Numerical

Cognition

Without

Words

Evidence

from

Amazonia

Peter

Gordon

et

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AAAS

REPORTS

Numerical

Cognition

Without

Words

Evidence

from

Amazonia

Peter

Gordon

Members

of

the

Piraha

tribe

use

a

one-two-many

system

of

counting

I

ask

whether

speakers

of

this

innumerate

language

can

appreciate

larger

numerosities

without

the

benefit

of

words

to

encode

them

This

addresses

the

classic

Whorfian

question

about

whether

language

can

determine

thought

Results

of

numerical

tasks

with

varying

cognitive

demands

show

that

numerical

cognition

is

clearly

affected

by

the

lack

of

a

counting

system

in

the

language

Performance

with

quantities

greater

than

three

was

remarkably

poor

but

showed

a

constant

coefficient

of

variation

which

is

suggestive

of

an

analog

estimation

process

Is

it

possible

that

there

are

some

concepts

that

we

can

not

entertain

because

of

the

language

that

we

speak

At

issue

here

is

the

strongest

version

of

Benjamin

Lee

hypothesis

that

language

can

determine

the

nature

and

content

of

thought

The

strong

version

of

hypothesis

goes

beyond

the

weaker

claim

that

linguistic

structure

simply

influences

the

way

that

we

think

about

things

in

our

everyday

encounters

For

example

recent

studies

suggest

that

language

might

affect

how

people

mentally

encode

spatial

relations

-LRB-

-RRB-

and

how

they

conceive

of

the

nature

of

individual

objects

and

their

material

substances

-LRB-

-RRB-

However

of

these

studies

suggest

that

linguistic

structure

prevents

us

from

entertaining

the

concepts

that

are

available

to

speakers

of

alternative

linguistic

systems

The

question

of

whether

linguistic

determinism

exists

in

the

stronger

sense

has

two

parts

The

first

is

whether

languages

can

be

incommensurate

Are

there

terms

that

exist

in

one

language

that

can

not

be

translated

into

another

The

second

is

whether

the

lack

of

such

translation

precludes

the

speakers

of

one

language

from

entertaining

concepts

that

are

encoded

by

the

words

or

grammar

of

the

other

language

For

many

years

the

answer

to

both

questions

appeared

to

be

negative

Although

languages

might

have

different

ways

in

which

situations

are

habitually

described

it

has

generally

been

accepted

that

there

would

always

be

some

way

in

which

one

could

capture

the

equivalent

meaning

in

any

other

language

-LRB-

-RRB-

Of

course

when

speaking

of

translatable

concepts

we

do

not

mean

terms

like

Bmolecule

-LSB-

or

Bquark

-LSB-

which

would

not

exist

in

a

culture

without

advanced

scientific

institutions

Failure

to

know

what

molecules

or

quarks

are

does

not

signal

an

inability

to

understand

the

English

Department

of

Biobehavioral

Sciences

Columbia

University

West

Street

New

York

NY

USA

E-mail

pgordon@tc.columbia.edu

language

surely

people

were

still

speaking

English

before

such

terms

were

introduced

On

the

other

hand

one

would

question

command

of

English

if

they

did

not

understand

the

basic

vocabulary

and

grammar

Words

that

indicate

numerical

quantities

are

clearly

among

the

basic

vocabulary

of

a

language

like

English

But

not

all

languages

contain

fully

elaborated

counting

systems

Although

no

language

has

been

recorded

that

completely

lacks

number

words

there

is

a

considerable

range

of

counting

systems

that

exists

across

cultures

Some

cultures

use

a

finite

number

of

body

parts

to

count

or

body

tags

-LRB-

-RRB-

Many

cultures

use

particular

body

parts

like

fingers

as

a

recursive

base

for

the

count

system

as

in

our

system

Finally

there

are

cultures

that

base

their

counting

systems

on

a

small

number

between

and

Sometimes

the

use

of

a

smallnumber

base

is

recursive

and

potentially

infinite

For

example

it

is

claimed

that

the

Gumulgal

South

Sea

Islanders

counted

with

a

recursive

binary

system

and

so

on

-LRB-

-RRB-

The

counting

system

that

differs

perhaps

most

from

our

own

is

the

Bone-two-many

-LSB-

system

where

quantities

beyond

two

are

not

counted

but

are

simply

referred

to

as

Bmany

-LSB-

If

a

culture

is

limited

to

such

a

counting

system

is

it

possible

for

its

members

to

perceive

or

conceptualize

quantities

beyond

the

limited

sets

picked

out

by

the

counting

sequence

or

to

make

what

we

consider

to

be

quite

trivial

distinctions

such

as

that

between

four

versus

five

objects

The

Pirah

are

such

a

culture

They

live

along

the

banks

of

the

Maici

River

in

the

Lowland

Amazonia

region

of

Brazil

They

maintain

a

predominantly

hunter-gatherer

existence

and

reject

assimilation

into

mainstream

Brazilian

culture

Almost

completely

monolingual

in

their

own

language

they

have

a

population

of

less

than

living

in

small

villages

of

to

people

They

have

only

limited

exchanges

with

outsiders

using

SCIENCE

primitive

pidgin

systems

for

communicating

in

trading

goods

without

monetary

exchange

and

without

the

use

of

Portuguese

count

words

The

Pirah

counting

system

consists

of

the

words

BhFi

-LSB-

-LRB-

falling

tone

Bone

-LSB-

-RRB-

and

Bho

-LSB-

-LRB-

rising

tone

Btwo

-LSB-

-RRB-

Larger

quantities

are

designated

as

Bbaagi

-LSB-

or

Baibai

-LSB-

-LRB-

Bmany

-LSB-

-RRB-

I

was

able

to

take

three

field

trips

ranging

from

week

to

months

living

with

the

Pirah

along

with

Daniel

Everett

and

Keren

Everett

two

linguists

who

have

lived

and

worked

with

the

tribe

for

over

years

and

are

completely

familiar

with

their

language

and

cultural

practices

Observations

