Problem Solution

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Problem Solution

• October 24, 2002

2
Where are we?

• Problem Selection
• Problem Solution
• Role of Creativity in both

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Creativity(Tod Perry)

• Creativity, in its truest sense, is
  self-expression, such as for an artist.
• This comes from work -- the Mona Lisa was not
  painted on the first try.
• One can also be creative in solving a problem,
  and that requires work, knowledge, commitment,
  diligence, focus, passion, motivation, etc.
• Creativity is a breakthrough in thinking, an
  ability to reframe a project, a new way to
  connect ideas.
• Creativity is an attitude that every person can
  work to achieve.

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Creativity (Csikszentmihalyi)

• Creativity can be observed only in a system made
  up of three parts
• domain a set of symbolic rules and procedures
• field all the individuals who act as
  gatekeepers to a domain
• person an individual that, using the symbols of
  a domain, has a new idea or sees a new pattern,
  and when the novelty is selected by the
  appropriate field for inclusion into the relevant
  domain.

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Creativity Defined(Csikszentmihalyi)

• Creativity is any act, idea, or product that
  changes an existing domain, or that transforms an
  existing domain into a new one.
• A creative person is someone whose thoughts or
  actions change a domain, or establishes a new
  domain.
• Creativity results from the interaction of a
  system composed of three elements
• a culture that contains symbolic rules
• a person who brings novelty into the symbolic
  domain
• a field of experts who recognize and validate the
  innovation

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Problem Definition

• We want to solve the right problem, we want to
  solve it right, and we want to do both
  creatively.
• Values should be developed that you use to assess
  the quality of a research program or a consulting
  assignment.
• Select a problem that you are motivated to solve.
  
• Effective Problem Selection, Definition, and
  Solution may/will require iteration.

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Problem Solution

• Four Steps (Polya)
• Understand the Problem
• Devise a Plan of Attack
• Carry Out the Plan
• Examine the Solution

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Understand the Problem

• Dont try to solve a problem you dont understand
  or dont need to solve.
• What is known? What is unknown? What are the
  data? What is the condition?
• What are the facts? What are assumptions?
• Is it possible to satisfy the condition?
• Separate the various parts of the condition.
• Write something down.

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Devise a Plan of Attack

• Developing the plan well is challenging, but
  doing it well is very important to provide a
  basis for a good solution.
• Have you seen the problem before?
• Do you know a related problem?
• Look at the unknowns think of a familiar
  problem having the same unknowns.
• Restate the problem differently.
• Imagine a more accessible related problem.
• Can you solve a part of the problem?
• Can you break the problem down into sub-problems
  that are easier to solve.
• Write it down!

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Carry Out the Plan

• Easier than devising the Plan. The greatest risk
  is forgetting the plan. If carrying out the
  plan provides information that changes the plan
  or the problem definition, iterate (but do it
  consciously).
• Check each step carefully as you go.
• Concentrate on the step until you see that its
  correct.
• Can you see clearly that each step is correct?
• Can you prove that it is correct?

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Examine the Solution

• Look back at the solution and reexamine the path
  that lead to the result -- you can provide
  greater assurance of accuracy and enhance your
  ability to solve problems.
• Can you check the overall result?
• Can you derive the result differently?
• Can you estimate the result using alternate
  methods?
• Can you explain it to someone else?

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Guidelines for Solving Problems

• Does the problem have a solution? How do you
  know?
• List all possible solutions. Is the list
  exhaustive? How do you know?
• List all your assumptions about the problem. Are
  there inconsistencies?
• Ask others to criticize your assumptions. Are
  some unnecessarily limiting?
• Think of the optimal or near-optimal solution.
• Think of an approximate solution.
• Abstract the problem to a simpler formulation.
• Can you derive a solution from a related problem?
• Construct, develop, and test a working
  hypothesis.
• How sensitive is the solution to changes in the
  problem definition or data?

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Types of Thinking

• Various terms are used to define thinking that is
  focused on a single solution
• convergent
• vertical
• conventional
• Other terms are used to define thinking that
  provides an expansive look at opportunities
• divergent
• lateral
• full spectrum
• Both are required to achieve a full solution to a
  problem.

