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Problem Solving

Analysis and Design Process

Why do we write problem statements?

• to solve some problems hopefully

What kinds of problems?

• developing a shared understanding
• discovering the best possible solution

What information do we capture?

• all the costs, benefits and trade-offs
• what we don’t know
• possible solutions
• there must always be more than one solution

How do we organize this information?

• each potential solution gets a column
• each problem gets a row
• each characteristic we care about gets a row

Analysis and Design Template

Spreadsheet Sections

• each of these can be its own sheet within the workbook

Description (Symptoms)

• avoid too much curation
• stay connected to problems felt by people

Problems

• may be combined with Description sheet
• distillation of description which should identify root causes, not merely symptoms
• keep meta problems separate (e.g. process problems that led to this state)

Solution Space (Decision Matrix)

Comparison Characteristics

• one characteristic per row
• sorted in priority order (top-to-bottom)

Possible Solutions

• one solution per column
• useful to capture current state or solution for comparison
• must have more than 1 alternative solution

Pitfalls

• it’s easy for “solution” to creep into problems one subtle and hard-to-catch way is when we list problems as deviations from “best practices” or good design sensibilities
  • e.g. solution lacks generality
  • generalization is a solution to a problem!
  • we must always remain connected to the problem

Reflection

What’s wrong with how I’ve always approached ADRs?

• ADRs are for recording the outcome of a decision-making process
• they are not the record of the deliberative process itself
  • decision support artifacts
    • problem statements
    • comparison spreadsheet
• ADRs are fine as summaries of the decided solution and enumeration of consequences
  • can link to decision support artifacts for those interested in the deliberations

Problem Solving Advice

From Rich Hickey (Paraphrased)

On stating problems…

• let’s see where what we’ve done is too limited
  • e.g. what about the data model is just wrong or too restricted
• make a map of where we are, where we want to go
  • we’re not going to enumerate where we are, just have a sense
  • startup context
    • people have intuitions
      • independent team, charge is to go deliver
      • make what they need to make the features
    • we’re a startup, move fast, grow
      • burn money and go get customers
      • build an overall set of tools and services that satisfies all the missions
• possible misfits
  • model for the existing system
  • inherent data model in the world
  • service flow on top of those things
• during the why game, don’t introduce words that require more whys
  • e.g. +”extra hop”+ -> speed
• when walking up to an analysis task, let’s make the artifacts we’d like to see (if they don’t already exist)
  • we don’t need to look too far beyond what we have/want
  • enumerate the problems
  • what is the data model
    • model independent of service
    • example problems:
      • i have no place to store it
      • i have a place to store it, but the service won’t let me
• it’s not possible to make a distributed system where everyone’s knowledge is perfect
• get to semantics early
  • get away from mechanical / representational things
    • so you can do a new mapping to a different representational thing
  • try to stay in the semantic space as long as possible
  • cardinality matters
    • e.g. $log_n$ hops on disk
  • there’s nothing semantic about bytes
    • the only time I care is when over the wire or writing to disk
  • add units, break things down
    • e.g. 1.2 GBs == approximately how many thingies?
• ask questions about processing
  • why are you loading things?
  • why are they in memory (versus disk)?
  • why aren’t you asking a service?
• you don’t always need a uniform solution

How to Solve It

Process

State the Problem

Ask Questions

• what is the unknown?
• what are the data?
• what is the condition?

Visualize the Problem

Introduce Suitable Notation

Improve Understanding

Isolate the Principal Parts of the Problem

Problem to Prove

• hypothesis
• conclusion

Problem to Find

• unknown
• data
• conditions

Hunting for a Helpful Idea

• consider the problem from multiple sides
• have we used all the data?
• attempt to make contact with prior knowledge

Carry out the Plan

• start from the idea
• make sure you have a solid grasp of the main connection

Looking Back

• start from the solution
• verify completeness and correctness
• hunt for a helpful idea (see above)
• consider the details
  • are they as simple as they can be?
  • survey extensive parts and try to make them shorter
• can you modify parts of the solution
  • can they be made more intuitive?

