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Comment by ummonk | Hacker News Reader

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.

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I think this is the paper it's all coming from: 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.

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_ro... ). An iterative Newton's method would be pretty unlikely.

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 which just says "this is an excellent approximation"

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.

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

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

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