6 ms·

I've yet to see this brought up, but I hope a wandering historian might speak up about this along with reference a book I can read more about this. Wasn't the

I've yet to see this brought up, but I hope a wandering historian might speak up about this along with reference a book I can read more about this. Wasn't the marvel to Arabic-Hindu (edit) numerals the math system behind them? Beyond counting, no one really discusses the actual use of these other number systems. Maybe the actual number representation with our modern numerals is the worst way to track count, but the way to manipulate those numbers is the best that ever was from what I can tell. All thanks to the folks that laid down the foundation to Arabic-Hindu numerals. Using our current methods of math does not translate directly to other numerals systems... so it's just hard for me to gain an appreciation of these other numeral styles? Years ago I watched a documentary that focused on, I think on Cuneiform writing or maybe another ancient writing system. What was known on how accounting was done, the mathematic usage of that system was a complete pain in the ass. It made me think about how much we take for granted how easy it is to add and subtract, let alone multiply and divide, with our current system. This used to be a specialized skill. Now it's considered the beginning to even knowing anything remotely useful. Weird scatterbrained rant, but is anyone able to point to a good, recommended resource on the history of math, ideally comparing other methodologies?

FlyingSnake 6y ago
> All thanks to the folks that laid down the foundation to Arabic numerals. As an Indian, it is particularly weird for me to see the achievements on Indian pioneer mathematicians attributed to a totally different group of people. Brahmagupta, Pingala, Aryabhatta etc. should be correctly attributed and celebrated for their towering contributions to laying the foundations of Maths as we see today.
- NoOneNew 6y ago
  Right, yes, sorry. I'm just a casual to the history of math. My bad.
- reaperducer 6y ago
  As an Indian, it is particularly weird for me to see the achievements on Indian pioneer mathematicians attributed to a totally different group of people. Unfortunately, the internet is full of this sort of thing. Wikipedia is especially rife with revisions that change inventors and originators in jingoistic ways. See also: The eight thousand tiny museums in villages scattered across the U.K. all celebrating the local "inventors" of different things that were already invented in other countries long before.
  - scythe 6y ago
    The Internet did not trick Leonardo "Fibonacci" of Pisa into calling the number system he was advocating "Arabic" in the thirteenth century.
    - NoOneNew 6y ago
      I just wanted to have a casual, nerdy discussion of math god damn it. That's all. How did this turn to a politically correct issue already?
    - jacobolus 6y ago
      Fibonacci called them "Indian figures" and arithmetic the "Indian method". So you are technically correct that the internet did not trick him into calling them "Arabic": he was not tricked at all on this point! > As my father was a public official away from our homeland in the Bugia customshouse established for the Pisan merchants who frequently gathered there, he had me in my youth brought to him, looking to find for me a useful and comfortable future; there he wanted me to be in the study of mathematics and to be taught for some days. There from a marvelous instruction in the art of the nine Indian figures, the introduction and knowledge of the art pleased me so much above all else, and I learnt from them, whoever was learned in it, from nearby Egypt, Syria, Greece, Sicily and Provence, and their various methods, to which locations of business I travelled considerably afterwards for much study, and I learnt from the assembled disputations. But this, on the whole, the algorithm and even the Pythagorean arcs, I still reckoned almost an error compared to the Indian method. Therefore strictly embracing the Indian method, and attentive to the study of it, from mine own sense adding some, and some more still from the subtle Euclidean geometric art, applying the sum that I was able to perceive to this book, I worked to put it together in xv distinct chapters, showing certain proof for almost everything that I put in, so that further, this method perfected above the rest, this science is instructed to the eager, and to the Italian people above all others, who up to now are found without a minimum. If, by chance, something less or more proper or necessary I omitted, your indulgence for me is entreated, as there is no one who is without fault, and in all things is altogether circumspect.
krastanov 6y ago
Tangentially related: in modern math we do have alternative number systems to use for problems that are cumbersome with Arabic-Hindu numerals. Check out p-adic numbers on Wikipedia, for instance.
- lambda_obrien 6y ago
  Yes, if I remember correctly, any n-ary number system is equivalent and you can translate any proof between them. It's just easier to work in one or another system.
  - tgb 6y ago
    p-adic is quite different though. It's not really that relevant to this conversation though as far as I can tell as it's not just about representing the integers or rationals in a different way. https://en.wikipedia.org/wiki/P-adic_number https://en.wikipedia.org/wiki/P-adic_number
thaumasiotes 6y ago
> Maybe the actual number representation with our modern numerals is the worst way to track count, but the way to manipulate those numbers is the best that ever was from what I can tell. All thanks to the folks that laid down the foundation to Arabic-Hindu numerals. Hmm? The manipulation and the written form are fully independent. Before the introduction of Arabic numerals to Europe, this manipulation was already common; that's what an abacus was for. It's just that you wrote your result down in Roman numerals rather than as a picture of an arrangement of beads.
