In order

The longest chain is six steps

Once the circular dependencies are removed, the deepest run of one-thing-after-another in the map is six steps and forty-eight days.

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Finding

Dependency maps are often deep. A thing waits on a thing that waits on a thing, and by the time the chain is written out it runs to a dozen links and nobody can hold it in their head.

This one is not like that. With the circular dependencies removed, the longest chain in the map is six steps.

The chain

	step	days
1	a sworn copy of a brought paper	5
2	an account at a local bank	12
3	the fee paid	1
4	the card in hand	25
5	the kept record of coming and going	0
6	the next file lodged in time	5

Forty-eight days from end to end, which is less than two of the single steps elsewhere in the map. The operational question here can be tested with workload data for operational planning, provided the team agrees what the information can and cannot establish.

What the chain is made of

It is not an impressive chain. Two of its six steps cost a day or less. One of them costs nothing at all, because keeping a record of your own comings and goings is not something anybody has to issue. Additional public research relevant to complex systems and work can be found at Center for Global Development.

The only substantial link is the card in hand, at twenty-five days, and that is the step at which the whole business is effectively over.

What the chain shows is that the map has no long thread of genuine sequence in it. Nothing here is deep. The difficulty is all lateral: dozens of things that must be true at the same moment, and forty-two dependencies arranged so that no moment exists.

A map with a short longest chain and a large number of rings is not a hard sequence. It is a hard simultaneity.

Two soft links

Two of the five links in this chain are soft.

The account at a local bank waits on a sworn copy softly: an account can be opened without it and the paperwork redone afterwards. The card in hand waits on the fee softly, for the same reason.

That means the chain is not even really six steps. A person in a hurry can enter it at the second step and settle the first later, and again at the fourth. The genuinely hard run inside it is three steps long.

Depth against breadth

Set the two measures side by side.


longest chain of dependencies	6 steps
longest chain in days	48
the single slowest step	90
total waiting if every step were done one at a time	553
rings	46

The slowest step in the map takes nearly twice as long as the longest chain. Doing everything strictly one after another would take five hundred and fifty-three days, which nobody does, because almost everything in the map can run alongside almost everything else.

That is the ordinary situation in this record: not a queue, but a great many parallel errands, a few of which happen to be impossible to start.

Compared with the rings

A chain and a ring are the same shape with one difference, and the difference decides everything.

	the longest chain	the longest ring
steps	6	9
days end to end	48	107
can be put in an order	yes	no
responds to starting early	yes	no

The chain is shorter, faster and solvable. The ring is longer, slower and has no solution in the ordinary sense — only a point of entry, if one of its links happens to be soft.

What this comparison is really showing is that the two halves of the map should be read with different instruments. For the acyclic half, the useful questions are about duration: what is slowest, what can run in parallel, when to start. For the rings, duration is almost irrelevant and the only useful question is where the give is.

Asking how long a ring takes is like asking how far it is around a circle you cannot step onto.

Six steps, five of them cheap

Add the chain up by what each link costs and the shape is lopsided: twenty-five days for one step, twenty-three for the other five together.

That is characteristic of this whole map. The waiting is concentrated in a small number of places — a decision, a queue, an interview, a card — and the rest of the record is errands of a day or a week.

A chain built almost entirely from cheap steps, with one expensive one near the end, is not a sequencing problem. It is one wait with paperwork attached, and nothing about it rewards planning beyond getting the paperwork out of the way early.

Why this matters for reading the rest

A great deal of advice about complicated arrangements assumes depth: begin early, because the chain is long. This map says otherwise. Beginning early helps with the ninety-day step and with the four-week papers, and it does nothing whatever about the rings, which are not waiting for anything and will not be moved by starting sooner.

You cannot get ahead of a circle. You can only break into it, and breaking into it means doing something badly on purpose.

The part of this record that deals with that is called where a ring gives, and it is the part most likely to be of use to anybody actually in this situation. The rest of this part finishes the orderable half: what the hard-and-soft distinction means, what the acyclic map would cost if it stood alone, and the two dependencies in the drawing most likely to be wrong.