Short Dictionary of Heuristic

Analogy

• a kind of similarity
• analogous objects agree in certain relations
• analogies are ubiquitous
• it may pay to solve a simpler, analogous problem
  • we can sometimes reuse the method, the result, or both

Auxiliary Elements

• elements we introduce in the hope they will further the solution
• as we progress, our conception of a problem increases
• sometimes this helps us reuse some known result
• we should only introduce elements with a purpose

Auxiliary Problem

• a different problem we expect will help us solve the original
• there should be a relationship between the problems
  • either the result or the method may be useful
• the problems may also be equivalent

…many more…

TODO: continue to capture some of the most important heuristics

The Socratic Method: A Practitioner’s Handbook

Chapters 1-5

• TODO: back-fill notes for initial chapters…

Elements of the Socratic Method

1. proceeds by question and answer
   • some questions are open ended (especially in the beginning)
   • e.g. propose a definition
   • the person being questioned is the partner of the inquirer
2. focus on consistency of statements
   • consistency is probed with the elenchus
   • partner should feel compelled to refine their statements or abandon them
3. questions should aim to identify the principles behind statements
   • then show principle covers things it shouldn’t or omits things it should
4. use concrete examples to drive reasoning
   • use ordinary examples from everyday interactions
   • make headway on hard problems by talking about specific cases
5. don’t claim expertise
   • Socrates constantly confesses his own ignorance
   • dialogues often end at an impasse, without an answer

Takeaways

• denying what someone says is the act of a friend
• the Socratic method should make your more humble and aware of your own ignorance

The Elenchus

Etymology

elenchus

search

• testing, refutation, shame, ridicule
  • the latter two should be reserved for introspection

Process

• make a claim
• agree to other propositions (possibly logical conclusion)
• demonstrate inconsistencies
  • something has to give
  • often a modification of the original claim
  • finding these inconsistencies is the point

Consistency and Truth

• elenchus is a tool for finding inconsistencies
  • falsification, tearing down bad claims (negative logic)
• is it possible to build claims using this technique? (positive logic)
  • in science, the strength of our belief in a proposition is proportional to the evidence supporting it and the number of assaults it survives
  • Vlastos’ solution
    • everyone holds at least some true beliefs (axiom)
    • beliefs that survive consistency checks with everything else you believe are likely to be true
    • broad agreement within a belief system
• accumulation of a set of mutually consistent beliefs is a worthy project
  • cumulative consistency
• internal inconsistency between two ideas means one of them has to be wrong
  • persuasiveness
    • if ideas conflict with new data, one might doubt the data
    • if ideas conflict with each other, can’t attack the author

Reliability of Consistency

• is consistency enough? what about being consistent but wrong?
• can a repellent set of ideas be internally consistent?
  • unlikely: bedrock principles will conflict with some other held truth

Shame

• the “pain in the ribs” one feels at embarrassing propositions
• fear of what others will say or think has no place in moral reasoning
  • threat to honest inquiry
• the good kind of shame is that which you’d feel by adopting a morally bad position, forcing you to reconsider your claims or positions
• discomfort from:
  • realizing you don’t know what you’re talking about
  • you were overconfident, too sure of yourself
• teaches humility

Uses

• to poke holes in ideas, showing them to be faulty
• to fend off attacks of ideas by showing holes in their counters
  • indirect support of a claim

Example

• courage is mental persistence
• would you agree courage is admirable? (yes)
• what about unintelligent mental persistence? (e.g stubbornness)
  • isn’t that harmful or dangerous? (yes)
  • are harmful things admirable? (no)
• so this kind of persistence isn’t courage? (no)
• conclusion: original claim or definition needs revision

