# Complexity and illusion

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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.

#### Complexity

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.

So:

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.

#### Next

Theory, empirical data, appearances and illusion

Metaphysics of time

Time and Illusion 1

Notes

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.