Re: Numbers

[Tom Ford <tomford@THESCIENCESOURCE.COM>]

The deeper we did, that is excavate, the farther back seems to be the
threshold of counting, enumerating, writing and currency (in the value
sense -- not the precious metal sense). As soon as domestication of animals
and hoarding of produce were attempted, in ancient times, there was a need
to keep track. If the herd that I took to pasture differed from the herd I
sheltered at night, I  wanted to know about it. So, it occurred to me to
carry a small pouch with some clay balls in it, one ball for each animal in
the herd. I learned to scratch a mark on the clay ball to tell sheep from
goats and to make them personal. I did not even know I was counting when I
poured out the balls and put them back into the pouch, one at a time as
each animal walked by me into the pasture. When I decided to trade some
sheep, I gave away the balls with them and showed how I had been using
them. By the next time, I was worried that someone would make extra balls
on their own and come to me looking for more sheep, so I sealed the  balls
for the next deal in a hollow clay ball. That way the balls would have to
stay all the same. There was a problem with that too. I could not remember
nor prove to anyone else how many balls were in the larger hollow one.
Since by now each of the balls was marked in my own way to show sheep and
goats, I decided to let each one mark the outside of the hollow ball. I
made the next hollow ball, leaving a small opening  that I could easily
pinch shut. As I traded away the sheep one at a time, I pressed the proper
ball against the outside of the hollow one, leaving a mark in the damp
clay. When we were finished, I pinched the hollow ball shut and let it dry
by the campfire. That sealed the deal, and as the other trader walked away
carrying the record of our transaction, it occurred to me that I had just
invented "writing." I did not know what numbers were, but I had counted out
the proper number of balls and sheep in a way that anyone could check and
compare. Over the years, I did this so often that I was sure that when I
was gone, (thousands of) years later, someone would find some of these
hollow balls with the marks I had pressed on the side.

Tom Ford

At 10:43 PM 11/3/03 -0700, Jim Green wrote:
> That history lecturer from UCLA seemed to say tonight that in the Middle
> Ages  people paid little attention to counting let alone arithmetic -- and
> that there is not much value in the numbers eg time spans -- given in
> historical accounts.
>
> When did counting begin?
>
> When did simple arithmetic begin?
>
> Jim
>
>
> Jim Green
> mailto:JMGreen@sisna.com
> http://users.sisna.com/jmgreen