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(No Transcript)
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Lateral Thinking

• We are trained and schooled to think vertically.
• You have to work to be effective at lateral
  thinking.
• Two challenges of lateral thinking
• To get started and get some movement
• To escape the natural or obvious train of thought
• Develop and practice your capacity to think
  laterally.

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Techniques for Lateral Thinking

• Generating alternatives
• Challenging assumptions
• Suspending judgments
• Identifying dominant ideas and crucial factors
• Decomposing the problem (simplify)
• Using the reversal method (rearrange information)
• Brainstorming
• Using Analogies

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Pre-Conceived Ideas

• Pre-conceived ideas can ruin your ability to
  come up with good solutions.
• You must allow your mind to consider other
  avenues other than the one you initially find
  attractive or the one that seems obvious.

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Problem Solution in Consulting
Upon award, begin process of refining and
re-understanding the problem/need.
Consultant with Client
Devise a Plan of Attack
Consultant
Carry out the Plan
Consultant
Examine the Solution
Consultant with Client
Get next job!
Consultant
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Consulting

• Two primary kinds of problems
• One right answer find it WHAT?
• One abstract need lots of possible answers,
  find the best one HOW?
• Another common problem is one that has a very
  specific question, but the question is not
  related to the real problem.

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What versus How
Ambiguity
Kind of Consulting
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ConsultingUnderstand the Problem

• Restate the problem clearly to the client, as
  many times as necessary to assure agreement.
• Break the problem down into tasks that are easier
  to perform. This will provide a clear
  recognition of progress.
• Understand the expectations how creative do you
  need to be?
• Communicate with the client verbally and in
  writing.

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Devise a Plan of Attack

• Continue to break down the problem into sub-tasks
  that allow clarity link to how creative the
  solution needs to be.
• Develop plans on a task or sub-task level.
• Write it down.
• Make sure that the team understands the big
  picture, how each piece fits together, and what
  is expected. All need to be committed.
• Review schedules, commitments, and risks.
• Learn by performing and refine as you go.
• Iterate within the team and with the client, when
  necessary.
• Be fearless, try new things, when necessary.
• Communicate with the client.

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Carry Out the Plan

• Stay focused.
• Unless all agree, discourage side journeys.
• Make sure the team continues to be on the team.
• Learn quickly from things that dont go well.
• Solve the problem as well as it needs to be
  solved. Dont go overboard.
• Communicate with the client.

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Examine the Solution

• Check in with all on the team. Resolve any
  differences.
• Assure that the answer is correct.
• Write the report.
• At this point, the objective is to get done on
  time, within budget, etc. but also to assure a
  good relationship and a high likelihood for more
  work.
• Communicate with the client.

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One Right Answer Find It

• Clear steps that must be followed in this order
• Get the facts verify that what you think are
  facts are really facts.
• Develop hypotheses what could the answer be?
• Do analysis test the various hypotheses.
• Form conclusion choose the correct solution or
  iterate back to hypotheses.
• Verify solution make sure that it is correct.
• This commonly will use vertical thinking to
  converge on the correct answer.

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One Right Answer Find It

• These are rarely pure What? questions.
• The reason why the What? exists must be
  explored.
• This is (or should be) a How?. How did we get
  into the situation associated with the question?
• A Consultant should pursue the real root issue
  with a client to look for the How part of the
  question.

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One Abstract Need

• Worked commonly as a team.
• Ability for lateral thought usually helpful.
• Understand, but dont be affected by what your
  client thinks is the right answer.
• Still need to have facts to start.
• State the desired outcome (not the answer).
• Develop alternatives.
• Analyze/evaluate the alternatives.
• Form conclusion choose the best alternative.

