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PROFESSOR: OK, good afternoon.
Today's lecture is going to
be on child development.
How they go from infancy and
head towards adulthood.
Next Thursday we'll talk about
development after infancy and
into adulthood and over age.
And this amazing thing about
babies and how do they get
going, and how do scientists
discover from babies and young
children how their minds
are fundamentally
different than adults.
And how your mind was
fundamentally different than
it is as an adult.
And then the last thing will
be a dangerous experiment,
where my wife will come over
with my two-year-old and my
four-year-old and we'll try
to do a developmental
demonstration in front of you.
But I should warn you
that live children
have their own will.
So we'll see how that
goes, okay?
All right.
So one thing that people are
struck by babies is that
babies are cute.
And it's not just--
It's thought to be not just
fun, but kind of a really
important biological thing.
We talked about motherese
before.
Singsong talk to babies that
help them learn a language.
There's something about adults
finding babies cute that makes
them want to help babies.
Parents and friends--
The cuteness is thought to be
an evolutionary reward for
dealing with a baby.
And people have said, well what
is it that's a little bit
different about a baby's
face than an adult?
They have rounder heads, they
have foreheads that protrude
more towards--
that slope back more.
They have larger eyes
proportionately.
Smaller jaw bones
proportionally.
And people use the term neotony
to describe this kind
of infant proportions, or
properties, of faces, which
are universal.
And, of course, a lot of
people discover this in
advertising or cartoons.
And so here's an interesting
example of how Mickey Mouse
has, over the years, from the
original version of Mickey
Mouse to the current super
cute, super tested, super
Disney version of Mickey Mouse,
has become increasingly
neotonized.
And how much the cartoonists
literally know that, or just
have kept saying, what makes
cuter, and cuter, and cuter,
and ended up with a lot of the
same proportions in Mickey
Mouse's face that make infants
so cute and desirable.
We don't really know.
But the world kind
of feels this.
Even adult research-- there's
a little funny line of
research-- that says adults who
look more baby-faced get
treated a little bit
different socially.
So here's Leonardo DiCaprio.
And baby-faced adults in
experiments are perceived as,
just by their faces, as more
naive, more honest, more
helpless, more kind,
more warm.
People think, this is going
to be a nice warm person.
Guessing from faces they're
using the cues of neotony.
Other studies have found that
people who are baby-faced are
statistically more likely to be
found innocent in cases of
intentional wrongdoing.
So where they're trying to prove
if somebody on purpose
tried to do something
bad, they go, not
that cute little person.
But there's no difference if
it's cases that involve
negligence.
Something where you should
have done something.
Because we know babies aren't
super responsible
for how they behave.
And they're less likely to
receive votes in elections.
So people have done--
I won't even tell you this-- but
people have done all kinds
of analyses of faces that
win elections in the US
and around the world.
And there's two dimensions
that people look for.
What looks like somebody's
empathetic and what looks like
somebody's competent.
So you want babies when it's
fun, but when you have to
figure out how to balance the
budget that doesn't seem like
a baby task.
So it's kind of funny.
And a lot of voters go by
instincts as well as by facts
or stated values.
So in the development of infants
into adults, the
classic debates about how our
mind grasps the world have
played out, yet again,
in a powerful way.
You know, the nature-nurture
debate.
What's in our genes
and gets us going?
What's acquired from
the environment?
Philosophers who say that
knowledge starts with innate,
or genetic, or more evolved
capacities.
Other ones who've emphasized
that we pick it up from the
world empirically as measuring
scientists.
So, for example, Aristotle
wrote, "There's nothing in the
intellect which was not first
in the senses." that's the
empirical view.
It's out there in the world
and you solve it.
And starting with
a blank slate.
And, in fact, the behaviorists
believed in this with a
vengeance in psychology.
So Watson wrote, "Give me a
dozen healthy infants, well
formed, and my own specified
world to bring them up.
