Monthly Archives: August 2012

Complexity and illusion

Previous: Illusion 

Previous: What does an illusion of x show?

Previous: Three concepts of content and one of constitution.

Say we have two structures, one more complex than the other.What does it mean to say that one of these has ‘more’ than the other, such that we say it is more complex (and the other less complex)? The intent of this entry is to discuss the ideas that (a) complexity comes in degrees; one can compare the complexity of two things and hold that one is more complex than the other, (b) something can be complex or simple and (c) use this to sort illusions into two kinds.


The complexity of X is determined by the number of mutually independent intrinsic properties, intrinsic relations and elements which constitute X. The relations in which X is a relatum, extrinsic relations, and relational or extrinsic properties do not determine X’s complexity (although they can contribute to the complexity of something else of which X is an element)[1].

In contrast to complexity, the simplicity of X is defined in relation to the complexity of some other entity. X is simple in relation to some Y, if it is less complex than that Y; X is constituted by fewer mutually independent intrinsic properties, intrinsic relations and elements than Y. (One might also say that X more simple than Y, although that can be misleading).

The number of intrinsic properties, intrinsic relations, and elements can be used as a number by which one can measure the complexity, and against which some the complexity of other entities can be compared. The difference in these is what allows one to say one is more complex than another.

So, say that two entities, A and B, are constituted by very simple entities in relation to anything in our world: Each entity has only one kind of property, spatial location, and both A and B exist in a very simple world: this world is entirely contained within the same one-dimensional line. This world is otherwise wholly uninteresting, containing no other properties, relations or entities. If A has four such simple elements, and so is located at four spatial points along the line via these elements, and B has two such simple elements, i.e., is located at two spatial points along the line via these elements, then A is more complex than B: A has complexity 4 but B has complexity 2.

But say, also, B has different colours for each of its elements, and these colours are intrinsic and independent of each other, but A does not have any colours for any of its elements. Then the complexity of B increases by 3 (from the properties) and A stays the same. B then has complexity 5; thus, B is more complex than A.

What are we tracking by the number assigned to complexity? What we are tracking is difference or variation (I suppose you might call this information, given a certain understanding of that term). If something has more properties than something else, it has a greater variety of properties or its structure is differentiated to a greater degree. Any difference or variation at all will do: difference in shape, size, properties, relations, particular constituents. Whatever you include in your theory or description, this complexity tracks the amount of it needed for a particular entity, and allows comparison between different entities. This does not mean that you can compare them, of course. If the difference or variation in X can be described, then the complexity of X can be described. (If the difference or variation in X is indescribable, its complexity is indescribable).

When talking about something as being complex, this can mean two things: It either means it appears on the scale of complexity, but nothing more; it can be compared in complexity with something else, even if it has no structure at all (like a bare particular, however coherent that is). Or it is complex relative to something; something is not just complex, it is complex relative to some other x. In that latter sense, we can contrast it with something being simple.  Something is not just simple, it is simple relative to some other x.

Relative to some M, a mid-point in complexity between S and C (S is less complex than M, M is less complex than C), S can be called simple and C can be called complex. This is true of any point between the two, so M can lie anywhere between them. But for structures more complex than C, using just these two terms, both S, M and C are simple; for structures less complex than S, using just these two terms, both S, M and C are complex. The situations of interest are those which can be M, as these distinguish complexity and simplicity [2].

With illusions, the issue is the difference between two situations where we refer to complexity. These are situations of apparent complexity and real complexity. In this project, it is easier to talk about entities as just being complex or simple, as if they are not relational properties. This is the same as talking about things as small or big, without defining what it is that they are small or big in relation to. As will be discussed, the difference in complexity between what is apparent and what is real is one way in which there can be illusions. But further: the difference gives rise to two importantly different ways in which there can be an illusion, ways which have very different consequences for what ones theories.

