One must agree on a common standard.
And the standard therefore has to be something
which is reproducible
and should be convenient.
And should also be permanent.
And since so many measurements did depend on feet,
and indeed we still use the word foot to indicate one of our basic units.
Have a look at this picture.
Which comes from a German book on geometry of about 1550.
And here you see
a group of men, lined up,
and the only time I've ever seen people lined up like that
were not men, but girls in a beauty competition.
Well, obviously, they are no beauties.
So why are they doing it?
You see, they are all standing heel to toe
along this line.
And the purpose of that was indeed to carry out
what someone had found, and really it was very brilliant idea,
of getting an average foot.
Because this was a way in which the average foot in one village,
could be more nearly to the size of an average foot in another village,
by having not, just picking one man at random in each village,
but by taking a number of them.
And there was a very precise drill.
You waited until church service on a Sunday morning.
You stopped the first 16 men coming out.
Now that was rather dangerous procedure in a way,
in that there was an element of selection about it.
They might easily be the first 16 anxious to get across the local public house for a drink.
But nevertheless you picked them and you told them to,
to step up... to stand along a line.
And we will do this, not with 16 because it would take rather a lot of time,
there isn't much room, but with eight.
Can I have eight volunteers, to imitate the gentlemen in this picture?
And what we do, is you all stand, as best you can like that, heel to toe.
All in a line.
You don't have to have both feet, but one foot as there like that.
One, two, three, four five, six, seven, eight.
Yes, we've got eight, Bill.
Oh sorry. - That's OK.
Now.
What the next instruction was, that whoever was the man responsible in the village,
had to take a piece of string and stretch it out,
from the heel of the last man, to the toe of the first. Right?
Cut it like that and now you see, we've got a piece of string,
which is equal in length to the sum of eight feet.
In this case 16 feet, taken at random.
And then to get the average down to one of the eight, or one of the 16.
This very beautiful and very simple trick.
Was just to take the string like this.
And now that is exactly half, so it's four feet.
That is now down to two feet.
And you had to use very flexible string so as not to lose much in the bend.
And there is the average foot taken from our eight volunteers here.
A very beatiful trick. Again you see the scale of two coming in.
And that was why specifically it was 16 men you had to take
in order to get an average which would be on the average a square root of 16,
four times as less variable than if you had taken one man alone.
Right, so, there was the way in which if you hadn't got a standard,
an actual physical standard, you could indeed,
you could indeed get a reasonable average.