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Comment by geysersam | Hacker News Reader

It does't sound like a lot of work. However, multiplying two six digit numbers by hand isn't that easy!

They might have used Newtons algorithm (not using that name probably), but then they would have had to divide, which is even more horrible by hand.

Consider that their notation was probably far worse than what we are used to today, and it all becomes quite a hassle.

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I would expect that, while it is a hassle, somebody would do it. And you only need to do the computation once. Then, stamp it on a square tablet and you can sell it!

Probably make a whole set for different aspect ratios. Carpenters might like them.

“I used to buy 1.5 ft cuttings of wood at the market to make the diagonals on my cabinets, but thanks to geysersam’s number blocks, I buy 1.42 ft cuttings of wood. It’s like every 17’th cabinet is free!”

I bet that a single digit, 1+25/60, is already more precise than any materials you're likely to buy.

Heck, just 1+2/5 is likely sufficient.

Someone else pointed out that they likely were doing astronomy predictions/measurements so you actually need the precision.

That's cool!

I was specifically talking about the carpenter use case.

That crazy

I guess for them it would be more like a three - four with the leading one - digit number, would it not? Did they have a 60 x 60 multiplication table at hand? I am almost tempted to try it out, I would guess that it should be doable in two hours in modern notation.

I assume it was in their head.

I don't know exactly how large of a times table I have in my head, but it's larger than 10x10, more like 15x15. A 60x60 table is 16 times larger than that, but I also learned my times table in elementary school and being a scribe or whatever the job title was for a guy who multiplied was very likely a full time job for a grown Babylonian. Learning your times tables up to 60x60 seems totally plausible.

15x15 plus 10xInfinity ;-)

There's some other odd ones like 16x16 but the table gets pretty sparse after the 15's.

We know that by 300bc at the latest that they had abacuses, so I imagine they used these

Sumerians invented it circa 2800-2500BC. 300bc is a thousand years after the tablet in question. I believe the oldest extant example is 300bc.

It's not that hard in base 10. It might take 5 minutes with the long multiplication technique. I'm assuming that there is an equivalent in the Babylonian base 60 system

Newton's method is in fact what is described in the Twitter thread.

x → x – f(x)/f'(x) with f = x² – N does in fact give you

x → x – [x² – N]/(2 x)

Which quickly simplifies to,

x → (x + N/x)/2.

With that said I am not sure that they knew this coverages quadratically or any of the machinery needed to make Newton's method work... It's a great way to approximate square roots!

> Newton's method is in fact what is described in the Twitter thread.

We might in fact have been looking at Nasir's method this whole time.

Who is Nasir?

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