TFA only mentions two of the mathematicians involved. The full paper being reported [0] makes it clearer that, as ever, there was a much richer nuanced history with many interacting players. It also describes the specific calculations involved.
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."
> 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.
(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.”)
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?
At one point he squares the distance 92 pedes, 9 untia, 0 minuta, 9 secunda. He writes this quantity as “.92909.”, and its square as “.8.6.3.2.0.8.2.2.8.1″
which is correct arithmetically, yet still not a clear application of dec point.
Assuming 'pedes' is steps, 'untia', 'minuta', and 'secunda' are some dec divisions of a step, then the result notation has too many points to keep the meaning.
Looks like more of a reading/spacing convenience for a whole number with many digits. Not much about decimal point.
>found use of a decimal point by a Venetian merchant 150 years before
Interesting a merchant was the one who so far started using it in the 1400s. Since Venice was based upon trade, I wonder if some older use could be found in The Ottoman Empire or one of the Arab or India Empires ?
> They could have said 150 years, but then, where's the point
I know jokes are generally discouraged on this forum but this one is clever and done really well with good taste. Seems appropriate for the kind of crowd we have here. Very well done, sir!
Windows South African regional settings used to use a period before changing it in Windows 8 to use a comma.
Total mess while we had a mix of Windows 7 and Windows 8+ developer machines.
I don’t even know why Microsoft changed it, my theory is that some idiot academic or government worker reported to Microsoft that “officially” we use a comma, with zero regard for the fact that practically everyone used a period. Total idiot.
In general I support countries maintaining their language-specific quirks, but I would encourage the decimal-comma countries to lose that habit.
A few reasons: programming languages have universally settled on '.', numbers frequently end up in CSV files, and languages can't really support both standards, because of the usual function notation `f(a, 100.5, "c")`, a comma would be ambiguous here as it would be in a CSV. It's difficult and error-prone to interoperate between decimal period and decimal comma, and the former has only advantages over the latter.
Basically, it creates problems which no one needs. I don't consider this to be a case of cultural chauvanism, it's just that it so happens that the English-speaking countries chose the more useful representation when it became time to program computers. Separating arguments and expressions using a comma is much more natural than using a full stop would be, and this can't be parsed in tandem with a decimal comma.
You can't really count this as a win for the English way of doing things, which predates computer programming, the only context in which the difference actually matters. Before that, it was an arbitrary distinction, now it's not.
Having moved to Sweden and from the '.' to the ',' what is even more confusing is then the thousand separator is switched around. Add to the confusion where a banking interface sometimes itself switches between the two and is not consistent what am I transferring.
But the thing that really got me was in Sweden my 9 year old wasn't even using the comma separator in his maths book it was the dot operator `·`. How confused was I that a 9 year old was working with dot products.
Also suggest US switches from crazy Month/Day/Year date formatting.
> it's just that it so happens that the English-speaking countries chose the more useful representation when it became time to program computers
English-speaking countries basically invented CSV so chose the symbols used in CSV files such that they work well with their way of writing numbers saved in these CSV
CSV with floats that use commas as decimal separator uses semicolons (well, it should be called SSV) or sometimes tabs (TSV, which actually is an official name).
Practically, all 3 versions need to be supported.
But the actual problém (well, one of many problems of CSV) are non-quoted strings with commas or semicolons.
It’s not so arbitrary. I’ve grown up in a country which uses commas, but it’s still really confusing even to me, when writing e.g. f(1,2). Is that function applied to 2 arguments or 1? For this reason I always use period as decimal point.
Maths is typically written fast, so subtle spacing is too weak a signal to distinguish meanings. Where I studied maths, we even crossed our zeds horizontally to make it easier to distinguish from carelessly written 2s. Similarly, even though the country uses commas, the uni uses periods, for the benefit of clarity. Almost noone uses semicolons in function application in writing.
[0] https://www.sciencedirect.com/science/article/pii/S031508602...