Complexity and illusion

Let us say one of the following happens: I take a drug of some sort; a neuroscientist stimulates parts of my brain; a psychologist presents me with a special image on a computer screen, a magician shows me something as part of an act. In all of these, I am surprised because how things seem is not how things are. With this in mind, there are two further ways we might distinguish how appearances differ from reality:

(1) By one of those means, I end up seeing what is presented to me as (a) a perfectly smooth sphere; (b) a single unambiguous rich shade of red, which (c) lies at rest on a table before me. But the object I see as being this way is, in fact, one or more of the following: (~a) roughly spherical thing: either squashed and bent so that it is not a perfect spherical shape and/or roughly surfaced like an orange or a golf ball; (~b) multiple colours, perhaps different shades of red, but perhaps even other hues (green, blue, and so on); (~c) moving around or even hovering above the table.

We can ask: which is more complex: appearance or reality?

— For (a): The answer may be difficult for shape: but we might say the following: where there appears to be a simple or easily defined shape, a sphere, with every point on its surface equidistant from its centre, there is really a relatively complex or difficult to define shape, with many points at its surface at different distances from its centre. In that case, what is real is more complex than what is apparent; what is apparent is less complex than what is real.

— For (b): Apparently, there is just one shade of red; really, there are multiple shades and even perhaps hues. Again, in that case, what is real is more complex than what is apparent; what is apparent is less complex than what is real.

— For (c): given that being at rest, having no variation over time in its location, is less complex than being in motion, having variation over time in its location, and, given that the object’s being on the chair, two objects at no distance from each other, is less complex than the object hovering above the chair, two objects at some distance from each other, then, again:  what is real is more complex than what is apparent; what is apparent is less complex than what is real.

If these analyses are right (which can be questioned[3]) they are all cases where appearance is less complex than reality. There is more to what is real than what is apparent. Apparently, there is complexity S; really, there is complexity C.  C is not S; C>S(as discussed below). This lets us say this: relative to C, S is simple; relative to S, C is complex.

Based on what has already been said about illusion:  illusion(x) <-> apparently(x)  and ~x. Here, apparently(simplicity) and (~simplicity); thus, illusion(simplicity). So, I will call such a case of illusion a simplicity-illusion.[4]

Now, let us reverse the relationship between appearances and reality.

(1) Let us say that that I end up seeing what is presented to me as (a) roughly spherical thing: either squashed and bent so that it is not a perfect spherical shape and/or roughly surfaced like an orange or a golf ball; (b) multiple colours, perhaps different shades of red, but perhaps even other hues (green, blue, and so on) which (c) is moving around or even hovering above the table. But the object I see as being this way is, in fact, one or more of the following: (~a)  a perfectly smooth sphere; (~b) a single unambiguous rich shade of red; (~c) lies at rest on a table before me.

We have the reverse situation to the simplicity illusion. The discrepancy is between complex appearances (‘a’, ‘b’ and ‘c’) and simple reality (‘~a’, ‘~b’ and ‘~c’). As such, since appearances are more complex than reality, we can say that this is an illusion of complexity. So, I will call such a case of illusion a complexity-illusion.


1. A simplicity-illusion is an illusion where how things seem/what seems to be the case/what is apparent/appearances  is less complex than how things are/what is the case/what is real/reality.

2. A complexity-illusion is an illusion where how things seem/what seems to be the case/what is apparent/appearances  is more complex than how things are/what is the case/what is real/reality.


Theory, empirical data, appearances and illusion

Metaphysics of time

Time and Illusion 1


1. Otherwise, what we would otherwise call a simple, e.g., something with the most basic properties and constitution, would greatly increase its complexity by just in a world with many other things to which it is related, or which define properties for it. One might argue for such a thing, but I don’t see the need, and I think it would unnecessarily complicate the matter (which, despite the content of this post, is not, I think, a good thing).

2. I am aware that, even though both S and C are complex, or S and C are simple, C is still more complex than S, S less complex than C.  One can always say that. The issue here is only to say which is complex and which is simple. M, an exclusive point between S and C, allows one to say that, by defining the complexity/simplicity in relation to M.

