DISCUSS: What are examples of analogies you've encountered?
1. Ancient: parables, fables, Plato, Greeks.
2. Modern science: waves & sound, light, natural selection, lightning. Analogies everywhere.
3. Student's use of analogy: problem solving in statistics, computer programming.
4. Instructors use of explanatory analogies.
5. Uses of analogy:
1. Hesse: analogies in the philosophy of science.
My interest sparked by Darwin.
2. Early AI: proportional analogies A:B::C:D.
3. 1980's: Psychological experiments by Gentner and Holyoak. Subsequent attempts to give computational models.
4. Case-based expert systems: use a supply of cases to solve problem or provide explanation.
e.g. CHEF: create new recipes by analogy to old ones.
Cf. Harvard Business School, law school.
5. My approach: combine psychological experiments and AI simulations: use as tool to investigate cognitive processes.
See Holyoak and Thagard, The Analogical Mind.
6. Douglas Hofstadter and his colleagues have done research on fluid analogies.
7. Terminology:
Target analog: what you are trying to understand or solve.
Source analog: what you are hoping to use to solve a problem or provide an explanation.
1. No rules or concepts available to provide solution.
2. It's easier to adapt an existing case than to start anew.
3. Human mind is adept at the kinds of matching and comparison that are involved in analogy, more so than with deduction.
1. Pursue target
2. Find source that matches target:
a. given, or
b. search through memory: retrieve
3. Map source to target: find correspondences.
4. Adapt source to generate solution to target.
5. Learn from use of analogy: turn two analogs into a schema that can be useful later.
1. Purpose (pragmatic): what is the analogy used for?
e.g. problem solving, explanation, education, etc.
2. Similarity:
a. meaning of concepts
b. visual similarity
3. Structure: approximation to isomorphism
Preserve relational structure.
These constraints apply to retrieval, mapping, adaptation, learning.
But different constraints are of central importance to different stages:
retrieval: similarity
mapping: structure
adaptation: purpose
1. How are analogies represented?
a. verbally: propositions
b. pictorially: images, diagrams
2. Capture all the richness of particular cases, including solutions.
3. Don't need to have lots of evidence for generalizations to rules, don't have to worry about exceptions.
1. Problem solving: see above.
Useful in many domains, for both
cross-domain analogies (long-distance, more creative)
within-domain analogies
2. Learning:
a. every solution is learned, and can be used again
b. schematization: turn 2 analogs into schema.
e.g. two restaurant experiences -> script
3. Language: metaphor
1. There may not be previous experience to draw on.
Analogy not useful in unfamiliar territory.
2. Finding a relevant case may be difficult:
Too many cases each similar to each other, as
in law.
3. Adapting a case may involve all the aspects of rule-based reasoning, as you deal with the differences between the old and the new case.
4. Analogies may be very misleading if the cases used are not similar in relevant respects.
1. Education: worst analogy every made.
Other misleading analogies, e.g. atom/solar system, of limited use.
Some really bad analogies
2. Decision making: e.g. generals fighting the last war: horses rather than tanks.
3. Theorizing: get stuck with old ideas.
We need the generality of concepts and rules to avoid getting stuck with misleading particularities.
Computational Epistemology Laboratory.
This page updated Oct. 8, 2012