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Is there a waterfall visual after-effect with discrete inputs?

Is there a waterfall visual after-effect with discrete inputs?

If you watch a waterfall for several seconds and then suddenly change your gaze to a fixed object it appears to briefly move upward.

But if instead you're looking at a scrolling LED marquee sign, does the motion aftereffect still take place? In reality nothing is actually moving on the marquee sign because the LEDs are all fixed in place.

The answer to this question probably has interesting implications as to where in the visual pipeline motion is being processed. The difference between the actual waterfall and the scrolling LED marquee might also be a good way to separate out various aspects of motion processing. I'd be curious in hearing commentary on this.


The waterfall after-effect is an illusion falling into a broader class of visual illusionary apparent movements caused by watching a constant motion for an extended period of time. The motion after-effect can be explained by adaptation of visual neurons that respond selectively to movement. Motion-sensitive visual neurons are tuned to a specific direction. Exposure to a continuous motion in one particular direction fatigues specifically those visual neurons that are tuned to that direction as they continuously fire. When the visual stimulus stops, it alters the balance of activity in favor of cells tuned to the opposite direction, as these are the least fatigued by the stimulus and this causes the after-effect (Mather et al., 2008).

The motion-after effect does work well with more discreet stimuli too.

To start with, here is an example of a more standard waterfall effect illusion (see Fig. 1 for a related impression still image).


Fig. 1. Waterfall. source: Carlos Vasquez

And in this video an example is shown of the waterfall after effect with more discreet stimuli. Not particularly your standard marquee sign but it comes close and there's a definite motion after effect observable (Fig. 2).


Fig. 2. Movie still from this video

However, I think your question is specifically whether a motion after-effect occurs with chase-lighting as often seen in Marquees signs (Fig. 3).


Fig. 3. Marquees sign showing illusionary apparent motion. source: Old Turnpike School

The chasing-light stimulus in itself is a visual illusion, as there is no true motion involved. Instead, it is generated by using electronic circuitry to activate lights serially with a certain time delay in-between activations. Because there is no motion involved as such, I believe the after effect will not occur, or very weakly. At least, I couldn't observe an after effect after watching several chase lightings for a while. For example, the chase lightings in Fig. 1 become ambiguous when I look at it a while, i.e., the lights actually spontaneously reverse their direction when staring at it for a while. The only thing I see when I look away, personally, is a colorful blob, and no motion after-effect.

Reference
- Mather et al., Trends Cog Sci (2008); 12(12): 481-7


Is there a waterfall visual after-effect with discrete inputs? - Psychology

The hard problem of consciousness--the nature of phenomenal experience--is especially hard for people who believe that:

(1) Conscious perceptual experiences exist inside a person (probably somewhere in the brain) 1

(2) Nothing existing inside a person has (or needs to have 2 ) the properties one is aware in having these experiences.

The experience I have when I see (dream of, hallucinate) a large orange pumpkin is certainly inside me. Why else would it cease to exist when I close my eyes, awaken, or sober up? Yet, nothing inside me--certainly nothing in my brain--has the properties I am aware of when I have this experience. There is nothing orange and pumpkin shaped in my head. How, then, can I be aware of what my perceptual experiences are like--presumably a matter of knowing what qualities they have--if none of the properties I am aware of when I have these experiences are properties of the experience?

Surely, though, we are, in some sense, aware of our own conscious experiences. We have, if not infallible, then privileged, access to their phenomenal character. I may not know what it is like to be a bat, but I certainly know what it is like to be me, and what it is like to be me is primarily--some would say it is exclusively--a matter of the phenomenal qualities of my perceptual (including proprioceptive) experience. I am aware--directly aware--of what it is like to see (dream of, hallucinate) orange pumpkins. If such awareness is incompatible with (1) and (2), so much the worse for (1) and (2).

This is a problem that some philosophers have given up trying to solve. Others spend time tinkering with (2). The problem is real enough, but (2) is not the culprit. The solution lies in distinguishing between the fundamentally different sorts of things we are aware of and, as a result, the different forms that awareness (or consciousness 3 ) of things can take. Once these distinctions are in place, we can see why (1) and (2) are compatible with privileged awareness of one's own experience. We can have our cake and eat it too.

By way of previewing the argument for this conclusion, let o be an object (or event, condition, state--i.e., a spatio-temporal particular), P a property of o . We speak of being aware of o , of P , and of the fact that o is P . These differences in the ontological kinds we are aware of are reflected in differences in the corresponding mental acts of awareness. Awareness of P is a much different mental state from awareness of the o which is P , and both differ from an awareness of the fact that o is P .

