Thinking before you move

A working definition

Planning

Choosing a sequence of actions to reach a goal by simulating them before you act, rather than discovering the sequence by trial and error.

Two features separate planning from simply being clever. First, the work happens before the action. A planner who solves a puzzle in five moves has usually "seen" those five moves before touching anything. Second, a plan is a sequence. Picking the best single move is a judgement; picking the best order of moves, where each one changes what the next can be, is planning.

Psychologists usually treat planning as a higher-order executive function. The core executive functions are inhibition (stopping an automatic response), working memory (holding and updating information) and cognitive flexibility (switching between ways of thinking). Planning, reasoning and problem solving are built on top of these three. That is why a planning task feels like several things at once: you must hold imagined positions in mind, resist the obvious move, and switch approach when a line of thought dead-ends.

How a plan gets built

The problem space

From the late 1950s Allen Newell and Herbert Simon described problem solving as a search through a problem space: a set of states (every arrangement the puzzle can be in), operators (the legal moves), a start state and a goal state. Solving means finding a path from start to goal. Planning is doing some of that search in your head.

The three-ball Tower of London, the classic planning test and the model for our Towers of London game, has 36 possible arrangements on its three pegs. That sounds small, but even looking two moves ahead means comparing several imagined positions at once, as the figure below shows.

Means-ends analysis and subgoals

Newell and Simon's General Problem Solver used a strategy they called means-ends analysis: compare where you are with where you want to be, pick an action that reduces the difference, and if that action cannot be taken yet, set up a subgoal that makes it possible. People do the same. "Disc 3 must go to the bottom of peg 1, but disc 1 is sitting on it, so first I need somewhere to park disc 1" is means-ends analysis with a subgoal.

Subgoals are where planning gets hard. In a study of five-disc Tower of London problems, errors and planning time rose steadily with the number of subgoal chunks: runs of moves that are essential to the solution but do not place a disc in its final position. A move that makes visible progress is easy to find. A move that makes progress only three steps later has to be imagined.

The counterintuitive move

Sometimes the right move takes a piece away from where it wants to end up. Researchers call this a goal-subgoal conflict. In a study of patients with prefrontal damage solving the Tower of Hanoi, the patients' main difficulty was not looking ahead as such but seeing and resolving exactly this kind of conflict, which the authors linked to failing to inhibit a strong but wrong response. The same idea shows up in healthy adults: in a large study of executive functions, Tower of Hanoi performance was most closely related to inhibition, not to updating or switching.

Look-ahead depth

How far ahead can a person reliably plan? In one set of experiments, most people could accurately preplan up to two subgoals ahead on the Tower of London, but not three. The same study found that telling people to plan every move before starting made them think for much longer without making their execution any better. The practical point is that good planners do not simulate the whole solution in one go. They plan a chunk, act, and plan again.

Planning is not one number

Executive functions show "unity and diversity". In Miyake and colleagues' landmark study, individual executive tasks correlated weakly with each other, but the underlying abilities for inhibition, updating and shifting correlated at .42 to .63: related, yet clearly separable. Planning inherits this. Someone can be excellent at seeing five moves ahead and still be careless about decisions that cannot be undone. That is why we measure planning through three facets rather than one task.

Facet 1: Look-ahead

Look-ahead is the depth and accuracy of your mental simulation: how many moves you can run forward, and whether the position you imagine is the one you would actually reach. It is what the Tower of London was designed to measure, and it is the facet our Towers of London game feeds.

• Everyday: packing a car boot so the thing you need first comes out first.
• Work: sequencing a software release so that the database change ships before the code that depends on it.
• Tests: seating-arrangement puzzles where fixing one person's seat forces three others.

Facet 2: Irreversible decisions

Some moves cannot be taken back. Pushing a crate into a corner, sending an email, submitting an answer. Planning well here means noticing which of your options are one-way doors and slowing down for those, while moving briskly through the rest. Our ShiftMaze game, a push puzzle where a crate you shove stays shoved, feeds this facet. Push puzzles of this family are famously hard: deciding whether a Sokoban level can be solved at all is known to be PSPACE-complete.

• Everyday: booking a non-refundable ticket before checking the date of your exam.
• Work: deleting a production table, or signing off a design that other teams will build on.
• Tests: negative marking, where a guessed answer is a commitment with a cost.

