# Correlation

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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
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
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
– 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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Simultaneous by black object
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Color Signal for ‘spatial mean’
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of black color signal + red
color signal + white color
signal
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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
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
• 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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 views: 5 posted: 8/8/2012 language: pages: 49