Appendices: A & B
tpp pyramid-principle abduction problem-solving introductions scq-structure
Status: Notes complete
Overview
The book concludes with two appendices that extend core concepts from the main text.
Appendix A: Problem Solving in Structureless Situations expands Chapter 8’s analytical problem-solving framework by introducing Abduction — a form of reasoning coined by Charles Sanders Peirce in 1890. Where analytical problem solving addresses situations where the structure is known (you dislike the result the existing structure produces), Abduction addresses situations where the structure itself does not yet exist, is invisible, or fails to explain an observed result. Minto discusses both Analytical Abduction and Scientific Abduction, showing they follow the same five-step pattern.
Appendix B: Examples of Introductory Structures complements Chapter 4’s discussion of introductions by providing full worked examples of common SCQ patterns, drawn from real consulting cases in Chapter 8. It also explains two especially tricky introductory forms — proposals and alternatives — and shows how to describe changes to processes clearly using before-and-after visualization.
Appendix A: Problem Solving in Structureless Situations
The Three Structureless Situations
Standard analytical problem solving works when the structure causing an undesired result exists and can be found. But three kinds of situations lack an obvious structure:
- The structure does not exist — as when trying to invent something new (the telephone, underwater tunnelling)
- The structure is invisible — as in the brain or DNA, where you have only results to analyze
- The structure fails to explain the result — as when Aristotle’s definition of force did not explain the momentum of a cannonball, or when tools rust despite all precautions
In all three cases, the reasoning process required is Abduction.
Peirce’s Three Entities
C. S. Peirce identified that all reasoning involves exactly three distinct entities:
| Entity | Definition |
|---|---|
| Rule | A belief about the way the world is structured |
| Case | An observed fact that exists in the world |
| Result | An expected occurrence, given the application of the Rule in this Case |
The form of reasoning depends on where you start and what you already know:
| Form | Starting Point | Logic | Conclusion |
|---|---|---|---|
| Deduction | Rule + Case | If A then B; A is true | Necessarily B |
| Induction | Case + Result | A happened; B happened | If A then probably B |
| Abduction | Result + Rule | B happened; If A then B | Possibly A |
Example (price/sales):
- Deduction: “If price too high, sales go down” (Rule) + “We put the price too high” (Case) → “Sales will go down” (Result, necessarily)
- Induction: “We put price up” (Case) + “Sales went down” (Result) → “Price probably too high” (Rule, probably)
- Abduction: “Sales have gone down” (Result) + “Sales often go down because price is too high” (Rule) → “Let me check whether the price is too high” (Case, possibly)
Analytical problem solving as described in Chapter 8 exactly matches Abductive reasoning: notice an Undesirable Result, look for its cause in the Rule (structure of the situation), test whether you have found it (Case).
Analytical vs. Scientific Abduction
The major difference:
- Analytical: You already know the structure; the scientist (analyst) must find which part of it is causing the undesirable result
- Scientific: The structure does not exist yet; the scientist must invent a hypothesis about the structure before testing it
Scientific Abduction — the classical scientific method:
- Hypothesize a structure that could explain the result
- Devise an experiment that will confirm or exclude the hypothesis
- Carry out the experiment to get a clear yes-or-no answer
- Recycle: make sub-hypotheses or sequential hypotheses to define remaining possibilities
Generating Hypotheses
Hypotheses are not drawn from thin air. They are directly suggested by examining the structural elements of the situation that produced the problem.
The key insight: Productive envisioning requires seeing analogies between what you know about the problem and what you know about the world. Example — Alexander Graham Bell’s insight about the telephone:
“It struck me that the bones of the human ear were very massive indeed, as compared with the delicate thin membrane that operated them, and the thought occurred that if a membrane so delicate could move bones relatively so massive, why should not a thicker and stouter piece of membrane move a piece of steel?”
The insight that arrives is always a visual image.
Devising Experiments
After formulating a hypothesis, devise experiments with clear yes-or-no answers. Zelazny’s principle: “How odd it is that anyone should not see that all observations must be for or against some view, if they are to be of any service” (Darwin).
Galileo example: Aristotle said force produces velocity, so a cannonball should stop when force stops. But it doesn’t. Galileo identifies three structural elements (weight, distance, time of fall), forms three hypotheses about the relationship of force to each, then tests hypothesis 3 (force proportional to time) with an inclined plane — confirming that distance is proportional to the square of time, thus force produces change of velocity.
