What is Cognitive Science? Zenon Pylyshyn, Rutgers Center for Cognitive Science What’s in the mind? How do we know?

What is special about cognition? Cognition (from Latin “cogito”) refers to the capacity to know, and by extension to reason, perceive, plan, decide, solve problems, infer the beliefs of others, communicate by language as well as by other ways, and all the other capabilities we associated with intelligent activity. What is central to all such activity is that it relies on representations of the (actual or imagined) world. Cognitive science is the study of systems that represent and that use their representations rationally, e.g.,draw inferences. A computer is another such system, so computing has become the basic paradigm of cognitive science. In the last 40 years, The Representational Theory of Mind has become The Computational Theory of Mind

Cognitive science is a delicate mixture of the obvious and the incredible Granny was almost right: Behavior really is governed by what we know and what we want (together with the mechanisms for representing and for drawing inferences from these)

It’s emic, not etic properties that matter Kenneth Pike What determines our behavior is not how the world is, but how we represent it as being As Chomsky pointed out in his review of Skinner, if we describe behavior in relation to the objective properties of the world, we would have to conclude that behavior is essentially stimulus-independent Every behavioral regularity (other than physical ones like falling) is cognitively penetrable

It’s emic states that matter!

The central role of representation creates some serious problems for a natural science What representations are about is what matters But how can the fact that a belief is about some particular thing have an observable consequence? How can beliefs about ‘Santa Claus’ (or the ‘Holy Grail’) determine behavior when there is no Santa Claus? In a natural science if “X causes Y” then X must exist and be causally connected to Y! It’s even worse than that; even when X exists, it is not X’s physical properties that are relevant! e.g., the North Star & navigation

Is it hopeless to think we can have a natural science of cognition? Along comes The computational theory of mind “the only straw afloat”

The major historical milestones Brentano’s recognition of the problem of intentionality: Mental States are about something, but aboutness is not a physical relation. The formalist movement in the foundations of mathematics: Hilbert, Kurt Gödel, Bertrand Russell & Alfred Whitehead, Alan Turing, Alonzo Church, … provided a technique by which logical reasoning could be automated. Representational/Computational theory of mind: The modern era: Newell & Simon, Chomsky, Fodor

Intelligent systems behave the way they do because of what the represent But in order to function under physical principles, the representations must be instantiated in physical properties To encode knowledge in physical properties one first encodes it in symbolic form (Proof Theory tells us how) and then instantiates those symbolic codes physically (computer science tells us how)

How to make a purely mechanical system reason about things it does not understand or know about? The discovery of symbolic logic. (1) Married(John, Mary) or Married(John, Susan) and the equation or “statement”, (2) not[Married(John, Susan)]. from these two statements you can conclude, (3) Married(John, Mary) But notice that (3) follows from (1) and (2) regardless of what is in the parts of the equation not occupied by the terms or or not so that you could write down the equations without mentioning marriage or John or Mary or, for that matter, anything having to do with the world. Try replacing these expressions with the meaningless letters P and Q. The inference still holds: (1') P or Q (2') not Q therefore, (3') P

Cognitive Science and the Tri-Level Hypothesis Intelligent systems are organized at three (or more) distinct levels: The physical or biological level The symbolic or syntactic level The knowledge or semantic level This means that different regularities may require appeal to different levels

How can we find out? Given these broad constraints on cognitive theory, how do we go about discovering how it works?

Weak vs Strong Equivalence Is cognitive science concerned with anything more than developing models that generate the same Input-Output behavior as people exhibit in certain problem domains? A theory that correctly predicts I-O behavior is said to be weakly equivalent to the psychological process it is supposed to explain. It is what some people mean by “simulating behavior”. Everyone in Cognitive Science is interested in strong equivalence – we want to explain not only the observed behavior, but also how it is generated. The how will take the form of an algorithm.

Simulating the Input-Output function Black Box Output Can we do any better than I-O simulation without looking inside the black box? If all you have is observed behavior, how can you go beyond I-O simulation?

Modeling the Actual Process (the algorithm used) Input Black Box Output Index of process If all you have is observed behavior, how can you go beyond I-O simulation (mimicry)? Answer: Not all observations are Inputs or Outputs: some are meta-behavior or indexes of processes.

Example of the Sternberg memory search The initial input consists of the instructions and the presentation of the memory set (n items). On each trial the particular input to the black box consists of the presentation of a target letter. The output consists of a binary response (present or absent). The time taken to respond is also recorded. That is called the “Reaction Time”. The reaction time is not part of the output but is interpreted as an index of the process (e.g., an indication of how many steps were performed).