And I'll guarantee to take any
of them, one at random, and
train him to become any type of
specialist I might select.
A doctor, lawyer, artist,
merchant, chief, and, yes,
even beggerman and thief.
That it's all the environment
and a blank slate.
And who really knows?"
But infants are born with some
incredible things, an we'll
talk about them today.
One of them is this experiment
from Andy
Meltzoff, which is this.
That it seems like within
moments of birth, infants are
equipped with a desire
to imitate adults.
A desire to imitate.
And why people have been really
impressed by this is,
if you have that in your genes
and in your nature, it's a
good way to learn about the
world is to imitate people you
see around you.
It's kind of a driving
principal.
I'll imitate their language,
their social mores.
Here's what Meltzoff did.
Sticks out his tongue, opens
his mouth, purses his lips.
And here's the infant, one day
or a couple days old, tongue
out, mouth open, lips pursed.
Now, I should warn you
about one thing.
These are the greatest hits
pieces of that research.
People debate about
how perfectly this
happens, all right?
So I was frustrated when my
infant came home and I did all
this stuff and she would not
instantly do everything she
was supposed to do.
It's a statistical thing.
Because when you see these
pictures, they're showing you
the best moments.
They have to defend that it
happens above chances
statistically.
But it's not like every
expression you
make they copy you.
And that's why there's still
some debate about exactly
what's going on.
But they definitely, on average,
imitate an adult
within a day or two of birth
for completely arbitrary--
as far as we think--
expressions.
So it's a very powerful
mechanism for learning that
appears to be in place.
Because there's two ways that
we could imagine genetically
programmed learning.
One is that you know the
content of it already.
But another way is that
you just have stuff
that makes you a learner.
So being an imitator is a
general way to make you a
learner without being very
specific to the content.
So we talked a little bit
about this already, but
psychologists are unbelievably
brilliant--
I think, I'm really blown away--
about how they can
figure out when an infant knows
and doesn't know, or
young child knows
or doesn't know.
And they do this indirectly by
things like looking time.
And you've seen this.
I'll give you an
example or two.
And you'll see some
more examples.
As a measure of what
the baby knows, or
the young child knows.
And, of course, if they look
longer at something it could
be because they prefer it.
And, also, if it's based
on a memory task--
like you saw something,
you see it again--
that would tell you there's some
sort of discrimination .
They can tell things apart
based on memory.
And then, sometimes, people will
push this memory thing
with habituation or
familiarization, so if you
show something to a baby over,
and over, and over again, they
get sort of tired of it.
And at that moment they'll
change the stimulus.
And they'll see whether the
baby gets newly attentive.
Now, if it's something that the
baby doesn't grasp, they
won't get newly attentive.
You know, nothing's changed
in their mind.
If it's something the baby
understands, then they'll say,
wow, something interesting
is happening.
And they'll look longer.
So, here's an example.
Baby getting bored because
they're showing something over
and over, and something
new, oh!
That's the kind of things
that people measure.
And we're doing it
loosely here.
They measure it pretty
carefully.
I should tell you, the people
who do this kind of research--
they'll film it, they'll show
it to unbiased people like
you, maybe judges.
OK, to say, how long is
the baby looking?
Where's it looking?
You don't know where the baby
should be looking at or not.
So researchers take care to make
it not just that you're
convinced in your heart
of hearts that
they're looking more.
They film it.
They show it to people who don't
know what's going on.
They try to make it a blind
procedure in many ways, the
better research.
So how do we know things?
Even very young infants look
selectively at novel objects.
If something's new, even at
one day, if you show them
checkerboards with different
size squares, same size, same
size, same size, wait a couple
seconds, smaller squares.
They look more.
This shows you they saw the
difference in the squares.
They even remember, somehow in
their mind, the difference
between the squares.
Because when you switch it
they start looking more.
Something interesting has
happened based on perception
and memory.
Another thing that
we've mentioned--
I'll just remind you-- is that
infants, almost from birth,
seem to love to control, or
provoke, their environment.
