Bakhshali manuscript | Hacker News Reader

Bakhshali manuscript

en.wikipedia.org

94 pointstalonx24 comments

It's written in a script which didn't exist yet in the 3rd/4th century, which seems to rather disprove the earliest 224-383 dates, unless people want to argue that this script was in use hundreds of years before we thought it was.

It does seem to fit fairly well with the 680-779 dates, which also fits with when the 0 symbol started being used. 885-993 seems a bit too late, though not strictly impossible.

I'm a bit confused why the 224-383 date is even offered as a serious possibility by the researchers, because to me (admittedly as a non-expert) they seem highly unlikely and should have been dismissed as a fluke. This seems more driven by sensationalism and/or nationalism than anything else.

It’s in a proto-sharada script, which it seems can be dated to earlier than 5th century.

There’s no consensus on dating of the Bakhshali manuscript however: https://www.ams.org/publicoutreach/feature-column/fc-2018-06

According to the article the proto-script emerged more during middle of the seventh century.

Which article?

> unless people want to argue that this script was in use hundreds of years before we thought it was.

Is that script attested in hundreds of other (dated) works, such that this really is absurd... or is it attested by two or three other works which might have been misdated themselves? I ask because I genuinely do not know. With one sort of answer, it seems like it could be as absurd as you suggest, but with the other sort of answer it seems like there could be the possibility of it being that old.

I think carbon dating has undue influence because most other methods of dating things are rather wishy washy and open to interpretation compared to cold hard quantifiable radioisotope ratios. Most people don’t know how complicated radiocarbon calibration can be and when to question the data.

Under the `Date` heading:

> Prior to the proposed radiocarbon dates of the 2017 study, most scholars agreed that the physical manuscript was a copy of a more ancient text,

Perhaps, but that's not very relevant for the dating of this specific physical piece of text.

Can someone explain to me what problems and solutions this solved

https://mathshistory.st-andrews.ac.uk/HistTopics/Bakhshali_m... has some examples.

|One person possesses seven asava horses, another nine haya horses, and another ten camels. Each gives two animals, one to each of the others. They are then equally well off. Find the price of each animal and the total value of the animals possesses by each person.

| Two page-boys are attendants of a king. For their services one gets 13/6 dinaras a day and the other 3/2 . The first owes the second 10 dinaras. calculate and tell me when they have equal amounts.

Just for completeness, I noted in the description provided on that site:

> The Bakhshali manuscript is a handbook of rules and illustrative examples together with their solutions.

So, I guess these read like textbook examples because they basically are.

Wow, maybe a more obscure question, what drives this problem solving at that day and age?

Not sure about this particular text, but much of the earliest writing we have is record-keeping for taxes. You could definitely imagine this kind of math being important for tax collectors to learn, since they would typically travel around to collect taxes at some interval, and would have to calculate the amounts on the fly.

Yeah these could be very literal problems. The first seems useful for assessing the value of a taxable asset, and the second for paying back a loan or a penalty over time.

Math.

(As in, math is it's own motivation to some minds.)

These read to me like very abstract problems cast into everyday (for that time) language to make the concepts more approachable. Like "word problems" today the situations described would be apocryphal.

if I was a palace vizier, it might be helpful to know when people serving a king have imbalances / debts that can be exploited by others

https://en.wikipedia.org/wiki/Methods_of_computing_square_ro...

python implementation (for numbers >= 2)

def bakshali(S, iters=5, a=0, b=0):

    x = S//2

    print(f'inital approximation = {x}')

    for n in range(iters):

        a = (S - x**2) / (2*x)

        b = x + a

        print(f'{x}')

        x = b - (a**2)/(2*b)

    return x

Converges pretty fast!

Is this common in python to declare local variables as fake parameters? The downside is obvious: it clutters the function interface with red herrings. What is the upside?

The upside is that if you wanted a different "iter", "a" or "b", you could just specify it in the arguments.

The iter part I get, but I don't see how the caller can affect a or b. Whatever value supplied for a or b will be replaced by values in dependent of a and b during the loop. a is a function of S and x (which initially is a function of S) and b is a function of x and the just revised value for a.

No, it was just to shorten the code block length for the comment section (for a and b, iters makes more sense as one might want to allow the caller to change that) :)

> The rules are algorithms and techniques for a variety of problems, such as systems of linear equations, quadratic equations, arithmetic progressions and arithmetico-geometric series, computing square roots approximately, dealing with negative numbers (profit and loss), measurement such as of the fineness of gold, etc.

The first documented case of null pointer, the billion dollar mistake.

Wasn't 1965, part of ALGOL W, but somewhere in the previous millenium, in a language meant for object-oriented tax collection.

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