Analogy

Question 1

Analogy: Introduction

Answer 1

• Very common and widely applied form of reasoning
• “hallmark of human intelligence”
• Exists a segment of the measurement of intelligence field that has focused on analogies as the markers of intelligence.
• The Ravens Progressive Matrices is a good example of this approach. Many IQ tests use analogies as test items;
• Analogical reasoning is at once obvious when understood and at the same time for many obscure.
• As a form of logic analogy is prominent in the history of science and medicine;
  
  • Solar system and structure of the atom
  • The flow of electricity as a “current” of water
• It has been the basis of arguments from precedent, particularly in law and politics.
• One of the best mechanisms for effecting conceptual changes in people’s thinking.
• Analogical reasoning goes beyond the given and so is a form of induction.
• Analogical reasoning depends heavily on working memory. This is due to the requirement to create connections between concepts and to make leaps of insight while holding the ideas in focus.

Question 2

Defining Analogy

Answer 2

• Analogical reasoning
  
  • “the transfer of knowledge from one situation to another by a process of mapping..”
  • Two key terms used in literature
    
    • Source
      
      • The analogical resource for a possible solution from the past;
    • Target
      
      • The present problem to be solved.
  • Analogies are also seen in narrative contexts (e.g. similies and metaphors)
  • This lecture will concentrate on Analogical problem solving in which there is a problem to be solved as opposed to analogy as a means of illustration or literary device.
  • There are several difficulties inherent in this definition in terms of actual proves which will become apparent.
  • This form of reasoning has been very productive in a wide range of activities from physical sciences to philosophical analysis.

Question 3

Gick and Holyoak 1980 – Tumour Problem

Answer 3

• Variations along the same line
  
  • A surgeon wishes to treat a patient with a stomach tumour
  • Patient will die if not treated
  • Operation is impossible – kill patient
  • Resources are radiation machines that will kill the patient
  • High doses will also kill patient
  • How to save patient?
• The problem is ill-defined in that the path from problem to solution can take several forms.
• Participants allocated into 4 groups
  
  • Given the problem and asked for a solution
  • Given the problem and encourage to read a solved problem
  • Given problem, a solved problem, and a hint of the relevance of the solved problem to the unsolved problem
• Solved problem involved;
  
  • A general attaching a fort containing a tyrant
  • There were many small roads that lead to the fort but no big one
  • Had to send troops along many small roads
  • Assembled sufficient troops to capture Fort and defeat tyrant.
• The solution is to divide the treatment into several less intense rays and to coverge the total radiation dosage onto the tumour. By doing this the surgeon damaging healthy tissue and yet destroys the tumour.
• The results
  
  • Group 1.
    
    • 10%
  • Group 2
    
    • 40%
  • Group 3
    
    • 80%
• Mapping from solved to unsolved can be viewed as looking at a schema of the process which involves;
  
  • Goal
  • Resources
  • Operators
  • Solution plan
  • Outcome
• The features of the two problems must have some degree of correspondence mapping for an analogy to be of use in solving the problem.
• Robertson (2001, p135) points out that there are some objects and relations that do correspond but others are not useful for solving the problem.

Question 4

Stages in the analogical reasoning process

Answer 4

• Representation of Source and Target
• Retrieve useful information i.e. a useful source analogue
  
  • Activate a set of analogues
  • Select a relevant one
• Analogical mapping i.e. apply source to target
  
  • Match corresponding concepts
  • Transfer part of the structure from the source to the target.
• Schema induction is the construction of an inductive generalisation. This is a process of abstracting from a number of analogues a set of principles.
• Success depends on the solver’s ability to get beyond surface features that in the initial stage have been useful in selecting a potentially useful analogue.

Question 5

How to determine the appropriate Anolgy

Answer 5

• Analogical reasoning is sensitive to the ability of the problem solver to clearly unpack the structure of the target problem.
  
  • In the tumour problem the structure of the problem is best understood from the goal state backwards.
  • The goal state is the tumour destroyed with minimal or no damage to the healthy tissue
  • This highlights a constraint, i.e. the damage to healthy tissue. This is a critical part of the problem. In essence it is the heart of the problem. The surgeon has the ray machine that will destroy the tumour, she knows where it is etc.
  • In each problem we must be able to state the goal in terms of the constraints
• Once a problem is deconstructed so that the goal state can be described in terms of the constraints the selection of an appropriate analogue is more straight-forward.
• Selection of an analogue is not easy however. There are several personal limitations, such as the problem solvers;
  
  • General knowledge,
  • Cognitive style re flexibility,
  • Stress levels

Question 6

Exemplar theories of Analogy

Answer 6

• The problem solver is reminded from past experiences of similar instances which are used to guide solutions to the target problem.
• This approach asserts that previous examples essentially are transferred and so the limitation is that the example may contain distracting or contradictory information and so inhibit a solution being founf.
• Problem solvers thus tend to “plug in” variables and values in a rote manner.

Question 7

Principles-Cueing (constraint) theories

Answer 7

• In general these theories assert that people are reminded of the principle(s) from previous successfully solved problems and so apply those principles that they see as appropriate to the current target problem.
• The principle this becomes the lens through which the person can understand the target problem.

Question 8

Holyoaks Constraint satisfaction theory

Answer 8

• There are three conditions or aspects that must be present for an analogical connection to be effected when confronted with a novel problem:
  
  • Structural similarity = shared elements that mean similar things
  • Semantic similarity = shared elements that mean similar things
  • Pragmatic similarity = goals (end states) are similar
• To access i.e. retrieve an analogy there must be the perception of similarity. This perception can be of two types:
  
  • Positive = when the similarity is of use in solving the novel problem
  • Negative = when the similarity is not of use and may lead to an over-commitment to the ‘analogy’ e.g. Vietnam war is like preventing the dominos from falling
• Problem structure is critical aspect of the process. There are two sorts of structure;
  
  • Surface = where elements are similar e.g. numbers, names of persons
  • Deep = where the processes are focused on achieving the goal and goals [target and source] are sufficiently similar to be recognised.
• The theory faces a number of difficulties;
  
  • How does it explain the combination of multiple analogies and how they seem to be easily combined.
  • The concept of “similarity” does not seem all that explanatory of analogy since it seems somewhat the same as analogy.
• The application of the Constraint theory to AI and computers has raised some interesting questions. Humans do not seem to need many surface similarities but computers have to have identical attributes for the analogy to be useful. This is very important insight into the difference between human reasoning and AI. Humans exhibit much more flexibility than computers.
• When participants in experiments “get” the analogy there is often expressed an “ah ha” reaction. There is sudden and somewhat holistic sense of the analogies application to the problem. This process is very interesting and not understood.

Question 9

Relationship to problem solving

Answer 9

• Analogy has been used to illustrate several important issues in the realm of reasoning and problem solving
• Solving problems requires accurate representations of the goal states, processes and resources to achieve the goals and some sense of the constraints.
• Problems can be described as either
  
  • Well defined = by which is meant that all [?] the information needed to solve the problem is contained in the description and the end state is clear (i.e. it will be known when the problem is solved) and what actions are needed in order to solve the problem and finally what constraints there are on the solution or
  • Ill-defined = these are problems where you are told the initial and end states but not what operators you have and how they combine to solve the problem.
• Problems can also be:
  
  • Knowledge rich = these problems require quite an amount of knowledge to solve them and so draw heavily on LTM or other training.
  • Knowledge lean = these problems require very little knowledge to solve them and so they are easily solved provided you understand the end state, operators and constraint.