The action taking part
in any event involves
roles. 
Here we classify
three main roles as
"self," or the agent from
their own perspective,
"other," people or
other sentient
actors incidentally
involved with
the addressee in
one way or another,
and "things," which inanimate
objects, might be close
might be distant.
Let's focus on the
vertical access now or
functional transposition
represented in
our grammar diagram
here across the page.
So let's consider
the speaking "I."
The first person in
the conversation
is an embodied self.
It's me speaking.
This is now others
involved might be
the person with whom
I'm speaking, which
could be for example,
you, and people not with
us at the same time,
which might be they,
for example.
This "other" may
include creatures
whose sentience we
humans recognize - pets,
for interest, or
wild
animals or even insects.
Note how closely speeches
related to body
because our bodily
positions in
relation to each
other and our
gesticulations partly
configure these
self, other, thing
relationships. Speech is
always multi-modal.
This seems very
straightforward,
and what could be more
distinct and more
separate than you and
me and them? But in a
transpositional grammar,
we start to notice
that these are in
fact relationships
that are in
constant movement.
Now let me say
something which is
deceptively simple and
deceptively complicated.
Let's say we're speaking.
And when we are, I am a you,
and you are an I.
In our mind, we're
always swapping
things out like this.
When you say "I," it
means you to you.
And when I say
"you" it means I to
you. The meaning in
the conversation is
about swapping things out.
The transposition,
swapping out you and
I. Learning a new language,
for example, means
being able to make
these kinds of elementary
transpositions
in a fluent way during
a conversation.
I want to give you
another example
of functional
transposition,
now, how self and
other are so very
interconnected.
Let's say you are
telling me about your pain,
and I feel for you.
I'm in a way becoming you.
I have a feeling inside me
that is like the
feeling that you are
expressing. Or I'm
watching a movie where
the main character
is experiencing
pain so much so that
it makes me cry too.
Well, these are
transpositions
which in which
the meaning of
self puts itself in
the position of the other.
This is a transposition
that we call "empathy,"
an idea theorized by
the great philosopher
of meaning
Edith Stein. Form
to form, I actually
feel for what the other
person is feeling.
And I feel this
from what they are
saying in a conversation or
the situation they're
in if they're
a character in a movie.
Function to function,
I'm transposing
self and other.
The meaning is not in
our totally
separate persons -
you and me or
self and other,
but it's in our sociable
sharing of meaning.
Of course, your
real pain and
my empathized pain
are not the same,
and the action
that's playing
through in the
cinema of pain is
not the person the
actors on pain, but one
of an idealized
person that they're
acting. 
Your pain is real.
Mine and the actors
are idealized.
But by empathy, the
real and the ideal
come into connection.
These are just some
of the ways in which,
by transposition
between self
and other, we experience
shared meaning.
I also want to
mention here in
the process a role
transposition, there
is another place where text
and speech are so
very different.
The self and other of
the conversation
is present,
but the "I" in a text
is distant, which
means that although
the "I" of reported
speech would have been
the self of a participant
in its required dialogue,
it is actually an
"other" for a reader.
That's a huge difference.
Now I want to look at
role transpositions
in image. Picturing
is about getting someone
else to see something in
a way similar to yourself.
From the artist's
perspective,
they want to
transpose the other's
eye, the viewer's eye,
with their own.
From
the viewer's
perspective, they
are seeing something as
if they were the artist.
But what the artist
and the viewers see can
never be quite the same,
even though we can trace
a relationship. The
relation is transposition.
I want to talk now about
some of the ways
this happens.
So by example here is
the first known image of
Mary, mother of Christ,
a sixth century
icon from Saint
Catherine's monastery
in the Sinai Desert, Egypt.
It's not very
three-dimensional.
There are only two
planes, one for Mary and
one for the two angels
looking up at
the hand of God.
There are some shadows on
their faces but
not much else.
Now, I want to show you how
the impression of
three dimensionality
evolves in Western
imaging by showing
you three more Marys.
