What's the time, Mr Wolf?

Not suuper useful for time though, honestly

Would be nicer if we had an overall base-12 number system

You can easily count to 12 with just one hand, and you can count to 60 with both hands, in the babylonian style, by using the finger segments.

This, basically a lot of things were based on 12 in the olden times. But since the French were against everything British, including their imperial system they based their metric system on base 10. I heard there were even clocks in France that had only 10 hours

Everyone here assumes that midnight=12a.m. is valid everywhere but in a lot languages this is not the case (German and French just to name two). So maybe this is just something weird English speaking people do...

We have had clocks with the accuracy to display fractions of a second for about 120 years (pre-WW1 stop watches were accurate to the 1/10 of a second) and milliseconds for about 50 years but there is no real use as the second is the shortest practical amount of time the vast majority of humans need in their daily lives.

https://currentmillis.com/

It looks irritating to read time in the distance pic with the woman standing next to it.

I find it annoying that it has a 24 instead of a 0, and that it's at the top instead of the bottom.

Sure.

The way we mesure time around one day is in multiples of 12.

There is 24 hours a day. 12*2
And at many occasions, especially in english, we will count in half days of 12 hours each. We'll say that it is 3 (p.m) not 15 o'clock.

Then, there is the minute, 60 of them in an hour and 60 seconds a minute. 60 is 12*5.
Which means that for every twelfth of 60, you have 5, minutes or seconds.

Now, what is a clock?

We have a circle representing a unit of time.
A pointer showing us how much of the unit is past and how much is left ; that's the clock hand. It circles fully in one unit of time.

This clock is perfectly suitable for any unit of time and any division of this unit.
You can even read already that you are a quarter or a half past the beginning of the unit or a quarter before the next one. Just look for right angles with your desire point of departure for the unit.

So the clock, as simple as a blank circle and a clock hand, is already a very clever tool to mesure time.

Let's adapt it to our need to read time at the scale of half a day.

At the scale of half a day, we will use :

• hours and their subdivisions,
• minutes and their subdivisions,
• seconds.

We could go further, but the common clock don't do it. It's why we use words such as timer, chronometer and stopwatch to talk about more precise tools.

Starting with hours.

We first need to have a hand that circle in half a day, our unit.
We'll portion our circle into twelfths. That's convenient as 360, the number of degrees in our circle is a multiple of 12. Our portions will be of 30° each.
By convention, we will number a twelfth with a digit placed at the end of the portion; starting at portion #1, the numbers go up to 12. It better than starting the numeration at 0, because our languages (at least mine) can use 0 to represent midnight, the end of one of the halves of the day but not noon, the end of the other of the halves of the day.

A twelfth of half a day is called an hour.
We have successfully represented the hours on our clock.

So we have the hours but what about their subdivisions?

Our unit of time is now of an hour.
That's what represent the full circle.
The right angles for our desire beginning marks the quarters and half of hour already. We will need a second hand that circle fully in one hour but we can use the same circle. So, we can read the twelfths of the hour without making any change of it.

Remember, the number does not tell you about minutes. We don't care about minute for now.
We don't even now what a minute is! We haven't defined it.

So we have twelfths of hour. By convention, we will take the digit 12 as departure for our clock hand. This way, the twelfths of hour are numbered.

Twelfths of hour are convenient to find broader portions of hour that we didn't mark. For example, a third of an hour is 4 twelfths. So the number multiples of 4 on our clock (4, 8 and 12) portion the thirds of hour.

The twelfth of the hour is also an interesting unit of time. But somehow, we always call it five minutes, never "twelfth of hour".

It is time to define the minute as a sixtieth of an hour.

This subdivision of hour is wildly use and we may want to mark it on our circle.
Some clock don't have such marks, like the one described by LlamalnaTux. But many do, so we will add them. Starting, by convention, at the 12 digit. After ever portion that is a sixtieth of our circle (every 6°), we will add a mark, a line for example. Of course, every five portions, we'll find a digit. We don't need to add a line to mark what the digit already marks.

We have successfully represent the minutes on our clock.

To finish, we want to read the subdivision of a minute.

That's optional. Many clock don't go that far but it is not an uncommun feature and it we'll be quick.

Our unit of time is now the minute.
That's the meaning of the full circle and the time that takes our last hand to go back to departure.

Thanks to the technics and mark we have already, we can read :

• quarters and half,
• thirds
• twelfths
• and sixtieths of a minutes.

Let's defined the sixtieth of a minute as a second and the twelfths of a minute as five seconds and our clock is complete.

An analogic clock is a superior tool to a digital clock.

The clock we have design use three hands, and 59 marks to mesure the time at the scale of half a day in 9 different units -- not counting the half, quarters and thirds of half a day. It is precise to the second. Actually, even more as the mesure is continuous: it's our reading that is not more precise.

A digital clock will use the arabic numerals to write time.
It will need 6 digits to represent time to the second. The number shown will range between 000000 and 125959. Leaving every combinaison between 125960 and 999999 useless.

Only one dimension of the time is represented, a very complicated one at that : a number of hours added to a number of minutes added to a number of seconds. No quarter, no half, no third, no twelfth, no sixtieth of anything!

And we are losing what is most interesting about the arabic numerals system :

We can't actualy add up seconds to minutes to hours. So we have to keep them in sequence. Why choose then a positional notation? That's one of the great strength of the arabic numeral system but it is completly useless in this context.
The other interesting part of the arbic numerals, is the base ten. We use ten symbols, the digits (0,1,2,3,4,5,6,7,8,9) to write every number possible. Ten is a good base, it's our finger number but it is not how we count time. We count time in base twelve!

So to count hours in half a day, minutes in one hour or seconds in a minute, one digit is not enough, two is too much.
That's why in the range of 000000 and 125959, many numbers will never be used such as 006512 or 113299. And deciding to represent the full day rather that a half exacerbate the problem of unuse numbers within the range.

And the clock is innocent of the faults of Coordinated Universal Time and Greenwitch Mean Time.

A clock can be use with solar time as easily as it can with Coordinated Universal Time. Also, not every place in the world has 12 hours of day time and 12 hours of night.