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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 0 20 40 60 80 100 120 140 377 392 407 422 437 452 467 482 497 512 527 542 557 572 587 602 617 632 647 662 677 692 707 0 20 40 60 80 100 120 140 160 377 393 409 425 441 457 473 489 505 521 537 553 569 585 from the color signal. 601 617 633 649 665 681 697 713 0 10 20 30 40 50 60 70 The Theory: 377 391 405 419 433 447 461 475 489 503 517 531 (?represent?) the spectral reflectance 545 559 573 587 601 615 • It is the task of visual system to recover 629 643 657 671 685 699 713 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) 0 1 2 3 4 5 6 7 8 0 50 100 150 200 250 377 377 391 392 405 407 419 422 433 437 447 452 461 467 475 482 489 503 497 517 512 531 527 545 542 D65 559 557 573 572 587 587 601 602 615 617 629 632 643 647 657 662 671 685 677 699 692 713 707 Color Signal for illuminated by D65 Color Signal reflected SimultaneousbyContrast black object 8 7 Color Signal reflected Contrast Simultaneous by black object 6 5 illuminated by D65 4 3 2 1 0 377 391 405 419 433 447 461 475 489 503 517 531 545 559 573 587 601 615 629 643 657 671 685 699 713 250 200 150 Color Signal for ‘spatial mean’ 100 of black color signal + red color signal + white color signal 50 0 377 392 407 422 437 452 467 482 497 512 527 542 557 572 587 602 617 632 647 662 677 692 707 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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