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After a harrowing chase, 
Ethic, Hedge, and their new ally Lemma

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find themselves 
in a cavernous control room.

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Here the last artifact—
the Node of Memory—

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is suspended within a force field 
and powering a supercomputer.

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Ethic is about to deactivate the force
field when Lemma stops her.

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She explains, a decade ago, 
she was assigned a research task:

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to use the world machine to create 
something that would make everyone happy.

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After many failed attempts, Lemma 
discovered a compound that, when ingested,

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made people motivated, happy, creative, 
loving… in short, their best selves.

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It was rushed into production.

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Soon, the entire nation’s food supply 
came from Huxenborg,

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with the compound mixed in.

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The first year was paradise.

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The second, not so much.

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Side-effects began to emerge: memory-loss,
listlessness, and self-absorption.

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In the third year, 
the government dissolved,

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leaving the robots running everything 
in a self-sustaining loop.

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By this point things were too far gone
for Lemma to reverse.

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People had become dependent 
on the compound,

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and the few who refused it 
formed a resistance to try to fix things.

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It took 10 years for Lemma to find a cure.

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This factory contains everything 
she’ll need to make it,

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but the second they take 
the Node of Memory,

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the security system will alert the robots,
and they’ll have to run.

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If, instead, they first reconfigure 
the factory to manufacture the cure,

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the people can be saved.

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Lemma has the whole factory redesign 
planned out.

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The problem is… 
it’s a little hard to read.

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Her schematic shows all the steps 
in the manufacturing process

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needed to make the cure.

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An arrow from “add nitric acid” 
to “shake vigorously”

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means that the acid addition 
has to happen before shaking.

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If a single step is performed 
out of order,

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the cure won’t work, or worse.

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There aren’t any circular references,
where step A requires step B

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and step B eventually requires step A.

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Here’s where Ethic and Hedge come in.

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Lemma needs Hedge to translate 
the tangled diagram

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into a sequence of steps.

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That’ll be the order that things happen 
in the factory.

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Once input into the central computer,

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the factory will reassemble 
itself as instructed.

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Hedge’s ability to store information 
in a table will help here.

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So how does Ethic program Hedge 
to turn out a correct sequence

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that can reconfigure the factory?

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Pause now to figure it out yourself.

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Rules in 3

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Rules in 2

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Rules in 1

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Hint in 3

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Hint in 2

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Hint in 1

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It may help to first think about 
this problem as a human,

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rather than a machine.

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Given this diagram, it’s clear to start 
with getting a bowl,

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since no arrows point to it.

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How might you mark up the diagram 
to figure out what to do next?

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Pause now to figure it out yourself.

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Solution in 3

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Solution in 2

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Solution in 1

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Diagrams like the one Lemma has drawn
are called directed acyclic graphs.

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A graph is a representation of data 
that shows different elements

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and how they’re related to each other.

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Directed means that direction matters—
as indicated by the arrows.

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Here A leads to B, 
but B doesn’t lead to A.

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And acyclic means that there 
aren’t any loops.

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Which is fortunate, because if there were,
this problem wouldn’t be solvable.

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There’s a simple way to navigate 
the graph as a human:

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start with a step that doesn’t have 
any arrows pointing to it.

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Once you do that, cross out that step 
and all arrows leading from it.

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Choose another step with no arrows 
pointing to it,

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and repeat until you’ve hit every step.

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There are two things here that are tricky
to translate for a robot.

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First, how do you keep track 
of the information?

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And second, what do you do if there
are multiple options at the same time?

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For the first challenge,

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a convenient way for machines 
to store information is in a table.

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In this case, you can have Hedge 
list every step in the headers

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of both the rows and columns.

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Then he can go through 
the rows one at a time.

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On the schematic, what points to mix?

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Both shake and titrate.

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So Hedge should make a mark 
in both of their columns.

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He can do the same for every row, 
one at a time, to make a table like this.

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Of course the full table 
will be much bigger.

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Like a human, 
Hedge will also want to start

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from one of the steps that has 
no arrows pointing to it—

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which is the same as having no marks 
in its row.

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If there’s more than one,

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a convenient way to choose is to pick 
the one that’s alphabetically earliest,

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though other selection methods 
can work just as well.

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Next, Hedge can add that step 
to his running-order list,

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delete its entire column from the table—

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thus removing all the times 
it was a dependency––

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and loop back to the start.

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Because there are no circular 
references in the graph,

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each time we get here there’ll be at least
one step with no remaining dependencies.

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Hedge can add the alphabetically earliest 
to his running-order list,

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remove it from the table, 
and loop back to the start again.

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So now we have a working loop,

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and it’ll run through all the elements 
in our table until none are left.

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Hedge drifts back and forth 
over the schematics,

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and soon he starts spitting 
out instructions,

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which Ethic uses to configure 
the assembly lines.

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With the three working together,

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they churn out thousands of doses 
of the cure in no time.

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Ethic finally plucks the Node of Memory

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from its holding field 
and trips the alarm.

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Within seconds bots are everywhere.

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As Ethic falls in shock, the Node 
restores not only her own memories,

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but reveals the last, missing pieces
of the puzzle.

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Ethic built Hedge with a singular purpose:

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to construct a maze that would protect 
the world machine

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from a corrupt government.

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But in her haste, 
she made a critical mistake.

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She forgot to set the condition 
that would end the loop

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which told Hedge 
how large the maze should be.

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So Hedge built and built 
until he could build no longer.

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And then he was conflicted.

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He had to build a maze.

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But he couldn’t build further 
without hurting people

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or flying over the Bradbarrier,

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both forbidden by his programming.

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So he wandered the land 
and searched for a solution,

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until he happened upon the Node of Power, 
the Node of Creation,

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and the Node of Memory.

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He recognized their true, 
collective power

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to grant self-awareness 
to those who lack it.

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With all three he’d be able 
to change his programming

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and fulfill his drive to transform 
the entire world into a giant maze.

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It wouldn’t be easy:

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the Nodes had safeguards to prevent 
robots from taking and using them.

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But if Hedge could find the right human

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and manipulate her 
with the promise of a heroic quest…

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well that would be a different story.

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A very different story.