were

informed

by

their

background

of

continuous

and

extensive

immersion

in

the

Pirah

culture

During

my

visits

I

became

interested

in

the

counting

system

of

the

Pirah

that

I

had

heard

about

and

wanted

to

examine

whether

they

really

did

have

only

two

numbers

and

how

this

would

affect

their

ability

to

perceive

numerosities

that

extended

beyond

the

limited

count

sequence

Year

Initial

observations

On

my

first

week-long

trip

to

the

two

most

up-river

Maici

villages

I

began

with

informal

observations

of

the

Pirah

use

of

the

number

words

for

one

and

two

I

was

also

interested

in

the

possibility

that

the

one-two-many

system

might

actually

be

a

recursive

system

that

their

limited

number

words

might

be

supplemented

by

more

extensive

finger

counting

or

that

there

might

be

taboos

associated

with

counting

certain

kinds

of

objects

as

suggested

by

Zaslavsky

in

her

studies

of

African

counting

systems

-LRB-

-RRB-

Keren

Everett

developed

some

simple

tasks

to

see

if

our

two

Pirah

informants

could

refer

to

numerosities

of

arrays

of

objects

using

Pirah

terms

and

any

finger

counting

system

they

might

have

Instructions

and

interactions

with

participants

were

in

the

Pirah

language

When

it

was

necessary

to

refer

to

the

numerosity

of

an

array

Keren

Table

Use

of

fingers

and

number

words

by

Piraha

participant

The

arrow

-LRB-

Y

-RRB-

indicates

a

shift

from

one

quantity

to

the

next

No

of

objects

Number

word

used

hoi

-LRB-

-RRB-

hoi

-LRB-

-RRB-

aibaagi

-LRB-

many

-RRB-

hoi

-LRB-

-RRB-

hoi

-LRB-

-RRB-

aibai

-LRB-

many

-RRB-

aibaagi

-LRB-

many

-RRB-

aibaagi

-LRB-

many

-RRB-

hoi

-LRB-

-RRB-

aibaagi

-LRB-

many

-RRB-

No

of

fingers

Y

Y

aibaagi

-LRB-

many

-RRB-

Y

This

use

of

one

might

have

been

a

reference

to

adding

one

rather

than

to

the

whole

set

of

objects

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Everett

used

the

Portuguese

number

words

embedded

in

Pirah

dialogue

Such

terms

are

understood

by

the

Pirah

to

be

the

language

of

Brazilians

but

their

meaning

is

not

understood

In

addition

to

this

short

session

during

the

first

year

trip

I

continuously

took

opportunities

to

probe

for

counting

abilities

in

everyday

situations

The

outcome

of

these

informal

studies

revealed

the

following

-LRB-

i

-RRB-

There

was

no

recursive

use

of

the

count

system

the

Pirah

never

used

the

count

words

in

combinations

like

BhFi-ho

-LSB-

to

designate

larger

quantities

-LRB-

ii

-RRB-

Fingers

were

used

to

supplement

oral

enumeration

but

this

was

highly

inaccurate

even

for

small

numbers

less

than

five

In

addition

BhFi

-LSB-

and

Bho

-LSB-

the

words

for

Bone

-LSB-

and

Btwo

-LSB-

were

not

always

used

to

denote

those

quantities

Whereas

the

word

for

Btwo

-LSB-

always

denoted

a

larger

quantity

than

the

word

for

Bone

-LSB-

-LRB-

when

used

in

the

same

context

-RRB-

the

word

for

Bone

-LSB-

was

sometimes

used

to

denote

just

a

small

quantity

such

as

two

or

three

or

sometimes

more

An

example

of

the

use

of

counting

words

and

finger

counting

is

given

in

Table

in

one

of

the

informal

sessions

with

an

informant

who

appeared

to

be

in

his

Videotaped

extracts

from

the

session

are

included

in

the

supporting

online

materials

-LRB-

movie

-RRB-

The

interpretation

of

these

observations

is

limited

by

their

informal

nature

and

small

sample

size

However

the

observations

are

supplemented

with

years

of

observation

by

the

Everetts

as

trained

linguists

in

their

analysis

of

the

Pirah

language

One

particularly

interesting

finding

is

that

BhFi

-LSB-

appears

to

designate

Broughly

one

-LSB-

or

a

small

quantity

whose

prototype

is

one

Most

of

the

time

in

the

enumeration

task

BhFi

-LSB-

referred

to

one

but

not

always

An

analogy

might

be

when

we

ask

for

Ba

couple

of

Xs

-LSB-

in

English

where

the

prototypical

quantity

is

two

but

we

are

not

upset

if

we

are

given

three

or

four

objects

However

we

surely

would

be

upset

if

given

only

one

object

because

the

designation

of

a

single

object

has

a

privileged

status

in

our

language

There

is

no

concept

of

Broughly

one

-LSB-

in

a

true

integer

system

Even

the

informal

use

of

the

indefinite

article

Ba

X

-LSB-

strictly

requires

a

singular

reference

In

Pirah

BhFi

-LSB-

can

also

mean

Bsmall

-LSB-

which

contrasts

with

Bogii

-LSB-

-LRB-

big

-RRB-

suggesting

that

the

distinction

between

discrete

and

continuous

quantification

is

quite

fuzzy

in

the

Pirah

language

Year

Experiments

in

nonverbal

numerical

reasoning

On

my

second

visit

to

the

Pirah

villages

for

a

period

I

developed

a

more

systematic

set

of

procedures

for

evaluating

the

numerical

competence

of

members

of

the

tribe

The

experiments

were

designed

to

require

some

combination

of

cognitive

skills

such

as

the

need

for

memory

speed

of

encoding

and

mental-spatial

transformations

This

would

reveal

the

extent

to

which

such

task

demands

interact

with

numerical

ability

such

as

it

is

Details

of

the

methods

are

available

on

Science

Online

-LRB-

-RRB-

There

were

seven

participants

who

included

all

six

adult

males

from

two

villages

and

one

female

Most

of

the

data

were

collected

on

four

of

the

men

who

were

consistently

available

for

participation

The

tasks

were

devised

to

use

objects

that

were

available

and

familiar

to

the

participants

-LRB-

sticks

nuts

and

batteries

-RRB-

The

results

of

the

tasks

along

with

schematic

diagrams

are

presented

in

Fig.

