Problem solving and creativity
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Problem solving and Creativity. Problem solving. What is problem solving? Weak and strong methods Much of our life is spent solving problems? Homework problems Managing money Video games Ending conflict. What makes these problems?. Four aspects to a problem Goal

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Problem solving and creativity

Problem solving and Creativity


Problem solving

Problem solving

  • What is problem solving?

  • Weak and strong methods

  • Much of our life is spent solving problems?

  • Homework problems

  • Managing money

  • Video games

  • Ending conflict


What makes these problems

What makes these problems?

  • Four aspects to a problem

  • Goal

    • What is to be accomplished?

  • Givens

  • What is known from the start of the problem?

    • Means of transformation

  • How can the initial state be modified?

    • Obstacles

  • Something that stands between the initial state and the goal.

  • What would happen if one of these aspects were missing?


Types of problems

Types of problems

  • Well-defined problems

    • All four aspects of the problem are specified.

      • Towers of Hanoi

      • Mazes

  • Ill-defined problems

    • One or more of the aspects of the problem are not well specified.

      • Stopping a war


How do we solve problems

How do we solve problems?

  • Sometimes a problem is novel

    • Then we use general problem solving strategies

      • “weak” methods

  • Sometimes a problem is more familiar

    • Then we can use our background knowledge

      • “strong methods”


Problem solving as search

Problem solving as search

  • Consider a well-defined problem

    • The givens are known

    • The means of transformation are known

    • The goal is known

  • The obstacle is generally that there are so many possible solutions it is hard to find the right one

    • We must search for the right solution


What if the search space is too large

What if the search space is too large?

  • It is not possible to enumerate the entire search space for all well-defined problems.

    • Chess: After a few moves, there are too many possible moves and counter moves to consider all of them.

  • We must use constraints

    • Heuristics (general guidelines)

  • It is likely to lead to a good solution, but not guaranteed to work


Hill climbing

Hill climbing

  • Find some measure of the distance between your present state and the end state.

    • Take a step in the direction that most reduces that distance.

  • A potential local minimum problem.


Means end analysis

Means-end analysis

  • Try to reduce the largest difference between the initial state and the goal state first.

  • How should you get from UNT to the Empire State Building?

    • Fly from Dallas to New York

  • That takes care of the biggest difference, but now creates new sub-problems

    • Getting from UNT to the airport

    • Getting from a New York airport to the Empire State Building

  • Each of these new sub-problems needs to be solved


Working backward

Working backward

  • Sometimes it is hard to solve a problem by starting at the initial state

    • Many puzzles are intentionally designed to be hard to solve from the givens.

  • It can be useful to start at the end state and work backward


Summary of weak methods

Summary of Weak Methods

  • Problems involve overcoming obstacles

  • Weak methods of problem solving

    • Domain general heuristics for solving problems

    • Best for well-defined problems

  • No real mechanisms for dealing with ill-defined problems

  • Domain knowledge needed for this.


Phenomena in problem solving

Phenomena in Problem Solving

  • Insight Problems

  • Functional Fixedness

  • Using external representations


Why study problem solving

Why study problem solving?

  • Important questions

    • How do great problem solvers work?

    • How do people solve very difficult problems?

  • Could we get a computer to do this?

    • What are people’s limitations in solving problems?

  • Separate fact from fiction in problem solving

    • There are many stories about the way great problem solvers work that are just not true.


Myths of insight

Myths of insight

  • Weisberg has debunked a number of myths

    • Coleridge and Xanadu

      • The story is that the poem was written in a single (perhaps drug-induced) session

    • Kekulé and the benzene ring

      • Chemists were search for the structure of benzene

      • Kekulé was said to have visualized a snake eating its tail

  • These stories are just myths.

    • There are many surviving drafts of Xanadu

    • The story of the snake biting its tail was told 35 years after Kekulé discovered the structure of benzene


Characteristics of insight problems

Characteristics of insight problems

  • People initially have no idea how to solve the problem

  • There is no linear “feeling of warmth”

    • There is no sense that one is getting closer to solving the problem.

  • Often, there is a period of “incubation”

    • Perhaps you walk away from the problem for a while

  • The solution comes in a flash

    • Often, it feels as though the solution is fully formed


How to study insight

How to study insight?

  • Insight problems are hard to study.

    • Cannot ask people for their intuitions

    • There is no feeling of warmth

  • People have an “aha” experience

  • What we want to know is what causes the “aha”

  • Insight problems are rare

  • There are only a few laboratory examples that work

  • They are are also rare in real life


Functional fixedness

Functional Fixedness

  • Why does incubation help?

  • We may get locked into a way of thinking about the objects in a problem

  • Time away from the problem

    • We may eventually be able to see objects in a new way


Using external representations

Using External Representations

  • Sometimes organizing information is the problem.

