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					     Problems for Many
         Sciences.
• How do we observe / experiment on
  the internal workings of something
  (I.e. cognition)?
"Once we understand the biology of
 Escherichia coli, we will understand
    the biology of an elephant".
           Jacques Monod.
Animal Model hall of fame:
                ‘Model’?
• A Model is a description of some
  phenomena / on
 A model is verdical insofar as corresponds to
 the actual phenomena it seeks to model.

 A model, just like a ‘law’ or a ‘theory’ explains
 phenomena / on and can be used to make
 predictions about novel / unobserved aspects
 of the phenomena it seeks to model.
 Therefore, it is plays the same roll as ‘law’ or
 ‘theory’ in the H-D method or D-N model of
 explanation.
Models
Categorization of different
    Models / Systems:
                   Modeling

 Formulae                       Investigation of
 relating                       underlying
 observables                    structure
‘Mathematical
Models’ in Psych    Discovered Models    Invented Models
  V = d/t             ‘Experimental        Mathematical
                        Systems’            Symbolic
                                          Neural Network

                                             F=ma
1st use: positing unobservables
   Performed by Jameson and Hurvich in
   1957. A test light is shown to a subject.
   If the light appears greenish, a red-
   appearing light is added until the test light
   no longer appears at all greenish.
Jameson and Hurvich
      Results
Cone Sensitivity Curves
Mathematical Transformation
of Cone Sensitivity Functions



• We decorrelate the responses of the L, M and
  S cones by weighting each signal with a
  constant, and combining those results:
   C1(l) = 1.0L(l) + 0.0M(l) + 0.0S(l)
   C2(l) = -0.59L(l) + 0.80M(l) + -0.12S(l)
   C3(l) = -0.34L(l) + -0.11M(l) + 0.93S(l)
Opponent Processing Model
                   Modeling

 Formulae                       Investigation of
 relating                       underlying
 observables                    structure
‘Mathematical
Models’ in Psych    Discovered Models    Invented Models
  V = d/t             ‘Experimental        Mathematical
                        Systems’            Symbolic
                                          Neural Network

                                             F=ma
2 nd   use: relating observables

• The most simple use of a mathematical
  model is to fit a mathematical function to
  some data collected in an experiment.
  That function can then be used to make
  predictions about novel or unobserved
  behavior.

• Sternberg’s Memory Scanning Model
  – Response Time = 398 + 38(Memory Set Size)
• De Castro and Brewer
  – Intake of food = s(Number of People
    Present)0.22
Sternberg’s Experiment
      Sternberg’s Results




Response Time = 398+38(S)
Gravitational Force =
  (A constant called G) x (mass of first
  object) x (mass of second object)
  (the square of the distance between them)
   Common use: Theory v.
         Model
• ‘Model’ is often distinguished from
  ‘Theory’ along the lines of
  something like ‘generality’ and/or
  positing a mechanism.
  – Example: Color constancy-
    • Theory= the visual system recovers the
      stable spectral reflectance from the color
      signal
    • Model= exactly how the visual system gets
      the information about the spectral
      reflectance from the information in the
      color signal
                    Non-Constant
                    Representation




Filtered Daylight       Florescent   Halogen
                      A Schema
• The received schema of color
  perception in psychophysics:




•   Note: The word ‘Alchemy’ was used by Christine Ladd-Franklin
    in 1937. The transduction of light to nervous impulses is much
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                                                                                                                                                     The Theory:




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                                                                                                        (?represent?) the spectral reflectance




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                                                                                                      • It is the task of visual system to recover




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          y=1/x; x < 4, y < 4
The product of two numbers is 1. Both numbers are
less than 4. What are they?
         When Success?
• When the visual system has good
  information regarding the illuminant:
  • If the visual system has information about
    the ambient light, so we would expect
    success:
     • When the iluminant is the ambient light.
   explains the intuition that color constancy is
    very good in ‘natural lighting conditions’ –
    I.e. Judd’s and Katz’s conjectures
  • explains the Gelb effect and Newton’s spot
    lights

• In Brainard’s ‘nearly natural viewing’
            When Failure?
• In what conditions does the visual system
  represent changes in the illuminant as
  changes in the spectral reflectance?
• When the visual system has bad
  information about the illuminant:
  – When illuminant is not the ambient light:
     • Spot lights
     • Explains Newton’s observation
     • And the Gelb effect
  – Lighting conditions outside the parameters of
    the system (I.e. outside our evolutionary
    niche?) (explains the intuition of Katz & Judd)
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707                        Color Signal for
                                                                        illuminated by D65
                                                                                         Color Signal reflected
                                                                                         SimultaneousbyContrast black object
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7                                                         Color Signal reflected Contrast
                                                         Simultaneous by black object
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                                                                  illuminated by D65
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                                                                                                                                                                            of black color signal + red
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       Estimating the Illuminant
Brainard’s success suggests that color constancy is a matter of
estimating the illuminant. So how does the visual system do
this?

