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?
G
ar
Qra
u
eickT
ph
need
ics
im
ed
e™
deco
toan
se
md
pre
ea
th
ssor
is picture.
HAMILTON AND SANFORD (1978)
1.8
B
B
1.7
RTcorrect (sec)
f(x) = -.044x+1.56
1.6
B
REACTIONTIME(SECONDS)
1.5
1.4
B
B
1.3
B
B
B
1.2
B
B
1.1
B
1
B
B
B
11
12
B
0.9
1
2
3
4
5
6
7
8
9 10
DISTANCEBETWEEN LETTERS
13
14
Distance Effect
ABCDEFGHIJKLMNOPQRSTUVWXYZ
Accuracy  f(distance)
AccuracyCL > AccuracySU
Reaction Time  f(distance)
RTC
< RTS
HAMILTON AND SANFORD (1978)
4
B
RT correct (sec)
B
REACTION TIME (SECONDS)
3.5
3
B
2.5
B
B
B
2
1.5
B
B
1
2
3
4
5
6
RUN-THROUGH LENGTH
7
8
Magnitude Effect
Accuracy  f(magnitude)
Reaction Time  f(magnitude)
ABCDEFGHIJKLMNOPQRSTUVWXYZ
AccuracyCF > AccuracyKN > AccuracySV
RTC < RTK < RTS
Which number is larger?
9 or 4?
2 or 3?
640
B
620
RT (msec)
B
Moyer & Landauer (1967)
REACTION TIME (MSEC)
600
B
580
B
560
B
B
B
540
B
520
B
500
1
2
3
4
5
6
7
DIST ANCE BETWEEN NUMERALS
8
BUCKLEY AND GILMAN (1974)
900
J
850
B
RT: digits
J
RT: Random Dot Patterns
J
800
J
REACTION TIME (MSEC)
750
J
700
f(x) = 58.33x + 436.2
J
650
600
J
B
550
500
450
J
B
J
B
B
B
B
B
f(x) = 13.1x + 429.8
B
400
1
2
3
4
5
FIRST DIGIT
6
7
8
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
List One
List Two
List Three
List Four
Seven-Item Lists
QuickTime™ and a
decompressor
are needed to see this picture.
SUBSET TEST: WITHIN LISTS
A B  C  D E F  G
SAMPLE
(Required order):
B E
SUBSET:
E
ALL
SUBSETS:
B
AB AC AD AE AF AG
BC BD BE BF BG
CD CE CF CG
DE DF DG
EF EG
FG
SUBSET TEST
A1  B 1  C1  D1 
E1  G1  F1
A2  B2  C2  D2  E2  G2  F2
A3 
B3  C3  D3  E3  G3  F3
A4 
B4  C4  D4  E4  G4  F4
SAMPLE SUBSETS (Required order):
B1F4
E3G1
E3
G1
B1
D 4  G3
G3
D4
F4
B3D3
B3
D
[WITHIN LIST]
S
9
L
J
R
7
E
ACCURACY to 1st Item of Subset
100
80
70
MONKEYS(n=4)
FOUR 7-ITEM ARBITRARY LISTS
4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)
60
Chance
50
DISTANCE:
1
2
3
4
5
6
SUBSET
A
AF
BG
AE
BF
CG
A
BE
CF
DG
AC
BD
CE
DF
EG
40
AB
BC
CD
DE
EF
FG
PER CENT CORRECT
90
ACCURACY to 1st Item of Subset
100
80
70
MONKEYS(n=4)
FOUR 7-ITEM ARBITRARY LISTS
4 LISTS: RANDOMLY SELECTED PAIRS (BETWEEN LISTS)
60
4 LISTS: RANDOMLY SELECTED PAIRS (WITHIN LISTS)
Chance
50
DISTANCE:
1
2
3
4
5
6
SUBSET
A
AF
BG
AE
BF
CG
A
BE
CF
DG
AC
BD
CE
DF
EG
40
AB
BC
CD
DE
EF
FG
PER CENT CORRECT
90
Terrace, Son, Brannon, Psychological Science
(2003)
RTs to 1st ITEM OF SUBSET
3000
REACTION TIME (msec)
2750
2500
2250
2000
MONKEYS(n=4)
Trained on four 7-item arbitrary lists
BETWEEN LISTS
1750
1500
1
2
3
DISTANCE
4
5
6
Terrace, Son, Brannon, Psychological Science (2003)
RTs to 1st ITEM OF SUBSET
3000
REACTION TIME (msec)
2750
2500
2250
2000
MONKEYS (n=4)
