Use of decimal point is 1.5 centuries older than historians thought

https://phys.org/news/2024-02-decimal-centuries-older-historians-thought.html

by andsoitis • 2 years ago

81 36 2 years ago

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.

[0] https://www.sciencedirect.com/science/article/pii/S031508602...

blensor• 2 years ago

They could have said 150 years, but then, where's the point

kinix• 2 years ago

Glad you got here before me, it put a full stop to me making the same comment

robertlagrant• 2 years ago

I believe that would cover the same period, yes.

mapreduce• 2 years ago

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!

Terr_• 2 years ago

Significant Digits are besides the point.

caxco93• 2 years ago

I think that is exactly the reason why they went with 1.5

stareatgoats• 2 years ago

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• 2 years ago

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

ithkuil• 2 years 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• 2 years 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/S031508602...) doesn’t make that error.

(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.”)

throw0101b• 2 years ago

More important question: comma or period?

weebull• 2 years ago

I'd like to understand where this difference originates from. It can be very confusing working with Germans (for example).

throwawayben• 2 years ago

Wikipedia has a quite detailed history section: https://en.m.wikipedia.org/wiki/Decimal_separator

ysofunny2• 2 years ago

the answer is the same as tabs or spaces

GrumpySloth2• 2 years ago

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.

throw0101c• 2 years ago

the answer is the same as tabs or spaces

Not when—as a sibling comment notes—you're dealing with CSVs.

samatman• 2 years ago

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.

timc3• 2 years ago

I completely agree.

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.

ReleaseCandidat• 2 years ago

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.

heavenlyblue• 2 years ago

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

beefield• 2 years ago

I'd propose a compromise. Euros switch to decimal point and Americans to metric system. Win-Win.

jonathanlydall• 2 years ago

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.

jmclnx• 2 years ago

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 ?

zoomablemind2• 2 years ago

Anyone tried to translate the example given in the TFA manuscript excerpt image?

There are way too many dots in the text.

fhars• 2 years ago

The paper is linked in the article, from it:

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″

zoomablemind2• 2 years ago

Thanks.

Well, roughly this is equivalent to

  92909**2 = 8632082281

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.

DeathArrow• 2 years ago

In many countries the decimal point is actually a comma.

moi2388• 2 years ago

Yes but their commas are decimal points so it’s all good

fuzzfactor• 2 years ago

Can't read the article but which one predates which?

I can only imagine there's a reason they're called decimal points.

Use of decimal point is 1.5 centuries older than historians thought

Related Stories