   •Unfortunately, it is not that easy:
      – The visual system doesn’t have ‘direct’
      information about the ambient light, and
      – Humans are very bad at estimating the
      ambient light directly.
   •So, how might we estimate the illuminant?
      –   ‘Classical’
      –   Buchsbaum: ‘gray world’ & spatial mean
      –   Maloney & Wandell: subspace
      –   Forsyth: linear model + physical constraints.
      –   Brainard: Bayesian decision theory
                   Modeling

 Formulae                       Investigation of
 relating                       underlying
 observables                    structure
‘Mathematical
Models’ in Psych    Discovered Models    Invented Models
                      ‘Experimental        Mathematical
                        Systems’            Symbolic
                                          Neural Network
   The importance of
  Mathematical Models:
Quick: what is the most
famous mathematical model
in the US right now?
   The BCS Formula as
sample Mathematical Model
• A matter of ‘Fit’?
• Data: team record, opponent’s
  record (‘strength of schedule’), poll
  rankings over the season, team
  losses & ‘quality wins’.
 Example: Oklahoma 2000?
• AP & Coaches poll end of season rank =
  1.
• Average rank over the course of the
  season= 1.86.
• Average of AP & Coaches poll + average
  over season = 2.86.


• (Thanks to Richard Billingsley at ESPN
  for the explanation).
     Strength of schedule
• Add the opponent’s records together
  = 73 Wins, 62 losses.
• Drop wins against teams that were
  not 1-A, and you have 70W.
• Drop losses from opponent’s
  schedule that were against OK, and
  you get 50 losses.
• Total: 70 Wins, 50 losses.
    Opponent’s winning %.
• The winning percentage is 70/120 =
  58.3% or 0.583.
• 0.583 * 2/3 = 0.3889
• Do the same ‘opponent’ calculation for
  each of the opponent’s opponents and
  weight it by 1/3 = 0.1749

• Add these 2 together and you get 0.5638
                 Now…
• Rank all the teams according to this
  ‘strength of schedule’. OK is 11th

• Finally, take that rank / 25 = 0.44.

• Add ‘Team losses’ (0 for OK) and ‘Quality
  wins’ (0 for OK).
• Add that to ‘Poll average’ and you get
  3.30.
       ‘Mathematical’?
– Obvious: algebra / calculus
– Recursive functions (cognitive science)
– Game Theory (decision theory /
  political science)
        Other models:
• Symbolic
• Neural Network
• Animal
Animal Model hall of fame:
When animal models go
        bad:
Cont’d
 The Thalidomide Tragedy
• Thalidomide is a anti-inflammatory and
  immunosuppressant that was prescribed
  to expectant mothers in the 1950s
• Thalidomide is a teratogen in a few rabbit
  breeds and in seven species of primates.
• It is not a teratogen in at lest 10 rat
  strains, 15 mice strains, 11 rabbit breeds,
  two dog breeds, three hamster strains,
  and eight species of primate.
            In reverse:
• Aspirin, insulin, epinephrine, and
  certain antibiotics (I don’t know
  which) are known to cause
  malformations in rodents
   Argument from analogy
• A and B are alike with respect to
  properties {1, 2, 3…}
• A has property n
• Therefore, B should have property n
  as well.
   Argument from model:
• A and B are functionally isomorphic
  with respect to properties {1, 2,
  3…}
• A has the functional property n
• Therefore, B should have functional
  property n as well.
            A Question:
• Is the Thalidomide story a case of
  pseudo-science, or just science
  done badly?
• Is this evidence that animal models
  are unreliable, or is it just that these
  studies were poorly performed?
   So… Lessons learned?
1. Animal models tell us nothing.
2. Animal models suffer from the
   same sampling errors as
   sociological studies (note that the
   teratogenic effect of Thalidomide
   is seen in rabbits)
3. Animal models must be used in
   conjunction with other strategies.
   Orchestrating strategies
• Remember Gizmo?

• Investigating mechanisms- that is,
  investigating what’s in the ‘black box’
  requires multiple methods – observation
  and correlation to establish the function –
  intervention, lesioning, stimulating and
  activating to hypothesize – modeling to
  refine – observation and correlation to
  test the functional isomorphism –
  orchestrated together.
         Corroboration

• Each confirming experiment corroborates
  the experiments of the other – in Quine’s
  terminology, the form a ‘web of belief’
  which can only be falsified as a whole.
• BUT that doesn’t necessarily mean that
  it’s not science – and not genuine
  knowledge! It doesn’t mean, for example,
  that all science is the equal of Creation
  science.
      What it does mean:
• Lakatos’ demarcation procedure:
  – Degenerative v. Progressive research
    program
• Can be cast in new light: A
  progressive program is one that (a)
  is continually suggesting novel
  corroborations in different
  methodologies and (b) predicts novel
  testable phenomena.
             Reduction
• Nomological Reduction
  – 1-1 relations
  – Many-1 relations (supervenience)
    • Functions & mechanisms?
• Emergence
  – The problem of epiphenomenalism
• Attribute dualism (synchroncity)
• Substance dualism
    Mechanistic viewpoint
• Isn’t the whole question of reduction
  misguided?
  misguided?

				
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