3. Motion, in particular, may be questioned. That something is in motion is defined relative to a frame of reference. Saying that A varies in its spatial location, e.g., it is here, then it is there,  may be true for B but not for A, according to which there is no motion of A, e.g., it is here, then it is here (but B has moved in this case). The answer is: if you define something as moving, you must assume a shared rest in both what is apparent and what is real.

[That you may not need to do this, or even cannot do this, leads to situations where one need not have an illusion of motion. But that involves a another factor ignored here — it involves showing that, in fact, appearances (motion) can correspond to reality (motion), because there is that motion according to something which can ‘do the required work’* of being a frame in perception. This is a very similar question to a question I have about illusions of duration, about which I’m currently writing a paper for peer review publication; given the outcome of that publication process, I’ll discuss this in a later post.

*I’m deliberately leaving what it means for anything to do that ‘work’ undefined for now). In my 2010a, and my recent talk at IMMA, I call something similar to this the ‘occupant’. I think it might conceivably be the same thing as the occupant. Anyway, I’ll leave it alone here.]

4. For reasons that will be discussed in a later post, this may motivate one to insist that, in fact, there is strictly speaking no illusion here.


What does an illusion of x show?

Previous post: what perceptual theories should explain about illusions.

Previous post: universal illusory counterparts

I assume that I am not under a universal illusion. Of course, I would assume that even were I under a universal illusion.

Just as I cannot assume that how things seem is how things are, so I cannot assume that how things seem is not how things are. I agree with Levin 2000 that, although it is possible that I am under a universal illusion, it is also possible that I am not under a universal illusion; further, it is difficult to find evidence that would decide for the former.

If I assume that, then the possibility that I am under such a universal illusion is not something I will try to prove or disprove. What then is the point of discussing universal illusion? To illustrate the following: there can be illusions; a subject of an illusion can fail to detect that they are under an illusion; just because something is apparent does not mean that it is how things are. Thus, if one is naive, and takes all appearances to be how they are (colour? Shape?), one could be misled without knowing it(about colour? Shape?).[1]

And so one might think this: although there may not be evidence of a universal illusion, surely there is evidence that we are capable of being under such a universal illusion. That is, there is no evidence that, for everything I seem to have experienced, all of the object and properties that are or have been apparent to me, are illusory; but there is evidence that I am capable of such illusory experiences, regarding any objects and properties that are or have been apparent to me. That is, based on how I am constituted in this world, I am capable of being misled regarding anything that is apparent to me.

But are we sure there is evidence for such a capacity for universal illusion?

What sort of evidence is there? Well, how about: people hallucinate — even do so easily, given the circumstances, such as a sensory deprivation tank; people experience distortions in sound, smell, sight, and touch; people dream so vividly that they believe, on waking, that it was no dream. People have false memories (and of course false expectations, but this would be a different meaning for ‘illusion’); people have after-images, which they do not know as being ‘in the mind’ (or whatever is going on there) and interpret as being out in the world. By my own analysis (Power 2011, and discussed in the footnotes of this post), Perky’s results suggest people can even have illusions in their imagination.

This plenitude of distortion and misleading appearances suggests that these are only a sample of what goes wrong, for any mode of perception, and that the list of illusions which our perceptual system is capable of extends much further. So, from this, we might conclude that,  our perceptual system is capable of any illusion. For any veridical appearance, there can be a non-veridical, illusory counterpart appearance, i.e., we can assume a principle of universal illusory counterparts.