Example of the input-output of a computational model of the Sternberg task Inputs: Memory set is (e.g.) C, D, H, N Inputs: Probe (e.g., C or F) Output: Pairs of Responses and Reaction Times (e.g. output is something like “Yes, 460 msecs”) Does it matter how the Output is derived? It doesn’t if all you care about is I-O behavior It does if you care about Strong Equivalence (i.e., HOW it works)

Example of the input-output of a computational model of the Sternberg task Inputs are: (1) Memory set = C,D,H,N (2) Target probe = C (or R) Input-Output prediction using a table: Input to model Model prints out C Yes 460 ms N 530 ms R No 600 ms H 520 ms M 620 ms Is this model weakly- or strongly-equivalent to a person?

Example of a weakly equivalent model of the Sternberg task Store memory set as a list L, assign set size = n Read target item I (If I = “end” quit) Check if I is one of the letters in the list L If found in list, assign R=“yes” otherwise R=“no” If R=“yes”, set T= 500 + K * n  Rand(20  x  50) If R=“no”, set T= 800 + K * n  Rand(20  x  50) Print R, Print T Go to 2 Is this the way people do it? How do you know?

How do you know? Because in this case time should not be one of the computed outputs, but a measure of how many steps it took. The same is true of intermediate states (e.g., determined by what subjects say), error rates, eye tracking, judgments about the output, and so on. Question: Is time always a valid index of processing complexity?

Results of the Sternberg memory search task What do they tell us about how people do it? Is this Input-Output equivalent or is it strongly equivalent to human performance?

Results of the Sternberg memory search task What do they tell us about how people do it? Is this Input-Output equivalent or is it strongly equivalent to human performance? Exhaustive search Self-terminating search

More examples – arithmetic How can we tell what algorithm is being used when children do arithmetic? Consider these examples of students doing addition and subtraction. What can you tell from these few examples? 32795 21826 + + - - - ?? 54621 53511 10969 11179 11875 How else could we try to find out what method they were using?

Studying human arithmetic algorithms Arithmetic (VanLehn & Brown. “Buggy”) Buggy – a model of children’s arithmetic – has about 350 “rules” which help uncover “deep bugs” Newell & Simon’s study of problem solving Problem behavior graph and production systems Use of protocols, eye tracking Information-Processing style of theory. Computational but not always a computer model.

Examples from language. Does intentionality (and the trilevel hypothesis) only apply to high-level processes such as reasoning? Examples from language. John gave the book to Fred because he finished it John gave the book to Fred because he wanted it The city council refused to give the workers a permit for a demonstration because they feared violence The city council refused to give the workers a permit for a demonstration because they were communists

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Representation in perception What does perception (especially vision) tell cognition? What is the “output” of the visual system?

This is what our conscious experience suggests goes on in vision…

This is what the demands of explanation suggests must be going on in vision…

Completions … Where’s Waldo?

Standard view of saccadic integration by superposition

Does intentionality (and the trilevel hypothesis) only apply to high-level processes such as reasoning? Examples from vision seeing as: It’s what you see the figure as that determines behavior – not its physical properties. What you see one part as determines what you see another part as.

Is it possible to specify a set of ways of physically presenting a visual stimulus for it to be perceived in a certain way?

Can you think of other ways of presenting a stimulus so it is perceived as e.g., a Necker Cube?

Errors in recall suggest how visual information is encoded Children have very good visual memory, yet often make egregious errors of recall Errors in relative orientation often take a canonical form Errors in reproducing a 3D image preserve 3D information

Errors in recall suggest how visual information is encoded Children more often confuse left-right than rotated forms Errors in imitating actions is another source of evidence

Ability to manipulate and recall patterns depends on their conceptual, not geometric, complexity Difficulty in superimposing shapes depends on they are conceptualized Look at first two shapes and superimpose them in your mind; then draw (or select one) that is their superposition

Many studies have shown that memory for shapes is dependent on the conceptual vocabulary available for encoding them e.g., recall of chess positions by beginners and masters

Other examples showing that it is how you represent something that is relevant to cognitive science Examples from color vision. “Red light and yellow light mix to produce orange light” This remains true for any way of getting red light and yellow light: e.g. yellow may be light of 580 nanometer wavelength, or it may be a mixture of light of 530 nm and 650 nm wavelengths. So long as one light looks yellow and the other looks red the “law” will hold.