The Common Pattern (Exhibit A-2)
Both analytical and scientific problem solving follow the same five-step pattern:
| Basic Question | Analytical Approach | Scientific Approach |
|---|---|---|
| 1. What is the problem? | Visualize the difference between result now and result wanted | Define the discrepancy between result got and result expected given prevailing theory |
| 2. Where does it lie? | Visualize structural elements causing the result | State traditional assumptions of the theory that might give rise to the discrepancy |
| 3. Why does it exist? | Analyze each element to determine if and why it causes the result | Hypothesize alternative structures that would eliminate the discrepancy |
| 4. What could we do? | Formulate logical alternative changes that could produce the desired result | Devise experiments that will exclude one or more hypotheses |
| 5. What should we do? | Create a new structure incorporating changes that will produce the most satisfactory result | Reformulate the theory on the basis of experimental results |
Key insight from Herb Simon: Solving a problem simply means representing it so as to make the solution transparent. The representation itself — the image — is the solution.
Appendix B: Examples of Introductory Structures
The Four Standard Questions
Most introductions answer one of four standard questions (Exhibit B-1):
- What should we do? — covers solving problems, getting desired action, evaluating alternatives, auditing, recommending change
- Should we do what we plan to do? — covers whether it’s the right action, whether there will be a problem, whether the solution will work, letters of proposal
- How do/did we do something? — covers implementing solutions, telling how to do things properly, giving direction, progress reviews
- Why did it happen? — covers progress review No. 1, later progress reviews
Common patterns with S/C/Q structures for each — Exhibit B-1 provides a comprehensive reference table with 17 named patterns across the four question types, each showing the Situation, Complication, and Question.
Common Patterns of Introduction (Worked Examples)
What should we do? (Simmons & Smith)
- S = Have X approach to selling to markets now
- C = Expect much higher growth, face other problems; afraid X approach will not continue to work
- Q = How change?
- A = S&S should adopt a separate distribution approach for each market.
Should we do what we are thinking about doing? (Diffraction Physics)
- S = May have problem
- C = If so, will have to change
- Q = Do I have to change?
- A = Diffraction Physics should launch a major unbundled effort now, to capitalize on long-term industry trends.
How should we do what we want to do? (City of San Sebastiano)
- S = Have problem
- C = Know solution, difficult to implement
- Q = How do we implement the solution?
- A = The City should begin with actions that can be initiated by local efforts.
Do we have a problem? (Anielski Airlines)
- S = Change taking place
- C = Want to mitigate likely adverse impact
- Q = What will adverse impact be?
- A = Deregulation will act as the key catalyst in creating a truly common market.
Which alternative should we choose? (Colefax Supermarkets)
- S = Had plan to do X
- C = Suggestion that Y might be better
- Q = Which?
- A = Colefax would be better served by making the system branch-based rather than centralized.
Our solution hasn’t worked, what should we do? (Jackson Foods)
- S = Had problem, implemented solution
- C = Solution hasn’t worked
- Q = What should we do?
- A = Jackson must transform the supply chain into a source of competitive advantage.
Difficult Introductory Forms
Proposing Steps to Solve Problems (Consulting Proposals and Project Plans)
Both consulting proposals and project plans require defining the problem in the introduction. The standard firm headings (Introduction, Background, Objectives and Scope, Issues, Technical Approach, Work Plan and Deliverables, Benefits, Qualifications, Timing/Staffing/Fees) encourage lists that overlap and obscure actual thinking.
Better approach: Structure the document either around:
- The steps in the approach (if a familiar client confirming scope): Exhibit B-2 — pyramid with apex “To help you solve your problem, we would…” branching into Step One, Step Two, Step Three, Step Four. Qualifications and Timing/Staffing/Fees sit outside the main structure.
- The reasons to hire you (if a competitive situation): Exhibit B-3 — apex “You should hire us to solve your problem” branching into (1) We understand your problem, (2) We know how to go about solving it (with steps), (3) We have extensive experience, (4) Our timing/staffing/fees make sense.
In the “reasons” approach, the opening paragraph presents the four key reasons, then section 1 explains the problem in detail using Situation-R1-R2 structure.
