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Lu Abel, you wrote:
"I for one would love an explanation of how/when we came by our 24 hour day
with 60 minutes per hour and 60 seconds per minute.   Yeah, I've heard all
about how it comes from the Sumerian/Babylonian sexagesimal system, but with
the European world presumably counting in decimal since 500 BC or so, why
did all those smart people suddenly say "hey, let's confuse all those kids
learning to tell time by using base 60!" "

While it's true that there were situations where base ten math was used in
the Classical period, it certainly wasn't obvious that this was a
universally preferred choice. Even today, in many commercial settings, it's
common to count by twelves (and a "gross" is twelve twelves). The concept of
a "dozen" is quite old and continues to be useful for pretty much the same
reason that the sexagesimal system for angles and time was originally
useful.

The chief advantage of the number 12 (and even more so 60) is that it has
many factors. If I give you a dozen eggs and ask you to split them equally
between you and me, that's easy: 12 is evenly divisible by two. If I instead
ask to divide them among you, me, and Bill, again, that's no problem: 12 is
evenly divisible by three. Same goes for batches of four or batches of six.
Now let's try the same thing with a box containing seven eggs. You can
divide those up among seven people, but for any other division, you'll be
cracking shells. This is a very real practical advantage. It does leave an
open question, of course: what do you do if you only have seven eggs?!

If you're a fan of science fiction, there's a very nice story demonstrating
the value of the number sixty and its many factors near the beginning of the
novel "Imperial Earth" by the (recently) late Arthur C. Clarke. It had a
significant impact on my own understanding of this issue as a teenager when
I read it back in 1976.

And finally, go to Google Books and dig up an old copy of Bowditch. There
are several from the 19th century. Here's the 1826 edition:
 http://books.google.com/books?id=KcVBAAAAIAAJ
Like other navigation manuals from that era, he includes many definitions
for strange things. In the "signs and abbreviations" section, you will learn
that a double hash-mark is used to denote "seconds". Sure, we all know that.
A single hash after the number implies "minutes" and a second hash-mark
signifies "seconds". Get it: a second mark for seconds? Now suppose we put a
third hash-mark. That signifies "thirds" which are the "sixtieth parts of
seconds" according to Bowditch. So an angle of ten and half seconds would be
written as
  10''30'''
and read as "ten seconds and thirty thirds". Luckily, that never caught on,
and fractions of seconds are almost universally expressed in decimal terms
today.

 -FER


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