These

are

roughly

ordered

in

terms

of

increasing

cognitive

demand

Any

estimation

of

a

numerical

competence

will

always

be

confounded

with

performance

factors

of

the

task

Because

this

is

unavoidable

it

makes

sense

to

explore

how

performance

is

affected

by

a

range

of

increasingly

demanding

tasks

In

the

matching

tasks

-LRB-

A

B

C

D

and

F

-RRB-

I

sat

across

from

the

participant

and

with

a

stick

dividing

my

side

from

theirs

I

presented

an

array

of

objects

on

my

side

of

the

stick

-LRB-

below

the

line

in

the

figures

-RRB-

and

they

responded

by

placing

a

linear

array

of

AA

batteries

-LRB-

cm

by

cm

-RRB-

on

their

side

of

the

table

-LRB-

above

the

line

-RRB-

The

matching

task

provides

a

kind

of

concrete

substitute

for

counting

It

shares

the

element

A

Line

Match

Prop

Correct

B

Cluster

Line

Match

Prop

Correct

C

Orthogonal

Line

Match

Prop

Correct

Target

Target

Target

D

Uneven

Line

Match

Prop

Correct

E

Line

Draw

Copy

Prop

Correct

F

Brief

Presentation

Prop

Correct

Target

Target

Target

G

Nuts-in-Can

Task

P

ro

p

C

o

r

r

e

c

t

H

Candy-in-Box

Task

Prop

Correct

Target

Target

Fig.

Results

of

number

tasks

with

Piraha

villagers

-LRB-

n

-RRB-

Rectangles

indicate

AA

batteries

-LRB-

cm

by

cm

-RRB-

and

circles

indicate

ground

nuts

Center

line

indicates

a

stick

between

the

author

's

example

array

-LRB-

below

the

line

-RRB-

and

the

participant

's

attempt

to

make

it

the

same

-LRB-

above

the

line

-RRB-

Tasks

A

through

D

required

the

participant

to

match

the

lower

array

presented

by

the

author

using

a

line

of

batteries

task

E

was

similar

but

involved

the

unfamiliar

task

of

copying

lines

drawn

on

paper

task

F

was

a

matching

task

where

the

participant

saw

the

numerical

display

for

only

about

s

before

it

was

hidden

behind

a

screen

task

G

involved

putting

nuts

into

a

can

and

withdrawing

them

one

by

one

-LRB-

participants

responded

after

each

withdrawal

as

to

whether

the

can

still

contained

nuts

or

was

empty

-RRB-

task

H

involved

placing

candy

inside

a

box

with

a

number

of

fish

drawn

on

the

lid

-LRB-

this

was

then

hidden

and

brought

out

again

with

another

box

with

one

more

or

one

less

fish

on

the

lid

and

participants

had

to

choose

which

box

contained

the

candy

-RRB-

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of

placing

tokens

in

one-to-one

correspondence

with

individuals

in

a

to-be-counted

group

The

first

matching

tasks

began

with

simple

linear

arrays

of

batteries

This

progressed

to

clusters

of

nuts

matched

to

the

battery

line

orthogonal

matching

of

battery

lines

matching

of

battery

lines

that

were

unevenly

spaced

and

copying

lines

on

a

drawing

In

all

of

these

matching

experiments

participants

responded

with

relatively

good

accuracy

with

up

to

or

items

but

performance

deteriorated

considerably

beyond

that

up

to

to

items

In

the

first

simple

linear

matching

task

A

performance

hovered

around

up

to

the

largest

quantities

Matching

tasks

with

greater

cognitive

demands

required

mental

transposition

of

the

sample

array

to

the

match

array

without

benefit

of

tagging

for

numerical

quantity

Performance

dropped

precipitously

to

for

the

larger

target

set

sizes

in

these

tasks

One

exception

was

task

D

with

unevenly

spaced

objects

Although

this

was

designed

to

be

a

difficult

task

participants

showed

an

anomalous

superiority

for

large

numerosities

over

small

Performance

initially

deteriorated

with

increased

set

size

up

to

items

then

shot

up

to

near

perfect

performance

for

set

size

through

A

likely

interpretation

of

this

result

was

that

the

uneven

spacing

for

larger

set

sizes

promoted

recoding

of

arrays

into

smaller

configurations

of

two

or

three

items

This

allowed

participants

to

use

a

chunking

strategy

of

treating

each

of

the

subgroups

as

a

matching

group

When

time

constraints

were

introduced

in

task

F

-LRB-

exposing

the

array

for

only

s

-RRB-

performance

was

drastically

affected

and

there

was

a

clear

correlation

between

set

size

and

accuracy

beginning

at

set

size

A

line-drawing

task

-LRB-

E

-RRB-

was

highly

affected

by

set

size

being

one

of

the

worst

performances

of

all

Not

only

do

the

Pirah

not

count

but

they

also

do

not

draw

Producing

simple

straight

lines

was

accomplished

only

with

great

effort

and

concentration

accompanied

by

heavy

sighs

and

groans

The

final

two

tasks

-LRB-

G

and

H

-RRB-

required

participants

to

keep

track

of

a

numerical

quantity

through

visual

displacement

In

one

case

they

were

first

allowed

to

inspect

an

array

of

nuts

for

about

s

The

nuts

were

placed

in

a

can

and

then

withdrawn

one

at

a

time

Participants

were

required

to

say

after

each

withdrawal

if

there

were

still

any

nuts

left

in

the

can

or

if

it

was

empty

Performance

was

predictably

strongly

affected

by

set

size

from

the

very

smallest

quantities

The

final

task

involved

hiding

candy

in

a

box

which

had

a

picture

of

some

number

of

fish

on

the

lid

The

box

was

then

hidden

behind

the

back

and

two

cases

were

revealed

the

original

with

the

candy

and

another

with

one

more

or

one

less

fish

on

the

lid

For

quite

small

comparisons

such

as

three

versus

four

performance

rarely

went

over

chance

responding

There

is

a

growing

consensus

in

the

field

of

numerical

cognition

that

primitive

numerical

abilities

are

of

two

kinds

First

there

is

the

ability

to

enumerate

accurately

small

quantities

up

to

about

three

items

with

only

minimal

processing

requirements

-LRB-

-RRB-

I

originally

termed

this

ability

Bparallel

individuation

-LSB-

-LRB-

-RRB-

referring

to

how

many

items

one

can

encode

as

discrete

unique

individuals

at

the

same

time

in

memory

Without

overt

counting

humans

and

other

animals

possess

an

analog

procedure

whereby

numerical

quantities

can

be

estimated

with

a

limited

degree

of

accuracy

-LRB-

-RRB-

Many

researchers

believe

that

large-number

estimation

although

based

on

individuated

elements

is

coalesced

into

a

continuous

analog

format

for

mental

representation

For

example

the

discrete

elements

of

a

large

number

array

might

be

represented

as

a

continuous

length

of

a

line

where

a

longer

line

inexactly

represents

a

larger

numerosity

When

people

use

this

analog

estimation

procedure

the

variability

of

their

estimates

tends

to

increase

as

the

target

set

size

increases

The

ratio

of

average

error

to

target

set

size

is

known

as

fraction

and

can

be

indexed

by

a

measure

known

as

the

coefficient

of

variation

the

standard

deviation

of

the

estimates

divided

by

set

size

-LRB-

-RRB-

Although

performance

by

the

Pirah

on

the

present

tasks

was

quite

poor

for

set

sizes

above

two

or

three

it

was

not

random

Figure

shows

the

mean

response

values

mapped

against

the

target

values

for

all

participants

in

the

simple

matching

tasks

A

SCIENCE

B

C

and

F

The

top

graph

shows

that

mean

responses

and

target

values

are

almost

identical

This

means

that

the

Pirah

participants

were

trying

hard

to

get

the

answers

correct

and

they

clearly

understood

the

tasks

The

lower

graph

in

Fig.