Facet 3: Keeping options open

When many choices interact, a good planner makes the most constrained decisions first and avoids choices that close off later ones. In constraint-satisfaction research this is called the fail-first principle: try first where you are most likely to fail. Our Number Builder game, where every digit you place limits the digits left, feeds this facet, along with Numerosity on the reasoning shelf.

• Everyday: choosing the one restaurant that suits the friend with the strictest diet, before debating the rest.
• Work: scheduling the meeting with the busiest person's calendar first.
• Tests: arithmetic target puzzles, and the logical-reasoning sets in CAT and bank exams.

How our planning score is built

The weights reflect how directly each game isolates planning. Towers of London is the purest planning task we have. Number Builder and Numerosity also lean heavily on arithmetic, so they count for less here.

1. 1883

   Édouard Lucas publishes the Tower of Hanoi puzzle, later a standard problem-solving task in psychology.

2. 1957–61

   Newell, Shaw and Simon build the General Problem Solver, which plans by means-ends analysis.

3. 1972

   Newell and Simon's Human Problem Solving sets out the problem-space view of thinking.

4. 1982

   Shallice introduces the Tower of London to study planning after frontal-lobe damage.

5. 1990

   Owen and colleagues publish a computerised tower task, separating thinking time before the first move from thinking time during the solution.

6. 2000

   Miyake and colleagues show that executive functions are related but separable, and link Tower of Hanoi to inhibition.

2 practice questions

1. A candidate solves a tower puzzle in the minimum number of moves, but only after taking a disc off the peg it must finish on. What skill did that first move show?
2. According to Phillips and colleagues, how far ahead could most people accurately preplan on the Tower of London?

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Remember

• Planning means simulating a sequence of actions before committing to it.
• It is built from inhibition, working memory and flexibility, and adds sequencing on top.
• Subgoals and counterintuitive moves are what make a plan hard, not the raw number of moves.
• Our planning score has three facets: look-ahead, irreversible decisions, and keeping options open.

Sources

1. Diamond, A. (2013). Executive functions. Annual Review of Psychology, 64, 135–168. PMC4084861
2. Newell, A., & Simon, H. A. (1972). Human Problem Solving. Prentice-Hall. Background on means-ends analysis and the General Problem Solver: Wikipedia
3. Ward, G., & Allport, A. (1997). Planning and problem-solving using the five-disc Tower of London task. Quarterly Journal of Experimental Psychology, 50A(1), 49–78. doi:10.1080/713755681
4. Goel, V., & Grafman, J. (1995). Are the frontal lobes implicated in "planning" functions? Interpreting data from the Tower of Hanoi. Neuropsychologia, 33(5), 623–642. PubMed 7637857
5. Miyake, A., Friedman, N. P., Emerson, M. J., Witzki, A. H., Howerter, A., & Wager, T. D. (2000). The unity and diversity of executive functions and their contributions to complex "frontal lobe" tasks. Cognitive Psychology, 41(1), 49–100. PubMed 10945922
6. Phillips, L. H., Wynn, V. E., McPherson, S., & Gilhooly, K. J. (2001). Mental planning and the Tower of London task. Quarterly Journal of Experimental Psychology, 54A(2), 579–597. doi:10.1080/713755977
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8. Kaller, C. P., Rahm, B., Spreer, J., Weiller, C., & Unterrainer, J. M. (2011). Dissociable contributions of left and right dorsolateral prefrontal cortex in planning. Cerebral Cortex, 21(2), 307–317. PubMed 20522540
9. Friedman, N. P., & Miyake, A. (2017). Unity and diversity of executive functions: Individual differences as a window on cognitive structure. Cortex, 86, 186–204. PMC5104682
10. Sokoban: rules and computational complexity (Culberson, 1997, PSPACE-completeness). Wikipedia
11. Haralick, R. M., & Elliott, G. L. (1980). Increasing tree search efficiency for constraint satisfaction problems. Artificial Intelligence, 14(3), 263–313. doi:10.1016/0004-3702(80)90051-X
12. Owen, A. M., Downes, J. J., Sahakian, B. J., Polkey, C. E., & Robbins, T. W. (1990). Planning and spatial working memory following frontal lobe lesions in man. Neuropsychologia, 28(10), 1021–1034. PubMed 2267054
13. Tower of Hanoi: history and rules. Wikipedia