hermes-agent/optional-skills/creative/creative-ideation/references/methods/polya.md
SHL0MS d799284b15
feat(optional-skills/creative-ideation): expand to v2.1.0 method library (#42402)
The optional-skills copy was still the v1.0.0 constraint-dispatch skill
(SKILL.md + full-prompt-library.md only). This brings it up to the current
tool: a situation-routed library of 22 named ideation methods drawn from
working artists, scientists, designers, and writers.

SKILL.md becomes a 4-step router (extract PHASE/DOMAIN/SPECIFICITY signals
→ apply overrides → route phase-then-domain → resolve ambiguity), with
anti-slop operating rules and an anti-default check.

Adds:
- 22 method files under references/methods/ — oblique-strategies (Eno/Schmidt),
  oulipo, scamper, lateral-provocations (de Bono), triz (Altshuller),
  leverage-points (Meadows), pattern-languages (Alexander), compression-progress
  (Schmidhuber), analogy-and-blending, pataphysics, first-principles, polya,
  biomimicry, volume-generation, creative-discipline, premortem-and-inversion,
  defamiliarization, derive-and-mapping, affinity-diagrams, jobs-to-be-done,
  story-skeletons, chance-and-remix. Each: when/when-not, the actual
  cards/principles/operators, a procedure, a worked example, anti-slop notes.
- references/method-catalog.md (index + when-to-use), heuristics.md (extended
  decision tree), anti-slop.md (rules applied to every output), exercises.md
  (time-boxed exercises).
- full-prompt-library.md restructured into domain-affinity sections (general /
  software / physical / social / lists) so the no-direction default isn't
  developer-biased.

Frontmatter: name aligned to directory slug (creative-ideation, folding in
the fix from #18084); version 2.0.0→2.1.0; platforms field preserved.

Original wttdotm-derived constraint dispatch is kept as the default path.
Supersedes #19295 (which targeted the pre-move skills/ path).

Co-authored-by: SHL0MS <SHL0MS@users.noreply.github.com>
2026-06-19 15:40:02 -07:00

3.5 KiB

Pólya's Heuristics

George Pólya, How to Solve It (Princeton UP, 1945). Four-phase problem-solving framework + dictionary of heuristic moves. Written for math but applies to any well-defined "find X such that..." problem.

When to use

  • Math, physics, theoretical problems
  • Algorithm design, debugging
  • Any problem with a clear target (find X such that...)
  • Teaching problem-solving

Don't use when

  • Open-ended creative problems with no defined target
  • Difficulty is understanding the problem space, not solving within it (use dérive or compression-progress first)
  • Solution is more about taste than analysis
  • Real-world problems where data is incomplete and conditions vague

The four phases

1. Understand the problem

  • What is the unknown?
  • What are the data?
  • What is the condition linking them?
  • Is the condition sufficient? Insufficient? Redundant? Contradictory?
  • State in your own words.
  • Draw a figure. Introduce notation.

This phase is most often skipped. Most problem-solving failures are upstream of method — they're failures to understand the problem precisely.

2. Devise a plan

Find the connection between data and unknown. Heuristic moves:

  • Have you seen this problem before? Or in slightly different form?
  • Do you know a related problem?
  • Look at the unknown — find a familiar problem with the same or similar unknown.
  • Could you use a related problem's result? Its method?
  • Restate.
  • If you can't solve the proposed problem, solve a related one:
    • More general
    • More specific
    • Analogous
    • A part of the problem
    • With a condition relaxed
  • Did you use all the data? All the conditions?

3. Carry out the plan

  • Can you see clearly that each step is correct?
  • Can you prove it?

4. Look back

  • Check the result. Check the argument.
  • Can you derive it differently? See it at a glance?
  • Can you use the result, or the method, for some other problem?

The looking-back phase is the learning phase — what makes Pólya's method an educational method, not just a problem-solving one.

Key heuristics from the dictionary

  • Decompose and recombine. Break into parts; solve each; combine.
  • Generalization. The general case is sometimes easier than the specific because it forces you to identify essential structure.
  • Specialization. Try the smallest case, the simplest case, the case where one parameter is zero. Look for pattern.
  • Analogy. Find a related problem with same structure, different surface.
  • Auxiliary problem. Solve a related problem first; use its result.
  • Working backwards. Start from the unknown and work back. Forward direction often has too many branches; backward is more constrained.
  • Setting up an equation. Most word-problem failure is in translation, not algebra.
  • Reductio ad absurdum. Assume the conclusion is false; derive contradiction.
  • Pattern recognition. Small cases → conjecture → prove.
  • Symmetry. Where there's symmetry in the problem, there's usually symmetry in the solution.

Anti-slop notes

  • Reciting the four phases without doing them = slop. The structure is fine; the value is in actually executing each phase.
  • Don't pretend you've understood when you haven't. State the unknown, the data, the condition concretely.
  • Don't claim "Pólya'd it" without consulting specific heuristics.
  • Don't apply to fuzzy problems. Pólya assumes clear problem statements.

Source: Pólya, How to Solve It (Princeton UP, 1945; current edition 2014).