5 ms·
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 goo
by jlarsen 7y ago
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.
"
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.
- taejo 7y ago> it really isn't simpler with 10 and 100. Only if you ignore the complexity of teaching a whole population to do arithmetic in a different base.
- jlarsen 7y agoNot 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.
- taejo 7y agoRepeating 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.
- dirktheman 7y agoDo 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.
- jlarsen 7y agoI 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.
- masklinn 7y ago> 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.
- lifthrasiir 7y agoBut 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. [1] https://en.wikipedia.org/wiki/Preferred_number https://en.wikipedia.org/wiki/Preferred_number
- jacobolus 7y agoThe 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.
- garmaine 7y agoActually 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.
- jarfil 7y agoIf binary has taught me anything, is that you can count up to 1024 with 10 fingers...
- masklinn 7y agoIf 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)
- Anarch157a 7y agoUsing your hands to signal 4 in binary could put you in a lot of trouble.
- rakoo 7y agoNot a single person I've met has ever used knuckles as a way to count anything, especially time.
- garmaine 7y agoYou obviously haven’t lived in ancient Babylonia. (Pro tip: different cultures have done things differently across time and space!)
- cm2187 7y agoI 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?
- granshaw 7y agoThat’s the same problem inches and feet suffer from now and it’s horrible
- ginko 7y agoThis seems about as convincing as the arguments that inches and feet are somehow more intuitive.
- swebs 7y agoBy that logic, you must really love the imperial measurement system.
- mysterydip 7y agoPart 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
- 116 7y agoGood thing you have 12 phalanxes and a thumb to point at them. That way you can count to 12. It's uncommon but doable.
- Anarch157a 7y agoYou 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.
- BlueTemplar 7y agoSadly, 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.)
- mrguyorama 7y ago>While TV screens are in centimeters, as expected. This is not my experience in America. We have both computer monitors and TV screens in diagonal inches
- BlueTemplar 7y agoI know - guess whose fault is it that those measurements in diagonal inches are still around ?