HARVARD ARQUIECTURA - ARANZA MARTINEZ(1)

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Perspective:
And then, he would finish and paint over the silver perspectival
image of the baptistery, so that when he held the image up
before the baptistery, he could match exactly the image to the actual thing
and see that it was a scientifically constructed linear perspective.
So perspective as a system brings together self and the world.
It brings them all together and organizes them
according to a single point of view.
It's important that perspective anticipates
a modern rationalized conception of space,.
One of the major ways that buildings are depicted
is in perspective.
The basic distinguishing feature of perspective is that these are
drawings-- or, in fact, a way of seeing the world--
in which parallel lines converge at infinity, way off in the distance.
The first thing for us to think about is that perspective is actually
a construct.
It's part of the Western artistic tradition.
It starts in the late 14th century and is really
developed in the 15th century, especially in Florence
by Filippo Brunelleschi.
Different historical periods and different cultural traditions
will depict space differently.
So for instance, in the Japanese tradition,
you often see objects arranged in space.
So there'll often be gold leaf or a colored
plane that separates the objects.
So it's acknowledging that the objects are distinct.
They're not touching, that there is a space between them.
But it's a different way of depicting that space than with perspective.
As I mentioned, the most significant thing with perspective
is that parallel lines, lines that you would normally see parallel
to each other, obviously, are actually converging
at a very, very distant point.
And that means that things that are closer to you will seem larger
and things that are farther away will seem much smaller,
even if these two objects are actually the same size.
The place where these lines converge, which
we can think of as being infinity, or far,
far, far away, is actually called a vanishing point.
And it's placed on what we call the horizon.
There are three major kinds of prospective drawings
that we're going to look at.
And what differentiates these three kinds--
and we call them one point, two point, and three point--
are the number of vanishing points that are used on the drawing.
In the simplest form, we'll use one vanishing point.
So if we look at this drawing, let's imagine, first of all,
that a line is drawn.
And that's the horizon.
On the far, far, far, distance-- so at infinity-- at this horizon,
we place a point.
And that's the vanishing point.
Now, let's imagine that we're constructing
a room, so an object that's in the space that's
between us, the viewer, and the horizon, and the vanishing point.
We start.
We draw a window.
We draw a frame.
And now we're going to put in a floor, walls, and a ceiling.
And since these surfaces and the lines that
define them are parallel to each other, we now
see how these lines are actually converging at the vanishing point.
So we can populate the space with tables and with furniture.
And we see objects that are the same size, that we know
are the same size, actually look different.
The chair that's in the foreground is much larger
than the chair that's farther back, in the background.
Why?
Because again, their lines that are parallel are converging at infinity.
Perhaps the most important thing that we notice with a one point perspective
is that, as a viewing subject--
the person who's looking at the drawing--
we notice how our viewpoint is looking right at the vanishing point.
So where we're looking is where all these lines are converging.
The second kind of perspective drawing is a two point perspective.
It's very similar to at one point, except now, we
have two vanishing points.
So let's look at this in the same way.
First, we draw a horizon line.
And now, we're going to place two vanishing points--
one on the left, and one here, on your right.
Now, let's imagine an object that's place
in the space that's between the horizon and you, the viewer.
So let's take here.
We have a simple farmhouse that we're going to draw.
We notice how the farmhouse has two sides that
are perpendicular to each other.
The parallel lines on one of these sides are converging at the left vanishing
point, while the parallel lines on the other side
are converging here at the right vanishing point.
Once again, the parts of the building that are closest to us
are appearing larger, whereas the parts that are farther away appear smaller.
A final perspective we can make is a three point.
This is very similar to the two point, except we've now
added a third point, where the vertical lines are going to converge.
This is especially useful when you think about how tall buildings
appear, or at least, how we generally depict tall buildings.
Since the top is far away, it appears smaller.
So we've got the same drawing, except let's
now imagine we're using a larger building, for instance, a tower.
IDEAL CITY 
And then finally, he says, "The result was
a translation of psychophysiological space into mathematical space;
in other words, an objectification of the subjective."
So Panofsky puts to a very powerful point a point
that we made earlier, which is that perspective,
in an almost unique conceptual system, brings subject and object together,
brings viewer and the world together.
Now, if we're going to think of perspective as this structure,
as this template, as this mechanism for constructing knowledge about the world,
not just for describing a world that already exists,
then we need a couple of things.
We need a system.
And the system should have both a structure,
and that structure should relate elements one
to another within the system.
So imagine the perspective of a city.
In that perspective of the city, you not only
would use perspective to regulate buildings or to describe buildings,
perspective would also relate buildings to one another,
and indeed, following Panofsky, would open up,
would expand almost to infinity the possibility of spatial perception
and spatial experience.
What I'd like to do as one final example of perspective