The year

The Shortest Disagreement In The Record

Twenty-one days a year, in two pieces: a fortnight in spring and a week in autumn. The smallest seam and the hardest to diagnose.

The brief and extended regimes disagree for twenty-one days a year. Three hundred and forty-four days out of three hundred and sixty-five, they are exactly where each other expects. For the remaining twenty-one they are an hour out.

Those twenty-one days are not one run. They are fourteen consecutive days in the spring and seven in the autumn — a fortnight and a week, at opposite ends of the year.

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The smallest seam against the largest

plain: the pair is at its nominal offset
hatched: it is not

Two pairs drawn. The worst of them spends 323 days of the year at an offset that is not the one either end would quote.

Two pairs of ordinary rules. One is adrift for three weeks of the year and the other for all but six.

Computed from the two regimes. The shift dates are the record's own, chosen so that they differ; no place's rule is named.

Where the asymmetry comes from

The extended regime shifts earlier in spring and returns later in autumn: its shifted season is simply longer at both ends. The brief one sits inside it. The spring gap between their start dates is fourteen days; the autumn gap between their end dates is seven.

Nothing deeper is going on. Two rules with slightly different dates produce two seams of slightly different lengths, and the lengths have no relationship to each other.

Why this is the hardest one to find

Consider what it looks like from inside.

For eleven months of the year, everything works. Meetings land where they should. Nobody has any reason to suspect the arrangement. Then, for a fortnight, somebody is consistently an hour out — and the obvious explanation is that somebody has made a mistake, because that explanation is correct ninety-nine times out of a hundred in ordinary life.

The mistake is apologised for. It happens again the next day, which is slightly odd. It happens for a fortnight, by which point somebody is irritated. And then it stops, which removes any remaining pressure to find out why.

Six months later the same thing happens for a week.

Twenty-one days a year is small enough to be absorbed as bad luck and large enough to poison an arrangement. That combination is worse than a fault which is simply always present.

The contrast

The brief and inverted regimes disagree for three hundred and twenty-three days of the year. That pair is at an unexpected offset for all but six weeks, which means the "expected" offset is the exception and everybody discovers this almost immediately.

A fault that is present nearly all the time gets fixed, because it is the normal state and gets treated as such. A fault present for six per cent of the year does not, because it never becomes the normal state.

Pair	Days adrift	Pieces	Likely to be diagnosed
brief with extended	21	2	no
brief with inverted	323	3	immediately

Three weeks, priced

Twenty-one days is about four working weeks' worth of days, or three if the weekends are taken out. What that costs depends on where the arrangement sits.

A pair at a nominal gap of two, drifting to three for those days, lose one hour of overlap out of six. Across three working weeks that is fifteen hours of shared time, which is noticeable and survivable.

A pair at a nominal gap of seven, drifting to eight, lose everything for those days. Three working weeks with no simultaneous time at all, arriving without warning, twice a year.

The second case is the one that matters, and it is more common than it sounds: arrangements at the edge of the workable range are exactly the ones that were set up carefully, with a protected hour, by people who knew the overlap was thin. That care is what makes the seam devastating rather than annoying.

The thing that makes it recur

Every mechanism that would normally fix a recurring problem fails here.

It does not persist long enough to be investigated. By the time somebody is annoyed enough to look into it, there are three days left.

It does not repeat soon enough to be remembered. The autumn seam arrives six months after the spring one, by which point the spring one has been forgotten or attributed to something else.

It has a plausible wrong explanation available. Somebody is being careless. That explanation is correct for most such incidents in ordinary life and is available immediately.

And it fixes itself, which removes the last of the pressure. A problem that goes away is a problem that did not need solving.

Four independent reasons, each sufficient on its own, all pointing the same way. The result is a fault that can run for the entire life of an arrangement without ever being named.

This is not a hard problem. It is an easy problem with excellent camouflage, and the camouflage is doing all the work.

The only defence

Know the dates. Not approximately — exactly, because the whole character of the problem is that it arrives without warning and leaves before the investigation finishes.

A pair in this position should expect, every year, a fortnight in spring and a week in autumn during which the gap is not what they think it is, and should plan the recurring commitments that fall in those weeks accordingly. That is the entire remedy, and it is available only to somebody who already knows the seam exists.