So we already mentioned to you
that 20 month olds prefer a
mobile that responds to their
bodily movements.
They like things that
they control.
If they take a two-month-old,
and they put a string on their
wrist by which they can control
a showing of Sesame
Street, they kind
of like that.
And if you stop Sesame Street,
they show anger on their face.
Hey, I was in charge here, who
has the remote control now.
And four and five month olds,
a little bit older, remain
angry when the video comes back
on because that's not
what they wanted.
They wanted to control the
presentation of the video.
So infants have this apparent
craving to explore and feel
like they have some control over
their environment, at an
age when they don't control a
lot because of their limited
physical capacity.
In the first three or four
months, infants explore the
world a lot by their mouths.
That's why people worry to not
leave around things that they
will put into their mouth and
swallow, that are dangerous.
Because their visual and
auditory systems, and their
system with their hand,
are slowly developing.
By five or six months around
the world, they start to
explore with their hands and
their eyes around them.
As their motor system
gets more mature.
As their visual system
gains acuity.
And we already know that infants
use social cues to
guide exploration.
One of the big changes this
happened in the last 10 years,
I'd say, in infant studies or
child studies, has been a lot
of appreciation about the
intersection between cognition
and social interaction.
There used to be like two
different worlds of people who
studied language.
They would have algorithms and
formulas about the language.
And then the social people who'd
study how babies were
cute or something, right?
But there's been more and more
thought that a deep thing in
us that helps cognition grow,
is the social relations that
an infant is drawn to parents
and caretakers.
So, for example, a
six-month-old, if their mother
rolls or pounds a ball, they
tend to copy, they tend to
imitate that action.
They follow the eyes
of a person.
Joint attention.
You know, eyes are the
windows on the soul.
We know eyes mean a lot.
Where are people putting
their attention?
What are they paying
attention to?
Infants pick up on this
very early on.
And if somebody looks over there
they look over there.
If you look at them they
know your attention
is focused on them.
And sometimes people
will say--
because psychologists love to
test everything-- is it just
the way the head is turning?
So if you cover somebody's
head they
don't follow it anymore.
They know it has to be the eyes
reflecting where the mind
is putting its attention.
It's not the head direction.
It's the eyes.
Here's something, infants who
are a little bit better at
following eyes--
either maturing faster
or something--
also learn language faster.
They get words faster,
and syntax faster.
It's as if part of that social
interaction is helping to
drive the language learning.
So that's how these social
things and language things
interact very substantially.
And we already said that a
12-month-old will stop at a
visual cliff, but if the mother
smiles there they go.
So constant learning
that mixes in the
cognitive and the social.
Now the epic name in
developmental psychology is
Jean Piaget.
Because prior to him, roughly
speaking, in the science of
child development, people just
thought children were sort of
boring and dumb.
They need a lot of attention.
Please finish MIT so we can talk
with you intelligently.
I guess people were not
that interested.
Partly is the world was
different in so many ways.
There was no-- practically
no--
formal psychology
experimentation or thought
about what really children's
mental lives were like.
And Piaget--
I have a wrong year
there, 1886--
developed--
he himself was a child prodigy,
trained in biology.
Very early interest in whether
categories are in our heads or
in the world.
Tried poetry.
Worked with Binet on
intelligence testing.
Became interested in patterns
of errors and successes.
You'll see that in many ways,
what he discovered about how a
child mind is different than
yours fundamentally, is based
on the patterns of
their errors.
And he said, there's two
basic things going on.
This is a huge idea.
One is assimilation, you
incorporate new knowledge into
existing cognitive structures.
It's basically ways you
think about the world.
And new knowledge is added.
That's important.
But he thought the dramatic
thing that happens in infancy
and childhood is what he
called adaptation.
That the fundamental ways in
which you understand the world
are shifted, through
development, to accommodate
new evidence.
So there's a wonderful book if
you come across it called The
Scientist in the Crib.
