[MUSIC]
We are the paradoxical ape,
bipedal, naked, large brained.
Long the master of fire, tools and language.
But still trying to understand ourselves.
Aware that death is inevitable.
Yet filled with optimism.
We grow up slowly.
We hand down knowledge.
We empathize, and deceive.
We shape the future from
our shared understanding of the past.
Carta brings together experts from diverse disciplines to
exchange insights on who we are and how we got here.
An exploration made possible by
the generosity of humans like you.
[MUSIC]
Thank you and thank you for inviting
me to this fascinating symposium.
I will be addressing the today's topic
in the domain of quantity and number.
Many animals have the capacity to
discriminate quantities and amounts,
for example, while foraging,
looking for fruits that are
ready to be eaten from those or not,
or let's say looking at predators,
amount of predators or prey.
The question is, are these phenomena in the domain of
the perception of quantity or conception of number?
These are questions that are normally addressed
in the domain of numerical cognition.
With respect to today's symposium,
we could place this in the area
of comparative numerical cognition.
But here we have to step back a little bit in the sense
that different fields take
the term comparative, slightly different.
For example, in the domain of comparative anatomy,
it is very clear that we can do
interspecies comparison, for example,
looking at the size of
the skull in different species, for example.
But as you move along down to a
comparative to neuroscience where you would need,
let's say, a nervous system,
as you move along down this list,
you would have comparative linguistics,
which involves only human languages.
The question for us today is going to be, well,
what about comparative numerical cognition?
Where would that fall along this list?
What do we know? Well,
certain things we know, for example,
many species are able to
discriminate small amount of things.
For example, dots.
When they're in a small range,
what we call two or three or one,
but as soon as you have more elements,
then it's much harder to discriminate these amounts.
This is called subitizing
and it's a phenomenon that's been
studied by experimental psychologists since the 1940s.
Another capacity that humans share with
many other animals is the capacity to
discriminate proportions, for example,
of black dots versus
white dots when the proportions differ substantially,
but when they don't and
they relatively similar to each other,
then it's much harder to discriminate these amounts.
This capacity is called a large quantity discrimination.
Some people and some domains in some fields
interpret these as being already mathematical capacities.
People's speak of monkey mathematical abilities
based on this ability in these capacities,
or numerical and arithmetic abilities
in non-primate species,
or let's say, numerical cognition
in bees and other insects.
Then of course, the media sometimes
publish splashy titles like New York Times saying
many animals can count some better than you or
referring to the origins of numbers when
you look at animal data.
Let's say a title like this one fish as
good as college students in number tests.
But there's a different source of data with
different kinds of interpretation that look at
many human cultures that do not have their practice of
counting and they don't have terms
for numbers beyond the subitizing range.
Many of them exist in
the Amazon area and also in Aboriginal Australia.
This had been referred to, for example,
by Caleb Everett as
anumeric cultures and anumeric languages.
Here, we seem to have a clash
between the data that comes from, let's say,
from animal cognition saying that
bees and other insects can
count and then at the same time
having the problem of
human cultures with very sophisticated languages and
smart people adapting in
various challenging environments not counting.
In the first group you have primarily
data coming from animal cognition, child psychology,
and cognitive neuroscience and
I put here a tilde
indicating that it's not all of them,
but is many people with more nativist approach.
On the other hand,
we have more anthropology and
linguistic typology bringing the data
I was just describing.
We seem to have an impasse between what is being
reported and particularly when
we want to address the question,
is there an evolved capacity for number?
The group on the left would tend to say that there is
a biologically evolved capacity that is
specific for number and arithmetic.
Whereas on the other side,
we would have a capacities for numbers are
emerged from cultural practices
and learning and language.
What do we find when we read these articles?
Is that quite a bit of
a confusion in the use
of the terms, for example, numeral,
which is assigned for number, not number itself,
or the definition of counting or
what is arithmetic and what is mathematics.
When we look at the literature,
we see sloppy and inconsistent concepts within
and across disciplines leading to different views.
We want to do comparative work
we need unambiguous and terminology,
clear concepts and sound theories.
