Distance & Magnitude Effects In Rhesus Macaques & College Students In collaboration with: Elizabeth Brannon (Duke University) Lisa Son (Barnard College)

Which is bigger? a fly or an elephant? a jaguar or a cheetah? Which city is further from San Francisco? Sacramento or Dallas? Sacramento or Santa Cruz? How do we represent such comparisons? Propositionally? requires language Imagistically? requires pictorial and/or spatial thinking

Which letter comes first in the alphabet? N or X? K or F?

Distance Effect A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Accuracy  f(distance) Accuracy CL > Accuracy SU Reaction Time  f(distance ) RT C < RT S

Magnitude Effect A B C D E F G H I J K L M N O P Q R S T U V W X Y Z Accuracy CF > Accuracy KN > Accuracy SV RT C < RT K < RT S Accuracy  f(magnitude) Reaction Time  f(magnitude )

Which number is larger? 9 or 4? 2 or 3?

Moyer & Landauer (1967)

Distance & Magnitude Effects Distance and magnitude effects are psychological and not psychophysical processes. Differences in RTs cannot be explained by any physical parameter of stimuli. They cannot be explained by associative processes which, indeed, predict the opposite of the observed effects. They cannot be explained by iterative processes, which predict the opposite of observed effects.

How do we make relative judgments of size, distance, weight etc? Prothetic continua intensitive differences (loudness, brightness, etc.) Weber’s law applies Logarithmic (Fechner) or power (Stevens) functions Metathetic continua qualitative differences (hue, pitch, etc.) Weber’s law does not apply

Seven-Item Lists List One List Two List Three List Four

A  B  C  D  E  F  G E B SUBSET TEST: WITHIN LISTS SAMPLE SUBSET: (Required order): B  E AB AC AD AE AF AG BC BD BE BF BG CD CE CF CG DE DF DG EF EG FG ALL SUBSETS:

A 2  B 2  C 2  D 2  E 2  G 2  F 2 A 1  B 1  C 1  D 1  E 1  G 1  F 1 A 3  B 3  C 3  D 3  E 3  G 3  F 3 A 4  B 4  C 4  D 4  E 4  G 4  F 4 SUBSET TEST SAMPLE SUBSETS (Required order): E 3 G 1 B 1 F 4 E3G1E3G1 D4G3D4G3 B1F4B1F4 G3D4G3D4 B3D3B3D3 [WITHIN LIST] B 3 D 3

E S L 7 R J 9

Terrace, Son, Brannon, Psychological Science (2003)

REQUIRED SEQUENCE SAMPLE CONFIGURATION

“…the number faculty largely emerges through the interaction of central features of the language faculty with other cognitive capacities relating to the recognition and manipulation of concrete objects and collections.” (Hurford, 1987)

D A D C B B A C Arbitrary sequence Numerical sequence

A B A C D C B D Arbitrary sequence Numerical sequence

Brannon & Terrace (JEP:ABP, 2000)

Milliseconds Percent Correct Numerical Distance LATENCYACCURACY Brannon & Terrace, (unplublished)

Numerical

Arbitrary Numerical

Random Dots (Human) (Buckley & Gillman,1974) Arabic Numerals (Human) (Buckley & Gillman, 1974) Arabic Numerals (Human) (Moyer & Landauer, 1976) Arbitrary Numerical

F 2  C 4 E1E1 G 3  A 1  B 1  C 1  D 1  E 1  G 1  F 1 A 3  B 3  C 3  D 3  E 3  G 3  F 3 A 2  B 2  C 2  D 2  E 2  G 2  F 2 A 4  B 4  C 4  D 4  E 4  G 4  F 4 Two-item subset test