Trained on four 7-item arbitrary
BETWEEN LISTS
1750
WITHIN LISTS
1500
1
2
3
DIST ANCE
4
5
6
Terrace, Son, Brannon, Psychological Science (2003)
7-ITEM LISTS: WITHIN- & BETWEEN-LIST SUBSETS
3750
WITHIN -LIST SUBSETS
3500
3000
2750
2500
2250
2000
1750
MONKEYS N=4
1500
DISTANCE:
1
2
3
4
5
6
SUBSET
AG
BG
AF
CH
BF
AE
EF
DG
BE
AD
EG
DF
CE
BD
AC
FG
EF
DE
CD
BC
1250
AB
REACTION TIME (msec)
3250
Terrace, Son, Brannon, Psychological Science (2003)
7-ITEM LISTS: WITHIN- & BETWEEN-LIST SUBSETS
3750
WITHIN -LIST SUBSETS
BETWEEN -LIST SUBSETS
3500
3000
2750
2500
2250
2000
1750
MONKEYS N=4
1500
DISTANCE:
1
2
3
4
5
6
SUBSET
AG
BG
AF
CH
BF
AE
EF
DG
BE
AD
EG
DF
CE
BD
AC
FG
EF
DE
CD
BC
1250
AB
REACTION TIME (msec)
3250
REQUIRED SEQUENCE
1
2
3
4
5
6
7
8
SAMPLE CONFIGURATION SAMPLE CONFIGURATION
5
4
8
1
2
8
6
3
7
2
3
6
5
7
4
1
QuickTime™ and a
Photo - JPEG decompressor
are needed to see this picture.
RT to1ST ITEM OF SUBSET
2800
REACTION TIME (msec)
2700
2600
2500
2400
2300
2200
2100
2000
A
B
C
D
POSITION
E
F
G
RTs: Subsets from Human 8-Item Arbitrary Lists
REACTION TIME (msec)
2750
2500
2250
2000
1
2
3
4
DISTANCE
5
6
7
3500
REACTION TIME (msec)
3000
2500
2000
1500
1000
MONKEY 7-ITEM
500
0
AB BC CD DE EF FG
AC BD CE DF EG
AD BE CF DG
SUBSET
AE BF CG
AF BG
AG
4000
3500
REACTION TIME (msec)
3000
2500
2000
1500
1000
MONKEY 6-ITEM
500
MONKEY 7-ITEM
0
AB BC CD DE EF FG
AC BD CE DF EG
AD BE CF DG
SUBSET
AE BF CG
AF BG
AG
4000
3500
REACTION TIME (msec)
3000
2500
2000
1500
1000
500
HUMAN 7-ITEM
MONKEY 6-ITEM
MONKEY 7-ITEM
0
AB BC CD DE EF FG
AC BD CE DF EG
AD BE CF DG
SUBSET
AE BF CG
AF BG
AG
“…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)
Arbitrary
sequence
B
C
D
A
Numerical
sequence
C
A
B
D
Arbitrary
sequence
B
C
D
A
Numerical
sequence
B
A
D
C
QuickTime™ and a
decompressor
are needed to see this picture.
Brannon & Terrace (JEP:ABP, 2000)
Brannon & Terrace, (unplublished)
LATENCY
1400
ACCURACY
1300 J
J
1100 B
B
1000
JB
900
JB
JB
JB J
800
B JB
700
J
JB B
JB 100
J B
J
J
J
B
J B
90
B
80
B
70
600
B
MONKEY LESS (n=2)
500
J
HUMAN LESS (n=11)
60
400
50
1
2
3
4
5
6
7
8
1
2
3
4
5
Numerical Distance
6
7
8
Percent Correct
Milliseconds
1200
6
NUMERICAL PAIR
7
1.9
5
1.8
2.9
4
1.7
2.8
3.9
1400
1.6
2.7
3.8
4.9
3
1.5
2.6
3.7
4.8
5.9
2
1.4
2.5
3.6
4.7
5.8
6.9
Distance:
1
1.3
2.4
3.5
4.6
5.7
6.8
7.9
400
1.2
2.3
3.4
4.5
5.6
6.7
7.8
8.9
REACTION TIME (msec.)
Brannon & Terrace, (unplublished)
2000
1800
1600
MONKEY
1200
1000
800
600
8
200
0
6
NUMERICAL PAIR
7
1.9
5
1.8
2.9
4
1.7
2.8
3.9
1400
1.6
2.7
3.8
4.9
3
1.5
2.6
3.7
4.8
5.9
2
1.4
2.5
3.6
4.7
5.8
6.9
Distance:
1
1.3
2.4
3.5
4.6
5.7
6.8
7.9
400
1.2
2.3
3.4
4.5
5.6
6.7
7.8
8.9
REACTION TIME (msec.)