Systole and Diastole

Defining Terms

• make a claim, state the principle behind the claim
  • show it is either too restrictive or too broad
  • by examining expansion and contraction, we arrive at better approximations
• two skills of the mind are required
  • detecting similarities among things that seem different
  • detecting differences among things that seem similar

systole

drawing together

• in book: finding commonality, a general case or principle

diastole

separation

• in book: finding distinction, what separates this from that

• note: the examples given to these words are at odds with the medical meanings
  • systole is the contraction of the heart (narrowing)
  • diastole is the expansion or relaxation of the heart
  • my opinion: probably best not to get hung up on these Greek labels
    • better to talk about finding commonality or making distinctions

Know It When You See It (KIWYSI)

• priority of definition: the claim that you can’t know something if you can’t define it precisely
  • known (fairly or not) as the Socratic fallacy
• KIWYSI is legitimate: we can often identify examples before we have a good definition
  • we should understand our knowledge to be provisional
• definitions provide clarity, especially useful for hard or edge cases

Collection and Division

• putting a subject into one of two categories
• subdividing that category into more categories

diairesis

a form of classification used in ancient (especially Platonic) logic that serves to systematize concepts and come to definitions

• perhaps not the best way to define something, but can still be useful to compare things and learn about them
• reflection: might also be useful for finding alternative solutions to problems

Analogy

• analogies aren’t arguments, but can make reasoning more clear
• they can be used to compare abstract ideas to more familiar ones
  • used to show how a claim works
• fill-in-the-blank: start an analogy and let partner finish it
  • can move an conversation forward
• begin with distinctions and examples that are easy and familiar, then try to map onto harder examples
• extended analogies compare two things at length to make an idea more vivid
  • established analogies can also be turned to make a very strong point
• offering choice between analogies can also be powerful
• analogies look like observations, but actually make claims
  • sometimes the best response is to reject the analogy

epagoge

an argument in which specific examples lead to a general conclusion

• inductive reasoning

Socratic Rules for Dialogue

Seek Truth

• seek truth rather than merely try to win an argument (dialectic not eristic)

  dialectic

  formal system of reasoning that arrives at the truth by the exchange of logical arguments

  eristic

  given to disputation for its own sake and often employing specious arguments

Examine People As Well As Claims

• examine people (myself and others) not just claims
  • it isn’t easy (or desirable?) to separate people from ideas
  • care of the psyche, mind, intelligence
  • testing consistency is testing the holder of claims as well as compatibility

Judge Arguments on Their Merits

• judge arguments on their merits, not by their author
  • primacy of reason
  • “I shall be very grateful if you refute me and deliver me from my foolishness.”
  • claims are judged strictly by the quality of the reasoning and evidence that supports them

Speak Candidly

• speak candidly: say what you think, not what others may want to hear
• you can’t seek truth if you’d shy away from speaking it
• rather than merely agree if you don’t understand, disagree by default unless you’re sure
  • this way the argument can be refined or approached from a different angle until one is satisfied
  • it’s better to seem slow than to persist in confusion
• also prevents weasel-y backtracking “well I never really meant that”
  • changing one’s mind in light of persuasion or evidence is fine
• important difference: sometimes the questioner must play “Devil’s advocate” to examine a claim deeply

One-Witness Principle

• numbers count for nothing
• the whole world in favor or against speaks not at all to the veracity of a claim
• Christopher Hitchens: “One person with a right opinion outweighs a majority.”
• interlocutor must be the one to assent
• the crowd is not to be trusted, especially when a horde can be summoned instantly
  • Twitter, anyone?

