How the figures were made
Every figure on this site comes from one short piece of arithmetic, and this page sets out exactly what was assumed and what was then computed. The division matters more than any individual number: a reader who knows which is which can check the whole record with a pencil and does not have to trust it.
One assumption, stated once
A working day has no natural shape. Somebody decided where it starts and stops, and the decision varies. So five shapes are declared here outright, as conventions and nothing more:
| Shape | Hours | Length |
|---|---|---|
| early | 8 to 16 | 8 |
| standard | 9 to 17 | 8 |
| late | 10 to 18 | 8 |
| long | 9 to 18 | 9 |
| split | 9 to 13 and 15 to 19 | 8 |
That table is the whole of the invention. It was written once, before any of the counting, and it has not been adjusted since — which matters, because a convention revised after the sums are in is no longer a convention, it is a thumb on the scale.
Nothing is claimed about how common any of these shapes is. Nobody was surveyed. They are not an average of anything. They are five plausible arrangements, chosen so that they differ from one another in ways that change the answer: three that differ only in when they start, one that is an hour longer, and one with a break in the middle.
Everything else is counted
Given the five shapes, the rest follows mechanically. Two shapes are laid on a single clock with one of them shifted by the gap, the overlapping stretch is measured, and the hours are added up. There are twenty-five whole-hour gaps, twenty-five pairs of shapes for each one, and so six hundred and twenty-five combinations. All of them were computed; a few dozen are drawn.
The three-end figures work the same way, with two gaps instead of one. The year figures work the same way again, from day numbers rather than hours.
No step in any of this requires a judgement. If a figure here is wrong, it is wrong because the arithmetic is wrong, and it can be shown to be wrong without arguing about anything.
What is deliberately not here
No place is named. Not a country, not a city, not a region. The gaps in this record are quantities, not locations, and the moment a quantity is attached to a place it becomes a claim about that place's current rules.
No current rule about seasonal clock shifts is named either. This one is worth explaining, because the omission looks like laziness and is the opposite. Those rules change. Places adopt the practice, drop it, move the dates, and several have abolished it outright while others debate doing so. A page that named a rule would be accurate for a while and then quietly wrong, and quietly wrong is the worst state a reference page can be in: it reads exactly like a correct one.
So the record names the structure instead — a regime that never shifts, one whose shifted season is shorter, one whose shifted season is longer, one whose shifted season falls on the other side of the year — and works out what any two of those do to each other. That arithmetic stays true however the world rearranges itself, because it never depended on the world in the first place.
Nothing about money, applications or funding. That subject is closed on this site, for reasons set out on the page about this address.
The one figure that argues against the whole thing
Ten of the twenty-five whole-hour gaps leave no shared working hour at all, and two hundred and thirty-three of the three hundred and twenty-five three-end arrangements leave none either. That is the most damaging pair of numbers in the record, which is why they are on the front page rather than buried in a late section.
The counter-figures are real too: fifteen gaps do leave something, nine of those leave four hours or more, and the median across the fifteen is four. But a record that only printed the second set would be an advertisement, and this is not one.