3 ms·

The details on the method are paywalled in his Substack, and it's not clear whether he has any evidence that the method he is proposing are actually how the Bab

by ummonk 4y ago

The details on the method are paywalled in his Substack, and it's not clear whether he has any evidence that the method he is proposing are actually how the Babylonians actually calculated square root 2.

tiborsaas 4y ago
I'm sure they didn't use floating point decimals :) I don't understand his confidence that this THE method.
- adrian_b 4y ago
  Actually they were using floating point sexagesimals (base 60), where the exponent was usually not written, but understood from the context.
Mathnerd314 4y ago
The substack loaded for me but all it says is that they used (a special case of) Newton-Raphson. No second tablet is mentioned showing that the Babylonians calculated that way. There is a link to https://www.jstor.org/stable/10.4169/j.ctt19b9k86 https://www.jstor.org/stable/10.4169/j.ctt19b9k86 which just says "this is an excellent approximation"
ffssffss 4y ago
I think this is the paper it's all coming from: https://www.sciencedirect.com/science/article/pii/S0315086098922091?via%3Dihub https://www.sciencedirect.com/science/article/pii/S031508609... They've found some tables of similar estimations, which apparently match the results you get when you apply the author's algorithm, suggesting that's what the Babylonians used as well. I don't think the method itself is actually attested anywhere in known texts.
- Mathnerd314 4y ago
  Well if you read that, the one attested computation is said to be mathematically equivalent to Heron's method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Heron's_method https://en.wikipedia.org/wiki/Methods_of_computing_square_ro... ). An iterative Newton's method would be pretty unlikely.
c7b 4y ago
I suppose by scholarly standards we don't know that any Babylonians knew this method (the first of whom we're sure would be a 1st century Greek mathematician), and the result on the stone is generally attributed to an unknown source (wikipedia). But I guess you could call the attribution folk knowledge, I have often seen this method called something like Babylonian root-finding.

by ummonk 4y ago

tiborsaas 4y ago

I'm sure they didn't use floating point decimals :) I don't understand his confidence that this THE method.

adrian_b 4y ago
Actually they were using floating point sexagesimals (base 60), where the exponent was usually not written, but understood from the context.

Mathnerd314 4y ago

The substack loaded for me but all it says is that they used (a special case of) Newton-Raphson. No second tablet is mentioned showing that the Babylonians calculated that way. There is a link to https://www.jstor.org/stable/10.4169/j.ctt19b9k86 https://www.jstor.org/stable/10.4169/j.ctt19b9k86 which just says "this is an excellent approximation"

ffssffss 4y ago

I think this is the paper it's all coming from: https://www.sciencedirect.com/science/article/pii/S0315086098922091?via%3Dihub https://www.sciencedirect.com/science/article/pii/S031508609... They've found some tables of similar estimations, which apparently match the results you get when you apply the author's algorithm, suggesting that's what the Babylonians used as well. I don't think the method itself is actually attested anywhere in known texts.

Mathnerd314 4y ago
Well if you read that, the one attested computation is said to be mathematically equivalent to Heron's method (https://en.wikipedia.org/wiki/Methods_of_computing_square_roots#Heron's_method https://en.wikipedia.org/wiki/Methods_of_computing_square_ro... ). An iterative Newton's method would be pretty unlikely.

c7b 4y ago

I suppose by scholarly standards we don't know that any Babylonians knew this method (the first of whom we're sure would be a 1st century Greek mathematician), and the result on the stone is generally attributed to an unknown source (wikipedia). But I guess you could call the attribution folk knowledge, I have often seen this method called something like Babylonian root-finding.