shows

that

the

standard

deviation

of

the

estimates

increases

in

proportion

to

the

set

size

resulting

in

a

constant

coefficient

of

variation

of

about

after

set

size

three

as

predicted

by

the

dual

model

of

mental

enumeration

This

value

for

the

coefficient

of

variation

is

about

the

same

as

one

finds

in

college

students

engaged

in

numerical

estimation

tasks

-LRB-

-RRB-

Data

for

individual

tasks

and

individual

participants

were

consistent

with

the

averaged

trends

shown

in

Fig.

Graphs

are

available

in

the

supporting

online

materials

-LRB-

figs

and

-RRB-

The

results

of

these

studies

show

that

the

Pirah

s

impoverished

counting

system

limits

their

ability

to

enumerate

exact

quantities

when

set

sizes

exceed

two

or

three

items

For

tasks

that

required

additional

cognitive

processing

performance

deteriorated

even

on

set

sizes

smaller

than

three

Participants

showed

evidence

of

using

analog

magnitude

estimation

and

in

some

cases

they

took

advantage

of

spatial

chunking

to

decrease

the

cognitive

demands

of

larger

set

sizes

This

split

between

exact

enumeration

ability

for

set

sizes

smaller

than

three

and

analog

estimation

for

larger

set

sizes

parallels

findings

from

laboratory

experiments

with

adults

who

are

prevented

from

explicit

counting

studies

of

numerical

abilities

in

prelinguistic

infants

monkeys

birds

and

rodents

and

in

recent

studies

using

brainimaging

techniques

-LRB-

-RRB-

The

analog

estimation

abilities

exhibited

by

the

Pirah

are

a

kind

of

numerical

competence

that

appears

to

be

immune

to

numerical

language

deprivation

But

because

lower

animals

also

exhibit

such

abilities

robustness

in

the

absence

of

language

is

already

established

The

present

experiments

allow

us

to

ask

whether

humans

who

are

not

exposed

to

a

number

system

can

represent

exact

quantities

for

medium-sized

sets

of

four

or

five

The

answer

appears

to

be

negative

The

Pirah

inherit

just

the

abilities

to

exactly

enumerate

small

sets

of

less

than

three

items

if

processing

factors

are

not

unduly

taxing

-LRB-

-RRB-

In

evaluating

the

case

for

linguistic

determinism

I

suggest

that

the

Pirah

language

is

incommensurate

with

languages

that

have

counting

systems

that

enable

exact

enumeration

Of

particular

interest

is

the

fact

that

the

Pirah

have

no

privileged

name

for

the

singular

quantity

Instead

BhFi

-LSB-

meant

Broughly

one

-LSB-

or

Bsmall

-LSB-

which

precludes

any

precise

translation

of

exact

numerical

terms

The

present

study

represents

a

rare

and

perhaps

unique

case

for

strong

linguistic

determinism

The

A

Mean

SD

Target

CV

Mean

B

Target

Fig.

-LRB-

A

-RRB-

Mean

accuracy

and

standard

deviation

of

responses

in

matching

tasks

and

-LRB-

B

-RRB-

coefficient

of

variation

Figures

for

individual

tasks

and

individual

participants

are

available

in

the

supporting

online

materials

OCTOBER

VOL

Downloaded

from

on

May

SD

REPORTS

study

also

provides

a

window

into

how

the

possibly

innate

distinction

-LRB-

-RRB-

between

quantifying

small

versus

large

sets

of

objects

is

relatively

unelaborated

in

a

life

without

number

words

to

capture

those

exact

magnitudes

-LRB-

-RRB-

References

and

Notes

S.

C.

Levinson

J.

Linguist

Anthropol

-LRB-

-RRB-

P.

Li

L.

Gleitman

Cognition

-LRB-

-RRB-

S.

C.

Levinson

S.

Kita

D.

B.

M.

Haun

B.

H.

Rasch

Cognition

-LRB-

-RRB-

J.

A.

Lucy

Grammatical

Categories

and

Cognition

-LRB-

Cambridge

Univ.

Press

Cambridge

-RRB-

R.

W.

Brown

E.

H.

Lenneberg

J.

Abnorm

Soc

Psychol

-LRB-

-RRB-

K.

Menninger

Number

Words

and

Number

Symbols

A

Cultural

History

of

Numbers

-LRB-

MIT

Press

Cambridge

MA

-RRB-

C.

Zaslavsky

Africa

Counts

Number

and

Pattern

in

African

Culture

-LRB-

Prindle

Weber

and

Schmidt

Boston

-RRB-

R.

Gelman

C.

R.

Gallistel

The

Child

's

Understanding

of

Number

-LRB-

Harvard

Univ.

Press

Cambridge

MA

-RRB-

Materials

and

methods

are

available

as

supporting

material

on

Science

Online

S.

Carey

Mind

Lang

-LRB-

-RRB-

L.

Feigenson

S.

Carey

M.

Hauser

Psychol

Sci

-LRB-

-RRB-

B.

J.

Scholl

Cognition

-LRB-

-RRB-

T.

J.

Simon

Cognit

Dev

-LRB-

-RRB-

L.

Trick

Z.

W.

Pylyshyn

Psychol

Rev.

-LRB-

-RRB-

C.

Uller

G.

Huntley-Fenner

S.

Carey

L.

Klatt

Cognit

Dev

-LRB-

-RRB-

F.

Xu

Cognition

-LRB-

-RRB-

P.

Gordon

paper

presented

at

the

biennial

meeting

of

the

Society

for

Research

in

Child

Development

New

Orleans

LA

to

March

P.

Gordon

paper

presented

at

the

European

Society

for

Philosophy

and

Psychology

Paris

France

to

September

W.

H.

Meck

R.

M.

Church

J.

Exp

Psychol

Anim

Behav

Processes

-LRB-

-RRB-

H.