- jk7tarYZAQNpTQa 6y ago
  > The manipulation and the written form are fully independent. No, they are related. The optimal written form for a base 10 manipulation system is a base 10 numeral written system. > Before the introduction of Arabic numerals to Europe, this manipulation was already common; that's what an abacus was for. And the abacus was base 10, wasn't it? So the natural (and optimal) way to write down that result is in a base 10 notation. This Cistercian numerals are base 10000. Try doing a pen and paper multiplication or division using this system. No, seriously, try it. You'll understand why historically we settled on our decimal system. It's basically "divide and conquer" applied to mental math. The good news is that 10000 has 10 as a factor, so base 10000 numerals come sort of natural to us, the learning curve isn't that high.
  - thaumasiotes 6y ago
    > This Cistercian numerals are base 10000. Try doing a pen and paper multiplication or division using this system. Sure, in the same way that Babylonian cuneiform numerals are base 60, which is "they're in base 10, but you combine multiple symbols into the space of one glyph". The Cistercian numerals don't have 10,000 separate symbols. They have 10 symbols, and one glyph includes four positional slots in which a symbol appears. They're exactly equivalent to the Arabic numeral system we use now, and the pencil-and-paper multiplication system we use now transfers directly without problems.
    - kadoban 6y ago
gumby 6y ago
> What was known on how accounting was done, the mathematic usage of that system was a complete pain in the ass. Actually it wasn't that difficult and was even rather convenient given how they viewed the rest of the world (among other things they only had rationals, and a limited number) Decimal systems didn't take over the circle, or timekeeping (and for the circle sometimes radians are easier). Decimal stock trading in the US is only a couple of decades old and within my memory countries switched to decimal currencies replacing systems that had survived centuries. In fact the US uses a non-decimal measurement system which has numerous advantages (as well as disadvantages) for daily use.
anthony_romeo 6y ago
So one element which kinda wraps all of these concepts together is what some have called the "Golden Age of Islam".[1] The [literal] Empire which emerged from Muhammad's legacy became a source of great intellectual thinking (while Europe had just entered its dark age). This makes sense, being the place of some of the oldest civilizations on Earth, and surrounded by several other great civilizations. During this time (a few hundred years after the fall of Rome) the texts of the ancient Greek philosophers and scientists became quite popular among Muslim thinkers. One could argue that this Golden Age included a natural continuation of the works of Aristotle, Plato, etc. Furthermore, they adopted a new system of representing numbers from India which turned out to be a convenient language for formalizing the concepts of Algebra (done by Muhammad ibn Musa al-Khwarizmi in the early 800's [2]). Sadly I can't recommend any books -- this was conjured up from my memories of this subject from College some time ago (with the guiding help of Wikipedia to fill in some gaps). [1] https://en.wikipedia.org/wiki/Islamic_Golden_Age https://en.wikipedia.org/wiki/Islamic_Golden_Age [2] https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi
- mercer 6y ago
  For anyone interested in this era, I can recommend the four-part series hosted by Radio War Nerd: https://www.podchaser.com/podcasts/war-nerd-radio-subscriber-feed-1383559/episodes/radio-war-nerd-ep246-arab-conq-74764998 https://www.podchaser.com/podcasts/war-nerd-radio-subscriber.... The podcast in general is quite interesting, even if you're not as left-leaning as the hosts are. But this series in particular was fun to listen to.
Balgair 6y ago
Cuneiform math isn't the most terrible. It's 'column' based, like the modern arabic version we have. However, at some times they lacked the 0 representation. Roman numerals, however, are quite difficult. In addition to the problems with basic manipulations (27-9, or XXVI - IX), they also lacked any higher symbols than 1000 (M in Roman). So for 15,000 you have to write MMMMMMMMMMMMMMM. I'll spare you numbers like 1,000,000. Here's a good video on how to do math in Cuneiform, and a brief discussion on Roman numerals: https://www.youtube.com/watch?v=RR3zzQP3bII https://www.youtube.com/watch?v=RR3zzQP3bII Strangely, Numberphile has yet to do a video on Roman/Chinese number systems. Maybe because it's really hard to do math with them, and that's a bit boring to just show that it's hard. EDIT: I have been misinformed, Chinese numbers are in fact easy to work with.
- kccqzy 6y ago
  The Roman system is indeed difficult? What's difficult about the Chinese one? It seems basically identical to Arabic numerals except using different symbols.
whatgoodisaroad 6y ago
I'm slowly reading through a book called the "History of Mathematical Notations" by Florian Cajori and it sounds like just what you're looking for. It goes into far more detail than probably anybody would wish for on the histories of various symbols and ways of writing addition, roots, ratios etc. Many of these notations were used only by a few medieval scholars for a few decades but they usually try to optimize for efficiency or clarity in some creative way. Really fascinating stuff.