But it's kind of a pun.
It's written by scientists
who study infants.
But the idea is that, in a
sense, every infant is kind of
his or her own scientist--
as you were--
probing the world and
discovering the physical and
social laws of the world.
Because they don't know them
coming in and they're going to
pick up a lot of them.
They're going to probe them.
But fail to publish
the results.
So Piaget postulated that were
these big stages, what he
called the Sensorimotor age,
zero to two, where the world
is one of what you see and
the physical actions.
And there's not much
representation of ideas or
lasting thoughts.
And we'll see some examples
of these.
Between two and seven, you start
to be able to keep a
thought in your mind.
You still have an egocentric
prospective.
You see the world from your view
but not appreciating the
views of somebody else.
You start to use language.
A lot of flimsy discussion about
fantasy and reality.
I could tell you with my own
daughter, who you'll meet,
she's still working out
whether fairies
really exist or not.
This was chaotic because we
went to some skating show
where Tinkerbell was a human
dancing, and that totally made
the situation very
complicated.
She's still working on that.
Concrete, as you get 7 to 11,
organize logical thought.
Still concrete, as opposed
to sort of abstract.
And then you move to more adult
like cognition, which
we'll talk about next week.
So the idea is from birth to two
years, you would love to
have an infant just tell you
what do I think the world is
really like.
They have very modest language,
of course, so they
can't tell you what they see.
So the thought is they have
fleeting, disconnected sensory
impressions and motor
reactions.
It's all, what do I see?
How am I responding?
That their focus of thought is
centered on actions, not
things or intentions.
And I'll show you in a
very concrete way.
That there's no distinction in
their mind between things that
are stable in the world
and transient events.
No distinction between
themselves and the world
around them.
It's all just one big mush until
they connect abstract
representations that separate
these things out.
So let's talk about
object permanence.
I'm going to show you that you
have object permanence just by
saying, here's my pointer.
I need a volunteer.
This is so easy that you
will not feel scared.
I promise.
All right.
Thank you very much.
So you see this?
Where do you think it is now?
OK.
If I was really cool
teacher who did
magic it would be gone.
But yes, and you know
it's there.
That's object permanence.
If you turn your head
you believe it's
probably still there.
But that's going beyond the
fundamentals of perception,
that's your knowledge, and
representing in your head,
there's something I don't see
but I know it's there.
That is not available to
a zero to two year old.
So, for example, if they see a
rattle they feel a rattle.
But now if they look away, or
if you just put a sheet of
paper in front of it--
I'll show you a couple
of examples--
they behave as if the rattle
no longer exists.
Just like I did in
front of you.
If you just cover it up, it's
gone as if it doesn't exist.
Because their mind cannot
represent what they do not see
right in front of them.
So out of sight out
of existence.
So you can show them a toy they
love, and until about
eight months, you
could do this.
They'll start crying.
They'll protest.
But they won't reach for it,
even when it's easily within
their reach.
Out of sight, out of mind.
It doesn't exist.
They can't represent in their
mind what they don't see.
And then there's another one.
You'll see a film of this.
But let me tell you this.
Which tells you about actions
verses other things.
So imagine you hide a toy under
one location, the child
searches there, finds it.
You hide it again in
the same location.
You encourage the
child to search.
They find it.
They do it two or three times.
Now, in front of the child, you
take that same object that
you've shown them like
this several times.
They've grabbed several times.
And you simply, in front
of them, pick it up
and put it over here.
And they're viewing everything
in full view,
just like you did.
What do they do?
When it's their turn to
grab they grab here.
The wrong place.
The place where they
grab before.
Because what's in their mind
is the action they did.
Not the object as an independent
thing they can put
in their mind.
Does that makes sense?
And I'll show you several
pieces of this.
It's called the A-not-B
effect.
I put this A, A, A, A in
the front, full view.
Put it over here and they reach
over here to get it.
So this is this idea, that in
their head is not a toy.