Barth

N.

Kanwisher

E.

Spelke

Cognition

-LRB-

-RRB-

S.

Cordes

R.

Gelman

C.

R.

Gallistel

J.

Whalen

Psychon

Bull

Rev.

-LRB-

-RRB-

C.

R.

Gallistel

The

Organization

of

Learning

-LRB-

MIT

Press

Cambridge

MA

-RRB-

J.

Whalen

C.

R.

Gallistel

R.

Gelman

Psychol

Sci

-LRB-

-RRB-

S.

Cordes

R.

Gelman

C.

R.

Gallistel

J.

Whalen

Psychon

Bull

Rev.

-LRB-

-RRB-

S.

Dehaene

The

Number

Sense

-LRB-

Oxford

Univ.

Press

New

York

-RRB-

B.

Butterworth

What

Counts

-LRB-

Simon

Schuster

New

York

-RRB-

J.

S.

Lipton

E.

S.

Spelke

Psychol

Sci

-LRB-

-RRB-

M.

D.

Hauser

F.

Tsao

P.

Garcia

E.

S.

Spelke

Proc

R.

Soc

London

B

-LRB-

-RRB-

S.

Dehaene

E.

Spelke

P.

Pinel

R.

Stanescu

S.

Tsivkin

Science

-LRB-

-RRB-

J.

R.

Platt

D.

M.

Johnson

Learn

Motiv

-LRB-

-RRB-

Cordes

et

al.

-LRB-

-RRB-

suggest

that

analog

representations

exist

even

for

n

because

subjects

made

errors

on

a

task

in

which

counting

was

suppressed

during

rapid

button

pressing

However

errors

in

this

range

also

occurred

when

subjects

counted

and

might

have

been

the

result

of

perseveration

errors

rather

than

reflecting

numerical

representations

One

can

safely

rule

out

that

the

Piraha

are

mentally

retarded

Their

hunting

spatial

categorization

and

linguistic

skills

are

remarkable

and

they

show

no

clinical

signs

of

retardation

I

thank

D.

Everett

and

K.

Everett

for

making

this

research

possible

SIL

in

Porto

Velho

and

E.

Ramos

for

logistical

support

and

S.

Carey

L.

Feigenson

D.

Everett

C.

Tamis-LeMonda

M.

Miozzo

G.

Marcus

F.

Xu

and

K.

Adolph

for

comments

on

the

paper

Supporting

Online

Material

Methods

SOM

Text

Figs

to

Movies

and

References

December

accepted

July

Published

online

August

science

Include

this

information

when

citing

this

paper

Exact

and

Approximate

Arithmetic

in

an

Amazonian

Indigene

Group

Pierre

Pica

Cathy

Lemer

Veronique

Izard

Stanislas

Is

calculation

possible

without

language

Or

is

the

human

ability

for

arithmetic

dependent

on

the

language

faculty

To

clarify

the

relation

between

language

and

arithmetic

we

studied

numerical

cognition

in

speakers

of

Munduruku

an

Amazonian

language

with

a

very

small

lexicon

of

number

words

Although

the

Munduruku

lack

words

for

numbers

beyond

they

are

able

to

compare

and

add

large

approximate

numbers

that

are

far

beyond

their

naming

range

However

they

fail

in

exact

arithmetic

with

numbers

larger

than

or

Our

results

imply

a

distinction

between

a

nonverbal

system

of

number

approximation

and

a

language-based

counting

system

for

exact

number

and

arithmetic

All

science

requires

mathematics

The

knowledge

of

mathematical

things

is

almost

innate

in

usI

This

is

the

easiest

of

sciences

a

fact

which

is

obvious

in

that

no

brain

rejects

it

for

laymen

and

people

who

are

utterly

illiterate

know

how

to

count

and

reckon

Roger

Bacon

-LRB-

-RRB-

English

philosopher

and

scientist

Unite

Mixte

de

Recherche

Formal

Structures

of

Language

CNRS

and

Paris

VIII

University

Paris

France

INSERM

Cognitive

Neuroimag

ing

Service

Hospitalier

Frederic

Joliot

CEA/DSV

Orsay

Cedex

France

To

whom

correspondence

should

be

addressed

E-mail

dehaene@shfj.cea.fr

Where

does

arithmetic

come

from

For

some

theorists

the

origins

of

human

competence

in

arithmetic

lie

in

the

recursive

character

of

the

language

faculty

-LRB-

-RRB-

Chomsky

for

instance

stated

that

Bwe

might

think

of

the

human

number

faculty

as

essentially

an

Fabstraction

from

human

language

preserving

the

mechanisms

of

discrete

infinity

and

eliminating

the

other

special

features

of

language

-LSB-

-LRB-

-RRB-

Other

theorists

believe

that

language

is

not

essential

that

humans

like

many

animals

have

a

nonverbal

Bnumber

sense

-LSB-

-LRB-

-RRB-

an

evolutionarily

ancient

capacity

to

process

approximate

numbers

without

symbols

or

language

-LRB-

-RRB-

that

provides

the

conceptual

foundation

of

arithmetic

A

third

class

of

theories

while

acknowledging

the

existence

of

nonverbal

representations

of

numbers

postulates

that

arithmetic

competence

is

SCIENCE

VOL

deeply

transformed

once

children

acquire

a

system

of

number

symbols

-LRB-

-RRB-

Language

would

play

an

essential

role

in

linking

up

the

various

nonverbal

representations

to

create

a

concept

of

large

exact

number

-LRB-

-RRB-

To

elucidate

the

relations

between

language

and

arithmetic

it

is

necessary

to

study

numerical

competence

in

situations

in

which

the

language

of

numbers

is

either

absent

or

reduced

In

many

animal

species

as

well

as

in

young

infants

before

they

acquire

number

words

behavioral

and

neurophysiological

experiments

have

revealed

the

rudiments

of

arithmetic

-LRB-

-RRB-

Infants

and

animals

appear

to

represent

only

the

first

three

numbers

exactly

Beyond

this

range

they

can

approximate

Bnumerosity

-LSB-

with

a

fuzziness

that

increases

linearly

with

the

size

of

the

numbers

involved

-LRB-

law

-RRB-

This

finding

and

the

results

of

other

neuroimaging

and

neuropsychological

experiments

have

yielded

a

tentative

reconciliation

of

the

above

theories

Exact

arithmetic

would

require

language

whereas

approximation

would

not

-LRB-

-RRB-

This

conclusion

however

has

been

challenged

by

a

few

case

studies

of

adult

brainlesioned

or

autistic

patients

in

whom

language

dysfunction

did

not

abolish

exact

arithmetic

such

a

finding

suggests

that

in

some

rare

cases

even

complex

calculation

may

be

performed

without

words

-LRB-

-RRB-

In

the

final

analysis

the

debate

can

not

be

settled

by

studying

people

who

are

raised

in

a

culture

teeming

with

spoken

and

written

symbols

for

numbers

What

is

needed

is

a

language

deprivation

experiment

in

which

neurologically

normal

adults

would

be

raised

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O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O B O O O O O O B O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O B O O O O O O B O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O

