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So in this next lesson, I want to remind you about something we talked about

before, but briefly, and it's the inverse problem as it applies to geometry.

And I'm going to argue, as I did before, that the phenomenology of

what we're seeing in these different effects really stems from

the way the visual system has evolved to contend, not to solve.

You can't solve an inverse problem but you can contend with it as a workaround.

So to remind you of the dilemma that exists, the quandary for

vision that exists.

Here's a diagram that we've looked at before and

here are different objects in three dimensional space that we exist in.

And there objects are all different in the sense that this one is further away than

this one, it's a different size or these two are different sizes.

This one is at a different distance yet and it's at a different orientation.

So the objects that are different in size,

different in orientation, different in distance from the observer,

all project in the same way onto the retina.

And how is the observer to know whether the retinal

projection that's the initiator

of the percepts that we're going to see in response to these objects in space.

How is the observer going to know whether the object they're looking at is this one,

this one, or this one or

any of a myriad of others that we could put into such a diagram?

So that's a fundamental problem.

Again, it's called the inverse problem as it applies to geometry.

And the points that it makes, as I've mentioned before, but

let's go over them again now.

Is that image features and their significance for

the behaviors that we have to execute in the real world in

dealing with physical objects in three dimensional space.

Including for present purposes, their geometrical features.

It's just uncertain, it's inherently uncertain,

there's no way of getting around this problem.

This is again the fundamental nature of the inverse problem.

The implication is that real world geometry,

the geometry of the objects, whether it's a Müller-Lyer figure made out of wood or

whatever it might be, that we're looking at the railing in the lobby.

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The geometry that's out there in the real world is basically unknown by

any direct operation that you can imagine applying algorithmically,

logically to the retinal images.

It just can't be done.

You have to figure out how to work around that problem.

So the question is, how is it that we behave appropriately in

responding to geometry in the real world, which we obviously do.

As I said before,

we wouldn't be here to have this conversation if we failed in this task.

But how do we do it?

That's the point of this lesson.