If cognitive processes are at a different level of organization from the physical level, how can we ever find out what they are – i.e., how can we discover what algorithm is being used? We are limited only by the imagination of the experimenter, e.g., Relative complexity evidence (RT, error rates…) Intermediate state evidence Eye tracking Stage analysis (additive factors method) Event Related Potentials (EEG) fMRI clinical observations of brain damage Psychophysical methods (SDT) Etc…

Two other considerations that are special to cognitively determined behavior The Cognitive Penetrability of most cognitive processes. A regularity that is based on representations (knowledge) can be systematically altered by imparting new information that changes beliefs. The critical role of "Cognitive Capacity". Because of an organism's ecological or social niche, only a small fraction of its behavioral repertoire is ever actually observed. Nonetheless an adequate cognitive theory must account for the behavioral repertoire that is compatible with the organism's structure, which we call its cognitive capacity.

Strong Equivalence and the role of cognitive architecture

The concept of cognitive architecture If differences among behaviors (including differences among individuals) is to be attributed to different beliefs or different algorithms, then there must be some common set of basic operations and mechanisms. This is called the Cognitive Architecture The concept of a particular algorithm, or of being “the same algorithm” is only meaningful if two computers have the same architecture. Algorithm is architecture-relative. The architecture is the part of the system that does not change when beliefs change. So it defines the system’s Cognitive Capacity.

On the difference between explanations that appeal to mental architecture and those that appeal to tacit knowledge Suppose we observe some robust behavioral regularity. What does it tell us about the nature of the mind or about its intrinsic properties?

An illustrative example: Mystery Code Box What does this behavior pattern tell us about the nature of the box?

An illustrative example: Mystery Code Box Careful study reveals that pattern #2 only occurs in this special context when it is preceded by pattern A What does this behavior pattern tell us about the nature of the box?

The Moral: Regularities in behavior may be due to either: The inherent nature of the system or its structure or architecture. The content of what the system represents (what it “knows”).

Why it matters: A great many regular patterns of behavior reveal nothing more about human nature than that people do what follows rationally from what they believe. The example of human conditioning

Another example where it matters: The study of mental imagery Application of the architecture vs knowledge distinction to understanding what goes on when we reason using mental images

Examples of behavior regularities attributable to tacit knowledge Color mixing, conservation of volume The effect of image size ? Scanning mental images ?

Color mixing example

Conservation of volume example

Our studies of mental scanning (Pylyshyn & Bannon. See Pylyshyn, 1981) There is even reason to doubt that one can imagine scanning continuously (Pylyshyn & Cohen, 1998)

Can you rotate a mental image? Which pair of 3D objects is the same except for orientation?

Do mental images have size. Imagine a very small mouse Do mental images have size? Imagine a very small mouse. Can you see its whiskers? Now imagine a huge mouse. Can you see its whiskers? Which is faster?

Why do so many people deny these obvious facts about mental imagery? The power of subjective experience (phenomenology). The mind-body problem is everywhere: but subjective experience does not cause behavior! (e.g., conscious will) The failure to make some essential distinctions Content vs form (the property of images vs the property of what images are about) {compare the code box example} An image of X with property P can mean (An image of X) with property P or An image of (X with property P) Capacity vs typical behavior: Architecture vs knowledge

Are all the things we thought were due to internal pictures actually due to tacit knowledge? Other reasons for imagery phenomena: Task demands: Imagine that X = What would it be like if you saw X?

Are there pictures in the brain? There is no evidence for cortical displays of the right kind to explain visual or imaginal phenomena

So what is in the brain? The best hypothesis so far (i.e., the only one that has not been shown to be clearly on the wrong track) is that the brain is a species of computer in which representations of the world are encoded in the form of symbol structures, and actions are determined by calculations (i.e., inferences) based on these symbolic encodings.

So why does it not feel like we are doing computations? Because the content of our conscious experience is a very poor guide to what is actually going on that causes our experiences and our behavior. Science is concerned with causes, not just correlations. Because we can’t assume that the way things seem has much to do with how it works (e.g., language understanding) As in most sciences, the essential causes are far from obvious (e.g., why does the earth go around the sun? What is this table made of ? etc.). In the case of cognition, what is going on is a delicate mixture of the obvious (what Granny or Shakespeare knew about why people do what they do) and the incredible

We can’t always be sure we have the right method or instrument

If all else fails there is always parsimony and generality…(they worked well in physics and linguistics!)