Computation and representation

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Computation and representation

• Joe Lau

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Overview of lecture

• What is computation?
• Brief history
• Computational explanations in cognitive science
• Levels of description

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What is computation?

• A computational process a formal operation on
  representation.
• Representation
• A meaningful symbol
• makes certain information explicit
• Formal
• Described by precise rule
• Can be carried out without knowing the meaning of
  the symbols

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Initial comments

• No restriction on what the symbols represent.
• The definition of computation is independent of
  the material basis of the process.
• The physical constitution of the process does not
  matter.
• X can be simulated on a computer ? X carries out
  computations.

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An example

• Consider this process
• input a finite string of symbols containing
  only symbols from 0123456789
• output the same string with an additional 0
  added to the end
• e.g. 1237 gt 12370
• meaning the symbols are decimal numerals
  representing numbers
• process computes x10.

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Another example

• Input names of people
• Output yes, no
• Process looks up the input in a book. Output
  yes if there is a matching entry, no if not.

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Brief history

• Mathematical theory
• Alan Turing and others (1930s)
• Precursors
• Concept of algorithm 12C Islamic mathematician
  Al Khowarizmi
• Reasoning as symbol manipulation 17C Thomas
  Hobbes
• Analytic engine 19C Charles Babbage

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The computational approach in cognitive science

• Assumption computational processes are
  necessary for explaining mind and behavior
• Reason
• perceptual and cognitive processes involve
  information processing
• info. processing requires computations.
• So perception and cognition requires computations.

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Comment on argument

• This is an empirical argument.
• The assumptions could turn out to be wrong.
• Perhaps it is possible to do information
  processing without computations.
• But no plausible alternative proposals so far.
• Having a mind might require more than
  computations.

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Examples of computational theories in cognitive
science

• Computational theories are prevalent in all areas
  of cognitive science, e.g.
• Perception
• Mental imagery
• Reasoning
• Language
• etc.

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Mental Imagery
Are these the same objects?
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Syntax

• The VC told the wardens to stop drinking at
  midnight.
• stop drinking at midnight
• stop drinking at midnight.

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Styles of computation

• Parallel versus serial architecture
• Analog vs. discrete representation
• Electronic vs. other (e.g. chemical) medium
• Classical vs. quantum computation

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Describing a computational system

• Three levels of description (David Marr)
• level of computation what is computed and why
• level of algorithm the procedure and
  representations used
• Level of implementation the physical hardware
• Higher level is independent of the lower one.

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Illustration

• What is computed x10
• Two different algorithms
• Add 0 to the end of the decimal numeral.
• Add the number to itself ten times.

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Churchlands criticisms of Marr

• Criticism 1 There are more than three levels.
• Criticism 2 The higher levels are not
  independent of the lower levels.

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Criticism 1
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Reply to criticism 1

• Marr does not have to say that there are exactly
  three levels.
• Those are three kinds of levels.

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Criticism 2

• Some AI people think that independence of levels
  means that they can understand intelligence
  without studying neurophysiology.
• Churchland
• This is not possible.
• The higher level is not independent of the lower
  levels.

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Reply to criticism 2

• Distinguish between conceptual and epistemic
  independence
• Might not be epistemically independent To
  discover which algorithm is used one might have
  to know the hardware.
• But can still be conceptually independent The
  algorithm can be defined and described
  independently of the implementation.

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Summary

• What is computation?
• Why use computational explanations?
• Three levels of describing a computational system
• Remaining issues
• Theoretical objections to approach.
• Further explanation of the concept of computation
  and representation.