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Metric time

Albert

By Albert
in The Jim Smith Room

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Albert

Albert

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Bit bored now waiting for Saturday, so I thought I'd have a think about the old concept of Metric or Decimal time.

It's one of those concepts that seems odd when you've been raised with our system of time, but it's worth understanding where ours come from. Some say the reason for the second is that it's roughly the human heartbeat, but the reason is actually quite different.

From memory the Egyptians were one of the first to develop the concept of hours, breaking the movement of the sun in the sky up into 10 units, plus 2 twilight sections, one in the morning and one in the evening. The ancient near east also broke the time the sun was up into 12 parts, and in many systems at the time the length of an "hour" would change with the length of the day. Some speculate that the role of the 12 lunar cycles of the year may have played a role in such systems becoming commonplace. That's not to say there were other systems, China for a long time used a unit called the ke which represented one hundredth of a day.

In any case, it was the Sumerians who introduced splitting hours into divisions of base 60 (60 minutes in an hour, 60 seconds in a minute). There were other systems, but ultimately this is the one that stuck in the West. Sexagesimal numbers were used quite often in the near east at the time. Some might wonder, why use 60 as a base? One proposed reason is actually quite similar to our use of base 10. Whilst the simplest method of counting by hand is simply holding up (or down) fingers in count, you can actually use other, more complicated methods, one method using the bones in the fingers is as follows:

- For one, place the thumb on the first bone on the index finger

- For each added number, move to the next bone

- Move through all twelve bones on the 4 fingers

- For thirteen, count "1" on the other hand

- Count back through twelve on the first hand again

- Add one to the other hand and restart the count on the other

This, for someone with all their fingers, will allow you to count to 60 using your hands. The Sumerians used Sexagesimal numbers for general use, and breaking up hours into base 60 in their case would be similar to us breaking numbers up into tens. That is, the way they wrote numbers was in place value notation, with 59 different characters (later 60) for the numbers, using place value notation in the same way as us. That is, writing 138 (that is, 1 group of a hundred, 3 tens and 8 ones, or 1:3:8) would be for them 2:18 (2 sixties, 18 ones).

So basically we broke up our days into two sets of 12s, one for the day and one for the night, then happened to use Sumerian and Babylonian counting to break those units up into base 60 numbers. The question is whether this is actually best?

Well... probably not, we're used to it, and I seriously doubt it could ever change. The concept of reading clocks is so hard wired into modern society it almost certainly couldn't be touched. But that doesn't stop us discussing it. Instead of discussing how others did it though, here I will just go through the obvious answer:

Break the day up into units based on base 10. The first obvious unit is a "deciday" or a tenth of a day of course (2.4 hours). As people are used to using time in the format H:MM:SS, it would make sense to make an analogue, so here it could be:

Deciday: 2.4 hours

Milliday: 1.44 minutes or 86.4 seconds

Tock (1/100,000th of a day): 0.864 seconds

Here I gave the 1/100,000th unit a placeholder name, Tock, as there really isn't a good metric prefix for hundred thousandth. There are some fun things about this though, for one, the "average" human heartbeat, ~70-75 beats per minute, is pretty much spot on 1 beat per tock. So that's a "fun" reference to the original mention of the false definition of the second.

There is also a very useful unit, the centiday, which is the same as the Chinese Ke, 1/100th of a day, or 1000 tocks (kilotock), which comes out as being pretty much 15 minutes (there are 96 'quarter of an hours' in a day, 100 centidays in a day). From this you can quickly estimate the equivalent decimal time from a 12 hour clock time:

- Take the hour number and times it by 4

- If this number is over 12, add 1 to it, over 36, add 2

- Take roughly however many quarters of an hour past the hour is it (i.e. if it's 4:15, that's 1, 4:30 is 2, 4:45 is 3) and add that many centidays

- If it is am, leave it as is, if pm add 50

- That is the number of centidays, so to find the decidays (the analogue of hours), divide by ten

For example, 7:36 am:

- 7*4 is 28

- It's over 12 so add one to make it 29

- It's closest to 7:30, so add another 2, so 31

- It's am so no change

- Dividing by ten converts it to 3.1 decidays

- 7:36 am is about 3:10 decidays (it is actually ~3:17, but close enough for a quick estimate)

So then, what are the overall advantages then?

- A convenient unit that is about a heartbeat

- Easy conversions from unit to unit

- A logical construction

- Useful subunits that mimic times people currently use (such as centidays being ~15 minutes)

It also offers an ease of conversions from multiple timezones and the ability to write appointments as dates easily. For example, say you need to be somewhere on the 24th of May at 3 pm, that would be 2014:5:24.625. On those time zones, this property is particularly handy. Consider the time difference between the UK and Australia as 9 hours, this would be 0.375 days. This means that 2014:5:24.625 in London would be 2014:5:25.00.

Long story short, if education and change over wasn't an issue, it would actually be quite a nice system. It has been tried before... but let's not talk about them. It would be something to consider if possible, but not really anything more than a pointless thought experiment these days. We'll probably keep using the ancient throwback for a long time to come, but still a way to occupy the mind while waiting for 2014:5:24.625 in London.

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Albert

Albert

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You really are bored Albert :lol:

What makes it worse is it is now even easier to come up with how long is left.

10:20 am goes to about 4:30, or in terms of a date 23.43, with the game being at 24.625, meaning that 1.195 days are left...

Speaking of football though, you could easily just make a match 6 centidays (86 minutes, 24 seconds) with a 1 centiday half time (14 minutes, 24 seconds) break and if extra time is needed, make it 2 centiday halves. 3 minutes of injury time is about 2 millidays and so forth. Not a huge amount of change for nice round units.

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GboroRam

GboroRam

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What makes it worse is it is now even easier to come up with how long is left.

10:20 am goes to about 4:30, or in terms of a date 23.43, with the game being at 24.625, meaning that 1.195 days are left...

Speaking of football though, you could easily just make a match 6 centidays (86 minutes, 24 seconds) with a 1 centiday half time (14 minutes, 24 seconds) break and if extra time is needed, make it 2 centiday halves. 3 minutes of injury time is about 2 millidays and so forth. Not a huge amount of change for nice round units.

"It's a game of 6 centidays" sounds wrong though.
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Albert

Albert

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Was having trouble sleeping but this helped a lot.

Cheers Albert!

Not sure what time to set the alarm for though, my clock doesn't have centidays.

It's actually quite a simple method for finding the time.

- Find the hour you want to wake up, say 9:30 am

- Times the hour number by 4, here this would be 36

- For number greater or equal to 12, add one, greater or equal to 36, add 2. Here add 2 as it is 36 to make it 38

- Add another 1 for every quarter hour past the hour it is, so in this case add 2, making it 40

- Divide by ten for centidays, giving: 4:00

Enjoy your sleep.

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