The Annual Clock
I can plan a day and I cannot plan a year. So I mapped the year onto a clock face and borrowed the intuitions I already had.
Will Chen6 minMotivation
I can plan a day and I cannot plan a year. The units are the problem rather than the discipline.
- Below the day, intuition is dense and free. We spend every waking hour inside hours and minutes, so twenty minutes carries a felt size, a cost, and a sense of what fits inside it.
- Above the day it thins out fast. A year has twelve months the way a kilometre has a thousand metres, which is the fact without the feel. Three months in I could not say whether I was ahead or behind without doing arithmetic, and nobody accumulates enough Marches to fix that.
- The shortage is not information. The calendar has all of it.
You cannot look up a feeling, and you cannot practise your way into one for a unit that comes round twelve times a year. You can borrow. Express the year in hours and minutes and whatever I already knew about hours and minutes arrives with it, and the problem reduces to arithmetic I do once.
The projection
Every planning system I had built before this one asked for something back, in filling in and reviewing. A borrowed intuition asks for a unit conversion and nothing else, done once.
A day has 1440 minutes and a year has 365 days. Squeeze the whole year 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. Every other figure falls out of that one.
| 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.
The first row is recorded two ways in two places, one second apart. 1440 divided by 365 is 3.945 minutes, which is three minutes and 56.71 seconds, so 57 is the correct rounding and 56 is a truncation. It changes nothing downstream, and a quantity that appears in your own files with two values is worth resolving before anything is derived from it.
It runs backwards too. A minute on the clock is six hours of your actual life, a quarter of a day, so the conversion that makes a year feel small makes an afternoon feel large.
Month boundaries
A conversion is only worth having if you can run it without a calculator, which turns on where the month boundaries fall. A month comes out at almost exactly two hours, so the first of each month lands near an even hour all the way down the year. That falls out of the scale factor rather than being a property anyone chose.
Near an even hour is not on one. 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.
The landmarks land where the borrowed intuition would put them:
- midsummer at lunchtime
- the end of the first quarter at six in the morning, about when you would want to have got up
- September, when everyone goes back to work, at four in the afternoon
Choosing the clock face
All of that depends on projecting the year onto a full twenty-four hours, and the objection is one I made to myself the same night. 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, with the year mapped onto the part of a day you actually schedule.
Two reasons for twenty-four.
- The small reason is the numbers. 1440 to 365 divides into figures that are nice to hold, those being four minutes, half an hour, two hours and 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 preserves proportion and sixteen does not. Sleep eight hours a night and you spend a third of every day asleep, which on a twenty-four hour Annual Clock is eight hours of the year spent asleep, counted cumulatively. The fraction is preserved by 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. 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
The test is whether the conversion runs unprompted, and the evidence is a line in an unrelated journal entry about compiler work:
we're already 15 minutes in the first hour of the annual clock this year
Four days is fifteen minutes and forty-seven seconds, so the number was right. What matters is that it arrived without a calculator and without being consulted. Fifteen minutes into a day is a feeling already owned, and it had attached itself to a date in January.
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. Having written enough systems that were supposed to change behaviour, the claim I can support is narrow: this changes what a date feels like, and that is all the evidence covers.
What makes it worth the one division is that the proportions survive the projection, which is a property you can check rather than a feeling you have to trust.