Analogical Reasoning

1. Analogical Reasoning

2. Types of reasoning • Content free reasoning: • Deductive reasoning • Reasoning by similarity • Inductive reasoning • Analogical reasoning: • analogical transfer: solving problem in one domain based on solution in another domain • Analogical inference: generalizing properties/relations from one domain to another

3. Analogical transfer Reason from base problem (previously solved) to target problem • Recognition: identify a potential analog • Abstraction: abstract general principle from base problem • Mapping: apply principle to target

4. Radiation Problem • Problem • Patient has an abdominal tumor (in center of body) • Radiation will kill tumor • But rays strong enough to kill tumor will also destroy healthy tissue that rays pass through on way to tumor • Solution?

5. Solution INCORRECT CORRECT

6. Gick & Holyoak (1980) Only 20% solved it Participants were more likely to solve the problem if they were given an analogy.

7. Fortress Problem • Army general wants to attack a fortress in center of forest. • Many roads lead to fortress like spokes of a wagon wheel. • All the roads have land mines that are triggered by heavy traffic. • If entire army travels down a road, land mines will go off. • Solution?

8. Solution The general sends small groups of soldiers down each of the roads, co-ordinating their movements so that they all arrive at the fortress at the same time.

9. Structural Similarities Fortress Problem Radiation Problem Fortress  Tumor Mined Roads  Surrounding tissue Attacking troops  Rays varying in intensity Small groups of troops Converging on fortress  Weak rays focused on tumor

10. Recognition Process • Radiation problem hard problem: • Preceded by Fortress problem, 20% solved it • If given hint that problems are related, 92% solved it • Subjects do not produce corresponding solutions with any great frequency unless given a hint • These results demonstrate the difficulty of recognizing the relevance of one problem and its solution to another Gick & Holyoak (1980)

11. Transfer aspects of fortress problemto radiation problem • Fortress problem was given with three different solutions: • Dispersion: the general’s army approaching the fort from several roads at once. • Tunnel: a general digging a tunnel to the fort • Open-route: a general attacking the fort via a supply route

12. Problem Solutions Solutions to the Radiation problem fell into three main categories: The DISPERSION solution, in which small doses of radiation are aimed at the tumor from different directions so that the radiation accumulates and destroys the tumorous tissue; The TUNNEL solution, in which an incision is made which leaves the tumor in place but which allows direct delivery of radiation. The OPEN-ROUTE solution, in which radiation is delivered to the tumor through the esophagus (tube leading from the throat to the stomach);

13. Distribution (%) of Solutions What do the results show?

14. Abstraction Process • Does performance improve if principle of base problem is stated? No • Showing diagrams helps? No • Showing multiple problems with related solutions helps? Yes

15. Analogical Inference “An atom is like the solar system” TARGET BASE Knowledge about the base domain can be used to reason about the target domain. Structure mapping theory is a theory for how this could work.

17. Structure Mapping Theory(Dedre Gentner, ’83, ’89) Theory on how to interpret an analogy 1) set up correspondences 2) focus on matches of relations, not attributes 3) focus on higher-order relations 4) extend knowledge about target by mapping relations from source to target

18. ALIGN RELATIONS

19. BASED ON ALIGNED RELATIONS, ALIGN OBJECTS “the nucleus is like the sun”

20. Mental Models • Knowledge structure used to understand how objects and physical processes work • Sometimes, mental models are based on poor analogies and can lead to incorrect predictons • Example: thermostats. How to heat up a room quickly? Current temp. Desired temp. | | 50 | | 60 | | 70 | | 80 | | OR? Kempton, ‘86

21. if you said “80”, what might your mental model be based on?

22. Children’s Mental Models “there are two earths, one is flat, the other is a sphere out in space” • Children were told facts: • Columbus sailed around the earth • Shown space photographs • What is their Conception of earth given these facts? Nussbaum ‘79

23. Intuitive Physics Kaiser, McClosky & Profitt ‘86 • Intuitive physics is based on naive mental models of physical processes • The diagram shows a curved tube, lying flat on a table. A ball is shot into the opening and out the other end. What is the ball’s path after it shoots out the tube? ? OR

24. Kaiser, McClosky & Profitt ‘86 Results (The C-curve problem is the same but shows just the C part of the spiral)

25. Explanation by Kaiser et al. • Grade school children start constructing theories of motion • Theories of persistence of motion: “an object persists in the way it is moving, unless there is friction”. E.g., bouncing ball continues to bounce • Theory is wrongly applied to spiral problem: overgeneralization

26. Intuitive Physics with a set of gears What is the direction of this gear? Suppose we swing this gear in this direction Schwartz & Black, 1999

27. ? Suppose we swing this gear in this direction Schwartz & Black, 1999

28. HINT: ? Suppose we swing this gear in this direction Schwartz & Black, 1999

29. Time A Time B Path Z Path X Path Y From McCloskey, 1983

30. Mental models might be initially be based on perceptual simulations (e.g., turning the gears in your mind) After training, these models might shift to more abstract rules to solve problems