cpprosem2
sapir whorf hypothesis
sapir whorf


Vol 441 | 15 June 2006 | doi : 10.1038 / nature04766 LETTERS Cortical substrates for exploratory decisions in humans Nathaniel D. Daw1 * , John P. O'Doherty2 * , Peter Dayan1 , Ben Seymour2 & Raymond J. Dolan2 Decision making in an uncertain environment poses a conflict between the opposing demands of gathering and exploiting information . In a classic illustration of this ` exploration exploitation ' dilemma1 , a gambler choosing between multiple slot machines balances the desire to select what seems , on the basis of accumulated experience , the richest option , against the desire to choose a less familiar option that might turn out more advantageous -LRB- and thereby provide information for improving future decisions -RRB- . Far from representing idle curiosity , such exploration is often critical for organisms to discover how best to harvest resources such as food and water . In appetitive choice , substantial experimental evidence , underpinned by computational reinforcement learning2 -LRB- RL -RRB- theory , indicates that a dopaminergic3 ,4 , striatal5 9 and medial prefrontal network mediates learning to exploit . In contrast , although exploration has been well studied from both theoretical1 and ethological10 perspectives , its neural substrates are much less clear . Here we show , in a gambling task , that human subjects ' choices can be characterized by a computationally well-regarded strategy for addressing the explore/exploit dilemma . Furthermore , using this characterization to classify decisions as exploratory or exploitative , we employ functional magnetic resonance imaging to show that the frontopolar cortex and intraparietal sulcus are preferentially active during exploratory decisions . In contrast , regions of striatum and ventromedial prefrontal cortex exhibit activity characteristic of an involvement in value-based exploitative decision making . The results suggest a model of action selection under uncertainty that involves switching between exploratory and exploitative behavioural modes , and provide a computationally precise characterization of the contribution of key decision-related brain systems to each of these functions . Exploration is a computationally refined capacity , demanding careful regulation . Two possibilities for this regulation arise . On the one hand , we might expect the involvement of cognitive , prefrontal control systems11 that can supervene12 over simpler dopaminergic/striatal habitual mechanisms . On the other hand , theoretical work on optimal exploration1 ,13 indicates a more unified architecture , according to which actions can be assessed with the use of a metric that integrates both primary reward and the informational value of exploration , even in simple , habitual decision systems . We studied patterns of behaviour and brain activity in 14 healthy subjects while they performed a ` four-armed bandit ' task involving repeated choices between four slot machines -LRB- Fig. 1 ; see Supplementary Methods -RRB- . The slots paid off points -LRB- to be exchanged for money -RRB- noisily around four different means . Unlike standard slots , the mean payoffs changed randomly and independently from trial to trial , with subjects finding information about the current worth of a slot only through sampling it actively . This feature of the experimental design , together with a model-based analysis , allowed us to study exploratory and exploitative decisions under uniform conditions , in the context of a single task . We asked subjects in post-task interviews to describe their choice strategies . The majority -LRB- 11 of 14 -RRB- reported occasionally trying the different slots to work out which currently had the highest payoffs -LRB- exploring -RRB- while at other times choosing the slot they thought had the highest payoffs -LRB- exploiting -RRB- . To investigate this behaviour quantitatively , we considered RL -LRB- ref . 2 -RRB- strategies for exploration . These strategies come in three flavours , differing in how exploratory actions are directed . The simplest method , known as ` 1-greedy ' , is undirected : it chooses the ` greedy ' option -LRB- the one believed to be best -RRB- most of the time , but occasionally -LRB- with probability 1 -RRB- substitutes a random action . A more sophisticated approach is to guide exploration by expected value , as in the ` softmax ' rule . With softmax , the decision to explore and the choice of which suboptimal action to take are determined probabilistically on the basis of the actions ' relative expected values . Last , exploration can additionally be directed by awarding bonuses in this latter decision towards actions whose consequences are uncertain : specifically , to those for which exploration will be most informative . The optimal strategy for a restricted class of simple bandit tasks has this characteristic1 , as do standard heuristics14 for exploration in more complicated RL tasks such as ours , for which the optimal solution is computationally intractable . We compared the fit of three distinct RL models , embodying the aforementioned strategies , to our subjects ' behavioural choices . All the models learned the values of actions with the use of a Kalman filter -LRB- see Supplementary Methods -RRB- , an error-driven prediction algorithm that generalizes the temporal-difference learning algorithm -LRB- used in most RL theories of dopamine -RRB- by also tracking uncertainty about the value of each action . The models differed only in their choice rules . We compared models by using the likelihood of the subjects ' choices given their experience , optimized over free parameters . This comparison -LRB- Supplementary Tables 1 and 2 -RRB- revealed strong evidence for value-sensitive -LRB- softmax -RRB- over undirected -LRB- 1-greedy -RRB- exploration . There was no evidence to justify the introduction of an extra parameter that allowed exploration to be directed towards uncertainty -LRB- softmax with an uncertainty bonus -RRB- : at optimal fit , the bonus was negligible , making the model equivalent to the simpler softmax . We conducted additional model fits -LRB- see Supplementary Information -RRB- to verify that these findings were not an artefact of our assumptions about the yoking of free parameters between subjects . Having characterized subjects ' behaviour computationally , we used the best-fitting softmax model to generate regressors containing value predictions , prediction errors and choice probabilities for each subject on each trial . We used statistical parametric mapping to 1 Gatsby Computational Neuroscience Unit , University College London -LRB- UCL -RRB- , Alexandra House , 17 Queen Square , London WC1N 3AR , UK . 2Wellcome Department of Imaging Neuroscience , UCL , 12 Queen Square , London WC1N 3BG , UK . Present address : Division of Humanities and Social Sciences , California Institute of Technology , 1200 East California Boulevard , Pasadena , California 91125 , USA . * These authors contributed equally to this work . 