value of pi and 22/7

[Steven D'Aprano]

On Mon, 20 Jun 2016 08:25 am, Gregory Ewing wrote:

> Ian Kelly wrote:
>>  Remember, the cubit was based on the length of the
>> forearm, so it's not like it was a terribly precise measurement to
>> begin with;
> 
> Let's not sell them short. Just because it was based on a forearm
> doesn't mean they didn't have a precise standard for it, any more
> than people who measure things in "feet" do it by plonking down
> their own foot.
> 
> No doubt it wasn't as precise as what we have nowadays, but
> it was probably a lot better than human body part variations.

And let's not make the mistake of presentism, judging the past by the
standards of the present.

The biggest problem with the cubit is not that it is *inaccurate*, as that
different places had their own idea of what a cubit was. I dare say that on
any specific building site, the foreman would ensure that everyone was
working with more or less the same idea of what a cubit was. But once you
moved from one village or town to another, chances are that they were using
a different idea of a cubit that was not quite the same as yours.

To be honest, I don't actually know much about the situation in Ancient
Egypt. For all I know, every tradesman did measure his bit of the pyramid
by laying his forearm down on the rock and adjusting by eye. (But I doubt
it.) And they did have two distinct measures, what we today call the "Royal
cubit" and the "short cubit". So I expect that there actually was quite a
bit of day to day confusion and frustration due to the lack of accurate and
consistent measurements.

One of the most underrated yet critical functions of government is to
standardise weights and measures, and that function evolved very slowly
over time. I doubt that the Egyptian Pharoahs cared about it, although
their scribes probably did, a bit.

If you look at, say, Medieval and even Renaissance Europe, one of the
biggest problems people faced was the lack of standard definitions of
units. Every village and town had their own idea of what a hogshead was, to
say nothing of unscrupulous merchants who would deliberately underweigh or
undermeasure. It was a big enough problem that governments eventually
evolved entire bureaucracies to ensure that when you ordered 10000 yards of
cloth, you got 10000 yards of cloth, and not an argument about what a yard
actually is.

But even today, we still have lack of agreement at the national level:
1,000,000 US gallons are about 832,674 UK gallons. Similarly for miles: US
statute miles are ever-so-slightly less than UK miles.

But at least the metric system is the same everywhere.


>> they might not have understood significant figures, but
>> they probably wouldn't have been overly concerned about the difference
>> between thirty and thirty-one.
> 
> If you're building something the size of a pyramid, that could
> add up to quite a lot of error.

Indeed.


-- 
Steven