Very interesting article, would definitely like to read the paper when I get the time.
Something I would like to understand is how these old systems scaled the reference measurements to order of magnitude larger/smaller weights to measure. Up until recently (before the SI redefinition of weight to physical constants) this was an issue even with the modern definition of the kg where for measuring larger and larger weights we essentially have to resort to larger reference weights. And in doing so the manufacturing complexity grows significantly if you want to hold the same uncertainty (as a %). And of course, this applies when measuring masses significantly smaller than the reference 1kg prototype.
Is it really that hard? You make a lever/beam with notches at regular intervals. Move the hooks to set the ratio, and you can compare weights of arbitrary ratios. Sure there's some loss of precision at each step, but assuming you minimize the stacking of errors and return to the master reference whenever possible, I'd imagine it to be precise enough for pre-scientific uses.
Note that many old measurement systems use factors other than 10, which happen to be easy to multiply/divide with ratios of 2 and 3, which happens to be very easy to make levers/beams for.
Given the simple balance pictured in the article, it should be fairly easy to scale up or down by small integer ratios.
First, you can put two equal weights on the scale, then swap them to make sure they are the same, AND the scale is fare.
Next, you could make duplicates of that weight. You could then use some small number of them to make a heavier standard.
You could also make some smaller weights, slightly heavier than 1/2 of the weight, and grind them down until they add up to 1 standard unit. You could then work on duplicating the heavier one, and then shave both of them down a bit at a time until they are equal, and match the standard weight.
With time, you could probably come up with a fairly good set of standards, each up/down would be correct to a tolerance of the sensitivity of the scale.
In other words, the use of standard measures that were portable and external to a society's local norms tracked closely the diffusion of settled agricultural civilisations and specialist societies. This is unsurprising.
You don’t have to be so dismissive. The research suggests that there was a common standard of weights from the near East to the Aegean, which is indeed surprising; there is no reason to believe that, in the absence of a centralizing force, the weights should standardize.
> there is no reason to believe that, in the absence of a centralizing force, the weights should standardize.
In the absence of trade there would be no reason for them to stabilise, but with trade there is every incentive for them to do so even over long distances and between people groups who don't know of each others existence.
We already knew about ancient trade across the region, specifically due to analytical metallurgy. Bronzes in particular. Tin content thereof in particular. Often sourced from Afghanistan/England IIRC and evidence also early.
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[ 3.7 ms ] story [ 42.4 ms ] threadSomething I would like to understand is how these old systems scaled the reference measurements to order of magnitude larger/smaller weights to measure. Up until recently (before the SI redefinition of weight to physical constants) this was an issue even with the modern definition of the kg where for measuring larger and larger weights we essentially have to resort to larger reference weights. And in doing so the manufacturing complexity grows significantly if you want to hold the same uncertainty (as a %). And of course, this applies when measuring masses significantly smaller than the reference 1kg prototype.
Note that many old measurement systems use factors other than 10, which happen to be easy to multiply/divide with ratios of 2 and 3, which happens to be very easy to make levers/beams for.
First, you can put two equal weights on the scale, then swap them to make sure they are the same, AND the scale is fare.
Next, you could make duplicates of that weight. You could then use some small number of them to make a heavier standard.
You could also make some smaller weights, slightly heavier than 1/2 of the weight, and grind them down until they add up to 1 standard unit. You could then work on duplicating the heavier one, and then shave both of them down a bit at a time until they are equal, and match the standard weight.
With time, you could probably come up with a fairly good set of standards, each up/down would be correct to a tolerance of the sensitivity of the scale.
All of this without a modern beam balance.
In the absence of trade there would be no reason for them to stabilise, but with trade there is every incentive for them to do so even over long distances and between people groups who don't know of each others existence.
That force is commerce, and it has almost never been absent in human history.