876 2006 Nature Publishing Group NATURE | Vol 441 | 15 June 2006 LETTERS Figure 1 | Task design . a , Illustration of the timeline within a trial . Initially , four slots are presented . The subject chooses one , which then spins . Three seconds later the number of points won is revealed . After a further second the screen is cleared . The next trial is triggered after a fixed trial length of 6 s and an additional variable inter-trial interval -LRB- mean 2 s -RRB- . b , Example of mean payoffs that would be received for choosing each slot machine -LRB- four coloured lines -RRB- on each trial , demonstrating their independent random diffusion . The payoff received for a particular choice is corrupted by gaussian noise around this mean . identify brain regions in which neural activity was significantly correlated with the model 's internal signals . Consistent with previous studies7 9 was our observation that a prediction error was correlated significantly with activity in both the ventral and dorsal striatum -LRB- see Supplementary Table 3 -RRB- . Other , cortical , structures linked to this subcortical network15 also showed significant value-related correlations . Specifically , we found activity in medial orbitofrontal cortex to be correlated with the magnitude of the obtained payoff -LRB- Fig. 2a -RRB- , a Figure 2 | Reward-related activations . Activation maps -LRB- yellow , P , 0.001 ; red , P , 0.01 to illustrate the full extent of the activations -RRB- are superimposed on a subject-averaged structural scan . a , Region of medial orbitofrontal cortex -LRB- mOFC -RRB- correlating significantly with the number of points received . The coordinates of the activated area are -LSB- 3,30,221 , peak z 3.87 -RSB- . The bar plot shows the average BOLD response to outcome , binned by amount won -LRB- error bars represent s.e.m. -RRB- . b , Regions of ventromedial prefrontal cortex -LRB- vmPFC ; including medial and lateral orbitofrontal cortex and adjacent medial prefrontal cortex -RRB- correlating significantly with the probability assigned by the computational model to the subject 's choice of slot . The coordinates of the activated areas are as follows : medial orbitofrontal , -LSB- 23,45,218 , peak z 5.62 -RSB- ; lateral orbitofrontal -LRB- not illustrated -RRB- , -LSB- 45,36,215 , peak z 4.6 -RSB- ; medial prefrontal , -LSB- 23,33,26 , peak z 4.62 -RSB- . The bar plot shows the average medial prefrontal BOLD response to decision , binned by choice probability -LRB- error bars represent s.e.m. -RRB- . 877 2006 Nature Publishing Group LETTERS NATURE | Vol 441 | 15 June 2006 Figure 3 | Exploration-related activity in frontopolar cortex . a , Regions of left and right frontopolar cortex -LRB- lFP , rFP -RRB- showing significantly increased activation on exploratory compared with exploitative trials . Activation maps -LRB- yellow , P , 0.001 ; red , P , 0.01 -RRB- are superimposed on a subject-averaged structural scan . The coordinates of activated areas are -LSB- 227,48,4 , peak z 3.49 -RSB- for lFP and -LSB- 27,57,6 , peak z 4.13 -RSB- for rFP . b , rFP BOLD time courses averaged over 1,515 exploratory -LRB- red line -RRB- and 2,646 exploitative -LRB- blue line -RRB- decisions . Black dots indicate the sampling frequency -LRB- although , because sample alignment varied from trial to trial , time courses were upsampled -RRB- . Coloured fringes show error bars -LRB- representing s.e.m. -RRB- . finding consistent with previous evidence indicating that this region is involved in coding the relative value of different reward stimuli , including abstract rewards16 ,17 . Furthermore , activity in medial and lateral orbitofrontal cortex , extending into ventro-medial prefrontal cortex , was correlated with the probability assigned by the model to the action actually chosen on a given trial -LRB- Fig. 2b -RRB- . In the softmax model , this probability is a relative measure of the expected reward value of the chosen action , and the observed profile of activity is thus consistent with a role for orbital and adjacent medial prefrontal cortex in encoding predictions of future reward18 ,19 . The same quantity was negatively correlated with activity in a small area of dorsolateral prefrontal cortex -LRB- left : 239,36,42 , peak z 3.38 ; right : 36,33,33 , peak z 3.27 -RRB- ; that is , higher activity was seen there for lower-probability choices . We next sought to identify brain activity that selectively reflected whether actions were chosen for their exploratory or exploitative potential . To test for such a signature , we classified trials according to whether the actual choice was the one predicted by the model to be the dominant slot machine with the highest expected value -LRB- exploitative -RRB- or a dominated machine with a lower expected value -LRB- exploratory -RRB- . We then directly compared the pattern of brain activity associated with these exploratory and exploitative trials . We found no area that exhibited significantly higher activity for exploitative than exploratory decisions -LRB- employing whole-brain correction for multiple comparisons -RRB- . However , the opposite contrast revealed several activations . First , right anterior frontopolar cortex -LRB- Fig. 3a -RRB- was significantly more active during decisions classified as exploratory -LRB- P , 0.05 , corrected whole-brain for multiple comparisons with false discovery rate ; activation was noted bilaterally at P , 0.001 uncorrected but did not survive whole-brain correction on the left -RRB- . Average blood-oxygenation-level-dependent -LRB- BOLD -RRB- signal time courses from the region -LRB- Fig. 3b -RRB- demonstrated phasic increases and decreases in activity that were time-locked to subjects ' exploratory and exploitative decisions , respectively . Because the prefrontal cortex is the principal cortical region implicated in behavioural control20 , the signal we observed in anterior frontopolar cortex could reflect a control mechanism facilitating the switching of behavioural strategies between exploratory and exploitative modes . This most rostral of prefrontal regions is known to be associated with high-level control21 . This region sits atop a proposed hierarchy of nested prefrontal controllers22 and is implicated in mediating between different goals , subgoals23 or cognitive processes21 . Differential activation during exploratory trials was also observed bilaterally in anterior intraparietal sulcus -LRB- whole-brain corrected at P , 0.05 ; Fig. 4 -RRB- , bordering on the postcentral gyrus . The sulcus has repeatedly been implicated in decision making in both humans15 ,19 and primates24 26 , with different subregions being associated with different output modalities . In lateral intraparietal area LIP , associated with saccades , neurons also carry information about decision variables such as the reward expected for a saccade24 26 ; the area perhaps serves as an interface between frontal areas -LRB- where such information may be calculated -RRB- and motor output . The anterior border of the sulcus , close to our exploration-related activation , is associated with grasping and manual manipulation27 , raising the possibility that such information -LRB- here , that associated with exploration -RRB- might also reach parietal