Takahashi's Illusion Revisited

© Riccardo Manzotti, Milan, December 2017.
For any question, please write to riccardo.manzotti@gmail.com.

In December 2017, the world of perception and of curious readers has been taken by storm by yet another illusion that promises to show the difference between reality and what we see. The visual effect is called the ‘curvature blindness’ illusion, and it’s described in a new paper from psychologist Kohske Takahashi (https://www.ncbi.nlm.nih.gov/pubmed/29204264). Below you can see the suggested stimulus.

Original Takajashi's illusion

As you can see, every other line appears as a zigzag rather than a wave. In fact, all lines have exactly the same shape – a sine curve. I see a zigzag line where there is a wave. Isn’t this case a proof that we what we see is not what is there? Is it not the proof that we perceive something different from reality? It appears so but, alas … it is not. In fact, we see what is there. How is that possible? Follow me.
In a nutshell, the alternative solution is that the zigzag and the wave are actually different and that the slight difference in the phase of the darker and lighter portion of it makes them different lines. The property we perceive, the shape we perceive, is made of both geometrical shape and shading and thus we see something different. The above description of the illusion was misleading insofar it claimed that “all lines have exactly the same shape”. It is true that they have the same geometrical shape, but what we perceive as shape is the combination of both geometrical shape and shading and thus it is different. Look at then following animated version of the illusion. Does the illusion occur when the shift in color is at a precise point?

To understand the details of what is going on, we need to clean up the picture. First of all, we need to dispel everything that is not essential to the alleged illusion, as the tri-partitioned background, the alternate sequence of lines and the existence of multiple lines. So, once we have stripped the so-called illusion to its basic form, what we get is just the following.

As you can see, the effect is still there. The line appears closer to a zig zag than a sine curve. But now let me ask you: what is it that we perceive when we perceive a line? What is the property that we perceive? Since we have a geometrical concept of lines, we take it that such a property is the geometrical shape of the line. However, this is questionable because in many cases, the exact geometrical shape is difficult to perceive. And so? The visual system resorts to other cues such as a shading. In fact, the visual property we call “looking straight” is different from the geometrical property we call “being straight”. The former is a cluster of properties that can be visually pick up visually, the latter is an abstraction.
The visual property called “straight” is a combination of two physical properties: geometrical shape and shading. Usually they co-occur – something is straight if it has a certain shade or a certain shape, or both. However, in the case of Takahashi’s illusion, the shade is not consistent with the shape. The figure is designed in such a way that the difference in shape is small and difficult to see. Thus shading prevails. Shading is enough to instantiate being the visual “straight”.
Consider the following cases:

The first picture is closer to the physical world where shading and size are usually consistent. The other two pictures are more abstract because they present only one property at a time. In particular consider the last one. Is the difference in shape really relevant the dominant property here? It is not. In fact it is quite small if compared to the longer dimension:

Thus if the shape is reduced in size it becomes less and less visible until it becomes negligible and one perceives just shading, which is, in this case, consistent with a straight line. Ha, got it In fact, the Takahashi’s illusion occurs only when the size is small enough to make the shape difficult to perceive so that the shading is dominant (see below).

In conclusion. What we perceive when we look at a line is a combination of geometrical shape and shading. It is not geometrical shape alone. Mistakenly, there is the widespread notion that humans perceive geometrical shape. They don’t. Alas, the devil is in the detail. Humans perceive a combination of geometrical shape and shading. Call it, visual shape. Visual shape changes if we change shading and we make negligible reduce the size as it happens with as in Takahashi’s illusion.

Do we see something different from reality? No, we see just what is there. The lines look like they had different shape, because they have different visual shape.

Riccardo Manzotti, www.consciousness.it, December 2017, Lavagna.