The Annual Clock

Motivation

I can plan a day. I know what fits inside an hour, I know what it costs me to lose one, and I can tell roughly where I am in the day without looking at anything. A year does not work like that at all. I know a year has twelve months in the way I know a kilometre has a thousand metres, which is to say I know the fact and have no feel for it, and by March I could not have told you whether I was ahead or behind without doing arithmetic.

The units are the problem rather than the discipline. We spend every waking hour inside hours and minutes, so the intuitions about them are dense and free. Above the day, the intuitions thin out fast, and a year is mostly a number you look up.

Put that way it stops being a problem about character and becomes one about units. I was not short of information, because the calendar had all of it. I was short of the thing you have for an hour and do not have for a month. If I say twenty minutes, you already know roughly how much of an afternoon that is, what you could get done inside it, and how irritated you would be to lose it. You know all of that because you have spent thousands of twenty-minute stretches and paid attention during some of them. Nobody accumulates that many Marches.

You cannot look up a feeling, and you cannot practise your way into one for a unit that only comes round twelve times a year. What you can do is borrow. If the year were expressed in hours and minutes, whatever I already knew about hours and minutes would arrive with it, and the problem would reduce to arithmetic I could do once.

The projection

So on New Year's Eve of 2023 I tried a unit conversion instead of a system. A day has 1440 minutes and a year has 365 days. Squeeze the whole year down onto one 24-hour clock face and a single day of your life becomes 1440 divided by 365, which is three minutes and fifty-seven seconds. Call it four minutes.

Everything else falls out of that one number.

Real time	On the Annual Clock
1 day	3 min 57 sec, call it 4 minutes
1 week	27 min 37 sec, call it half an hour
2 weeks	55 min 14 sec, call it an hour
1 month, meaning a twelfth of the year	exactly 2 hours
1 quarter	exactly 6 hours

The last two rows are exact rather than rounded, which is the whole reason the thing is usable. A twelfth of 24 hours is two hours no matter what the scale factor is, so any calendar built on twelfths lands on even hours by construction. A calendar month of 30 days comes to 118 minutes and 21 seconds, which is where the small drift in the next table comes from.

My own two notes disagree about the first row by one second. 1440 divided by 365 is 3.945 minutes, which is three minutes and 56.71 seconds, so the vault note rounding to 57 is right and the handwritten note truncating to 56 is not. It makes no difference to anything, and I am recording it because a number that appears twice in your own files with two values is worth knowing about before somebody else finds it.

It runs backwards too, and this is the direction I did not expect. If a day is four minutes on the clock, then a minute on the clock is six hours of your actual life. A quarter of a day. The conversion that makes a year feel small makes an afternoon feel large, which was not the goal and is the part I have thought about most since.

Month boundaries

Because a month comes out at almost exactly two hours, the first of each month lands near an even hour all the way down the year. That is a gift from the scale factor rather than something I designed, and it is most of what makes the clock usable without a calculator.

Near, though, not on. Calendar months are 28, 30 or 31 days rather than the 30.4 that a twelfth of a year actually is, so the boundaries wander around the even hours instead of sitting on them. The computed positions, with the drift from the even hour in the last column:

First of	Clock time	Off the even hour by
January	00:00	0 min
February	02:02	+2 min
March	03:52	-7 min
April	05:55	-5 min
May	07:53	-7 min
June	09:55	-4 min
July	11:54	-6 min
August	13:56	-4 min
September	15:58	-1 min
October	17:57	-3 min
November	19:59	-1 min
December	21:57	-2 min

The worst case is seven minutes, and seven minutes on this clock is under two days of real time, which is inside the error you were going to make anyway when eyeballing where you are in a year. So the rule holds in the form you actually use it: the first of the month is that month's number minus one, doubled, in hours.

Midsummer is lunchtime. The end of the first quarter is six in the morning, which is about when you would want to have got up. September, when everyone goes back to work, is four in the afternoon, and it does feel like four in the afternoon.

Choosing the clock face

The obvious objection is one I made to myself the same night I wrote the thing down. Nobody plans their whole twenty-four hours. You plan the time you are awake. So the honest analogy might be a sixteen-hour clock, or even an eight-hour working day, and the year would map onto the part of a day you actually schedule.

I went with twenty-four for two reasons, and only the second one is interesting.

The small reason is that 1440 to 365 divides into numbers that are nice to hold. Four minutes, half an hour, two hours, six hours. A sixteen-hour face gives you two minutes and thirty-eight seconds per day, and every derived figure gets worse from there.

The real reason is that twenty-four hours preserves proportion, and sixteen does not. If you sleep eight hours a night you spend a third of every day asleep, and on a twenty-four hour Annual Clock that comes out as eight hours of the year spent asleep, counted cumulatively. The fraction survives the projection. That is the difference between a mapping and a decoration: on the full-day version you can ask what fraction of the year something occupies and get a true answer back, and on the waking-hours version you have quietly thrown away the denominator and are left with a metaphor that sounds nice and cannot be computed with.

I still think the sixteen-hour version would feel better and be worth less.

In use

Four days into 2024 I was writing an unrelated brain dump about compiler work, opened with the holidays being a write-off, and then wrote this without stopping to think about it:

we're already 15 minutes in the first hour of the annual clock this year

Four days is fifteen minutes and forty-seven seconds on the clock, so the number was right. What I care about is that the sentence was available at all. I did not consult anything, I did not convert. Fifteen minutes into a day is a real feeling that I already own, and it had attached itself to a date in January.

That is the whole thing, and it is the reason I like it more than the planning systems I have built. It adds no tracking, no review, and nothing to maintain. It changes what a date feels like by handing you intuitions you had already paid for, and then it gets out of the way.

What the projection changes

It will not make you do anything. A perspective is not a forcing function, and a year that feels short is not a year that gets used well. I have written enough systems that were supposed to change behaviour to be careful about the claim: this one changes what a date feels like, and that is all I have evidence for.

The thing I keep coming back to is how cheap it was. One division, done once, on the last night of the year. Whether it is worth anything depends entirely on whether the proportions survive the projection, which is checkable, and they do.