FlyingSnake 6y ago

> All thanks to the folks that laid down the foundation to Arabic numerals. As an Indian, it is particularly weird for me to see the achievements on Indian pioneer mathematicians attributed to a totally different group of people. Brahmagupta, Pingala, Aryabhatta etc. should be correctly attributed and celebrated for their towering contributions to laying the foundations of Maths as we see today.

NoOneNew 6y ago
Right, yes, sorry. I'm just a casual to the history of math. My bad.
reaperducer 6y ago
As an Indian, it is particularly weird for me to see the achievements on Indian pioneer mathematicians attributed to a totally different group of people. Unfortunately, the internet is full of this sort of thing. Wikipedia is especially rife with revisions that change inventors and originators in jingoistic ways. See also: The eight thousand tiny museums in villages scattered across the U.K. all celebrating the local "inventors" of different things that were already invented in other countries long before.
- scythe 6y ago
  The Internet did not trick Leonardo "Fibonacci" of Pisa into calling the number system he was advocating "Arabic" in the thirteenth century.
  - NoOneNew 6y ago
    I just wanted to have a casual, nerdy discussion of math god damn it. That's all. How did this turn to a politically correct issue already?
  - jacobolus 6y ago
    Fibonacci called them "Indian figures" and arithmetic the "Indian method". So you are technically correct that the internet did not trick him into calling them "Arabic": he was not tricked at all on this point! > As my father was a public official away from our homeland in the Bugia customshouse established for the Pisan merchants who frequently gathered there, he had me in my youth brought to him, looking to find for me a useful and comfortable future; there he wanted me to be in the study of mathematics and to be taught for some days. There from a marvelous instruction in the art of the nine Indian figures, the introduction and knowledge of the art pleased me so much above all else, and I learnt from them, whoever was learned in it, from nearby Egypt, Syria, Greece, Sicily and Provence, and their various methods, to which locations of business I travelled considerably afterwards for much study, and I learnt from the assembled disputations. But this, on the whole, the algorithm and even the Pythagorean arcs, I still reckoned almost an error compared to the Indian method. Therefore strictly embracing the Indian method, and attentive to the study of it, from mine own sense adding some, and some more still from the subtle Euclidean geometric art, applying the sum that I was able to perceive to this book, I worked to put it together in xv distinct chapters, showing certain proof for almost everything that I put in, so that further, this method perfected above the rest, this science is instructed to the eager, and to the Italian people above all others, who up to now are found without a minimum. If, by chance, something less or more proper or necessary I omitted, your indulgence for me is entreated, as there is no one who is without fault, and in all things is altogether circumspect.

krastanov 6y ago

Tangentially related: in modern math we do have alternative number systems to use for problems that are cumbersome with Arabic-Hindu numerals. Check out p-adic numbers on Wikipedia, for instance.

lambda_obrien 6y ago
Yes, if I remember correctly, any n-ary number system is equivalent and you can translate any proof between them. It's just easier to work in one or another system.
- tgb 6y ago
  p-adic is quite different though. It's not really that relevant to this conversation though as far as I can tell as it's not just about representing the integers or rationals in a different way. https://en.wikipedia.org/wiki/P-adic_number https://en.wikipedia.org/wiki/P-adic_number

thaumasiotes 6y ago

> Maybe the actual number representation with our modern numerals is the worst way to track count, but the way to manipulate those numbers is the best that ever was from what I can tell. All thanks to the folks that laid down the foundation to Arabic-Hindu numerals. Hmm? The manipulation and the written form are fully independent. Before the introduction of Arabic numerals to Europe, this manipulation was already common; that's what an abacus was for. It's just that you wrote your result down in Roman numerals rather than as a picture of an arrangement of beads.