In thinking about the mind's awareness of itself, these differences are important. For if e is some mental particular and P a property of e 4 , we must not confuse awareness that e is P with awareness of either e or P . For one can be aware of the former--aware, that is, that one's experience is P --without being aware of either the experience ( e ) itself or the quality ( P ) that helps make it that kind of experience.

Therein lies an answer to the puzzle generated by (1) and (2), the puzzle of how one can be aware of internal affairs--aware of what one's experiences are like--without being aware of these experiences themselves or the properties that give them their phenomenal character. The mind's awareness of itself is an awareness of facts about itself, an awareness that internal experience, e , is P . It is not an awareness of the internal object e or the property P out of which such facts are composed. The facts we are aware of in knowing what it is like to experience orange pumpkins are, to be sure, facts about internal affairs--thus the truth of (1)--but the properties we are aware of in achieving this awareness (being universals 5 ) exist nowhere. They aren't in the head. Thus the truth of (2).

1. Objects, Properties, and Facts

When an object is moving, I can be aware of: (A) the moving object (B) the fact that it is moving (C) the movement (D) all of the above (E) none of the above. Consider:

Case A: I study the minute hand of a clock. The hand is moving so the object I see, the object I am aware of, is a moving object. I do not, however, sense, I am not aware of, its movement. Nor (thinking the clock is broken) am I aware of the fact that it is moving . I am aware (I see) the moving hand, o , but I am aware of neither its movement, M , nor the fact that it is moving: that o is M .

Case B: I observe the minute hand on the clock for several minutes. I see that the hand is in a different position now than it was a moment ago. I thus become aware that it is moving. Nonetheless, I still do not perceive the movement. The minute hand moves too slowly for that. I know it is moving. but I cannot see it move. I am aware of o and that o is M but not M .

Case C: I observe the movement of a nearby vehicle and mistakenly take it to be my own movement. I stomp on the brakes. Nothing happens. In this case I was aware of both the neighboring vehicle and its movement without at the time being aware that it (the adjacent vehicle) was moving. I thought I was moving. Awareness of o and M , but not of the fact that o is M .

Case D: I observe the second-hand of another clock. Unlike the minute hand of the first clock, the movement of this object is plainly visible. I am aware of the moving hand, its movement, and also the fact that it is moving. When one becomes aware of the fact that o is M by awareness of both o and the M of o I call it direct fact-awareness. I am directly aware that the second hand is moving, but indirectly aware that the minute hand is moving.

Case E: I am aware of neither the object, its properties, nor the fact that it has those properties. There are unobservable objects (e.g., electrons) that have properties (e.g., spin) I am not conscious of. I am, to be sure, aware of the fact that electrons have this property (I read about it in a book), but there was a time I was not. There was a time, in other words, when I was unaware of o , the property S , and the fact that o was S (not to mention the fact that there were o 's).

I will call these three forms of awareness o -awareness (for object -awareness 6 ), f -awareness (for fact -awareness) and p -awareness ( property -awareness). When the kind of awareness is clear from context--when, for example, I am talking about an awareness (and, thus, a p -awareness) of properties--I will generally drop the distracting prefixes. There are times, though, when it is important to specify exactly which form of awareness is at issue, and on these occasions the prefixes will appear. Though I use movement (a relational property) to illustrate these distinctions, I could as well have used any other property. I can, for instance, be f -aware that the wine is dry (someone told me it was or I read the label) without being aware of the wine or its dryness (I do not taste the wine for myself). One sees a fabric in normal light--thus experiencing (becoming p -aware of) its color (blue, say)--without realizing, without being f -aware, that it is blue. One thinks, mistakenly, that the illumination is abnormal. The fabric, one thinks, only looks blue. And one can be aware of the color of Tim's tie--that particular shade of blue--without being o -aware of his tie or the fact that it is blue. One sees another object of exactly the same color. If it sounds odd to speak of being aware of an object's color without actually seeing the object, imagine someone pointing at another object (a color sample perhaps) and saying, " That is the color of his tie." 7 What you are made p -aware of when you see the color sample is the color of his tie. One might also be p -aware of the color of his tie while being aware of no object at all. Imagine hallucinating a homogeneous expanse of color that exactly matches the blue of his tie.

