The internet is plagued with -sometimes contradicting- theories aimed to answer your question.

The origin of the Sumerian/Babylonian sexagesimal system of counting has not yet been truely explained. However, most historians concur in that the decimal system was in use at the same time. Some exegetists conclude that the use of the decimal system could not serve to analyse circle geometry as related to astronomical observations.

I cannot comment on man's stupidity but it is apparent we haven't progressed much, since modern societies continue in using both systems...

From answers provided by the Reader's Digest:

The 24-hour day. The Egyptian stargazers noted that the night was marked off by the consecutive rising of 12 bright stars. Bent on symmetry, they divided the day to match.
It was the Egyptian Pharaoh Amenophis who asked his chief engineer to build a water clock to enable measuring time at nights. Primitive sundials gave the approximate time during daylight. Greeks and Romans later on developed the clepsydras as water clocks that were able to measure fractions of hours.

12 inches to a foot. The foot, as its name suggests, was once the distance from the heel to tip of the big toe. Ancient Egyptians standardized it as two thirds of a short cubit. The cubit, the measure used by Noah to build his ark, was originally the length from elbow to middle fingertip, about 18 inches. Ancient Egyptians divided it into fingers and palms. Four finger widths or digits, made a palm, and six palms nade a cubit. Later, about 4,000 years ago, they added a seventh palm, naming it the royal cubit, which became standardized at approximately 21 inches.

Originally the inch represented the width of a man's thumb, but it was standardized in clasic Rome as one-twelfth of a foot. In 1305 Edward I of England defined the yard as made of three 12-inch feet and decreed that the inch should be equal to three grains of dry barley laid end to end. Shoemakers still use the barleycorn unit of measurement.

Horses are measured in Hands. Four inches equals one Hand

Good Luck
johnwm
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For early societies (well maybe even current) there are other things than logic (I don't really know why decimal should be so logical? why not binary? I can count to a much higher number on my fingers than 10)
What did interest me recently was to learn of the Chinese Bell measures.
A truly clever system of creating traceable standards and transmitting them. It appears the Chinese decided to use a bell with a particular note as a standard for  volume measurement. Different notes, different volumes, and a string tuned to a certain note as a measure of length.
This has a certain prescience about it if we consider what is today the standard for length.

JMW
www.ViscoAnalyser.com

I guess that the bell must also have been a standard weight  (to provide the tension for the string).

M

--
Dr Michael F Platten

The string was that used in a stringed musical instrument, i.e. not related to the bell.

JMW
www.ViscoAnalyser.com

I believe the 60-minute hour was from the Babylonians, wha had a 60-base numbering system.  This is also responsible for the 360° circle.

Illogical?  Hardly.  60 and 360 are great numbers.  60 can be divided evenly by 2, 3, 4, 5, 6, 10, 12, 15, 20, and 30.  360 can be divided evenly by 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 30, 36, 40, 45, 60, 72, 90, 120, and 180.  Really useful properties for a measuring system.

The Sun takes 365 days to move completely around the sky, so it travels, relative to the fixed stars, just about 1 degree per day. This may have induced the Babylonians to chose 360 degrees to the circle.

It is reasonable to assume that since the days of the week are named after the five bright stars known by the Babylonians: Mercury, Venus, Mars, Jupiter, Saturn, plus the Sun and the Moon, gave rise to the seven-day week, with one of the planets "in charge" of each day.

Even up to these days imaginative suggestions are made as to the planets' influence on human beings as their position changes in respect to the stars and other planets, and foretelling of the future has evolved into astrology, its horoscopes believed by many (credulous) people.

It was the Egyptian priests who noticed that there were ±12 new Moons per year, so they had 12 months. They made each month 30 days long, disregarding the actual Moon phases. This made 360 days, to which they added 5 days at the end.

jmw,

I kind of assumed that the length standard was based on the tuning of a string to the same pitch as the bell. Am I right? In which case, how did they know how much tension to put on the string?

M

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Dr Michael F Platten

So far as the string goes, I think it is a bit too arbitrary. The mass per unit length of the string would directly affect the result.

I really like the proposal for the neolithic yard - based on the length of a pendulum with a certain period. I can't remember how they were supposed to time the pendulum though.

Cheers

Greg Locock

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here are a couple of links that i found:
http://www.japanese-incense.com/time.htm
http://www.uh.edu/engines/epi1676.htm
http://www.geocities.com/~thinkink/guide/bells.htm

JMW
www.ViscoAnalyser.com

The treatment of such a topic defies short tidbits here and there in a forum like this and so I direct you to one author who, In my opinion, has done a bang-up job in presenting the world's view on these topics.  Please read the first part of the Discoverers by Daniel Boorstin.  Boorstin was with the Library of Congress and has produced three such insightful books.  

I was just fascinated as I read his trilogy.

Regards,
Qshake

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