Here is Cimabue's
"Santa Trinita Madonna" of
about 1290 shown at
the Uffici Gallery
in Florence.
Here in this image
there are many planes
and the architectural frame
is three-dimensional.
Next, also in the Uffici, is
Giotto di Bondone's
Madonna of 1310.
Here Mary has gained
a more human body.
We can see the shape
of her breasts and
the shadows in the
folds of her clothing,
and her face is more realistic.
And finally, our fourth
Mary. Sandro Botticelli's
"Madonna of the Book"
of 1482.
This image feels like
a much more
realistic image of
Mary than the first
of these four images,
the sixth century icon.
This two-dimensional image
depicts a
three-dimensional world
of space - inside
the room, the world
outside, the window -
and everyday
objects - the bowl,
the flowers,
the book lying on the
side of the shelf.
The shelves recede
into the corner of
the room. One of the
main changes across
these Marys is
the development
of what we call linear
perspective, where
the distance
recedes across an
infinite progression of
planes. This is one
of the ways in which
a 3D world is transpose
onto a 2D image.
Here is a panel created
between 1425 and 1452, and by
the goldsmith
Lorenzo Ghiberti for
the doors of the baptistery
of the San Giovanni in
Florence. These
panels are depicting
a relief of Old
Testament scenes.
You could see these
wonderful doors today
in the museum of the
Duomo in Florence.
This is a
foundational work in
the development of
linear perspective.
The depth effect is created
by making things
in the background
smaller than things in
the foreground, and have
a look at the arches for
this effect. 
Ghiberti
theorized his art
and the art of
others in his book
"The Commentarii." 
Referring
to the baptistery door,
he said, "I strove to
observe every measure of
proportion, seeking
the closest possible
imitation of nature.
The figures are relieved
against the planes so that
the nearer figures appear
larger than thus
further out
just as they are in
reality." Architect
Filipo Brunelleschi was
a contemporary
of Ghiberti's.
Here is a depiction of
his 1425 demonstration
outside the Florence
Baptistery. Using a canvas
with a peephole
and a mirror,
he showed the
diminishing size of
the walls of the building
the more distant
they became. 
The central point
in a hypothetical
distance was
the "vanishing point,"
a centering
line of sight orientated
to the horizon.
The relative sizes
of seen objects
could be figured
mathematically. Scholars
today think this may
not have been such
an original idea
because these principles
had already been
figured out
mathematically by
the Arab thinker Alhazen
nearly 500 years before
in his Book of Optics.
The Florentines had
a translation of this
book available to them.
My point is this: realism is
an invention. From
form to form,
realistic images create
the effect of seeing
a 3D world on
a 2D plane. We think
it is realistic,
but if we look up, we would
discover that vertical
lines recede as well.
But if we do that it will
look like the buildings
are falling down,
and the columns we
know are straight.
This is also
one-eyed vision,
and we discover
that as soon
as we put on the
viewing glasses for
3D imaging. And then
our field of vision
is round, clear in
the middle and blurry
on the outside.
So realistic images give us
an impression that is
not true to reality
as we see it.
Realistic images
are in fact
an altered reality, and
realism is a visual trick,
an optical illusion.
Now I want to speak
about the transposition
on the functional plane
with realistic imaging,
in this case photography.
Here is a wonderful
photograph of
the great philosopher
and feminist
Simone de Beauvoir taken
by Henry Cartier Bresson
in 1946. We have
a complicated succession of
self-other
transpositions here.
His eye has become your eye.
The picture is taken
at the height of
the head looking at
his subject, and her eye,
or we might assume
that the
photographer assumes,
looking into some kind of
philosophical distance.
The camera never lies.
But of course
it always does
because the truth of
the photograph is
the thing that it shows,
or not only that,
it is the self-I in
the form of the seeing-eye
of the photographer
transposed into a scene.
And now you, the
viewer, a transposing
yourself into
that photographer's
eyes, that other self.
This is how we parse
these movements.
The meaning of these roles
is in the moves they make.
Each role begging to
be swapped out with another.
