a template that corresponds to the Ebbinghaus effect.

So let's talk about this in a little bit more detail so that you understand it.

But the general point is that the strategy we're using here is exactly the same

strategy for determining by analyzing laser scan,

data of the real free world, and

the frequency recurrence of projections from that world onto your retina.

What the incidents of different contexts and

circles it is in terms of the frequency of it's occurrence in your experience,

not just you personally, but as I've said many times before,

in the experience of our species over the eons of evolution.

So let's look at this template that we're going to use to get the data that we need,

using again, the same source of lots and lots of laser scanned 3D scenes and

the application of the relevant template many, many times,

millions of times, so that seem to get a probability distribution of how

often have different context with central circles appear.

So this is just an illustration of the template, so

the central circle is the same.

And now, we're going to test the central circle or the frequency of the occurrence

of the central circle in relation to circles that are smaller,

a little bit bigger, a little bit bigger, a little bigger, and fairly big.

So this was the Ebbinghaus effect.

When you saw the same circle,

the dotted line circle in the context of smaller circles,

it looked larger, somewhat larger, that's the Ebbinghaus effect,

that one that you're seeing in the context of larger circles.

Go back and look at the Ebbinghaus Effect, and

you'll see what I'm talking about here.

So getting the data is, in one sense, straightforward.

Just using a bunch of different size circles in the context and

asking how does the occurrence, or the frequency of occurrence of those

different contexts affect the overall frequency of occurrence of the Ebbinghaus

effect when the circles are small, a little bit larger, or large.

And that's what's being compared.

In the Ebbinghaus effect, you're comparing, an example of which,

the surrounding circles are small to a context,

a different context in which those surrounding circles are larger, and

that's what's causing, in some way, we don't know yet, but in some way,

the effect that makes the two central circles look somewhat different in size.

So we'll go back and look at the Ebbinghaus circles if you need to,

at this point, to understand what the effect is.

Here's just an example of the application of the template.

So here is the template when the circles are large.

Here is a template when the circles are small.

These are just examples of the natural seams from

the digital images of the laser-scanned images that we saw before and

talking about line lengths and angles.

So it's exactly the same strategy, but

now being applied in a different context to try and explain that whole raft

of classical size illusions as they're called.

And in this case, the Ebbinghaus effect, the Ebbinghaus illusion in particular.

So when we apply millions of terms, context of large circles again.

So I'll do a center circle that's the same size, and when you apply this template,

as I said, millions of times to get a probability distribution of how often

we are getting this context in our experience

of the circle that's in the center and how often we are being exposed to or

getting this context of the circle that's in the center.

So when you do that, these are the results that you get.

So this is a little bit complicated, let me try to explain it.

These different colored lines indicate the diameter

of the surrounding circles, little ones versus bigger ones.

That's the data that we are trying to get, and they're each color coded,

so a small surrounding circle is color coded in black,

a somewhat larger one in yellow, a somewhat larger one in green and so on.

And you can see again, not surprisingly.

I mean, I think you would expect this that the frequency of

occurrence of the same circle in different surrounds is different.

So take any particular size of a central circle,

which is what's illustrated here on the x axis of the graph.

So there's a different frequency of occurrence for

the central circle of any particular size

in the context of circles in the surround that are of different sizes.

That's just another way of saying or describing the Ebbinghaus effect,

but the point of doing this is that when you apply the templates to real

world scenes for frequency of occurrence of the different contexts for the same

central circle, the different circle sizes in the surround is very different.

And that's what the curves of each of these different-sized surrounding

circles is indicating, again, showing on this axis how this varies.

So let's go back to these classical effects.

The one we've been talking about here is the Ebbinghaus Effect.

As I said before, each one of these has a different name,

each one of these has a different effect.

But suffice it to say that each of the phenomenon,

if the circle is bigger or smaller in your perception,

depends on the frequency of occurrence of the circle in human experience,

your experience and the experience of the species or the eons of evolution.

So as we talked about before in the context of

explaining empirically the lengths of lines and why we see them so

strangely and why we see angles so strangely,

acute angles being perceived as generally larger and obtuse angles as smaller,

this is exactly the same empirical theory applied to these classical effects.

And suffice to say that each one of these