Their head is representing the
thing on the right that they
reached for.
Because they don't represent
ideas of things.
They represent actions
that they've done.
So here's object permanence.
Here's a child sees
a toy they like.
You put up, in front of them,
this thing and tragically,
it's disappeared.
It's gone out of existence
in the world.
Some people have done some
sort of NIRS imaging
suggesting that kids who get
past this stage are developing
some frontal maturation.
But I think the most compelling
things are the
videos of the kids themselves.
So let me show you another film,
again very cleverly, the
Renee Baillergon has been one
the leaders in this field--
very cleverly showing you what
infants grasp and don't grasp.
Not only the brilliance
of these experiments.
These infants are really trying
to figure out the
world, and coming up with
hypotheses that they're
confirming.
And then when they're broken
down they're upset with
what's going on.
So let's move on to age two to
seven, especially in the early
years, so-called a
preoperational stage.
And one of the coolest things,
and we'll try this and see how
it goes with some girls in a
few minutes, is this idea.
So if you see two glasses filled
with equal amounts of
liquid, and you pour one over
into the thinner, taller
glass, c, which will have
more water in it?
A or C?
The same.
But not if you're a two year
old or a four-year-old.
So it's called conservation
of liquid.
So, it's kind of fascinating,
isn't it?
It's kind of amazing.
If you do this with a three
year old it's virtually
guaranteed they'll do this.
All of you did it all
over the world.
And, in some sense, as far as we
can guess , all throughout
our species' history.
So brilliant ways of showing
that babies, or young
children, really see a little
bit of a different world than
you and I as adults.
So here's another very powerful
area of research,
which is taking perspectives
from the view that other
people have thoughts and
feelings besides yourself and
how you interact with them.
And people call this idea
theory of mind.
The idea that you understand
that other people out there
have their own thoughts, their
own feelings distinct from
yours, and in the most
challenging case, they can
even be false beliefs.
A person can have wrong
information in their head and
truly believe it, even when
you know it's wrong.
Because you, as an adult,
realize that thoughts are one
thing and physical reality
is another thing.
But that's not what
children think.
They think there's
just one reality.
That's why at the very youngest
age, they think if
they cover their eyes that you
don't know where they are,.
Because they think there's one
physical reality only.
And they don't realize there's
another prospective
besides their own.
So here's a very clever
experiment showing you that at
three months, children code the
word in terms of actions.
And by six to nine months,
they begin to understand
intentions, that people out
there-- animals too but we'll
just focus on people--
have intentions and
goals in their head.
So here's what the experiment
they do using this
habituation.
There's two pedestals here, and
a person reaches again and
again for a ball.
So now, what do you believe
the intention is?
To reach for the ball.
You see it 10 times, the
baby's losing interest.
Now comes their shocker to get
the baby crying, or laughing,
or drooling.
Get the baby's attention
that you can
measure by how they respond.
And in some conditions,
something goes down, and when
it goes back up the
person reaches.
But now they take
the same action.
They reach for the left
pedestal, but
it's a teddy bear.
Or another case, they reach
for the ball in
the opposite side.
Who, depending on their age,
sees these two different
changes in the scenario
as startling?
The three month olds are
startled when the person
reaches for the same object.
The three month old.
Because in their mind, the only
thing that was really
happening was reach for the
left, reach for the left,
reach for the left.
And now you're reaching
for the right.
The action changed.
Because the action is
independent of intention.
It's just what happened, what
happened, what happened.
They're shocked when
the person goes for
the ball over here.
By six to nine months,
they're shocked--
relatively speaking--
when the person reaches for the
same action but now the
goal is different.
Grabbing the teddy bear.
It's as if they understand the
intention of the person was to
get the ball, and these children
think the only thing
that's happening is physical
action, physical action,
physical action.
So very clever experiment by
this habituation and looking
time to show at three months
all you see is actions.