Brannon & Terrace,
(unplublished)
2000
1800
1600
HUMAN
MONKEY
1200
1000
800
600
8
200
0
4000
MONKEY: 7 ARBITRARY ITEMS
HUMAN: 8 ARBITRARY ITEMS
MONKEY: 6 ARBITRARY ITEMS
3000
2500
2000
1500
1000
500
DISTANCE:
1
2
3
4
5
6
7
8
SUBSET
9
1.
-1
.8
.8
A
H
-2
4.
9
BH
.8
A
E1.
5
D
H
-4
.8
A
F1.
6
-5
.5
-2
EH
9
BE
7.
6
4.
.3
-1
D
F-
.8
A
C
5
H
-7
G
4.
D
E-
1.
2
0
A
B-
REACTION TIME (msec)
3500
4000
MONKEY: 7 ARBITRARY ITEMS
HUMAN: 8 ARBITRARY ITEMS
MONKEY: 6 ARBITRARY ITEMS
MONKEY: 9 NUMERICAL ITEMS
HUMAN: 9 NUMERICAL ITEMS
3000
2500
2000
1500
1000
500
DISTANCE:
1
2
3
4
5
6
7
8
SUBSET
9
1.
-1
.8
.8
A
H
-2
4.
9
BH
.8
A
E1.
5
D
H
-4
.8
A
F1.
6
-5
.5
-2
EH
9
BE
7.
6
4.
.3
-1
D
F-
.8
A
C
5
H
-7
G
4.
D
E-
1.
2
0
A
B-
REACTION TIME (msec)
3500
MAGNIT UDE EFFECTS: HUMAN AND MONKEY
4000
3500
2500
2000
Numerosity of Geometric
Patterns (Human)
1500
Random Dots (Human:
Buckley & Gillman, 1974)
1000
500
Numerical
REACTION TIME (msec)
3000
Arabic Numerals (Human:
Buckley & Gillman, 1974)
Arabic Numerals (Human:
Moyer & Landauer, 1976)
0
1
2
3
4
5
6
MAGNIT UDE
7
8
MAGNIT UDE EFFECTS: HUMAN AND MONKEY
4000
Arbitrary 6-item (Monkey:
Terrace, et al., 1966)
3500
Arbitrary 7-item (Monkey:
Terrace, Son & Brannon,
2003)
Arbitrary 8-item (Human:
Terrace & Jaswall, 1998)
2500
2000
1500
1000
500
Letters (Human)
(Hamilton & Sanford,
1978)
Numerosity of Geometric
Patterns (Human)
Numerical Arbitrary
REACTION TIME (msec)
3000
Random Dots (Human:
Buckley & Gillman, 1974)
Arabic Numerals (Human:
Buckley & Gillman, 1974)
Arabic Numerals (Human:
Moyer & Landauer, 1976)
0
1
2
3
4
5
6
MAGNIT UDE
7
8
DIST ANCE EFFECT S: HUMAN AND MONKEY
3000
2000
1500
1000
Geometric Patterns (Human)
(Brannon & Terrace, 2001)
Numerical
REACTION TIME (msec)
2500
Random Dots (Human)
(Buckley & Gillman,1974)
Arabic Numerals (Human)
(Buckley & Gillman, 1974)
500
Arabic Numerals (Human)
(Moyer & Landauer, 1976)
0
1
2
3
4
5
6
DIST ANCE
7
8
DISTANCE EFFECTS: HUMAN AND MONKEY
3000
Arbitrary 6-item (Monkey)
(Terrace, et al., 1966)
2000
1500
1000
Arbitrary 7-item (Monkey;
Terrace, Son & Brannon,
2003)
Arbitrary 8-item (Human)
(Terrace & Jaswall, 1998)
Numerical Arbitrary
REACTION TIME (msec)
2500
Letters (Human)(Hamilton &
Sanford,1978)
Geometric Patterns (Human)
(Brannon & Terrace, 2001)
Random Dots (Human)
(Buckley & Gillman,1974)
Arabic Numerals (Human)
(Buckley & Gillman, 1974)
500
Arabic Numerals (Human)
(Moyer & Landauer, 1976)
0
1
2
3
4
5
6
DISTANCE
7
8
Two-item subset
test
G3 
E1
A1  B1  C1  D1  E1  G1  F1
A3  B3  C3  D3  E3
F3
F2 
 G3 
C4
A2 B2  C2  D2  E2  G2  F2
A4  B4  C4  D4  E4
 G4  F4