Problem Solving And Skill



Invention and Scientific Discovery

Show That Modern Theories of Problem Solving Can Explain

Invention (The Airplane)

Scientific Discovery

Herbert A Simon

Gary Bradshaw

Peter Cheng, University of Nottingham

• General

— Interesting phenomena in their own right

— Demystifying science and invention

• Psychological

— Extreme human endeavor

— Cognitive processes

— Social processes

Approaches and Evidence

(Peter Cheng)

• Personal

— Recollections

— Autobiographies

— Diaries

• Historical records

— Laboratory note books

— Publications (journals, books, proceedings)

— Letters, email

— Equipment (physical, designs)

— Computer programs

• Empirical

— Interviews

— Observation

— Surveys

Approaches and Evidence (Cont)

• Experimental

— Reasoning/problem solving tasks

— Simulated discovery environments

— Concurrent verbal protocols

• Simulations and Modelling

— Computational models

— Mathematical models

The Invention of the Airplane

Gary Bradshaw

How Did Two Bicycle Mechanics From Dayton, OH Succeed In Inventing the Airplane?

Many well financed research programs in Europe and US

Early Attempts To Build Heavier Than Air Aircraft

Ornithopters

The Correct Solution, Sir George Cayley, 1809

Lift from wings

Thrust from power plant and propeller

Tail to provide stability

Bradshaw’s Figure 1

[pic]



How Did the Wright Bother Succeed?

Very Careful Study and Complete Mastery of Previous Research

Problem Reduction Verses Generate and Test

Generate and Test

A new design was identified, the craft was constructed and then taken out to the field for testing. The results of the testing were used in making a new design, completing the loop. (Bradshaw website)

Hill Climbing

Time and distance in flight.

global performance metrics that reflect the properties of the craft as a whole

insensitive to the particular strengths and weaknesses of any particular design

Trail and Error Search Though a Huge Design Space Using Ineffective Heuristics

Problem Reduction

Lateral Stability

Wing warping

Design of

Wings that Generate Enough Lift

Propellers that Generate Enough Trust

Use of Wind Tunnel

Wonderful Mechanics

Light Very Powerful Gasoline Engine

Searching Smaller Spaces

Can Use Feedback to Guide Search

Wright Bother’s First Flight

[pic]

Task Environments

(Kinds of Problem Solving Tasks)

Closed Problems

Specific Goal

Well Defined Moves

Laboratory and School Tasks

Puzzles

Mathematics and Physics Problems

Games

Open Problems

Poorly Specific Goal

Ill Defined Moves

Real World Problems

Design

Real Science

“Plan a happy life”

“Solve the population problem”

Major Parts of Problem Solving Task

1) Finding the problem!

2) Understanding the problem!

What is the goal? (Goal State)

What is given? (Start State)

What can be done? (Rules, Actions, Moves, Operations)

Can the problem be broken up into simpler problems?

Problem Solving as Understanding

3) Solving the problem!

Problem Spaces

Search!

Search Methods (Heuristics)

Problem Solving as Search

Problem Solving As Search

Understanding Before Search

Understand What Goal Is

Know All of Moves

Know About Detours

Search Methods

Generate and Test (Trial and Error)

Difference Reduction-Similarity

Hill Climbing

Working Backwards

Means-Ends Analysis

Decomposing Original Problem Into Subproblems

Heuristic Search and Scientific Discovery

More search

— Persistence

— Diversity

Representations

— Understand representations

— Effective representations for making discoveries?

Heuristics

— Make state-space practical size to search.

— In science these are strategies of discovery.

— Weak methods and knowledge based approaches.

Posing Problems

— Finding a problem is a problem in itself.

— Reformulating questions.

— Modifying of representations.

— Kuhn's normal science versus revolutionary science.

Generate And Test

Problem solvers adhering to the generate-and-test paradigm use two basic modules.

> One module, the generator, enumerates possible solutions.

> The second, the tester, evaluates each proposed solutions, either accepting or rejecting that solution.

All Depends on Properties of Generator

A powerful intelligent Generator will only produce a few "good" solutions including the correct one.

Evolution is an example of Generate-and-Test

All controversies about Darwin and the application of evolutionary ideas focus on the claim that the generator is NOT intelligent.

Blind trial and error

Difference Reduction-Similarity

Select moves by comparing consequences of each move from the current state with goal. Pick move that leads to state that is "closer" (more similar to ) the goal.

“Measure” difference between current situation and goal

Pick more that you think will lead you closer to the goal

Hill Climbing

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