jk7tarYZAQNpTQa 6y ago
> The manipulation and the written form are fully independent. No, they are related. The optimal written form for a base 10 manipulation system is a base 10 numeral written system. > Before the introduction of Arabic numerals to Europe, this manipulation was already common; that's what an abacus was for. And the abacus was base 10, wasn't it? So the natural (and optimal) way to write down that result is in a base 10 notation. This Cistercian numerals are base 10000. Try doing a pen and paper multiplication or division using this system. No, seriously, try it. You'll understand why historically we settled on our decimal system. It's basically "divide and conquer" applied to mental math. The good news is that 10000 has 10 as a factor, so base 10000 numerals come sort of natural to us, the learning curve isn't that high.
- thaumasiotes 6y ago
  > This Cistercian numerals are base 10000. Try doing a pen and paper multiplication or division using this system. Sure, in the same way that Babylonian cuneiform numerals are base 60, which is "they're in base 10, but you combine multiple symbols into the space of one glyph". The Cistercian numerals don't have 10,000 separate symbols. They have 10 symbols, and one glyph includes four positional slots in which a symbol appears. They're exactly equivalent to the Arabic numeral system we use now, and the pencil-and-paper multiplication system we use now transfers directly without problems.
  - kadoban 6y ago

gumby 6y ago

> What was known on how accounting was done, the mathematic usage of that system was a complete pain in the ass. Actually it wasn't that difficult and was even rather convenient given how they viewed the rest of the world (among other things they only had rationals, and a limited number) Decimal systems didn't take over the circle, or timekeeping (and for the circle sometimes radians are easier). Decimal stock trading in the US is only a couple of decades old and within my memory countries switched to decimal currencies replacing systems that had survived centuries. In fact the US uses a non-decimal measurement system which has numerous advantages (as well as disadvantages) for daily use.

anthony_romeo 6y ago

So one element which kinda wraps all of these concepts together is what some have called the "Golden Age of Islam".[1] The [literal] Empire which emerged from Muhammad's legacy became a source of great intellectual thinking (while Europe had just entered its dark age). This makes sense, being the place of some of the oldest civilizations on Earth, and surrounded by several other great civilizations. During this time (a few hundred years after the fall of Rome) the texts of the ancient Greek philosophers and scientists became quite popular among Muslim thinkers. One could argue that this Golden Age included a natural continuation of the works of Aristotle, Plato, etc. Furthermore, they adopted a new system of representing numbers from India which turned out to be a convenient language for formalizing the concepts of Algebra (done by Muhammad ibn Musa al-Khwarizmi in the early 800's [2]). Sadly I can't recommend any books -- this was conjured up from my memories of this subject from College some time ago (with the guiding help of Wikipedia to fill in some gaps). [1] https://en.wikipedia.org/wiki/Islamic_Golden_Age https://en.wikipedia.org/wiki/Islamic_Golden_Age [2] https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi https://en.wikipedia.org/wiki/Muhammad_ibn_Musa_al-Khwarizmi

mercer 6y ago
For anyone interested in this era, I can recommend the four-part series hosted by Radio War Nerd: https://www.podchaser.com/podcasts/war-nerd-radio-subscriber-feed-1383559/episodes/radio-war-nerd-ep246-arab-conq-74764998 https://www.podchaser.com/podcasts/war-nerd-radio-subscriber.... The podcast in general is quite interesting, even if you're not as left-leaning as the hosts are. But this series in particular was fun to listen to.

Balgair 6y ago

Cuneiform math isn't the most terrible. It's 'column' based, like the modern arabic version we have. However, at some times they lacked the 0 representation. Roman numerals, however, are quite difficult. In addition to the problems with basic manipulations (27-9, or XXVI - IX), they also lacked any higher symbols than 1000 (M in Roman). So for 15,000 you have to write MMMMMMMMMMMMMMM. I'll spare you numbers like 1,000,000. Here's a good video on how to do math in Cuneiform, and a brief discussion on Roman numerals: https://www.youtube.com/watch?v=RR3zzQP3bII https://www.youtube.com/watch?v=RR3zzQP3bII Strangely, Numberphile has yet to do a video on Roman/Chinese number systems. Maybe because it's really hard to do math with them, and that's a bit boring to just show that it's hard. EDIT: I have been misinformed, Chinese numbers are in fact easy to work with.

kccqzy 6y ago
The Roman system is indeed difficult? What's difficult about the Chinese one? It seems basically identical to Arabic numerals except using different symbols.

whatgoodisaroad 6y ago

I'm slowly reading through a book called the "History of Mathematical Notations" by Florian Cajori and it sounds like just what you're looking for. It goes into far more detail than probably anybody would wish for on the histories of various symbols and ways of writing addition, roots, ratios etc. Many of these notations were used only by a few medieval scholars for a few decades but they usually try to optimize for efficiency or clarity in some creative way. Really fascinating stuff.