What is Computational Cognitive Science?

Lovelace textbook · CC BY-SA 4.0 · computationalcognitivescience.github.io/lovelace/home

Computational cognitive science builds formal models of mental processes, then tests them against behavioral data. A model is not a metaphor: it is a precise, runnable theory that makes falsifiable predictions. Marr's three levels give the framework: what is computed, how it is computed, and what implements the computation. (For an alternative organizing scheme that decomposes information processing into six functional roles, see The Natural Framework.)

Models vs. theories

A verbal theory says "people use context to disambiguate words." A computational model specifies exactly how context is represented, what operations run over it, and what predictions follow. The model can be wrong in ways a verbal theory cannot, because it commits to details. That precision is the point: being wrong precisely is more useful than being vaguely right.

Scheme

; A toy model: does the agent predict "bank" means
; river-bank or money-bank, given context?
; The model commits to a specific mechanism: word frequency.

(define (predict-meaning context)
  (let ((river-words '("water" "fish" "stream" "paddle"))
        (money-words '("cash" "loan" "deposit" "account")))
    (let ((river-score (length (filter (lambda (w) (member w river-words)) context)))
          (money-score (length (filter (lambda (w) (member w money-words)) context))))
      (cond
        ((> river-score money-score) "river-bank")
        ((> money-score river-score) "money-bank")
        (else "ambiguous")))))

(display (predict-meaning '("water" "fish" "loan")))
(newline)
; "river-bank" — the model commits to this prediction.
; A verbal theory would just say "context helps."

(display (predict-meaning '("cash" "deposit")))
(newline)
; "money-bank"

(display (predict-meaning '("tree" "cloud")))
; "ambiguous"

Marr's three levels

David Marr proposed that any information-processing system should be understood at three levels. The computational level asks what problem is being solved and why. The algorithmic level asks what representations and procedures carry out the computation. The implementational level asks how the algorithm is physically realized. These levels are logically independent: the same computation can be carried out by different algorithms, and the same algorithm can be implemented in different hardware.

Scheme

; Marr's levels applied to addition:
;
; Computational: map pairs of numbers to their sum.
; Algorithmic: carry-based decimal addition, or binary addition,
;   or repeated increment.
; Implementational: silicon logic gates, or neurons, or gears.
;
; Two different algorithms for the same computation:

; Algorithm 1: recursive increment
(define (add-by-increment a b)
  (if (= b 0)
      a
      (add-by-increment (+ a 1) (- b 1))))

; Algorithm 2: built-in addition (the hardware does it)
(define (add-direct a b) (+ a b))

; Same computational-level function, different algorithms
(display "increment: ")
(display (add-by-increment 3 4)) (newline)
(display "direct:    ")
(display (add-direct 3 4))

Simulation vs. explanation

A simulation reproduces the output. An explanation reveals why the output takes that form. A weather simulation can predict rain without explaining why low pressure causes precipitation. Cognitive science wants explanations: models that not only fit the data but illuminate the mechanism. The test is whether the model makes surprising, correct predictions beyond the data it was fit to.

Scheme

; Simulation vs explanation:
; Both models predict that reaction time increases with set size.
; Only one explains WHY.

; Model A (simulation): lookup table from data
; "I measured these reaction times"
(define (model-a-rt set-size)
  (cond ((= set-size 1) 450)
        ((= set-size 2) 500)
        ((= set-size 4) 600)
        ((= set-size 8) 800)
        (else 0)))

; Model B (explanation): serial search, ~50ms per item
; "Each item takes ~50ms to check"
(define (model-b-rt set-size)
  (+ 400 (* 50 set-size)))

; Both fit the original data:
(display "Set size 4: ")
(display (model-a-rt 4)) (display " vs ")
(display (model-b-rt 4)) (newline)

; But Model B predicts novel set sizes:
(display "Set size 16 (model A): ")
(display (model-a-rt 16)) (newline)  ; 0 — no prediction
(display "Set size 16 (model B): ")
(display (model-b-rt 16))            ; 1200 — testable prediction

Notation reference

Term	Meaning
Computational level	What is the goal of the computation?
Algorithmic level	What representations and steps achieve it?
Implementational level	What physical substrate runs it?
Model	A precise, runnable specification of a theory
Simulation	Reproduces outputs; explanation reveals why

Neighbors

David Marr — the neuroscientist behind the three levels
Computational theory of mind — the broader philosophical context

Translation notes

The Lovelace textbook is interactive and example-heavy. This page condenses the conceptual core: the distinction between verbal theories and computational models, Marr's levels as an organizing framework, and the simulation-vs-explanation test. The textbook also discusses historical context (behaviorism, connectionism, Bayesian revolution) which we pick up in later chapters.

Read the original: Lovelace, Chapter 1.

by june.kim Probability and Bayes · 2 of 8 →