Principle of Charity

• principle of charity: assume best intentions of the other
• construe their meaning in the most reasonable light
  • assume opponent is smart and well-meaning
• work to represent the position of the partner/opponent in the strongest possible terms
  • steel man vs. straw man
  • improve the other person’s argument if you can
• come up with the strongest objections to your own views
  • run towards the hardest problems, not away from them

Offensiveness

• strive not to give nor to take offense
  • it’s as bad to take offense as to give it
  • takes courage and commitment to seeking truth
  • in any case, “I’m offended” isn’t an argument
• people feel strongly about certain issues
  • politics, religion, etc
  • disagreement when feelings are at stake can be perceived as personal attacks
    • avoid lines of argument that tweak personal sensitivities
    • use examples that don’t strike close to home
    • when people are worried the other side will take offense, they don’t say what they mean
    • honest inquiry is difficult (if not impossible) under these conditions
• be polite
  • choose words carefully and attempt to convey personal respect
  • if the conversation gets heated, nothing wrong with clearing up what you meant
  • A gentleman is someone who gives offense only when he means to.

Ignorance

• Socratic inquiry begins with an awareness of our own ignorance
  • we begin and end in this state
    • along the way, hopefully, there is some progress
    • the difficulty of ascertaining truth should teach us humility
• journey is not from question to answer, but from question to question
• principal project: uproot conceit of certainty in one’s own mind
• Socrates really does have a low opinion of his wisdom
  • he has a lower opinion of the wisdom of others only because they have such a high opinion of their own
• knowing one is ignorant is better than being ignorant of one’s ignorance
  • this double ignorance is termed “stupidity” in Sophist 229cd
  • the remedy is education (perhaps especially philosophy)
• can be used as a tool for exploring ideas that are firmly rooted
  • pretend I know nothing, walk me through this point by point
  • I will ask questions, some may be naive
  • let’s see where the answers go
• intellectual midwifery: eliciting ideas from others

Aporia

aporia

to be at a loss what course to pursue, where to begin to end, what to say

• an irresolvable internal contradiction or logical disjunction
• literally “without a way”; a sense of disorientation and perplexity
• generally arrive here when all prior ideas have been refuted
• common ending for Socratic dialogues once reason has been exhausted
• we are not perplexed about things we know:
  • e.g. I have two eyes
• we are not perplexed by things we know we don’t know
  • e.g. I know nothing of ballet
• we are only perplexed by things we thought we knew, but didn’t
• aporia is a sign that we’ve departed the dreaded state of double ignorance
  • we must be purged of our prejudices before learning can begin
  • can also be powerful motivator, spurring us to think more

Socratic Goods

• Socratic method doesn’t meet needs most people feel, so why bother?
• it can help you see reality more clearly
• Socratic good: something not assigned much value by those don’t have experience of it, but regarded highly by those who do
  • endowment effect: the tendency to value something more highly once you have it
• ignoti nulla cupido: absence of a good keeps you from seeing why you want it
  • “there is no desire of the unknown”
  • you don’t know what you are missing
• Dunning-Kreuger effect: incompetence prevents one from seeing their incompetence
  • idiocy doesn’t recognize its own existence
• contemplate people you know who are ignorant of their own ignorance
  • then realize you must certainly look that way to someone else
  • the horror should spur one to action!
• our current understanding is in a state that we would regard with embarrassment with a little progress
• would you rather be a blissful simpleton?
• nobody walks through life feeling like an idiot, yet we all probably know a few
  • these states are all relative, so adopt humility not hubris
  • the sensation of one’s own wisdom is a stubborn, persistent feature of the human mind
  • this mistake makes all others more likely
• “he is not to be trusted who loves voluntary falsehood” (Cypher from the Matrix)
• “he who loves involuntary falsehood is a fool” (what does this mean?)
  • the untrustworthy and the ignorant have no friends
• ignorance is bliss: you don’t suffer what you don’t realize you’re suffering from
  • misfortunes of which the bearers are unconscious, but they would avoid if they knew
  • to know these people is to pity them (see also: mirror)
• Socratic injuries may be suffered culturally as well as individually
  • a culture can be slow to learn or forget truths it once knew
  • good point for debate
• “when the cost of confronting a truth goes down (or ignoring it goes up), people are more willing to ask and answer questions about it”

Socratic Ethics

eudaimonia

happiness. well-being. living well.

