, the limits of thought, concepts we can form and those that will remain for ever beyond us. Of course, I picked up this book as soon as I came across it. I won't say I'm completely disappointed—the actual research presented is interesting and convincing—but the presentation is pretty bad.
On the one hand, the style is academic: lots of end notes, carefully worded conclusions, absence of any ideas that are not directly supported by evidence. On the other hand, the level is basic: concepts that should be familiar to any follower of popular science are carefully explained with simple words, then repeated again and again and again until the reader loses count. And yes, lame number-based wordplay like that abounds.
All of that is annoying, but the real disappointment is the lack of an overarching idea, or rather its dimness. One does get the impression that numbers, as opposed to quantities, are a human invention, that they impacted the development of language, preceded the development of writing, and enabled human culture.
But the author leaves this conclusion and its shape for the reader to deduce and keeps any insights and leaps of understanding to himself. He sticks to careful, evidence-supported academic exposition and never strays from the straight and narrow. Essentially, his fault is a failure of nerve, which is a great pity.
Read
July 10, 2020About 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:
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.
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)
September 16, 2020
الكتاب غني بالأفكار التي قد تكون جديدة وتدفع لإعادة النظر في بعض مسلماتنا عن دور الأعداد في حياتنا.
لغة الكتاب جزلة والترجمة جيدة.
لغة الكتاب جزلة والترجمة جيدة.
August 31, 2021
Esta frase del mismo libro lo describe mejor:
Moldeamos correspondencias de cantidades abstractas en algo muy real pero muy poco natural, los números; y dado el efecto transformador en la historia de la humanidad, es justo decir que los números también nos hicieron a nosotros.
Moldeamos correspondencias de cantidades abstractas en algo muy real pero muy poco natural, los números; y dado el efecto transformador en la historia de la humanidad, es justo decir que los números también nos hicieron a nosotros.
June 9, 2018
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 & 3
2. 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 8
3. 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 on
4. Virtually all numerate cultures have number systems based on the number of fingers we have, e.g. decimal systems
5. There is a big difference between being numerate and developing abstract mathematics
6. 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
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 & 3
2. 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 8
3. 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 on
4. Virtually all numerate cultures have number systems based on the number of fingers we have, e.g. decimal systems
5. There is a big difference between being numerate and developing abstract mathematics
6. 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
This entire review has been hidden because of spoilers.
April 27, 2021
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 الاعداد
الاعداد 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..
يقدم لنا الكتاب معلومات وفيرة حول الاعداد
الاعداد 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..
June 21, 2017
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.
December 1, 2022
أخذت كورس في ( نظرية الأعداد ) لم يكن رغبتي وإنما كانت (الطبولوجيا) ولكنها لم تنزل ذلك السمستر. كانت نظرتي سخيفة جداً وسطحية عن عالم الأعداد. عندما حضرت الكلاسات الأولى أُبهرت بدكتور المادة فقد كان يلبس سترة صوف أنيقة بدا كأنه ممثل يؤدي شخصية دكتور رياضيات في أحد الأفلام البريطانية؛ فقررت استكمال الكورس لذلك السبب الغريب. ماهو العدد ؟ سؤال بدا لي بسيطا في ذلك الوقت لكني لم أستطع الإجابة تلعثمت ولم يجب أحد. علمت كيف أن عالم الأعداد معقد ومليء بالإثباتات والبراهين الباردة. ليس سهلاً كما يبدو. لكل عدد صفة وكيان وشخصية وهناك طبقية صارخة في عالم الأعداد. علمت لمَ أفلاطون هام بالأعداد فلها سحر غريب ويبدو بأنني وقعت في ذلك السحر. الكتاب يتناول تاريخ هذه الأعداد فهو عبارة عن بحث أنثروبولوجي ثقيل -كعادة مباحث الانثروبولوجيا- في تتبع أثر العدد على الإنسان. هل الأعداد موجودة بالفطرة -غريزيا -وإن كان كذلك فإلى أي حد تلك الدقة أو مدى تصورنا للكميات؟ وهل هناك شعوب لاعددية وكيف أثر عليها غياب الأعداد.مجموعة أبحاث عظيمة في محاولة لإيجاد إجابات أو مقاربات لتلك الأسئلة.
August 24, 2020
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?
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?
December 30, 2017
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.)
October 9, 2020
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!
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!
July 20, 2021
"En lo que se refiere a las ideas, heredamos mucho mas de lo que innovamos"
Nuestra historia con los números es mas que descubrimiento, es una larga serie de hechos y aportaciones de distintas culturas, el autor ahonda mucho en el papel fundamental de los números en nuestra vida, como afectan al lenguaje, a las relaciones e incluso al tiempo.
Si como en mi caso estas buscando un libro lleno de historias fantásticas sobre los números probablemente te veas decepcionado, incluso podría recomendar que solo leyeras la introducción y a partir del capitulo 6 en adelante, que aborda temas como experimentos sobre la predisposición de conocimiento numérico que podrían llegar a tener (o no) los animales, bebes y comunidades anúmericas, así como la clara relaciona entre nuestro propio cuerpo físico y nuestro conocimiento numérico, pero si en cambio lo que buscas en un libro bien documentado que alterne entre historias y descripciones que rayan en lo técnico sobre los números en niveles tan esenciales como el lenguaje, pues bueno, seguramente amaras este libro.
Nuestra historia con los números es mas que descubrimiento, es una larga serie de hechos y aportaciones de distintas culturas, el autor ahonda mucho en el papel fundamental de los números en nuestra vida, como afectan al lenguaje, a las relaciones e incluso al tiempo.
Si como en mi caso estas buscando un libro lleno de historias fantásticas sobre los números probablemente te veas decepcionado, incluso podría recomendar que solo leyeras la introducción y a partir del capitulo 6 en adelante, que aborda temas como experimentos sobre la predisposición de conocimiento numérico que podrían llegar a tener (o no) los animales, bebes y comunidades anúmericas, así como la clara relaciona entre nuestro propio cuerpo físico y nuestro conocimiento numérico, pero si en cambio lo que buscas en un libro bien documentado que alterne entre historias y descripciones que rayan en lo técnico sobre los números en niveles tan esenciales como el lenguaje, pues bueno, seguramente amaras este libro.
December 14, 2017
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.”
September 26, 2019
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.
May 29, 2020
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.
An interesting read--subject-wise--but not so much in other regards.
September 19, 2020
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.
October 24, 2018
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.
January 4, 2020
En 20 páginas pudo haber resumido lo que escribió en más de 200
July 29, 2020
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...
June 3, 2025
I learned so much. Really stretched my brain. Loved it.
August 4, 2025
GENIAL !! Puede que le faltara rigor y hubo un par de veces que estaba redactado como docuseries de Netflix (2016) pero en general estuvo muy interesante.
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March 20, 2021*** From anthology point of view**
Chapter 6, Quantity in the minds of Young Children
successor principle p160, typically acquires at age 4
Cardinal 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 dolphins
A 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.
Chapter 6, Quantity in the minds of Young Children
successor principle p160, typically acquires at age 4
Cardinal 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 dolphins
A 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.
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March 9, 2018513.211 E933 2017
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