What can be drawn from an illusion of x

We might conclude this, but it is worth being slow about it. To do so would be equivalent to concluding that, because there are so many ways you can pull apart an object, then one can actually pull it apart in any conceivable way. This would be a controversial assumption, and it ought to be for perception as well. We might conceive of an appearance of P without P being real, but this does not mean that, for any actual subject, there can be an appearance of that P without P being real. It would only follow if one assumed a principle of universal illusion; but the point here is not to assume the principle of universal illusion, but to provide evidence in support of universal illusion.[2]

Instead I think you should only draw the following (here, I mean by ‘y depends on x’, in cases of properties, that for there to be an instance of y, there must be an instance of x):

1. Trivially: each example of illusion, each illusion of an x is evidence that there can be an illusion of that x. That certainly has consequences just from that particular discrepancy between appearance and reality. For that x, its appearance does not mean that we conclude that there is an x. But this does not mean that an illusion of x shows we are capable of an illusion of anything other than x. Unless:

2. Since the appearance of x can occur without actual x, then if the appearance of something else, call it y, depends on the appearance of x, it can occur without there being an x.

To use an example from my 2011, a house can look like a giant castle if its appearance as a giant castle depends, on the one hand, on its apparent shape and, on the other hand, on its apparent distance. If its apparent distance is illusory, it’s ‘giant castle-ness’ will be illusory. One can easily demonstrate dependencies about distance, shape and size, e.g., as seen in Bernard Pras’ work:

Such illusions, however, do not show illusions which do not depend in this way on x, i.e., some z that is not y. The shape or size of something can be distorted by distortions in distance, but this does not mean that its colour or shade can; one must show something else for that. Nor do they show that these dependent illusions, the ‘y’s, are illusions of the other apparent properties; distance may show the size is distorted, but fail to show the shape is distorted.

Of course, other illusions might do this (and I can think of some that do for the particular examples) but that does not mean that the offered example of illusion shows it. And this should not be surprising. Consider the examples of illusions above, of the Ebbinghaus illusion and the ‘checker shadow’ illusion. From the Ebbinghaus illusion, one can safely infer that the relative size between objects (x) can be illusory. But it is not obvious that one may conclude from the Ebbinghaus illusion what is shown in the ‘checked shadow’ illusion, that a difference in shade can be illusory (y). Further, even if one did think this, it would be because they can show that the differences in shade (y) is in some way dependent on what is illusory in the Ebbinghaus, the differences in size (x), i.e., just the point made here.

3. The opposite dependency relation that is in ‘2’ is this: Unless the appearance of x itself depends on z, then the dependency of x on z does not guarantee that, from the appearance of x, there is a z.

Say that the shape, x, of an object O depends on z, a particular set of three-dimensional properties in physical space, e.g., an object’s apple-shape depends on the object’s ‘fairly-spherical’ three-dimensional properties (this is very rough, I know). If O merely appears to be x, that there is an illusion of x in perceiving O, then from the mere appearance of x, O’s apparent apple-shape, one cannot conclude that there is a z, that O has fairly-spherical three-dimensional properties.

Of course, it might still have those three-dimensional properties. But you can’t take that from its apparent apple-shape, because it really isn’t apple-shaped. If it was really apple-shaped, then you could conclude that it had those three dimensional-properties. But then there would be no illusion here of the apple shape, the x in this example.

From ‘1’, ‘2’, and ‘3’, one can draw other conclusions: mutually dependent properties are combinations of ‘2’ and ‘3’. The point is, other than these three conclusion, I am not sure what else one can draw from an illusion of x. (Suggestions are welcome).

Illusions of space and time

Someone might wonder: so what?  This is all very well if one did not know the following:

There can be illusions of fundamental properties, properties on which most other properties depend. These are properties of space and time — that is, there can be illusions of space and illusions of time.

Thus, there can be illusions of any properties dependent on their occurrence on spatial and temporal properties (or their appearance on the appearance of spatial and temporal properties).   Most properties, especially in the phenomenology of perception, depend on spatial and temporal properties.

And there are lots of instances of illusory spatial and temporal properties.


It’s Now Over There: illusions of space (there) and time (now)(in development)

Illusion and the embedded and extended mind debate

1. Some philosophers (e.g., Crane 2006, Tye 2007, and Harman(discussed in Lycan 1996)) claim that, in having an experience, what is apparent to us, e.g., what we seem to see, hear, touch, etc., seems not to belong to the experience itself, but only to belong to things in the external world, independent of experience itself. The experience’s own properties are not apparent to us at all. Tye refers to this as the ‘transparency’ of experience; Crane refers to it as the ‘diaphanousness’ of experience.

