distance & magnitude effects in rhesus macaques & college students in collaboration with:...

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?

QuickTime™ and aGraphics decompressorare needed to see this picture.

B

B

B

B

B

B

B

B

B

B

B B

B

B

1 2 3 4 5 6 7 8 9 10 11 12 13 140.9

1

1.1

1.2

1.3

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1.5

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1.8

DISTANCE BETWEEN LETTERS

B RT correct (sec)

HAMILTON AND SANFORD (1978)

f(x) = -.044x +1.56

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)

AccuracyCL > AccuracySU

Reaction Time f(distance)

RTC < RTS

B

B

BB

B

B

B

2 3 4 5 6 7 81

1.5

2

2.5

3

3.5

4

RUN-THROUGH LENGTH

B RT correct (sec)

HAMILTON AND SANFORD (1978)

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

AccuracyCF > AccuracyKN > AccuracySV

RTC < RTK < RTS

Accuracy f(magnitude)

Reaction Time f(magnitude)

Which number is larger?

9 or 4?

2 or 3?

B

B B

BB

B

B

B

1 2 3 4 5 6 7 8500

520

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DISTANCE BETWEEN NUMERALS

B RT (msec)

Moyer & Landauer (1967)

BB B B

B

B

B

B

J

J

J

J

J

J

J

J

1 2 3 4 5 6 7 8400

450

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FIRST DIGIT

B RT: digitsJ RT: Random Dot Patterns

f(x) = 13.1x + 429.8

f(x) = 58.33x + 436.2

BUCKLEY AND GILMAN (1974)

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 ListsList One

List Two

List Three

List Four

QuickTime™ and a decompressor

are needed to see this picture.

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:

A2 B2 C2 D2 E2 G2 F2

A1 B1 C1 D1 E1 G1 F1

A3 B3 C3 D3 E3 G3 F3

A4 B4 C4 D4 E4 G4 F4

SUBSET TEST

SAMPLE SUBSETS (Required order):

E3 G1 B1 F4

E3G1

D4G3

B1F4

G3 D4

B3D3

[WITHIN LIST] B3 D3

E

S

L 7RJ9

ACCURACY to 1st Item of Subset

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ABBCCDDEEFFG ACBDCEDFEG A BECFDG AEBFCG AFBGA

SUBSET

PER CENT CORRECT4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)

MONKEYS (n=4) FOUR 7-ITEM ARBITRARY LISTS

DISTANCE:

1 2 3 4 5 6

Chance

ACCURACY to 1st Item of Subset

40

50

60

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100

ABBCCDDEEFFG ACBDCEDFEG A BECFDG AEBFCG AFBGA

SUBSET

PER CENT CORRECT4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)

4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)

MONKEYS (n=4) FOUR 7-ITEM ARBITRARY LISTS

DISTANCE:

1 2 3 4 5 6

Chance

RTs to 1st ITEM OF SUBSET

1500

1750

2000

2250

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2750

3000

1 2 3 4 5 6

DISTANCE

REACTION TIME (msec)

BETWEEN LISTS

MONKEYS (n=4)Trained on four 7-item arbitrary lists

Terrace, Son, Brannon, Psychological Science (2003)

RTs to 1st ITEM OF SUBSET

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1750

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1 2 3 4 5 6DISTANCE

REACTION TIME (msec)BETWEEN LISTS

WITHIN LISTS

MONKEYS (n=4)Trained on four 7-item arbitrary



7-ITEM LISTS: WITHIN- & BETWEEN-LIST SUBSETS

1250

1500

1750

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2250

2500

2750

3000

3250

3500

3750

ABBCCDDE EF FG ACBDCE DF EG ADBE DGEF AE BF CH AF BG AGSUBSET


WITHIN -LIST SUBSETS

MONKEYS N=4

DISTANCE:

1 2 3 4 5 6


7-ITEM LISTS: WITHIN- & BETWEEN-LIST SUBSETS

1250

1500

1750

2000

2250

2500

2750

3000

3250

3500

3750

ABBCCDDE EF FG ACBDCE DF EG ADBE DGEF AE BF CH AF BG AGSUBSET


WITHIN -LIST SUBSETSBETWEEN -LIST SUBSETS

MONKEYS N=4

DISTANCE:

1 2 3 4 5 6

1 2 3 4 5 6 7 8

REQUIRED SEQUENCE

SAMPLE CONFIGURATION SAMPLE CONFIGURATION

5 4 8 1

7 2 3 6 5 4

8

17

2 36

QuickTime™ and aPhoto - JPEG decompressor


RT to1ST ITEM OF SUBSET

2000

2100

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A B C D E F G

POSITION


RTs: Subsets from Human 8-Item Arbitrary Lists

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2750

1 2 3 4 5 6 7

DISTANCE


0

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AB BC CD DE EF FG AC BD CE DF EG AD BE CF DG AE BF CG AF BG AG

SUBSET


MONKEY 7-ITEM

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SUBSET


MONKEY 6-ITEM MONKEY 7-ITEM

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SUBSET


HUMAN 7-ITEM MONKEY 6-ITEM MONKEY 7-ITEM

“…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

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Arbitrary sequence

Numerical sequence

A

B

A

C

D C

B

D

Arbitrary sequence

Numerical sequence

QuickTime™ and a decompressor


Brannon & Terrace (JEP:ABP, 2000)

Mill

isec

ond

sP

erce

nt C

orre

ct

Numerical Distance

LATENCY ACCURACY

B BB

BB B B B

J

J

JJ J

J J J

1 2 3 4 5 6 7 8400

500

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1000

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1200

1300

1400

B

BB

B B B B B

JJ

J J J J J J

1 2 3 4 5 6 7 850

60

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B MONKEY LESS (n=2)

J HUMAN LESS (n=11)

Brannon & Terrace, (unplublished)

0

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1.22.33.44.55.66.77.88.91.32.43.54.65.76.87.91.42.53.64.75.86.91.52.63.74.85.91.62.73.84.91.72.83.91.82.91.9

NUMERICAL PAIR

REACTION TIME (msec.)

