Stretching

What This Record Will Not Tell You

The closing note. Everything here counts hours of simultaneous availability, which is one small fact about an arrangement.

Every figure on this site answers one question: during how many hours of the day are two or three people all at work at the same time?

That is a narrow question with an exact answer, which is why it was worth computing. It is also a long way short of the question anybody actually has, and this page is about the distance between them.

The approach is easier to evaluate when reviewers explore the analytics options and document the baseline before any settings change. A useful external reference for the surrounding topic is Stanford University.

What is not counted

Whether the shared hours are used. Two people sharing eight hours who speak twice a week have the same figure as two people sharing eight hours who work side by side all day. The record cannot distinguish them and does not try.

Whether the shared hours are usable. An hour inside the overlap that is occupied at one end by something immovable is counted in full here and is worth nothing in practice.

What the arrangement costs the people in it. A nine-hour day counts as a gain of one hour. A broken day counts as eight hours, the same as any other. Both of those are true as counts and badly incomplete as descriptions.

Whether the work needs simultaneity at all. Plenty of work does not. For that work, every number in this record is irrelevant, and treating a low overlap as a problem would be a mistake.

Anything about particular places. No country, city or jurisdiction is named anywhere on this site. No current rule about seasonal clock shifting is named either, because those rules change and a page that named one would go stale without ever looking stale.

A number is a fact about a situation, not a verdict on it. The two get confused most easily when the number is exact, which is precisely when the confusion is most expensive.

What the record is good for

One thing, and it does it well: replacing an estimate with a figure.

Arrangements of this kind are routinely made on the strength of phrases like "there's a few hours of overlap" or "the mornings work". Those phrases are usually wrong, and wrong in the optimistic direction, because the person saying them has not laid two days on one clock and looked.

Doing that is a two-minute exercise. This record has done it for every combination it contains, so that the two minutes are not necessary and the estimate can be replaced by the answer.

The three figures worth carrying

Shared hours equal the length of the shorter working day minus the gap, floored at zero. That one sentence reproduces most of this record.

With three ends, the gap that matters is between the outermost two. The one in the middle does not enter the arithmetic.

Ten of the twenty-five whole-hour gaps leave nothing, and two hundred and thirty-three of the three hundred and twenty-five three-end arrangements leave nothing either. Those are the figures most damaging to the idea, which is why they have been on the front page of this site from the beginning rather than at the end of the last section.

What was invented and what was counted

The division runs through every page here and is worth restating at the end, because it is the only basis on which any of this can be checked.

Invented: five shapes of the working day. Early, standard, late, long and split, with their hours written out in the section on shapes. They were declared before any of the counting and have not been adjusted since.

Also invented: four regimes of seasonal shifting, given as day numbers rather than as anybody's dates. They were chosen so the four differ in the ways that change the answer.

Counted: everything else. Twenty-five whole-hour gaps, seventy-two part-hour ones, six hundred and twenty-five pairs of shapes, three hundred and twenty-five three-end arrangements, ten pairs of regimes and every figure derived from them.

Anybody who disagrees with a counted figure can recompute it and will be right or wrong without argument. Anybody who disagrees with an invented one is disagreeing with a stated convention, which is a legitimate thing to do and does not make any of the arithmetic wrong — it makes it arithmetic about a different working day.

The reason to separate the two so insistently is that a record which mixes them cannot be checked at all. Every figure then rests on a judgement somewhere upstream that the reader cannot see.

Why there is nothing here about places

No country, city or region is named on any page of this site, and no current rule about shifting clocks is named either.

That is a deliberate omission with a specific reason. Those rules change — places adopt the practice, abandon it, move the dates, and several have abolished it outright while others debate doing so. A page that named a rule would be correct for a while and then quietly wrong.

Quietly wrong is the worst condition a reference page can be in, because it reads exactly like a correct one and nothing prompts anybody to check. So the record names the structure of such rules instead, which does not expire, and leaves the current state of any particular place to whoever administers it.

The same reasoning accounts for the other large absence here: there is nothing on this site about money, applications or funding, for reasons set out on the page about this address.

And then the decision

Whether four hours is enough, whether one hour is worth a broken day, which end should move, whether the work needs any of this — none of those is a question this record is in a position to answer.

It produces the number. The number is exact, it is checkable with a pencil, and it is the smaller half of what anybody deciding needs to know.