## Sunday, August 01, 2010

### Decimalising Time

So say you were some sort of future-loving nut-case, or even a rampant scientist or mathematician who thinks all things 'imperial' are antiquated and need to be done away with. So you decide, since most other measures are already 'metric', why not time?

Why not have 100 seconds to a minute; 100 minutes to an hour, etc..?

Where to Start?

Okay, so there are actually two approaches to this. Which approach you go for depends on whether:

a) you want to keep the length of a second the same as it is now, or
b) you want to keep the length of a day the same as it is now.

The one I'll be using is approach (b), simply because (a) would mean the day lasting 8.64 'metric hours'. Which is just silly. But I'll come back to that later.

Defining Time

So as you know, units of time - in particular days and years - are defined in terms of astronomical events. A day is the time it takes the Earth to revolve once on its axis and a year is the time it takes the Earth to do one lap around the Sun - approximately equivalent to 365.25 days. Simple.

The point is, you can't change the length of a day without altering how the Earth moves through space. You can't change it, but you can redefine it. And that's what I'm going for.

The decision to divide the day into 24 chunks was fairly arbitrary. And the main benefit of 24 is that it's divisible by 24, 12, 8, 6, 4, 3, 2 and 1.

10 on the other hand is less nice because it's only divisible by 10, 5, 2 and 1. And I'm sure there are advantages to being able to divide the day up in 8 different ways as opposed to 4. Or something like that.

Similarly, dividing hours into 60 minutes and minutes into 60 seconds is equally arbitrary. So really there's no reason we can't and shouldn't change that.

Decimalising

For my system, I’ve decided I want 100 seconds in a minute, 100 minutes in an hour and 10 hours in a day.

Again, like the system we have, that's a fairly arbitrary choice. And really, there's nothing stopping you redefining the day in terms of any old number of seconds minutes and hours. But therein madness lies*.

So what my system means is a day will now last 100,000 'metric seconds', or mSeconds.

What we need to do now is work out a way of converting standard time into mTime. And the simplest way to do that is to say,
1 Day = 24 x 60 x 60 Seconds = 86,400 Seconds
And since one day in metric time is still the same length as one day in standard time,
100,000 mSeconds = 86,400 Seconds. Therefore 1 mSecond = 0.864 Seconds.
Or, alternatively,
1 Second = 1/0.864 mSeconds = ~1.16 mSeconds
And similarly,
1 mMinute = 86.4 Seconds [1 Minute 26.4 Seconds.]
1 mHour = 8640 Seconds [2 Hours 24 Minutes.]
Still with me?

Converting

So now the obvious question is, how do you convert the current time into metric?

For the sake of arguing, lets say it's 5:32pm exactly. [17:32]

The quickest way to do it, is to convert the time to seconds (since midnight),
17 x (60 x 60) + 32 x 60 = 63,120 Seconds.
So to convert that to mSeconds,
63,120 x (1/0.864) = 73,056 mSeconds.
Then to get the current metric time, the first digit is the mHours, the next two digits are the mMinutes and the last two digits are the mSeconds.

So the time is 7:30.56

It's that simple!

Implementation

That's all well and good, but having to convert by hand is a bit of a pain in the arse. What we need is a clock to tell us the current time in metric.

Well I'm glad you asked! Below is a screen-shot of a metric clock:

It's of an actual, working (JavaScript based) clock I made. And you can watch it tick and tell the time here.

Drawbacks

So this approach works wonderfully for having a nice, 10-hour, metric day.

You could even go so far as to make a week 10 days long, a month 10 weeks long; although a month is technically, loosely defined as the time it takes the moon to orbit the Earth. And besides that, 100 days in a month is shear madness.

But even if you do try that, you've still got 365.25 days in a year. You can't change that to a power of ten without changing the earth's orbit and/or it's rotational speed. And that sort of thing is best left to the mad scientists.

Not that it's entirely necessary to have everything as powers of ten. Having a metric day is good enough for me.

What's in a Second?

Okay, so at this point I should probably admit something - a second is the SI base unit of time. What that means is that - for scientific purposes, at least - time is in seconds, milliseconds, nanoseconds and, in theory, even kilo-seconds and mega-seconds.

In case you were wondering, a second is defined as:
"the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."
Which is approximately equal to 1/86400 the average time for one Earth rotation.

So that's already a well defined metric-friendly measure, and far be it from me to interfere with that.

A Different Approach

Where the previous approach fell down was it's insistence that astronomical periods should be kept constant. And the problem there is that it's a very geocentric approach. For example, a Mercury day is worth 58.7 Earth days, a Venus day is worth 243 Earth days, a Jupiter day is worth 9.8 Earth hours, and so on.

So it doesn't really make sense to be the length of our days and years etc. as the yard-stick for all planets and all of space. Instead, it would make more sense to have a system that's simple, generalised and Earth-independent.

So what we're left with is -
1 minute = 60 seconds, 1 hour = 3.6 kilo-seconds (ks), 1 Earth day = 86.4ks, and 1 Earth year = ~31.6 mega-seconds..

But, for all intents and purposes, the system we have is pretty much prefect. And this whole post was really just an excuse to show off my metric clock. I certainly hope it was worth me wasting your time.

Oatzy.

*[Bonus] - Say, for some monstrous reason, I wanted 75 seconds to the minute, 23 minutes to the hour and 19 hours to the day:

5:30pm now becomes 13:19.48

..and the world starts to make a little less sense.