Fun little snippet of history =), but something that seems to get missed often in time-keeping is that 12, 24, and 60 are not accidental, they're used for a good reason - they're highly divisible numbers.
12 is divisible by 2, 3, 4, 6
24 is divisible by 2, 3, 4, 6, 8, 12
60 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
Compare that to
10 (divisible by 2, 5) and
100 (divisible by 2, 4, 5, 10, 20, 25, 50),
and you start to see the problem. You can't split a 10 hour day into quarters without a decimal, and you can't split a 10 hour day into thirds without an infinite decimal or a fraction.
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But in 1793, the French smashed the old clock in favor of French Revolutionary Time: a 10-hour day, with 100 minutes per hour, and 100 seconds per minute. This thoroughly modern system had a few practical benefits, chief among them being a simplified way to do time-related math...
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isn't really true. Sub-dividing days and hours into smaller, equal pieces is a critical part of time-keeping, and it really isn't simpler with 10 and 100.
Do we really divide units of time that often, though? Only 'half an hour' and the quarters (in French at least) are used frequently. And with the decimal time system, 'quarter of an hour' would be just as meaningful as the Gregorian system, it would just signify 75 minutes instead of 45.
Keep in mind they introduced the entire metric system: distance, volume, weight, currency, etcetera, making this just one of many changes... Either way, apparently people weren't too stoked about having one day off every 10 days instead of one day off every 7 days.
I do. I sleep 8 hours, wake up 2 hours before work, work 8 hours, and spend 6 hours in the evening afterwards. That's 1/3, 1/12, 1/3, and 1/4 of the day, or 3.33, 0.83, 3.33, 2.5 decimal hours.
You have a good point about taking it in context with the 'decimalization' of other units of measure, but my point is really just that the article is overly generous towards decimal time, and ignores solid mathematical reasons for using 12/24/60 for time-keeping. I've never in my life needed to know when a day is "70% over", but I constantly need to subdivide my time into halves, thirds, or quarters.
> I do. I sleep 8 hours, wake up 2 hours before work, work 8 hours, and spend 6 hours in the evening afterwards. That's 1/3, 1/12, 1/3, and 1/4 of the day
You do realise that you use these approximations because they're the integral results of easy calculations, and you'd just use slightly different durations in a decimal time framework, right?
As in, metric countries don't use a 12.7mm wrench because that's what 1/2" is. They use a 13mm wrench (and the corresponding metric nuts). And their speed limits are 110/120/130, not 112.6/120.7/128.7.
But we still have preferred numbers [1] which never map neatly to the decimal or any other radixes due to their logarithmic nature. The ratios, sharing the same logarithmic nature, ARE one of the good reasons to select radixes if the decimal were not as pervasive as now.
The whole point of preferred numbers is fitting a rough logarithmic scale to a positional (e.g. decimal) number system.
For an alternative let me recommend just using binary logarithms written in base 12. (So that 1 corresponds to doubling, 1.7 corresponds pretty closely to tripling, and 2.4 corresponds roughly to quintupling. i.e. 0.1 (base 12) is an equal-tempered semitone.
I am not so sure of that. People are pretty comfortable using decimals for distances in the metric system. And you can always switch to the unit below.
[edit] In fact the reason we don't use decimals for time is probably precisely because it is not using a metric system. What does 1.3h means? 1h and 18 minutes or 1h and 30 minutes?
Not what I said. I said that, sub-dividing days is not really simpler with base 10, and that sub-dividing time is pretty important practical aspect of time-keeping.
Repeating the same thing you said before isn't the best way of clarifying what you mean, but fair enough, I do now understand what you're trying to say.
Actually the reason we have base-60 time is that we have 5 fingers on one hand, and 12 knuckles that can be pointed to by the thumb on the other. 5x12=60.
Of course why the Babylonians went with this two-mechanism system instead of doing the same thing on both hands is probably because of divisibility. Get a prime factor of 5 from one hand, and prime factors of 2 and 3 from the other.
(Also note that you can count 12 hours on one hand, a full 24 on both.)
EDIT: AFAIK the Babylonians didn't have a developed number theory, and I'm not sure they even had a formal idea of prime numbers. But we do know from surviving accounting "textbooks" (practice tablets & instructions) that both they and the near-contemporary ancient Egyptians understood the special divisibility of these numbers.
If you've got flexible hands and independent-enough fingers you can even count in ternary, up to 59048 (though binary can also take advantage of toes for a limit of 1048573)
I have not seen any evidence that ancient Mesopotamians counted phalanges using their thumbs.
I believe that counting method was devised by some fan of duodecimal arithmetic sometime within the past century, and has nothing to do with sexagesimal numeration per se.
If that is your evidence then you are tricking yourself, or to be generous speculating wildly.
The evolution here was: physical clay counters; physical clay counters sealed in a clay envelope; physical clay counters sealed in a clay envelope but also pressed into the outside of the envelope to indicate how many; clay tablet with counters pressed into the outside (since the envelopes with counters inside were redundant); clay tablets with little cuneiform symbols to represent quantities, differing by type of object being counted, and not all sexagesimal; more uniform written sexagesimal writing system.
There is no indication in the symbols about how people counted on their fingers.
Sadly, the dozenal system was basically done for after the release of "The Art of Tenths" by Simon Stevin in 1585, and the resulting adoption by traders and tradespeople.
But well, the decimal system is probably the second best...
My main gripe these days is the lack of consistency : while hours/minutes/seconds are not too bad, having computer screens in inches annoys me a lot ! (While TV screens are in centimeters, as expected.)
Part of me wishes the majority were born with 12 digits on our hands instead of 10, so base 12 would've been the norm and everything would have the divisibility benefits mentioned
You can do base6 (which is almost as good) with your fingers. Use one hand for units, the other for tens, this way, you can count to 50b6, which is 35 in base10.
12 is divisible by 2, 3, 4, 6
24 is divisible by 2, 3, 4, 6, 8, 12
60 is divisible by 2, 3, 4, 5, 6, 10, 12, 15, 20, 30
Compare that to
10 (divisible by 2, 5) and
100 (divisible by 2, 4, 5, 10, 20, 25, 50),
and you start to see the problem. You can't split a 10 hour day into quarters without a decimal, and you can't split a 10 hour day into thirds without an infinite decimal or a fraction.
"
But in 1793, the French smashed the old clock in favor of French Revolutionary Time: a 10-hour day, with 100 minutes per hour, and 100 seconds per minute. This thoroughly modern system had a few practical benefits, chief among them being a simplified way to do time-related math...
"
isn't really true. Sub-dividing days and hours into smaller, equal pieces is a critical part of time-keeping, and it really isn't simpler with 10 and 100.