And by six to nine months you
start to grasp that people
have intentions in their head
above and beyond their actions
that govern their actions.
So to make it really tricky,
there's this very clever
experiment that makes--
and we'll try it in
a few minutes--
this way.
This so-called Sally-Anne
problem because it's been so
widely cited and discussed.
So you tell a child
this story.
Imagine there's two girls
here, Sally and Anne.
And Sally takes a ball and
puts it in this basket.
And then she leaves the room.
Anne, who's a little bit of a
troublemaker takes the ball
out of here and puts it into
this box, and closes the box.
Here's the big question.
When Sally comes back and looks
for this ball, where
will she look?
And a three year old
says, in the box.
Now if she was out of the room
there's no way for her to look
that's in the box.
But for the three year
old, there's not
thoughts and reality.
There's just kind of reality.
Does that make sense?
The three year old can't
entertain the idea that Sally
has, in her head, wrong
knowledge of
where this ball is.
The she couldn't have known
where it is and she's going to
act on the knowledge
that's in her head.
That's the content
of her mind.
The three year old says there's
one reality, the ball
is over here.
I know it.
Everybody knows it.
What else is there to
even think about?
But that typical five-year-old
will say, Sally will look in
the wrong place.
She'll look in the basket.
She'll look in the wrong
place compared to
where the ball is now.
Because she believes
it's there.
She has the wrong idea
in her head.
That ideas can be independent of
physical, observable things
in the world.
This is a universal finding.
I'm going to have to
change my settings.
Sorry.
Your handout has this.
In practically every country
where they've tested this,
three year olds don't have
a theory of mind,
five year olds do.
Turns out--
and you could take a guess--
the older sibling you have,
the younger you become at
getting a good theory of mind.
Nobody really knows what the
answer but what's your guess?
The more siblings you
have that are older
than you, the younger--
by some number of months--
people tend to show that they
can understand that people have
all kinds of thoughts and
beliefs in their head.
What's your guess?
Yeah.
AUDIENCE: They have gone
through versions of the
Sally-Anne problem themselves.
PROFESSOR: They may have been
tortured by their siblings.
But on top of that, the
intuition is-- and we don't
really know, this is hard to--
they're living in a world,
because they have older
siblings who do unkind things
to them, who have superior
powers over them physically,
they're much more socially--
have to figure out what's going
on to survive happily
and make their way
in the world.
The big five year old, he or she
is dominant, and the two
year old is trying
to steer around.
Like, what is does that
five year old think?
How will I not get into
trouble with that
five-year-old and my mother
and my father?
A younger sibling has more
social pressures to figure out
what's going on and steer your
way around, and not get in
trouble with your
older siblings.
We'll come back to autism.
I'll just say a word
about this now.
You hear a lot about it.
The current guess is that it's
approximately 1 out of every
140 children.
A shockinging increase in
numbers to what people
believed it was many
years ago.
Mysteriously, there's
many more boys
than girls with autism.
Estimates are 4 to 1, or 10
to 1 range, all there.
It's hard to know for sure.
We'll talk more about that.
Autism is defined
by three things.
A sort of weakness, or
deficit, in social
interaction.
Children with autism, or adults,
have difficulty in
social interaction.
In communication.
And they have lots of repetitive
behaviors that can
be difficult to help in
interaction with others.
And when people test theory of
mind in children with autism,
it's typically delayed by five
or six years on average, for
those children who can
take the test at all.
They have a very slowly
developing, very delayed
theory of mind and understanding
what's in the
content of the thoughts
of other people.
And that's considered one of
their biggest challenges.
How they relate to
other people.
Understanding what the other
person's thinking and feeling.
Just for a couple minutes I'm
going to show you a video and
then we're going to try--
So the biggest challenges to
Piaget have been this idea
that there's these distinct
stages of thought.
That your mind shifts,
literally, how it's
constructed and understands
the world.
And that people have thought
that the process is much more
continuous than Piaget
had suggested.
