Shapes

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 actually sit.

Two split days against each other leave something at nineteen of the twenty-five whole-hour gaps. No other pairing reaches that far: two long days give out at a gap of nine, and every pairing of unbroken eight-hour shapes gives out at eight or sooner.

It is, on that measure, the best pairing in the record. It is also the worst pairing to have if the gap is small, and both facts come from the same property.

The next practical step is to compare the current capabilities, choose one real work cycle and compare the report with what was delivered. A useful external reference for the surrounding topic is Asana.

The far end

At a gap of nine hours, two days broken in the middle still share one hour. The reason is that the moved day's first block has slid onto the other day's second block. The pieces no longer line up with their own counterparts; they line up with the next one along, and that is enough to keep something alive at a separation where an unbroken day has been dead for two hours already.

Gap	split with split	long with long	standard with standard
7	3	2	1
8	2	1	0
9	1	0	0
10	0	0	0

At the three widest gaps that leave anything, the broken day beats everything else in the record outright.

The near end

Gap	split with split	standard with standard
0	8	8
1	6	7
2	4	6
3	3	5
4	2	4

At a gap of two, two broken days share four hours where two ordinary days share six. At a gap of four it is two against four — half as much.

So the pairing that survives longest is also the pairing that gives up the most, the fastest, right where most arrangements sit.

Reach and depth are bought with the same coin. Nothing in this record does well at both ends, and the shape that reaches furthest is the shape that empties quickest.

The one honest use

If the gap is wide enough that every other arrangement leaves nothing, this one is the only thing on the table. One shared hour at a gap of nine is the difference between a daily conversation and a daily handover, and a broken day is the price.

If the gap is small, adopting it is self-harm with a table to justify it. A pair at a gap of two who both break their days lose two hours of overlap and gain a two-hour hole in the middle of every afternoon.

Against an unbroken day it is simply worse

The figures above are for two broken days meeting each other. A broken day against an ordinary one is a different and much less flattering story.

Gap	split with standard	standard with standard
0	6	8
2	6	6
4	4	4
6	4	2
8	2	0
9	1	0

At no gap the broken day throws away two hours — its own break falls inside the other end's working day and removes those hours from the intersection. It never recovers them: six hours is the most this pairing ever delivers, against eight for two ordinary days.

What it does gain is reach. The two pairings are level at gaps of three and four; from a gap of five onwards the broken day is ahead, and it survives to nine where the ordinary pairing died at eight.

So one end breaking its day unilaterally is a pure loss below a gap of six and a modest gain above it. The large reach shown earlier requires both ends to break, which is twice the cost and a considerably harder agreement to reach.

The decision in one table

Gap	What is worth doing
0 to 4	nothing; the broken day costs more than it returns
5 to 7	one end breaking gains an hour; probably not worth it
8 or 9	both ends breaking is the only thing that works
10 or more	nothing in this record reaches

Three of those four rows say to leave the day alone. That is the honest shape of the recommendation, and it is considerably narrower than the headline figure about surviving nineteen of twenty-five gaps would suggest.

The best pairing in the record is the right choice in two rows out of four, and only when both people agree to a day that neither of them wants.

What the record does not weigh

A day with a two-hour break in it is not eight hours of work with a long lunch. It occupies eleven hours of the day, it is harder to arrange a life around, and for anybody with fixed obligations in the afternoon it is impossible.

This record counts shared hours and has no way to price that. The figures above are the strongest case that can be made for the broken day, and they are not the whole case.