What are the problems that we identify?
Well, on the one hand, we can see
that there's loose terminology as I was saying,
and unfortunately the term number is
used in everyday language
like in passport number or phone number,
and also in technical domains,
ordinal number or transfinite numbers and those
tend to be very different notions of number.
As we said, the literature is
filled with confusing terminology,
how numbers use and sometimes is referring to many of
these concepts here or
sometimes refers to something that is exact,
sometimes its approximate,
sometimes is symbolic, sometimes is non-symbolic.
When we comes to talk about numerical cognition,
then we have a problem of what really
is hidden under this term, numerical,
when we say numerical abilities or
numerical processing, numerical stimulus.
Another problem that we can identify is
an over-interpretation of trained animal data.
Results from training are often arduous
and require considerable environmental support,
intentionally concocted and designed by humans.
For example, if let's say we can
have monkeys learning how
to walk on stilts or a bicycle,
but the question with respect to
the evolution of locomotion in primates,
we need to ask,
is that really useful,
or what do we learn if we want to address the question?
Something similar happens when we train animals in
our environmentally humanly design environments,
when we put these animals in to these heavy trainings.
The training process usually follows
extensive and dedicated training,
which sometimes takes years to complete.
For example, a quote from a practitioner says, here,
training a monkey on a simple quantity match to
sample tests can take over
four months and 20,000 trials,
only to achieve discrimination of collections that are
three to four ratio with a 75 percent accuracy.
The trained animal data really
informed many interesting questions,
there's no doubt about that,
but it's not necessarily about
biological evolution and biological endowment.
Another source of problems is that there's been
pretty much a disregard for crucial human data.
While most numerical cognition studies have been done
in industrialized societies with writing practices,
well established curriculum and
schooling from young age and so on,
this poses a problem for evolutionary claims.
We want to know, for example,
how is quantity handled in non-industrialized societies?
In this case, we can see that all known cultures,
that use in one way or another,
natural quantifiers terms like English,
few, or several,
or many, and so on.
But by no means,
they all exhibit exact quantification.
For example, a recent study,
a survey in Aboriginal Australia over
nearly 200 languages from
13 different linguistic families,
reported that nearly 90 percent
of these cultures lack numerals beyond five.
This is words or terms or
expressions that go beyond the subitizing range,
and similar results have been observed in groups of
hunter-gatherer cultures in South America and in Africa.
In some language by itself does not lead to number,
appears to be necessary but not
sufficient for exact quantification,
which seems to be a cultural trait,
not a specific biological trait.
Some distinctions are needed here.
While we know that some animals have
the capacity to discriminate, let's say,
chromatic experiences, let's say red from green,
or the quantity, amount.
When we say that this group here, the top group,
has nine elements and the one on the bottom has eight,
we are involved in symbolic reference,
and this appears to be exclusively human capacity.
We could refer to this in other languages like nueve,
and ocho in Spanish,
or using Roman numerals or let's say
other bases in mathematical notation
to refer to these quantities.
What is really number when we take this counting classic,
familiar list of 1,
2,3, and so on?
Well, we have at least seven properties.
First is that number quantifies exactly,
it is abstract in the sense that it
transcends immediate perception on modality,
let's say visual or acoustic,
and so on, they are relational.
For example, numbers refer to each other like
eight is a product of
four and two and so on and so forth.
But importantly, for today's presentation,
is that numbers are referred to symbolically.
Really, number is exact symbolic quantification.
Now, that appears to be substantially different from
what we observe in untrained animals in the lab,
which whatever phenomenon we observe is
mainly achieved via associative learning.
Good science needs clear non-confusing concepts.
How to properly refer to biologically in doubt
quantity-related phenomena that do not
satisfy the prototypical number properties?
In other words, in this picture,
how do we refer to this part of the picture?
Well, we can't really call that numerical in
the sense that it lacks properties
like symbolic reference,
and it's not really quantitative in
the sense that is opposed to qualitative,
so we refer to it as quantical capacities.