One point I think could be drawn from the issue with illusion is that, even if it seems that way, that experience is transparent, that we only experience properties of external things, we possibility of universal illusion means that cannot be sure that it is that way. But, again, it does not mean that we cannot be sure that it is not that way either. My point throughout is that, without actual evidence for one or the other, I think one has to either throw up one’s hands and then sit on them about the whole affair, or draw on the only thing available to prefer one or ther other: appearances themselves, that it seems that way.

[A footnote to the footnote: on the claim that transparency/diaphanousness -> we do not experience the properties of experience themselves.

Because I am interested in the structure of experience, in how it is constituted and its spatiotemporal conditions, and, further, I am sympathetic to positions involving an object being necessary and presented for experience (somewhat in the spirit of naive realism and indirect realism) I tend to take it that, in one way at least, it should be an open possibility that we experience properties that  strictly (though indirectly) belong the experience.

These are properties of the object of experience under a conception of the experience/object relation as one where the object is a constituent of the experience. In that case, one might say that we experience a part or constituent of experience, the part being the object of the experience, or its properties. If we think of the whole inheriting the properties of its parts (e.g., a woolly mammoth is woolly — except, of course, only part of it is woolly(its tusks, eyes, and toes aren’t)), then we are in this sense experiencing properties of the experience.

I think is reasonable to think that is a metaphysical claim about experience; it is not a naive claim, or simply pointing out the phenomenology of experience, i.e., how we describe it. But I also think that the alternative is not a naive claim, a simple pointing out of the phenomenology, either: that, conceiving of experience as something that happens,  then experience is something completely separate to what we experience, what we experience is not part of experience.

After all, the very motivation for transparency/diaphanousness is that the phenomenology, in having an experience, is only of the object and its properties, of what we experience. In ignorance of the complex processes involved in experience, one might think that all there is to experience is what is experienced; all that is happening is only what we are experiencing. In that case, one experiences the properties of experience because the only properties experience has are the properties of what we experience.

Of course, I do not assume that this is true, nor do I expect anyone else to assume it in this debate. But I do not think it is false because experience is separate or separable from what we experience. It is my view that, for various reasons, one might want to develop an account of experience that says experience includes the properties of what we experience, and more, rather than excludes those properties (which are, again, the only ones of which we are aware in having an experience).

(I will say more about this in a later post)]

2. One might think that the fact we are talking about appearances means automatically that there can be an illusion. That is, an: appearance of x -> possibly ( illusion of x).

First, as the discussion so far should show, the issue doesn’t just concern the possibility of illusion. It concerns there being evidence that, given how our actual perception works, that, for a particular x, x can appear without being real.

Second, it is true that ‘appearance’ and ‘not real’ are compatible, that ‘apparent(x) and ~x’ is a coherent phrase, and that an entity can have the concept of ‘appearance’  and ‘unreal’ or ‘not real’ coherently applied to it (in contrast, the special concept I introduce as ‘obviousness‘ is not compatible with ‘not real’; ‘obvious(x) and ~x’ is incoherent — as incidentally is ‘obvious(x)’ and ~apparent(x)’). But that something is conceivable, again, does not mean we have to satisfy it with our explanations about how actual perception works (something similar is argued by Harman, discussed in Arstilla 2005). 

(I can think of at least one group of theorists should agree with this last point: those who hold that some apparent properties are only apparent, without there being any case where they correspond to something real, e.g., representational physicalists who agree that qualia  (1) are apparent and (2) are non-physical but reject having to accept them as something real (e.g., Dennett 1991, perhaps; Lycan 1996; discussed by Crane 2006).  For reasons that have been touched on so far, I think one should resist approaching the problems of consciousness in this way, but never mind that now).