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So in this next lesson, let's talk about the perception of angles.

And, let's begin with just a little better understanding of how we see angles,

and what we're talking about.

We've been talking in the previous lesson, of outlying lengths.

That's just a single line.

And angle, of course, is the coming together of two lines.

And the sub tense, the angular interval between them

given that the two lines come together.

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And this might be a good place to just define something I tend

to confuse which is the term oblique angle and obtuse angle.

An oblique angle is any angle that's different from a 90 degree angle.

That's what we've been talking about before, 30 degree angle, 120 degree angle,

they're different from 90 degrees and those are oblique angles.

An obtuse angle is an angle that's greater than 90 degrees,

and I'm going to be talking about acute and obtuse angles here.

And so these definitions are going to be significant.

So people have looked at the way we see angles for a long time.

And the information that's in this graph has been validated a number of times.

This is a specific example of that validation.

So let's look at the way people actually see angles, and

what this graph shows you is that the way we see acute angles here,

and the way we see obtuse angles here are quite different.

We see all of the angles going from 0 to 90 degrees as being a little

bit greater than they really are, so this is the magnitude of our perception.

Misperception if you like, and it shows that for

acute angles, and as I say, people have validated this many times,

we see them as a little bit bigger than they really are by three or four degrees.

And the peak here is somewhere around 30, 40, 45 degrees.

For obtuse angles these angles that are greater than 90 degrees.

We see those as a little bit

smaller than they really are physically as measured with a protractor.

Again the difference being three degrees or so.

Peaking out at angles of about 150 degrees or thereabouts.

So what's going on here?

Why should we see angles that are acute in one way, and

angles that are obtuse as perceived In the opposite way?

These are seen as being a little bigger.

These are seen as being a little bit smaller.

What's going on?

What could explain that?

Can we explain this perception of angles

in the same empirical way that we explained line length?

Well, not surprisingly, the answer is yes.

Let me first go back and show you how some of

these classical phenomena are actually seen by us.

This is probably the simplest angle effect that you can see.

Again a classical presentation called The Tilt Effect.

That when a vertical line is superimposed on an oblique line,

the vertical line appears to be tilted just a little bit to the left.

That's The Tilt Effect, and it's not very impressive, as I said.

But if you reiterate this effect, it was called The Zollner illusion, or

The Zollner Effect.

So here we have the same thing of vertical lines.

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Four vertical lines super-imposed on a bunch of oblique black lines.

But now I think you see an effect that's considerably more impressive.

These lines,

which are physically parallel, are no longer seen as physically parallel.

It's a littler harder to define what you see in your impression of them.

The parallel kind of jumps around as you move your eyes over the scene, but

it's clear that there's something going on here that's making these red lines

no longer look parallel as they really are when measured physically.

That's called the Zollner Effect.

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Here is one that we saw before.

This is the Hering Effect that I mentioned earlier.

And it's the case here that these red lines are physically parallel

when you superimpose the red lines on a series of radiating black lines.

The lines appear to be somewhat bowed in the middle.

And again, that's another sort of classic angular effect.

The angles made between the red lines and the black lines are making you see them

in this peculiar way.