• Socrates believes living well is the purpose of life.
  • equates happiness with virtue, living honorably and justly
• “It takes true goodness to make a man or woman happy.” (Gorgias 470e)
• virtue is the only real good, necessary and sufficient for happiness
  • known as the “identity thesis” (= happiness virtue wisdom knowledge)

akrasia

acting against your better judgement; having a failure of will

• a failure of will is really a failure of knowledge
• visceral understanding of all the consequences would cause you to act differently
• deeper kind of “knowing”; an enlightened understanding

Stoics

stoicism

a philosophical movement beginning approximately 100 years after the death of Socrates

• a set of specific teachings about living well
• Socratic approach, style of analysis
• used the method in practical matters as well as philosophy
• we are truly free in our minds, nowhere else

History

• Zeno of Citium (334-262 BC) founded school on the stoa, or public porch
• Cleanthes, Chrysippus subsequent heads of the stoic school
• all early Stoic writings are lost
• Epictetus (55-135 AD) born in Turkey, lived in Rome
  • moved to Greece when Domitian banned philosophers
  • “Discourses of Epictetus”
• Seneca the Younger
  • commanded by Nero to sit in a hot bath and open his veins
  • largest surviving body of work on Stoicism from the classical period
• Marcus Aurelius (121-180 AD)
  • Meditations
    • Mill “the highest ethical product of the ancient mind”

Socratic Ignorance

• the method starts with an understanding of how little one knows
• the first business of studying philosophy is to part with self-conceit
• resistance to false pride should not become a source of false pride
• unlike Socrates, the Stoics thought they could reason their way to important truths on which they did not hedge

Cross-Examination

• Stoics proceeded by question and answer
• Socrates forced his interlocutor to bear witness for him
• Epictetus uses a variation on the style; push through surface impressions that seem natural
• Epictetus is less likely to ask for definitions or abstract claims and then to challenge them
• more likely to go after the (ethical) assumptions of the students directly, or to use questions to make a point he wants them to understand
• Epictetus doesn’t seek aporia. He has views about the right and wrong way to look at a problem and pushes students toward those results.
• Topics are more specific, inquiries less complicated, results more practical

Consistency

• Stoics also elevated consistency to the “supreme desideratum in the search for truth”
• anything false you believe will collide with the true things you know
• since truths never collide, consistency of beliefs after long testing is a sign they are right
• “peace of mind depends on securing definite judgement; nothing is certain for people who rely on popular opinion-the most unreliable of standards”
  • book has “reply” (typo)
  • the first part is suspect

Virtue and Happiness

• eudaimonia (“happiness”, a good life) is the ultimate goal
• Seneca: “virtue is the only good; at any rate there is no good without virtue”
• health, wealth are indifferents (neutral)-not goods in themselves
  • they are good when put to good use
• there can be no true happiness in ignorance of good and evil
• Stoics extend Socrates by showing one’s apparent problems in the world are problems in one’s own thinking
  • when something aggrieves us, it is our opinions which are faulty
  • grief is an opinion of some present evil, joy of some present good
  • fear is an opinion of impending evil, lust of impending good
• bad behavior is a result of ignorance or misguided opinions
  • our attitude should be one of forbearance: people don’t (truly) know any better
  • remembering this makes us kinder
• Marcus Aurelius: Today I will meet with the busybody, the ungrateful, the arrogant, the deceitful, the envious, the unsocial. All these result from their not knowing what is good and what is evil.
• people who behave badly should be pitied
  • they are mistaken or ethically disabled: either way, a sad spectacle

Emotion

• Socrates sometimes criticized for taking too little account of emotion
• model of human functioning seems wholly intellectual
• Stoics: if you have an emotional reaction to a thing, the response is not to the thing itself, but your understanding of the thing.
  • arises from your knowledge (or lack of it) and might be changed
• objection: fails to account for emotion of animals, infants
  • Stoics avoid problem by relabeling: those are “passions” or “impulses”
  • unsatisfying, but doesn’t totally invalidate the prior point
• some beliefs are intellectual and can be dropped or revised in the light of evidence or reason
• some are deeper and harder to change even when we “know better”
  • these take time to root out because they’re more deeply ingrained
  • a principal goal of philosophy is to bring beliefs into a consistent state
  • note: biology, evolutionary instinct are powerful forces