If we have here a schematic representation of handling of
discrete quantity from small amounts
to larger amounts in center-periphery wise,
here on the bottom left we have,
let's say, subitizing and large quantity discrimination,
which we share with many animals,
and it's falling the non-symbolic domain.
But symbolic reference allows us to have another type of
handling which allows for
natural quantifiers and exact quantification.
Natural here like few, many,
and so on in white,
and then exact quantification in blue,
going from oral language to written practices into
increasingly more sophisticated mathematical notation.
The point is that
quantical cognition is biologically endowed,
while numerical cognition is not biologically evolvable.
Here I'm going to quote Terry Deacon, saying,
"Symbolic reference must be acquired by
learning and lacks both the natural associations and
trans-generational reproductive consequences that would
make such references biologically evolvable."
Exact symbolic quantification beyond subitizing range
appears to be motivated by cultural preoccupations,
tracking variables,
stock management, trading, accounting,
and so on and is supported and enhanced by
tools and offloading cognition.
It requires enculturation. For example,
Incas in South America
did not have writing as far as we know,
but they had material anchors
to support calculations, for example,
or grammatical and lexical tools has been
reported by Nick Evans in Path 1 languages,
or of course, writing technology,
which was invented only 6,000 years ago.
In any case, all these cases require
conventionalized symbolic reference
for exact quantification.
Now when there is number,
it's commonly expressed in Base 5 or Base 10.
Maybe because we have five fingers in our hands,
pentadactylism which is an anatomical trait.
The thing is that many mammals have this trait.
Pentadactylism is observed in gorillas,
in monkeys, and raccoons,
and, as I said, many,
many other more bats and seals and so on.
Here we have an evolved anatomical trait
that is present in many animals, however,
symbolic reference is not present,
so the hen cannot be
recruited symbolically for, let's say, counting.
Another important aspect is
that even in the case of humans,
is not that because we have symbolic reference,
we have one way that is genetically determined for how
to keep track of numbers using our bodies.
The work of Bender and Beller has shown
many variations across
human cultures of how, for example,
the number 8 is characterized
using our anatomical feature of pentadactylism.
What happens when there is written exact symbolic number?
Well, even in that case,
seems to be mediated by
culturally shaped cortical phenotypic plasticity.
For example, Tang et al., showed that with
a numerical task given to
English native speakers and Chinese native speakers,
you would have a different
recruitment of neural population,
for example, in the English speakers,
more activity in the perisylvian area,
Broca's area and Wernicke's area
compared to the Chinese group and so on.
Exact quantification, or number then,
is really is not a biological trait but a cultural trait.
It builds on biologically evolved preconditions like
subitizing and large quantity discrimination,
supported by symbolic reference,
which is not biologically evolvable,
brought forth by cultural practices and preoccupations,
along with biological phenomenon
that support teaching, learning,
and specific phenotypical plasticity;
biological enculturation.
Number with respect to our topic
today of in comparative anthropogeny, well,
although ubiquitous today in the industrialized world,
numerical cognition like geometry, music,
or visual arts, should not be taken at a face value.
The answer to the question of what it takes to move from
quantical to numerical cognition is not trivial.
Indeed, only some humans
in the right sociohistoric context,
and after tens of thousands of years,
have made that leap.
We have outstanding questions, of course,
for example, what selective pressures
may have given rise to quantical cognition?
What does it take to move from
quantical cognition to numerical cognition?
What is the role of natural quantifiers in
the consolidation of exact number in children?
Building on quantical cognition,
how does exact symbolic quantification
get grounded and neurally instantiated?
Ultimately, how does
biological evolution
accommodate and support enculturation,
symbolic learning,
and cultural evolution in the human species?
These are questions that now,
along with colleagues, Andrea Blender,
Francesco d'Errico, and Russell Gray,
we're starting to address with a recently awarded grant
by the European Research Council in our project QUANTA,
Evolution of Cognitive Tools for Quantification.
Thank you very much for listening.
Thank you for all the students who have supported
this work and the funding agencies.
I'm happy to take questions at the end of the session.
Thank you. [MUSIC]