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IANAM or historian for that matter, but shouldn't an article like this mention that the use of positional decimal fractions is much older? at least according to

IANAM or historian for that matter, but shouldn't an article like this mention that the use of positional decimal fractions is much older? at least according to the Wikipedia article on decimal separators: "Positional decimal fractions appear for the first time in a book by the Arab mathematician Abu'l-Hasan al-Uqlidisi written in the 10th century.[9] The practice is ultimately derived from the decimal Hindu–Arabic numeral system used in Indian mathematics,[10] and popularized by the Persian mathematician Al-Khwarizmi,[11] when Latin translation of his work on the Indian numerals introduced the decimal positional number system to the Western world. His Compendious Book on Calculation by Completion and Balancing presented the first systematic solution of linear and quadratic equations in Arabic."

codeflo 3y ago
The idea is a lot older than Al-Khwarizmi: positional base-60 fractions were already used by the Babylonians in *2000 BC*.
- ithkuil 3y ago
  Babylonians did indeed use positional notation. But they didn't use the "point" to separate integral and fractional parts of a number. Moreover they didn't even write zeros to indicate an order of magnitude! You just had to know the right scale out of context I'm going to write the numbers in base 10 just for simplicity (they used base 60 which has many more divisors and works much nicely): Numbers 20, 200, 2, 0.2 and 0.00002 would be written simply "2" The reciprocal of 2 would be 5 The reciprocal of 5 would be 2 If that doesn't seem to make sense, let's just reassert that a given "spelling" of a number actually represents infinite numbers: a base and a free "scale" parameter. Thus 5 is also 0.5 The reciprocal of 0.5 is indeed 2 and thus it works. It's like a kind of "modular" arithmetic but for scale. I know that it allowed them to consult tables with reciprocal numbers which helped them to actually perform divisions using just multiplication. I don't know what method they used to keep track of the scale. Was it some kind of out of band "context" or just using common sense to guess the magnitude of the result?
Someone 3y ago
I agree. Reading > The invention of the decimal point led to the development of the decimal system I think the writer didn’t grasp the difference between “writing numbers as a sequence of place-valued digits, using a separator between the integer and fractional parts” and using, specifically, a dot as that separator, which (as far as we know now) came much later. The paper (https://www.sciencedirect.com/science/article/pii/S0315086024000016?via%3Dihub https://www.sciencedirect.com/science/article/pii/S031508602...) doesn’t make that error. (https://en.wikipedia.org/wiki/Decimal_separator#Hellenistic–Renaissance_eras https://en.wikipedia.org/wiki/Decimal_separator#Hellenistic–... hints at the point ‘won’ being because of the invention of thypesetting, saying “Later, a "separatrix" (i.e., a short, roughly vertical ink stroke) between the units and tenths position became the norm among Arab mathematicians (e.g. 99ˌ95), while an L-shaped or vertical bar (|) served as the separatrix in England. When this character was typeset, it was convenient to use the existing comma (99,95) or full stop (99.95) instead.”)

codeflo 3y ago

The idea is a lot older than Al-Khwarizmi: positional base-60 fractions were already used by the Babylonians in *2000 BC*.

ithkuil 3y ago
Babylonians did indeed use positional notation. But they didn't use the "point" to separate integral and fractional parts of a number. Moreover they didn't even write zeros to indicate an order of magnitude! You just had to know the right scale out of context I'm going to write the numbers in base 10 just for simplicity (they used base 60 which has many more divisors and works much nicely): Numbers 20, 200, 2, 0.2 and 0.00002 would be written simply "2" The reciprocal of 2 would be 5 The reciprocal of 5 would be 2 If that doesn't seem to make sense, let's just reassert that a given "spelling" of a number actually represents infinite numbers: a base and a free "scale" parameter. Thus 5 is also 0.5 The reciprocal of 0.5 is indeed 2 and thus it works. It's like a kind of "modular" arithmetic but for scale. I know that it allowed them to consult tables with reciprocal numbers which helped them to actually perform divisions using just multiplication. I don't know what method they used to keep track of the scale. Was it some kind of out of band "context" or just using common sense to guess the magnitude of the result?

Someone 3y ago

I agree. Reading > The invention of the decimal point led to the development of the decimal system I think the writer didn’t grasp the difference between “writing numbers as a sequence of place-valued digits, using a separator between the integer and fractional parts” and using, specifically, a dot as that separator, which (as far as we know now) came much later. The paper (https://www.sciencedirect.com/science/article/pii/S0315086024000016?via%3Dihub https://www.sciencedirect.com/science/article/pii/S031508602...) doesn’t make that error. (https://en.wikipedia.org/wiki/Decimal_separator#Hellenistic–Renaissance_eras https://en.wikipedia.org/wiki/Decimal_separator#Hellenistic–... hints at the point ‘won’ being because of the invention of thypesetting, saying “Later, a "separatrix" (i.e., a short, roughly vertical ink stroke) between the units and tenths position became the norm among Arab mathematicians (e.g. 99ˌ95), while an L-shaped or vertical bar (|) served as the separatrix in England. When this character was typeset, it was convenient to use the existing comma (99,95) or full stop (99.95) instead.”)