And here's one compelling
example of that kind.
So this is the A-not-B
experiment.
There's a two food wells,
and something of
interest in this infant.
The seven month old looks
at the toy here.
It gets covered up.
It's placed in b, and b is
one of the two wells.
He continues to look at b
when both are covered.
He knows the toy
is over there.
And the toy has been placed
over and over again in a.
So he gets the A-not-B error.
He has the action.
And even though he sees the
toy is placed there.
It's covered up.
He's looking where the toy is.
When it's time to reach
he goes to this well.
So this is A-not-B error.
A part of his mind that guides
action is stuck and guides
what he reaches for.
But obviously another part of
his mind knows perfectly well
where the toy is.
So it's not as if it's all of
one, or all of another.
His mind is representing that
there's a toy down there, but
the part of his brain or mind
that guides his action is
still stuck at this early
developmental stage. it's if
he were two ages.
One guiding where
his eyes goes.
And one guiding the
ultimate action of
where his hands goes.
And as he gets a little older,
his eyes and hands will go in
the same place.
OK, last couple of things
about how infants are
mathematicians.
Because, of course, we focused
on language, or social
thought, but the ideas of
counting and, ultimately,
arithmetic or math also come
out of children's minds.
And a very clever experiment--
and I'll show you
two of them--
that shows even at six months,
infants are starting to
prepare themselves to become
mathematicians.
And here's how they begin
the counting.
They're shown displays of three
objects or two objects.
And then they hear two sounds
like boom boom.
And where do they look?
They tend to look at the
one with two objects.
So this is pretty impressive.
They're counting the two.
They're relating something in
sound to something in sight
that's arbitrarily related,
but that shares the
numerosity.
And if they get boom, boom,
boom, three boom sounds, then
they go, OK, now I like the
display with three things.
They understand, in some level,
twoness and threeness.
And so you start to have the
basis of having numbers.
And not only that, Karen Wynn
at Yale has shown quite
cleverly, not only do infants
have numbers.
They can do a little bit of
subtraction and addition.
So here's the experiment
she does.
She places an object
in a case.
The screen comes up.
Now comes the second object.
And the hand leaves.
OK.
The screen drops.
And there are two.
One plus one equals two.
And the infant goes,
OK, no big deal.
But if the screen drops and
there's one, the infant is
startled and looks longer.
And they can do it the
other way around.
They can do subtraction
as well.
So one plus one equals two, and
if there's one left by the
trickery of the kind you saw
earlier, they're disturbed
that the addition has not
occurred correctly.
Or the subtraction has not
occurred correctly.
And there's kind of a debate--
this is the last slide--
and here's the core idea,
though, which is this.
That our minds afford us, by
evolution, counting up to
about four objects
in the world.
And many animals do
that as well.
That sort of has to develop a
little bit, but we've at lot
running in us.
So that infants can do.
Because, of course, if you show
7-- if you give 77 booms,
they don't look for the display
with 77 versus 78.
They can't do that.
So they can operate in the world
of 1 to 3 or 1 to 4.
And then they discovered--
there's been a series of studies
in tribes, that are
relatively isolated in different
parts of the world,
where in their language they
only have words for
one, two, and three.
And everything after that
is really described as
many, or a whole lot.
They don't have words
for five and up.
There's no word in
their language.
Because they've never needed it,
apparently, in the worlds
they live in.
So they go to them and
they have them do
little counting tasks.
And as soon as they get beyond
about four they get very
inaccurate.
It's as if the mind naturally
can represent about four
things in the object world, four
things in the counting
world-- maybe because
of that--
and after that everything is a
cultural invention of higher
level mathematics.
It builds off one to four.
But you don't have it
unless your culture
teaches it to you.
Or your culture invents it.
And there's been brain imaging
studies too, suggesting that
counting one to four is very
different in the brain than
exact mathematics beyond the
number four or five.
That's all culturally learned
and invented.
It's based on an innate
one to four capacity.