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Problem Solution - Research

• Four Steps
• Understand the Problem
• Devise a Plan of Attack
• Carry Out the Plan
• Examine the Solution
• Classes of research
• Basic
• Applied
• Two classes of applied research

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Classes of Research

• Applied Research employer defined
• Usually have one result find it.
• But often have great latitude for innovation.
• Basic Research
• Usually have a more abstract need.
• Solution is not clear, even when the problem is
  defined.
• Applied Research researcher defined
• Intermediate abstract need but clear goal

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Understand the Problem

• Often problem can be understood, but
• Often problem is too complex to be fully
  understood.
• If it could be understood, then it is not
  research.
• But, still try to understand as well as possible.
• What are the facts? What are assumptions?
• Separate the various parts of the condition.
• Dont do the whole thing in one step.
• Iterate!!

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Understand the ProblemApplied Research

• Often the problem is ill-defined.
• BUT, the solution required is absolutely well
  defined.
• Critical to identify the solution required.
• Then determine as much of the problem as possible
  this will point the way to a solution.
• You must recognize the solution to know when it
  is reached.
• You do not need to understand the solution.
• Good research is not always complete
  understanding.

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Understand the ProblemBasic Research

• Often the problem is not clear.
• BUT, the implications of the solution are.
• Can not fully understand the problem.
• Far better to develop an intuition, and step
  through the whole process, iterating as you go.
• Recognize when you are in the understanding the
  problem step.
• Dont be afraid to re-examine your understanding.

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Understand the ProblemApplied Basic Research

• Often the problem is not clear.
• BUT, the solution is absolutely clear.
• Recognize when solution will be achieved.
• Determine what should be understood to achieve
  the solution.
• Balance achieving the solution with understanding
  it.
• Problem can be solved without understanding the
  solution need balance.

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Devise a Plan of Attack

• Only rarely can a single plan be developed right
  away.
• Only if problem is very clear, well understood.
• More often, need to iterate.
• Get started, do some experiments, calculations.
• Learn by investigating.
• Dont be afraid to iterate.
• Be fearless
• Dont rely on past experience.
• Dont be afraid to learn something completely
  new.
• Step outside of the box if necessary.
• Let experiment guide the way.

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Devise a Plan of AttackApplied Research

• Experimental program can be defined.
• Often depends on a team
• Everyone must do their part.
• Must constantly be prepared to iterate.
• Must constantly re-evaluate the plan.
• Must constantly evaluate whether the plan is
  really addressing the solution.
• Dont get lost in details and forget the goal.
• Dont be afraid to think differently.
• Dont be afraid to learn something completely new.

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Devise a Plan of AttackBasic Research

• Experimental program often cannot be defined in
  any detail.
• Need experiments to define experiments.
• Must constantly iterate right back to start.
• Must constantly evolve the plan know when you
  do it.
• Research plan often helps define the problem.
• Dont be afraid to think differently.
• Dont be afraid to learn something completely new.

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Devise a Plan of AttackApplied Basic Research

• Experimental program can be defined.
• Solution is well posed stay focused.
• Dont be afraid to branch out.
• Take branches to better understand issues.
• Balance understanding with progress towards goal.
• Understanding can lead to better solution.
• But dont get lost in understanding.
• Dont be afraid to learn something completely new.

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Carry Out the Plan

• Stay focused on ultimate goal.
• Stop and ask what ultimate goal is.
• Iterate
• Experiment can lead the way.
• Try many things.
• Dont be afraid to fail just restart quickly.
• Balance focus (vertical thinking) with
  exploration of new solutions (lateral thinking).
• Go only as far as you need then stop.

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Carry Out the PlanApplied Research

• Stay focused on ultimate goal.
• Understand only what absolutely needs to be
  understood.
• Constantly re-evaluate where you are in terms of
  solving the problem.
• Constantly check both directions.
• Have you found the solution?
• Are you moving forward with the current plan or
  does it need to be re-evaluated?
• Go only as far as necessary.

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Carry Out the PlanBasic Research

• Balance focus on solution with basic
  understanding.
• Constantly re-evaluate where you are in terms of
  solving the problem.
• Constantly re-iterate.
• Take side branches, but only if the side branch
  is better than current direction.
• Dont be afraid to re-direct, but only if the new
  direction is better than the old.
• How far you go is a value judgment.

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Carry Out the PlanApplied Basic Research

• Balance focus on solution with basic
  understanding preference to solution.
• Constantly re-evaluate where you are in terms of
  solving the problem.
• Constantly re-iterate.
• Do not take side branches.
• Do not go farther than necessary.