Full worked example (US telephone company selling software):
- Problem definition framework: Opening scene (Client-US telco + Telcos in developing countries), R1 (Opportunity to supply), R2 (Become profitable vendor), Disturbing Event (policy change — companies now willing to buy from other telcos)
- Resulting pyramid apex: “We will identify the best strategy for serving the market”
- Four Key Line points: Identify market segments and buying behaviours / Project annual spending in each area / Determine supplier positioning / Identify specific markets and marketing approaches
Dealing with Alternative Solutions
Strictly speaking, there are no true alternatives — either you recommend R2 or you don’t. “Alternatives” arise when R2 is vaguely stated, causing people to compare three or four courses of action without a clear decision criterion.
The right approach:
- Define R2 clearly at the outset
- If alternatives are known to the reader in advance, structure around comparing them to R2
- If alternatives are not known to the reader, present your recommendation and explain why the alternatives are not as good
- If the reader insists on alternatives despite a clear R2, either put them in the introduction (potentially unwieldy) or relegate to an appendix in a comparative matrix (alternatives listed down side, criteria across the top, check marks showing match)
Structure for genuinely alternative R2s:
- “Do X if what you want is earnings stability”
- “Do Y if what you want is fast growth”
- “Do Z if what you want is labor peace”
Describing Changes to Processes
When recommending changes to a process the reader knows, the introduction need only briefly describe the before-and-after; the document can be structured around the recommended changes.
The before-after analysis:
- S = Have X process now
- C = Not working
- D = How change?
Two difficult situations:
1. The Reader Knows Both the Old and New Process (DDT document example — Exhibit B-4): The reader knows both the current inefficient process (locate document → request → locate/copy → mail out = 7-10 days) and the desired new one (locate reference on screen → telephone central computer → see document = 1 hour). The question falls into “Is it a good solution?” or “Can we develop a low-cost system?” The restructured introduction uses the Problem Definition Framework to make this clear.
2. The Reader Knows Little or Nothing (Period Graph Books example — Exhibit B-5): The reader does not know the existing process. The writer must:
- Draw a picture of the present process (Financial Analysis system: 8 steps with errors noted; PBG Monitor Book system: 3 steps with data inconsistency problems)
- State what is wrong with each
- Draw a picture of the proposed system (streamlined: 3 steps, direct data link, computerized graph point generation, CFA validates)
- State the changes needed
- Explain the problem succinctly in the introduction
Exhibit B-6 (Visualize the individual processes): Shows three process flowcharts side by side — Financial Analysis system (8 boxes with error annotations), PBG Monitor Book system (3 boxes with error annotations), and Proposed system (4 boxes, clean and efficient). The visualization makes the problem (errors due to multiple systems and manual entry) and the solution (single direct link, computerized generation) immediately clear.
The Key Line changes become: (1) Create a data link to permit direct transmission to Corporate computer; (2) Create a reliable routine to computerize graph point generation; (3) Demand that changes made by presenters be revalidated before use.
Key Takeaways
- Abduction — reasoning from an unexpected Result and a known Rule to a possible Case — is the logical process underlying both analytical and scientific problem solving.
- The form of reasoning (Deduction, Induction, or Abduction) depends entirely on which of the three entities (Rule, Case, Result) you start with and what you already know.
- Scientific problem solving requires inventing a hypothesis (the missing structure) and then devising a clear yes-or-no experiment to test it.
- All great hypothesis-generation depends on seeing analogies between the problem situation and known structural patterns; the insight always arrives as a visual image.
- Both analytical and scientific problem solving follow the same five-step pattern: define the problem, locate it, explain why it exists, identify options, select the best action.
- Most introductions answer one of four questions: What should we do? Should we do what we plan to do? How do/did we do something? Why did it happen?
- Consulting proposals should be structured around either the steps in the approach (familiar client) or the reasons to hire you (competitive situation), not around traditional firm-defined headings.
- “Alternative solutions” is a symptom of an ambiguous R2; the cure is to define R2 clearly at the start and structure around that.
- When recommending process changes, draw both the before and after states visually before writing the introduction — this reveals what the actual changes are and makes the introduction clear.
Related Chapters
- ch08-problem-solving — Analytical problem solving framework that Appendix A extends to structureless situations
- ch04-introduction-story — SCQ introduction structure that Appendix B illustrates with full worked examples
- ch05-deduction-induction — Deduction and Induction as reasoning forms, contrasted with Abduction in Appendix A