distance & magnitude effects in rhesus macaques & college students in collaboration with:...
TRANSCRIPT
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
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
1.4
1.5
1.6
1.7
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)
B
B B
BB
B
B
B
1 2 3 4 5 6 7 8500
520
540
560
580
600
620
640
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
500
550
600
650
700
750
800
850
900
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
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
ACCURACY to 1st Item of Subset
40
50
60
70
80
90
100
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
70
80
90
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
2500
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
1500
1750
2000
2250
2500
2750
3000
1 2 3 4 5 6DISTANCE
REACTION TIME (msec)BETWEEN LISTS
WITHIN LISTS
MONKEYS (n=4)Trained on four 7-item arbitrary
Terrace, Son, Brannon, Psychological Science (2003)
Terrace, Son, Brannon, Psychological Science (2003)
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
REACTION TIME (msec)
WITHIN -LIST SUBSETS
MONKEYS N=4
DISTANCE:
1 2 3 4 5 6
Terrace, Son, Brannon, Psychological Science (2003)
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
REACTION TIME (msec)
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
RT to1ST ITEM OF SUBSET
2000
2100
2200
2300
2400
2500
2600
2700
2800
A B C D E F G
POSITION
REACTION TIME (msec)
RTs: Subsets from Human 8-Item Arbitrary Lists
2000
2250
2500
2750
1 2 3 4 5 6 7
DISTANCE
REACTION TIME (msec)
0
500
1000
1500
2000
2500
3000
3500
AB BC CD DE EF FG AC BD CE DF EG AD BE CF DG AE BF CG AF BG AG
SUBSET
REACTION TIME (msec)
MONKEY 7-ITEM
0
500
1000
1500
2000
2500
3000
3500
4000
AB BC CD DE EF FG AC BD CE DF EG AD BE CF DG AE BF CG AF BG AG
SUBSET
REACTION TIME (msec)
MONKEY 6-ITEM MONKEY 7-ITEM
0
500
1000
1500
2000
2500
3000
3500
4000
AB BC CD DE EF FG AC BD CE DF EG AD BE CF DG AE BF CG AF BG AG
SUBSET
REACTION TIME (msec)
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)
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
600
700
800
900
1000
1100
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
70
80
90
100
B MONKEY LESS (n=2)
J HUMAN LESS (n=11)
Brannon & Terrace, (unplublished)
0
200
400
600
800
1000
1200
1400
1600
1800
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.)
MONKEY
Distance: 1 2 3 4 5 6 7 8
Brannon & Terrace, (unplublished)
0
200
400
600
800
1000
1200
1400
1600
1800
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
Brannon & Terrace, (unplublished)
0
500
1000
1500
2000
2500
3000
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
REACTION TIME (msec)
MONKEY: 7 ARBITRARY ITEMS
HUMAN: 8 ARBITRARY ITEMS
MONKEY: 6 ARBITRARY ITEMS
DISTANCE: 1 2 3 4 5 6 7 8
0
500
1000
1500
2000
2500
3000
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
REACTION TIME (msec)
MONKEY: 7 ARBITRARY ITEMS
HUMAN: 8 ARBITRARY ITEMS
MONKEY: 6 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
500
1000
1500
2000
2500
3000
3500
4000
1 2 3 4 5 6 7 8MAGNITUDE
REACTION TIME (msec)
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
2000
2500
3000
3500
4000
1 2 3 4 5 6 7 8MAGNITUDE
REACTION TIME (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)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
2000
2500
3000
1 2 3 4 5 6 7 8DISTANCE
REACTION TIME (msec)
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
3000
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
500
1000
1500
2000
2500
3000
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