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Examine the Solution

• You are not done until you have written the paper
  or reported on the results.
• Provides critical test of the results.
• Ensures that you really understand the results
  and all their nuances.
• Often requires further work to reach final
  solution, but dont go too far, you dont need to
  do the final work.
• Iteration at this point is usually only back to
  the experiment stage.

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Examine the SolutionApplied Research

• Final product is a solution to the problem.
• Understand only what absolutely needs to be
  understood to solve problem.
• But more understanding may help future problems.
• Often have deadline for finishing.
• Dont be afraid to have working solution, even if
  it is not understood.

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Examine the SolutionBasic Research

• Final product is a paper.
• Proves that you really do understand the result.
• Often have to go back to collect more data to
  fully understand issues.
• But dont collect too much data evaluate what
  is really necessary.
• Evaluate what is the problem that was really
  solved iterate, but with honesty.

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Examine the SolutionApplied Basic Research

• Final product is a solution to the problem posed
  clear when it is reached.
• Can balance solution with understanding. luxury
  of this class of research.
• Collect only enough data to find solution.
• Know if you are collecting more than this.
• Dont iterate to problem stage at this point
  solve the problem you set out.

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Case Study Applied Research

• Exxon
• Problem
• New dispersant molecule gelled when mixed with
  detergent
• Could not be used in AdPack
• Goal was to prevent gelation, mix solution
• Constraints
• Had to use given molecule
• Had to use given colloid
• Had to use given mixing technology
• Identified problem
• Developed hypothesis Surface adsorption,
  increased effective volume
• Developed test X-ray scattering, light scattering

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Case Study Applied Research

• Success Had problem, potential rationale
• Problem Did not have a solution
• Rationale Understand problem before suggesting a
  solution
• Highly dependent on others in the organization
  for solution
• Experiments confirmed basic hypothesis
• Solution seemed at hand
• Examined solution checked with light scattering
• Basic solution was NOT confirmed
• Required re-examination of the problem
• Resulted in a new hypothesis
• Network of polymer and colloid
• Problem disappeared before solution implemented
• New molecule was not commercialized
• But knowledge was valuable for later formulations

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Case Study Basic Research

• Diffusing-wave spectroscopy
• Motivated originally by concept of light
  localization
• Driven by curiosity, passion to understand effect
• Was not clear where to start
• Began by doing experiments
• Just looked at scattering from strongly
  scattering samples
• Did not follow traditional scattering techniques
  not a scattering expert
• Began to get results then looked in literature
• Recognized that we had something new extension
  of traditional dynamic light scattering to
  multiple scattering
• Holy grail for 30 years
• Common approach brute force application of known
  ideas
• Instead, we used a conceptually new approach
• Main contribution recognition of significance

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Serendipity

• Role of chance in research is surprisingly
  common.
• Cannot be sole justification for research.
• But can make likelihood of serendipity higher.
• Be constantly looking for new things.
• Always ask why, but dont always answer it.
• Always ask what significance of things you dont
  understand.
• What is significance of result?
• Will working on it be better than what you are
  doing?
• Dont do both choose.

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Serendipity Case Study

• Microrheology Tom Mason
• Investigating rheology and scattering from hard
  spheres.
• Trying to understand both of them.
• Under pressure upcoming March meeting talk.
• Think completely differently.
• What is relationship between light scattering and
  rheology not usual way to think (Tom Mason)
• Recognition of importance, implications.
• Re-iterate to redefine basic problem.
• How to do this all the time?

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Risk

• All of us are born with two contradictory sets of
  instructions
• a conservative tendency, made up of instincts for
  self-preservation, self-aggrandizement, and
  saving energy, and
• an expansive tendency made up of instincts for
  exploring, for enjoying novelty and risk.
• We need to explore the conditions necessary for
  us to take and enjoy risk.