regions involved in the button-press actions in our task . Last , we used a multiple regression analysis to verify that differential activity in frontopolar and intraparietal regions during exploratory trials was not better explained by any of several potentially confounding factors such as switching between options or reaction times -LRB- see Supplementary Information and Supplementary Tables 4 and 5 -RRB- . Figure 4 | Exploration-related activity in intraparietal sulcus . a , Regions of left and right intraparietal sulcus -LRB- lIPS and rIPS -RRB- showing significantly increased activation on exploratory compared with exploitative trials . Activation maps -LRB- yellow , P , 0.001 ; red , P , 0.01 -RRB- are superimposed on a subject-averaged structural scan . The coordinates of the activated areas are -LSB- 229,233,45 , peak z 4.39 -RSB- for lIPS and -LSB- 39,236,42 , peak z 4.16 -RSB- for 878 rIPS . b , lIPS BOLD time courses averaged over 1,515 exploratory -LRB- red line -RRB- and 2,646 exploitative -LRB- blue line -RRB- decisions . Black dots indicate the sampling frequency -LRB- although , because sample alignment varied from trial to trial , time courses were upsampled -RRB- . Coloured fringes show error bars -LRB- representing s.e.m. -RRB- . 2006 Nature Publishing Group NATURE | Vol 441 | 15 June 2006 LETTERS These results have important implications for both computational and neural accounts of action selection . The finding of brain regions discretely implicated in exploration -LRB- and particularly that one of them is a prefrontal , high-level control structure21 -RRB- is consistent with a theory in which exploration is accomplished by overriding an exploitative tendency , but troubling for accounts such as uncertainty bonus schemes1 ,14 , which more tightly entangle exploration and exploitation . Such anatomical separation would be unlikely under these latter schemes , because they work by choosing actions with respect to a unified value metric that simultaneously prizes both information gathering and primary reward . Just such an explorationencouraging value metric has previously been suggested to explain why dopamine neurons respond to novel , neutral stimuli13 ; such anomalous responses in an otherwise typically appetitive signal remain puzzling in view of our failure here to find either behavioural or neural evidence for such an account . Exploration has a central role in the acquisition of adaptive behaviour in environments that change . Characteristic expressions of frontal pathology28 include impairments in task switching as well as behavioural perseveration , which might relate , at least in part , to a core deficit in exploration . As one might expect for such a critical function , subcortical systems are also implicated in the control of exploration , with noradrenaline being suggested as regulating a global propensity to explore29 ,30 , a factor captured in our model in terms of the parameter regulating competition in the softmax rule . Last , self-directed exploration of the form studied here is an example of a refined cognitive function that is ubiquitous but hard to pin down in regular designs -LRB- because exploratory and exploitative responses are apparently seamlessly mixed -RRB- . We were able to capture it only through a tight coupling of computational modelling , behavioural analysis and functional neuroimaging . METHODS Fourteen right-handed healthy human subjects participated in an fMRI scan -LRB- using a 1.5 T Siemens Sonata scanner -RRB- while repeatedly choosing between animated slot machines . One of three candidate reinforcement learning models for their behaviour was selected , and its parameters estimated , by maximizing the cumulative likelihood of the subjects ' choices given the model and parameters . Trials were classified according to the model as exploratory or exploitative , and trial-by-trial estimates of subjects ' predictions about slot machine payoffs -LRB- and the error or mismatch between those predictions and received payoffs -RRB- were generated by running the model progressively on the subjects ' actual choices and winnings . A general linear model implemented in SPM2 -LRB- Wellcome Department of Imaging Neuroscience , Institute of Neurology , UCL -RRB- was used to locate brain voxels where the measured BOLD signal was significantly correlated with these model-generated signals . Regions identified as significantly correlated with exploration were subjected to a subsequent multiple regression analysis to investigate whether other , confounding factors might better account for the observed activity . For a detailed description of the experimental and analytical techniques , see Supplementary Methods . Received 7 February ; accepted 30 March 2006 . 1 . 2 . 3 . 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Reward representations and reward-related learning in the human brain : Insights from neuroimaging . Curr . Opin . Neurobiol . 14 , 769 -776 -LRB- 2004 -RRB- . Gottfried , J. A. , O'Doherty , J. & Dolan , R. J. Encoding predictive reward value in human amygdala and orbitofrontal cortex . Science 301 , 1104 -1107 -LRB- 2003 -RRB- . Tanaka , S. C. et al. . Prediction of immediate and future rewards differentially recruits cortico-basal ganglia loops . Nature Neurosci . 7 , 887 -893 -LRB- 2004 -RRB- . Miller , E. K. & Cohen , J. D . An integrative theory of prefrontal cortex function . Annu . Rev. Neurosci . 24 , 167 -202 -LRB- 2001 -RRB- . Ramnani , N. & Owen , A. M. Anterior prefrontal cortex : Insights into function from anatomy and neuroimaging . Nature Rev. Neurosci . 5 , 184 -194 -LRB- 2004 -RRB- . Koechlin , E. , Ody , C. & Kouneiher , F. A . The architecture of cognitive control in the human prefrontal cortex . Science 302 , 1181 -1185 -LRB- 2003 -RRB- . Braver , T. 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D. , Servan-Schreiber , D. , Rajkowski , J. & Aston-Jones , G . The role of locus coeruleus in the regulation of cognitive performance . Science 283 , 549 -554 -LRB- 1999 -RRB- . Doya , K. Metalearning and neuromodulation . Neural Netw . 15 , 495 -506 -LRB- 2002 -RRB- . Supplementary Information is linked to the online version of the paper at www.nature.com/nature . Acknowledgements We thank J. Li , S. McClure , B. King-Casas and P. R. Montague for sharing their unpublished data on exploration , and Y. Niv , Z. Gharamani and C. Camerer for discussions . Funding was from a Royal Society USA Research Fellowship -LRB- N.D. -RRB- , the Gatsby Foundation -LRB- N.D. , P.D. -RRB- , the EU BIBA project -LRB- N.D. , P.D. -RRB- , and a Wellcome Trust Programme Grant -LRB- J.O.D. , R.D. -RRB- . Author Information Reprints and permissions information is available at npg.nature.com/reprintsandpermissions . The authors declare no competing financial interests . Correspondence and requests for materials should be addressed to N.D. -LRB- daw@gatsby.ucl.ac.uk -RRB- or J.O.D. -LRB- jdoherty@hss.caltech.edu -RRB- . 4 . 5 . 6 . 2006 Nature Publishing Group 879

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O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O

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