Tag Archives: Herring illusion

Spatial illusions and Temporal Illusions (I): Three Dimensions

Previous: what does an illusion of x show?

Previous: complexity-illusions and simplicity-illusions

Note: Most of the ideas here are developed further in my 2018 book, Philosophy of Time and Perceptual Experience.

This project concerns the relationship between time and illusion. However, a great number of impressive illusions demonstrate illusions of spatial properties. How one might otherwise categorize these spatial illusions depends on one’s metaphysical position on space. But, it also depends on one’s metaphysical position on time.

Three Dimensional Phenomenology

Wackermann writes that Geometric–optical Illusions (GOI) is ‘a covering term for a multitude of phenomena in which subjective perception of extents, angles or forms is affected by additional (contextual) elements present in the visual field’ (Wackermann 2012, p.89).

One may take this to be only discussing phenomena that are constrained to two dimensions of vision (a ‘visual field’). This may be a position, for example, of those who hold that our direct and immediate visual experience is of sense-data, and then that sense-data have two-dimensional properties (and not three-dimensional properties). Also, those who make a distinction between how something looks and how something is, and then hold that how something looks is two-dimensional. We see that in, for example, Noë, who talks about tilted coins looking elliptical, but being circular and tilted (see Noë; also, Leddington for, in my opinion, an excellent and critical discussion of the idea).

I don’t agree with this way of interpreting how things seem to us (and so agree with Leddington). I think that the world to us does not visually seem two-dimensional. I think that the world visually seems to be (a) three-dimensional (b) from a particular perspective. I would say: It is not two-dimensional and perspectiveless, but three-dimensional and perspectival. To adapt an example from Leddington,

What leads us to believe that:

    • We are seeing a circular coin, tilted away from us, and spinning through space – a three-dimensional entity related to us in space –


    1. The appearance of a circular coin tilted away from us, and spinning – a three-dimensional entity related to us in space –

and not

    1. The appearance of an elliptical thing seen head on, changing shape, shrinking and growing in thickness – a two-dimensional thing which has no properties dependent on where we stand.

Can I defend this view that appearances are three dimensional? I think someone can, and relatively easily, by simply pointing out what most people visually experience of the world. One might add the fact that our visual sense of things as three dimensional is so strong that even when we create two-dimensional art, we have to work to make them seem two-dimensional. This is a point of Lichtenstein’s pop art: through his co-option of comic-book art, he is interested in representational art that is as flat (i.e., 2D) as possible. And it is hard, is noteworthy, just because our experience is not like that.

But I’m not sure that I can defend the view that the world seems 3D from my experience.

Several years ago, near the beginning of my PhD, I went to the doctor because of a problem with my eyes. Testing my vision, the doctor claimed something about my vision which I did not know (and also had nothing to do with the problem that brought me there in the first place).

I have been told, and believed, that I was hypertropic: my vision of distant things is fine, but what I look at up close is blurry. When I was a kid, I couldn’t read properly without glasses; my eyes eventually adjusted, and so I didn’t need glasses anymore, but I still couldn’t read with my left eye closed.

However, the doctor told me that my eyes were fine. Instead, I had amblyopia in my right eye, a condition in which part of the brain receiving images from an eye does not process them properly. Since I can read without glasses, it seemed that the image from that eye was being ignored and only my good eye attended to consciously. This is why when I look out of my left eye alone I can read and see distant things, but not in my right. And it also meant this: I do not have proper stereopsis. I do not have proper three-dimensional visual experience of nearby things.

If this is true, then complete three-dimensional vision is not something I can claim to know what it is like to have. Just as colour-blind people don’t know what the visual difference between red and green is like, I don’t know what the visual difference between something a few inches from me and a few feet is like. At least, not as it is for people with normal three-dimensional vision.

Yet, it does seem to me as if I have some sense of three-dimensional depth when I look around me. The apparent distance of a model of a mountain, and the apparent distance of an mountain, seem different to me. When I lived in a flat in St. Luke’s in Cork, the view was an uncommon one to me: it overlooked much of the city, and so was of quite distant things. Some winter mornings, working at my desk near the window, I was surprised by something in the corner of my vision. It seemed to be an insect with large black wings flying by the window (like damselflies that used to fly about down by the river when I lived in Cambridge). Yet, when I looked properly, I’d see it was actually a rook lifting off from a distant roof. There was a different feel, in some way, between what it was like to see a small insect by the window and the larger bird in the distance.

This suggests that I don’t know what it is like to fully experience three visual dimensions. Still, I have some kind of experience of three dimensions, one which has no dependency on a difference between the eyes, e.g., of the difference between seeing a bird moving in the distance and an insect move nearby.

But others do seem to have the richer experience of three dimensions. In his chapter ‘Stereo Sue’, Sacks 2010 discusses the experience of stereopsis, stating that different people seem to have it to different degrees. Sacks claims that he himself has very strong stereopsis. Those who do get something from those 3D pictures that were popular in the nineties. Those who don’t — like me — don’t. And in fact I have never seen an image in one of those pictures. I don’t even know what it would be like to see that.