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Risk and Failure(Falson and Keyes)

• A creative organization must tolerate risks and
  be failure-tolerant to the right kind of
  failures!
• Whoever Makes the Most Mistakes Wins
• Treat success and failure the same they both
  provide learning opportunities
• Leaders must get engaged in the process, not just
  successes!
• You have to learn how to fail intelligently.

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Failures

• Good failures
• Excusable mistakes.
• Outcomes that can be understood and built upon.
• An interesting outcome that will provide insight
  into what will work.
• Bad failures
• Result from sloppiness.
• Compromise health and safety.
• Poorly thought out plans.

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Questions to Ask When a Project Falls Short of
Its Goals

• Was the problem well defined?
• Could the design of the project have been better?
• Could the failure have been prevented with more
  thorough research or consultation?
• Was the project collaborative? Was the input of
  the others understood clearly?
• Did you understand enough of the facts
  surrounding the issue before you moved on?
• Was the schedule (cost, deliverables, etc.)
  reasonable?
• What should we do differently next time?
• Others?

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Risk Taking

• Knowing how and when to take risks is generally
  more fun than not.
• You can train your organization to be more risk
  tolerant (or maybe you can't!).
• Match your interests to your organization.
• Be fearless relative to taking risks but also
  be good! Dont take stupid risks.
• Choose non-judgmental people to collaborate with.
• Take risks to solve problems, not to win.
• Competition within your team will reduce the
  quality of your solutions.

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Failure Tolerance in Consulting

• Consulting, generally, needs to utilize and
  manage risk better.
• If you want to do ground-breaking consulting,
  you have to take risks and you may fail.
• If you dont want to do challenging consulting,
  youre OK where you are now.
• Try to make your failures sub-task oriented and
  not too grand (no flames allowed).
• You must fail quickly and gracefully.
• The response to a failure is key to both the
  eventual great solution and the client
  relationship.

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Failure Tolerance in Academia

• Good research requires taking big risks high
  risk, high payback is best.
• If you take real risks, you must be prepared for
  the possibility of failure.
• University environment is surprisingly
  risk-adverse.
• But, funding depends on success, knowledge.
• Easiest to continue doing what you are known for
  does not inspire new things
• Hard to start new things

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Failure Tolerance in Academia

• Students are strongly risk adverse.
• Dont have the experience to understand failure.
• Need to learn about failure.
• But, they see colleagues getting results, want to
  get results just as fast.
• Unwilling to fail ? unwilling to take risks.
• Post docs also have a short time horizon.
• Makes doing high risk research much more
  difficult.
• The key is to recognize failure as early as
  possible and move on.
• Experience is essential.

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Creativity in Basic Research

• The most important and difficult task in basic
  research is the evaluation of the quality of the
  problem.
• This sets the metric for deciding when to work on
  a new problem.
• Creativity is essential to do this well.
• My criteria are
• Be the first, not necessarily the deepest.
• Start a field.
• Choose topics that have high impact.
• Do the early work, not the detailed final work.
• Be at the bottom of the S-Curve.

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Creative Problem Solving

• Five Steps
• Period of preparation, becoming immersed,
  consciously or not, in a set of issues that you
  find interesting.
• Period of incubation, during which ideas churn
  around below the threshold of consciousness.
• Insight, sometimes called the Aha! moment, when
  the pieces of the puzzle fall together.
• Evaluation, when the person must decide whether
  the insight is valuable and worth pursuing.
• Elaboration filling in the blanks!

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Creativity and Pressure

• Creativity is challenging to maintain during
  times of both high and low time pressure.
• In consulting, time pressures can often be high.
• In research, time pressure can often seem low.

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Creativity Under the Gun
Time Pressure
High
Low
Likelihood of Creative Thinking

• Creative thinking under low time pressure is more
  likely when people feel as if they are on an
  expedition.

• Creative thinking under extreme time pressure is
  more likely when people feel as if they are on a
  mission.

High

• Creative thinking under low time pressure is
  unlikely when people feel as if they are on
  autopilot.

• Creative thinking under extreme time pressure is
  unlikely when people feel as if they are on a
  treadmill.

