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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