    • Nurse A can only work after 2pm

    • Nurse B can only work Monday, Wednesday and Friday

    • Nurse C can work Tuesday and Thursday before Noon

    • Nurse D can work any day between 10am and 4pm

  • How should this schedule be arranged?

    • An external representation would be useful.


Problem solving and creativity

  • Times can be organized into a matrix

    • An external representation of the problem.

      Monday Tuesday Wednesday Thursday Friday

      9-10am

      10-11am

      11am-Noon

      Noon-1pm

      1pm-2pm

      2pm-3pm Nurse A

      3pm-4pm

      4pm-5pm

  • Minimizes the information that must be kept in the head.


Structure of problem

Structure of problem

  • Type of representation used must match structure of problem.

  • Matrix

    • Good for scheduling

    • Days of the week along the columns

    • Times along the rows

    • Entries are events.

  • Network

    • Good for relationships


Problem solving1

Problem solving

  • Using background knowledge

  • Analogical problem solving and access

  • Case-based reasoning


Weak and strong methods

Weak and strong methods

  • Just looked at “weak” methods

    • Domain-general ways of solving problems

    • Useful when a problem is unfamiliar

  • Now we look at “strong” methods

    • Domain-specific solutions

    • Often derived from past experience

  • Why are these strong?

    • It is always easier to solve a problem you have solved before


Using background knowledge

Using background knowledge

  • Gick & Holyoak (1980)

    • Had people read a story about a general attacking a fortress.

    • The roads around the fortress were mined

    • General split up his forces and had them converge on the fortress from many directions.

  • Later in the study, they were given Duncker’s radiation problem

    • Doctor with patient who has an inoperable tumor

    • Rays strong enough to kill the tumor would damage the healthy tissue

  • What should the doctor do?


Access failure

Access failure

  • About 10% of people solve the radiation problem spontaneously

  • About 30% of people solve it if they first read the story about the general

    • Not much of a gain

  • Is this an access problem or a use problem?

  • If given a hint to use the earlier stories, about 80% of people solve the problem

    • Suggests that it was an access problem


Analogical access

Analogical access

  • Finding relevant background knowledge is hard

  • There are many possible experiences that might be relevant

    • Which ones are most likely to be relevant?

    • Situations that are similar to ones you have seen before.

  • In many cases, using highly similar background knowledge is good

  • Purchase decisions

    • Knowing what brand of pickles you buy will not help you decide what ketchup to buy

  • Science (Dunbar)

    • Microbiologists use results from one bacterium to decide what studies to do on another bacterium

    • It is rare that distant similarities are useful


Retrieving analogs

Retrieving analogs

  • Gentner, Rattermann, & Forbus

  • People read a story

    • Hawk gives feathers to hunter for arrows in exchange for hunter not shooting hawk.

  • Later, people read another story:

    • Similar (S): Eagle gives feathers to archer…

    • Mere Appearance (MA): Eagle flies near archery tournament

    • Analogy (AN): One country gives missile guidance systems to another in exchange for not attacking it.

    • No Match (NM): One country has rivers, another does not.

  • People given S and MA retrieve story

  • People rate S and AN as similar


Models of access

Models of access

  • How do we access analogies?

    • Many models have been developed

    • Most of them are two-stage models.

  • Stage 1: Search through memory to find things that are generally similar

    • Things from the same domain are often retrieved

    • Only a small number of items pass this filter

  • Stage 2: Find things that are analogous

    • Determining analogies is effortful

    • Do this task only on items that pass stage 1


Access and use

Access and use

  • Similarities may also affect use of knowledge

    • Word problems (Ross)

  • Retrieval affected by domain similarity

    • Both similar and cross-mapped examples retrieved

  • People found it hard to apply cross-mapped examples


Overcoming access problems

Overcoming access problems

  • Experts are better at analogical retrieval

    • They are better at finding good analogies

    • They are less influenced by cross-mappings

  • Forming a schema may help access

    • Comparing a few analogs during learning helps retrieval

  • Learning about subgoals may help access

    • An example may be indexed by the sub-problems that it helps to solve


Case based reasoning

Case-based reasoning

  • An Artificial Intelligence technique

    • Solves problems based on known episodes

  • Stages of Case-based reasoning

    • Access

    • Adaptation

    • Evaluation

    • Updating of memory


Chef an example

CHEF: An example

  • Szechuan cooking (Hammond)

  • Had a failure cooking beef and broccoli

    • Broccoli came out soggy

  • Retrieve past knowledge about similar failures

    • Other cases of soggy vegetables

  • Find a case of beef and snow peas

    • When cooking beef, notice that meat sweats

    • Solution in that case: Cook vegetables first, put them aside, then cook beef.

  • Adapt case to current situation


Summary

Summary

  • Background knowledge is important for solving problems (Strong methods)

  • Accessing background knowledge is hard

  • Analogical access

    • Driven by surface similarities

  • Case-based reasoning


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