MONKEY

Distance: 1 2 3 4 5 6 7 8


0

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2000

1.22.33.44.55.66.77.88.91.32.43.54.65.76.87.91.42.53.64.75.86.91.52.63.74.85.91.62.73.84.91.72.83.91.82.91.9

NUMERICAL PAIR

REACTION TIME (msec.)

HUMAN

MONKEY

Distance: 1 2 3 4 5 6 7 8


0

500

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3500

4000

AB-1.2DE-4.5GH-7.8AC-1.3DF-4.67.9

BE-2.5EH-5.8AE-1.5DH-4.8AF-1.64.9

BH-2.8AH-1.81.9

SUBSET


MONKEY: 7 ARBITRARY ITEMS

HUMAN: 8 ARBITRARY ITEMS


DISTANCE: 1 2 3 4 5 6 7 8

0

500

1000

1500

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2500

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3500

4000

AB-1.2DE-4.5GH-7.8AC-1.3DF-4.67.9

BE-2.5EH-5.8AE-1.5DH-4.8AF-1.64.9

BH-2.8AH-1.81.9

SUBSET



HUMAN: 8 ARBITRARY ITEMS


MONKEY: 9 NUMERICAL ITEMS

HUMAN: 9 NUMERICAL ITEMS

DISTANCE: 1 2 3 4 5 6 7 8

MAGNITUDE EFFECTS: HUMAN AND MONKEY

0

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1 2 3 4 5 6 7 8MAGNITUDE


Numerosity of GeometricPatterns (Human)

Random Dots (Human:Buckley & Gillman, 1974)

Arabic Numerals (Human:Buckley & Gillman, 1974)

Arabic Numerals (Human:Moyer & Landauer, 1976)

Nu

mer

ical

MAGNITUDE EFFECTS: HUMAN AND MONKEY

0

500

1000

1500

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3500

4000

1 2 3 4 5 6 7 8MAGNITUDE


Arbitrary 6-item (Monkey:Terrace, et al., 1966)

Arbitrary 7-item (Monkey:Terrace, Son & Brannon,2003)Arbitrary 8-item (Human:Terrace & Jaswall, 1998)

Letters (Human)(Hamilton & Sanford,1978)Numerosity of GeometricPatterns (Human)

Random Dots (Human:Buckley & Gillman, 1974)

Arabic Numerals (Human:Buckley & Gillman, 1974)

Arabic Numerals (Human:Moyer & Landauer, 1976)

Arb

itra

ryN

um

eric

al

DISTANCE EFFECTS: HUMAN AND MONKEY

0

500

1000

1500

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2500

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1 2 3 4 5 6 7 8DISTANCE


Geometric Patterns (Human)(Brannon & Terrace, 2001)

Random Dots (Human)(Buckley & Gillman,1974)

Arabic Numerals (Human)(Buckley & Gillman, 1974)

Arabic Numerals (Human)(Moyer & Landauer, 1976)

Nu

mer

ical

DISTANCE EFFECTS: HUMAN AND MONKEY

0

500

1000

1500

2000

2500

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1 2 3 4 5 6 7 8DISTANCE

REA

CTIO

N T

IME (

msec)

Arbitrary 6-item (Monkey)(Terrace, et al., 1966)

Arbitrary 7-item (Monkey;Terrace, Son & Brannon,

2003)Arbitrary 8-item (Human)(Terrace & Jaswall, 1998)

Letters (Human)(Hamilton &Sanford,1978)

Geometric Patterns (Human)(Brannon & Terrace, 2001)

Random Dots (Human)(Buckley & Gillman,1974)

Arabic Numerals (Human)(Buckley & Gillman, 1974)

Arabic Numerals (Human)(Moyer & Landauer, 1976)

Arb

itra

ryN

um

eric

al

F2 C4

E1G3

A1 B1 C1 D1 E1 G1 F1

A3 B3 C3 D3 E3 G3 F3

A2 B2 C2 D2 E2 G2 F2

A4 B4 C4 D4 E4 G4 F4

Two-item subset test

BBB

BB

BBB

BBBBBBB

BBBBBB

BBBB

BBB

BB

B

BB

BB BJ

J J J J

J J J J

J

J J

JJ

J

HH

HHH HHH

HH

HHHHH

HHHH

HH

HH

HH H

H

HH

H

H

H

H

H

H

H

F

FF

F

FF

F

FF

F

F FF

F

FF

FF

F

F

F

F

F

F

F

F

F

F

0

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1000

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3500

B MONKEY: 9 NUMERICAL ITEMS (n = 2)

J MONKEY: 6 ARBITRARY ITEMS (n = 2)

H HUMAN: 9 NUMERICAL ITEMS (n =11)

F HUMAN: 8 ARBITRARY ITEMS (n = 40)

DISTANCE EFFECTS AT A CONSTANTMAGNITUDE OR POSITION

SUBSET

distance & magnitude effects in rhesus macaques & college students in collaboration with:...

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