Invulnerability

• nothing can “harm” a good man in life or in death
  • philosophical harm
  • no outside force can harm your inner understanding, will, choice
• seems extravagant: a sage can be perfectly happy while being tortured
  • Stoics concede no one has reached such perfection of mind
  • Socrates went to his death with his virtue intact

Skeptics

• philosophy was a direct extension of that of Socrates

skepsis

inquiry

History

• developed by heads of the Academy (“scholarchs”) after Plato
• Arcesilaus (264 BC)
• Carnaedes (167 BC)
• Philo last scholarch at the time of the destruction of the Academy
  • decamped to Rome, taught Cicero
• skeptics inquire (and inquire) without reaching a conclusion
• dread of “rash assent”, asymptotically approach truth without ever reaching it
  • skeptics regard this as the great failing of humanity

Question and Answer

• central Socratic lesson is the appreciation of our own ignorance
• affirm nothing yourself, refute the assertion of others
• Cicero: “This alone is the whole of wisdom, for a man not to think that he knows what he does not know.”
• Arcesilaus (Academy Skeptic) shows not that everyone was wrong, but that there were always good arguments both ways so that no such arguments should settle anything

epochē

withholding judgment because you can’t decide what to think since there are good arguments both ways

Aporia vs. Epochē

• aporia is an impasse because you don’t know what to think since all arguments are lacking
  • at a loss, frustrated
• in epochē, you can’t decide what to think because you’re suspended between alternative arguments that seem right
  • reserved judgment, detached
• similar experience: nothing you say is good enough
  • don’t give up, try harder even if you may never arrive at truth

Knowability

• skeptics believe nothing can be known; no one must make positive assertions
• Arcesilaus falls into the same trap: denying that anything can be known is a claim to a form of knowledge
• Descartes makes a compelling argument half a millenium later

  cogito ergo sum

  “I think, therefore I am.”

• did Socrates fall into this trap? he seems to claim he knows some things, including that he knows nothing of importance.
  • solution: Socrates isn’t claiming something is proven, rather that these propositions have not been disproven

Implications (and types) of Skepticism

• is skepticism a philosophy of despair?

Pyrrhonian Skepticism

• Pyrrho of Elis
• the result of suspending judgment was tranquility

ataraxia

tranquility and freedom from distress

• achieving ataraxia is the goal
• note: sounds a little Buddhist to me

Academic Skepticism

• Arcesilaus
• goal is not to find tranquility, but to find truth
• most of what anyone has ever believed has been wrong
  • people who claim to know anything are lazy or delusional
• don’t give up, rather become more diligent
• why? isn’t it futile?
  • you can still get asymptotically closer
  • the quest to grasp the truth is ennobling even if ultimate truth is not obtained

How to Decide What to Do

• if nothing can be known, are we stuck?
• Carneades: no, some things are more likely to be true
  • rely on “probability”

fallibilism

propositions concerning empirical knowledge can be accepted even though they cannot be proved with certainty

Skepticism vs. Stoicism

• rival groups
• skeptics didn’t specifically object to stoic moral teachings
  • sometimes complemented their teachings
  • they did object to the epistemological basis for those teachings

Finding Principles

• Socrates’ use of his method had a narrow focus, but it is broadly useful
• advice for devising Socratic questions
• we want to show claims are inconsistent with other beliefs
• this requires coming up with good questions on short notice
• there is no simple formula, but some patterns may be noted
• Socrates liked to make a point with simple and familiar topics (analogy)