Low
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Creativity Under the GunHigh Time Pressure

• High likelihood of creative thinking -- people
  feel as if they are on a mission.
• can focus on one activity for a significant part
  of the day
• believe that they are doing important work and
  are challenged.
• identify problems and generate or explore ideas.
• Protect people that need to be creative from
  interruptions.
• Communicate why the time pressure is necessary.

• Low likelihood of creative thinking -- people
  feel as if they are on a treadmill.
• feel distracted
• work-day highly fragmented with many activities
  and changes.
• dont get the sense that the work they are doing
  is important.
• tend to have more meetings and discussions with
  groups.
• Each day worse than the one before no hope!

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Creativity Under the GunLow Time Pressure

• High likelihood of creative thinking -- people
  feel as if they are on an expedition.
• show creative thinking that is more oriented
  toward generating or exploring ideas than
  identifying problems
• tend to collaborate with one person rather than a
  group
• Try to maintain focus to stay oriented to the
  work.
• Motivation necessary and needs to be reinforced.

• Low likelihood of creative thinking -- people
  feel as if they are on autopilot.
• receive little encouragement from management to
  be creative
• tend to have more meetings with groups rather
  than individuals
• engage in less collaborative work overall
• People doing their jobs but not really engaged in
  progress.

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Modeling

• Modeling is commonly used to assist in problem
  solving.
• Causes extreme focus on details.
• Can be used individually or with a team to
  develop and practice skills.

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Problem Solving

• Electrical Connection Problem

• A cable running from London to New York is made
  up of one hundred independent wires. A single
  individual desires to identify the ends of these
  wires by means of three operations. Any number
  of short connecting wires is available, along
  with a strong battery and meter to test the flow
  of current. An operation consists of making any
  number of connections between wires, checking the
  flow of current and labeling as is necessary on
  one side. So the individual, starting in New
  York, connects, tests, and labels goes to London
  and does the same and finally returns to New York
  to do more such testing and labeling and them
  finishes by having each wire similarly labeled in
  both cities. How?

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Electrical Connection Problem(with five cables)
NY
London
1 2 3 4 5
1-2 3-5 4 not connected 4 is e 5 is a (since e is
4 and a and e were connected) 3 is b (since a is
5 and 3 and 5 were connected) 2 is d (since b is
3 and b and d were connected)
a b c d e
a-e b-d c not connected c is 1
1 2 3 4 5
a b c d e
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Problem

• Two men meet on the street. They havent seen
  each other for many years. They talk about
  various things, and then after some time one of
  them says Since youre a consultant, Id like
  to give you a problem to solve. You know, today
  is a very special day for me All three of my
  sons celebrate their birthday this very day! So,
  can you tell me how old each of them is?
• Sure, said the consultant, but youll have to
  tell me something about them.
• OK. Ill give you some hints, replies the
  father of the three sons, The product of their
  ages is 36.
• Thats fine, said the consultant, but Ill
  need more than just this.
• The sum of their ages is equal to the windows
  in that building, says the father pointing to
  the structure next to them.
• The consultant counted the windows, thought, an
  then said, Still, I need an additional hint to
  solve your puzzle.
• My oldest son has blue eyes, says the other
  man.
• Oh, this is sufficient! Exclaims the
  consultant, and he tells the man the age of his
  three sons.

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Additional Reading

• Harvard Business Review, August 2002. Several
  articles on creativity and innovation that are
  excellent.
• Falson and Keyes, Whoever Makes the Most
  Mistakes Wins. Also extracted in HBR.
• Polya, How to Solve It. A classic on problem
  solving from 1945.
• DeBono, Lateral Thinking. A classic (1970)
  that defines vertical and lateral thinking.
• Michalewicz and Fogel, How to Solve It Modern
  Heuristics. An excellent overview of modeling
  in problem solving.
• Ulrich and Eppinger, Product Design and
  Development. An excellent reference on product
  design.
• Saaty, Creative Thinking, Problem Solving, and
  Decision Making.
• Csikszentmihalyi, Creativity, Flow and the
  Psychology of Discovery and Invention.
  Excellent description of creativity based on
  interviews with ninety-one creative people.
• Bock, Getting it Right, RD Methods for Science
  and Engineering. Overview on techniques for
  research.