As such, one can take the following discussion to include both kinds of three-dimensional appearances: those involved in stereopsis (call it strong 3d vision) and those involved in my kind of vision (call it weak 3d vision).

Illusions of Three Dimensions

Our experience of three dimensions can be used to explain why geometric illusions occur, something not lost on psychologists of perception. Gregory has argued that many geometric illusions can be understood as side-effects of appearances always being of a three-dimensional world, even where there is no third dimension involved. The appearances are a product of (or maybe just are) judgements about visual stimuli; these judgements are based on either learned or evolved propositions about the visual world.  For example, Gregory argues that the Muller-Lyer illusion (see below) occurs because we judge one line as being more distant than the other; this is based on how such shapes typically appear to us, something we might learn throughout our life.

If this is right, one may take geometric illusions to at least include phenomena where what we perceive seems also to be arranged in a third dimension. This is not to say it is arranged in three dimensions, of course, or that it is arranged in those dimensions as it seems to be arranged. In both cases, however, we have GOIs, where the geometry is three-dimensional.

Where three dimensions are in play, apparent three dimensions diverge from real three dimensions, and in that way we also get a geometric illusion. Dramatically, anamorphic images are illustrative cases of three dimensional distances bearing no relation to their apparent three dimensional distances, as happens for example with Bernard Pras’ work here. (See Clark for discussion about anamorphosis).

Common images also share this feature: what is depicted in them can be any distance from us. Yet what we actually or really see, or at least what is actually or really giving rise to our seeing, is constituted by elements that are all on one plane at a distance from us.

Some theorists have also argued that we are aware of spatial properties such as distance in other perceptual modes, such as sound (O’Callaghan 2011) or smell (Batty 2010). This suggests the following: GOIs can be generalised to any number of dimensions and perceptual modes. This is important for what will be said about the relationship between time and space.

So: when we look around us, it seems to us that we are at a place in the world, surrounded by objects distributed throughout three dimensions, and aware of their three-dimensional properties from that place in the world. If how this seems in particular cases is not how it is, then we are under an illusion.

Here, then, is a list of the sort of illusions that are said to be of spatial properties. I am describing them in a specific way so as to highlight what particularly interests me about them:

  • Muller-Lyer illusion(already mentioned above): different lines with the same length belong to different geometric structures. They seem to have different lengths.
  • (i) Ponzo illusion, (ii) Ebbinghaus illusion, (iii) Ames room: different objects of equal size belong to different geometric structures. They seem to be different sizes.
  • (i) Zollner illusion, (ii) ‘cafe wall’ illusion: different lines which are parallel to one another, i.e., that are equally distant to one another throughout their length, belong to different geometric structures. The lines do not seem to be parallel, i.e., they seem to be at different distances to one another throughout their length.
  • Hering illusion: different lines which are parallel to one another partially occlude otherwise visible radiating lines. The different lines seem to bulge as they pass in front of different parts of that radiation.

Demonstrations and discussions of these illusions are common, as the bibliography attests. Offhand, the easiest to find is the Wikipedia optical illusion entry, which has the images for all the above: http://en.wikipedia.org/wiki/Geometrical-optical_illusions. Michael Bach’s site is useful, and entertaining, although it focuses on more active illusions (to which we will turn). Also, in the ‘Links’ above, Lotto’s site demonstrates colour and shade illusions.

There are many many more of these illusions, named typically by their discoverers and suggestive in their regularity and description of some general principles which can be used to explain several of them at once.

Explaining these in the first place in terms of the appearance of three dimensions is commonplace (again, see Gregory; but also see Newman & Newman 1974 for experimental evidence the authors claim denies Gregory’s kind of explanation). What is of most interest to me is made explicit by how I describe these illusions. It is that these seem to be cases of complexity illusions: there is no difference between two things, but there seems to be a difference.

A difference is more complex than the absence of difference.

  • If you posit (a) an x and a y, then you only need to commit to x and y. But if you also posit (b) some distinction, e.g., an asymmetric relation, between x and y, then you also need to commit to that distinction, as well as x and y. ‘b’ is more complex than ‘a’.
  • If you posit (c) x and y, both with property P, then you only need to commit to x, y and P. But if you posit (d) x, with property P, and y with a different property, P’, then you also need to commit to P’. ‘d’ is more complex than ‘c’.


1. No difference between two things is either ‘a’ (no distinction) and/or ‘c’ (no different properties).

2. A difference between two things is either ‘b’ (some relation between them) or ‘d’ (each has different properties).

If what you commit to as being real is ‘a’ or ‘c’ while appearances are, respectively, ‘b’ and ‘d’, then you will have a complexity illusion.

Change your ontology, of course, and things can look very different. But how could you change your ontology with spatial illusion?

This seems to be obvious — you change what you hold to be true of space.

But I can imagine some objecting as follows: isn’t it too much to change one’s idea of space? Isn’t it easier and better to just stick with illusions? They are common after all. Changing one’s concept of space seems desperate.

Maybe. But I think there’s a possibility that, given how one intuits things in space, one should change it anyway.


What really surrounds you? The space we live in if we’re living in spacetime (in development)