When The Shared Time Arrives In Two Pieces

Shared time is usually a single stretch: it starts when the later day starts and ends when the earlier day ends, and there is nothing in between to interrupt it. In forty-nine of the six hundred and twenty-five arrangements in this record it is not a single stretch at all.

All forty-nine involve the split shape at one end or the other. Nine of the twenty-five pairings of shapes can produce a broken overlap, and every one of those nine has a split day in it.

A clear scheduling baseline makes distributed workforce management tools easier to evaluate because planned overlap, recorded time and delivered work can be compared over the same period. A useful external reference for the surrounding topic is GitHub.

Why only the split shape does this

An intersection of two unbroken stretches is itself an unbroken stretch — there is no way to cut a hole in it, because neither input has a hole. The split shape has a hole. Anything it meets inherits one.

Those are counted in one direction only; the mirror pairings bring the total to forty-nine.

The split-with-split case is the most interesting of them, because at a gap of three the shared time arrives in three pieces rather than two. Two days each broken once, offset against each other, can produce three separate windows of shared availability totalling three hours.

Three windows of one hour is not three hours of anything useful. It is three interruptions with the word "overlap" attached.

Why the count is not the answer

A pair sharing six hours in one stretch and a pair sharing six hours in two stretches have the same number in the table and very different days.

A single stretch supports anything: a long conversation, a piece of work done together, a meeting that overruns. Two stretches of three hours support two things of up to three hours each, and nothing longer, ever. The total is identical and the capacity is not.

This record counts hours because hours can be counted. It flags the broken cases because the count alone would mislead, and it does not attempt to say how much worse broken is, because that depends entirely on the work.

Reading it in practice

Three questions, in order, and the third one is the one people skip:

1. How many hours are shared?
2. Where in the day do they sit?
3. Do they arrive in one piece?

For every arrangement in this record that does not involve a split day, the answer to the third is always yes and the question can be dropped. The moment a split day is involved it cannot be.

What a broken overlap supports and what it does not

A single stretch of six hours and two stretches of three hours contain the same amount of time and support different work.

A single stretch supports anything that fits inside it. A three-hour session, a one-hour meeting that runs to ninety minutes, a morning of working through something together. The upper limit is the length of the stretch and nothing shorter.

Two stretches support only what fits inside the longer one. Nothing can span the gap between them, because one end is not at work during it. The practical ceiling is the longest single piece, not the total.

And each boundary costs something. Work resumed after a break is not work continued; there is a cost to picking up where something was left, and a broken overlap pays it once per break, every day.

So the useful number for a broken arrangement is not the total. It is the length of the longest piece, which the table does not report and which has to be read off the drawing.

Why the record does not try to discount it

It would be easy to invent a rule — count two pieces as three quarters of their total, say — and it would be dishonest, because the discount depends entirely on the work.

For work that proceeds in short exchanges, a broken overlap costs almost nothing: two windows of three hours support just as many short exchanges as one window of six. For work that requires long continuous sessions, two pieces of three hours may be worth nothing at all, because nothing that needs four hours can happen in either of them.

Any single discount factor would be right for one of those cases and badly wrong for the other. The record therefore reports the count of pieces as a fact and leaves the weighting where it belongs.

A number that has to be adjusted by judgement is better reported raw, with the judgement left visible. The alternative is a number that looks finished and has somebody's assumption baked into it.

The practical consequence

If either end works a broken day, the overlap figure needs a second look before anybody relies on it. The worst case in the record — three pieces at a gap of three — has a perfectly respectable-looking total of three hours and is almost certainly unusable for anything that needs continuity.

Next along

• All Six Hundred And Twenty-Five Pairs
  Five shapes at each end and twenty-five gaps: six hundred and twenty-five arrangements, all computed. The extr
• The Pairing That Fails Soonest
  An early day against a late one runs out two hours sooner than an identical pair. The two shapes have added a
• The Pairing That Survives Longest
  Two broken days still share an hour at a gap of nine. They pay for it by sharing least where most arrangements
• What Choosing A Shape Can And Cannot Fix
  Rearranging your own working day is the only lever either end controls without moving. Here is the exact size