Creating an Elenchus

• You make a claim
• Socrates solicits your agreement to a second claim
• then he shows inconsistency between the two things you claim to believe
• “He talked you into contradicting yourself.”
• the elenchus has two parts
  1. establishing the claim (part one)
     • this part is often overlooked
     • the first thing the interlocutor says may not be the bottom claim
     • question to clarify thinking and establish a firm claim
     • we need a claim on the table that lends itself to productive questioning
     • these questions are not designed to refute but to elicit
  2. ask questions to show the claim is wrong (part two)
     • next chapter

Find the Principle

• look for the generalization
• find the unconscious judgment that is the root and nerve of the claim
• move the debate to the level of a principle
• classic deductive arguments have a major premise and a minor one
  • major premise: All men are mortal.
    • general principle
    • often unstated and unexamined in an argument
    • smoke them out: they may be layered
  • minor premise: Socrates is a man.
    • specific case
  • conclusion: Socrates is mortal.
• the principle can either be the second half of the elenchus which is used to test the original claim OR
• the principle can be the subject of testing by the second half of the elenchus
• it may pay to find the point of departure from a principle on which you both agree

Concepts

• a major premise will either be a concept which needs to be defined or a proposition that needs to be defended
• point of defining isn’t to bicker over a word, it’s to understand a judgment
• people think they don’t care about concepts, when in fact they live and die by them (freedom, anyone?)
  • but they often haven’t taken the time to understand them very well
  • you hate something because of property X
  • but have not thought about what it is about X that makes it hateworthy

  -

The Thinker’s Toolkit

Structuring Analysis

• failure to consider alternatives is the most common cause of flawed analysis
• humans tend to be dismissive and closed-minded
• structuring one’s analysis is the quickest, surest path to opening the mind to alternatives
• structuring isn’t analysis; it is a technique for improving analysis
  • helps the mind make sense of complex problems
  • laying out problem visually engages more of the brain, enables focus

Problem Solving

• even the most complex problems usually arise from a few major factors, or causes
  • issues are points related to each factor that must be decided
• example: a car accident
  • factors
    • reckless driving
    • speeding
    • mechanical failure
    • DUI
  • issues
    • who was driving?
    • how fast were the cars traveling?
    • had the drivers been drinking?
• note that issues are questions
• factors and issues are the navigational aids to analysis
  • they tell you where analysis should lead

How to begin analysis of a problem

• create and maintain a list of major factors and issues
  • this presumes you know what the problem is!
    • identifying the problem is the real first step!!

Convergence and Divergence

• expand and contract
• both phases are important; one generates possibilities, the other narrows and selects

Taxonomy of Problem Types

• inverse relationship between number of facts and the amount of judgement required to solve a problem
  • should follow that as more judgement is required, there is a higher probability of error
  • and our confidence in the answer should decrease
• always be wary of conclusions based on judgements

Simplistic

• a single factual answer

Deterministic

• admits of a single answer, but requires application of a correct formula

Random

• different answers are possible, all can be identified

Indeterminate

• different answers are possible, are conjecture, not all can be identified

Thinking Tools

Problem Restatement

• divergent thinking: aim is to broaden perspective
• try to generate as many alternatives as possible without judgement
  • don’t try to critique every restatement in real time

Common Issues with Problem Statements

• too broad/vague
• too narrow/specific
• incorporates assumptions
• incorporates solutions

Techniques

• paraphrase without losing original meaning
• 180 degrees turn the problem on its head
  • e.g.
    • how can we encourage people to come to dinner? ->
    • how can we discourage people from coming to dinner?
• broaden focus
  • restate problem in a larger context
• redirect the focus
  • how can we boost sales? -> how can we cut costs?
• 5W2H questions
• simple, positive, active voice

Pros / Cons / Fixes

Divergent / Convergent Thinking

Sorting, Chronologies, and Timelines

Causal Flow Diagramming

Decision Matrix

Scenario Tree

Weighted Ranking

Hypothesis Testing

Devil’s Advocacy

Probability Tree

Utility Tree

Utility Matrix

Advanced Utility Analysis