This last claim may sound false--at least controversial. When a person hallucinates pink rats, isn't the person aware of colored images (shaped like rats)? Isn't awareness of properties (colors, shapes, sizes, orientations, etc.) always (and necessarily) awareness of objects having these properties? To insist on this point is a way of denying (2). It is a way of denying that there is nothing in one's head that has the properties one is aware of in having experience. Since I am here exploring the possibility of understanding conscious experience given the truth of both (1) and (2), I assume, to the contrary, that hallucinations are experiences in which one is aware of properties (shapes, colors, movements, etc.) without being o -conscious of objects having these properties. To suppose that awareness of property P must always be an awareness of an object (an appearance? a sense-datum?) having property P is what Roderick Chisholm (1957) called the Sense-Datum Fallacy. Following Chisholm, and in accordance with (2), I will take this to be a genuine fallacy. Hallucinating pumpkins is not to be understood as an awareness of orange pumpkin-shaped objects. It is rather to be understood as p-awareness of the kind of properties that o -awareness of pumpkins is usually accompanied by.

Awareness (i.e., p-awareness) of properties without awareness ( o -awareness) of objects having these properties may still strike some readers as bizarre. Can we really be aware of (uninstantiated) universals? Yes we can and, yes, we sometimes are. It is well documented that the brain processes visual information in segregated cortical areas (see Hardcastle 1994 for references and discussion). One region computes the orientation of lines and edges, another responds to color, still another to movement. 8 As a result of this specialization it is possible, by suitable manipulation, to experience one property without experiencing others with which it normally co-occurs. In the after-effect called the waterfall phenomenon , for instance, one becomes aware of movement without the movement being of any thing. There is no colored shape that moves. To obtain this effect one stares for several minutes at something (e.g., a waterfall) that moves steadily in one direction. In transferring one's gaze to a stationary scene one then experiences movement in the opposite direction. Remarkably, though, this movement does not "attach" itself to objects. None of the objects one sees appears to be moving. Yet, one experiences movement. As a psychologist (Frisby, 1980, p. 101) puts it, "although the after-effect gives a very clear illusion of movement, the apparently moving features nevertheless seem to stay still!" One becomes, he says, "aware of features remaining in their 'proper' locations even though they are seen as moving." This may seem paradoxical (Frisby describes it as contradictory), but it is nothing more than a p -awareness of one property (movement) without this movement being instantiated (as it normally is) in or by some object. One's movement detectors are active, but they are not made active by any object possessing the normal array of sensory properties (shape, color, texture, etc.).

Everyday perception is generally a mixture of object, property, and fact awareness. Usually we become aware of facts by becoming aware of the objects and properties that constitute these facts. I become aware that his tie is blue by seeing his tie and its color. I become aware that gas is escaping by smelling the escaping gas. Perceptual modalities being what they are, though, we are often made aware of facts by being made aware of properties altogether different from those involved in these facts. We become f -aware that the metal is hot by seeing it change color, not by feeling its temperature. Instruments, gauges, and natural signs (tree rings, tracks in the snow, cloud formations, etc.) have familiarized us with the various ways awareness of facts is mediated by awareness of objects and properties quite different from those involved in the fact. I see that the water is 92o by an awareness not of the water, but of a thermometer and the height of its mercury column. Use of language in communication is another source of f -awareness in which there is little or no connection between the objects (sounds and marks) and properties (spatial and temporal arrangement of symbols) we perceive and the facts (reported on) that communication makes one f -aware of. When f -awareness is achieved by awareness of properties and/or objects other than those involved in the fact, the f -awareness is indirect . Thus, awareness that your daughter has a fever is indirect when you use a thermometer, direct when you feel her forehead.

There is, then, a virtual 9 independence (conceptual, not causal) between f -awareness, o -awareness, and p -awareness when the awareness is perceptual. We can, and we often do, have one without the others. If this is also true--and why shouldn't it be?--of our awareness of mental affairs, this tells us something important about awareness of our own conscious states. I begin by describing what it tells us about a special class of conscious experiences-- perceptual experiences.

2. Perceptual Experience

Perceptual experiences are phenomenally rich in a way that beliefs are not. It is like something to have them. Unlike a belief or judgment (an f -awareness) that a pumpkin is moving toward you (something you can have without awareness of either the pumpkin or its movement), seeing a pumpkin move involves an experience that is phenomenally quite different from experiencing a green bean move toward you, a red tomato moving to the left, a ripe banana rotating in place, etc. The experience of a moving pumpkin, though it is caused by a pumpkin (and, according to causal theorists, must be so caused in order to be rightly classified as an experience of a pumpkin) is detachable from external causes in the sense that the very same kind of experience--an experience having the same phenomenal character--could occur (and in pumpkin hallucinations does occur) without a pumpkin.

This much, I hope, is philosophical (not to mention psychological) common sense. Disagreement arises when we turn to questions about our awareness not of pumpkins, their properties 10 , and facts about them, but of our experience ( e ) of a pumpkin, its properties, and facts about it . Letting P stand for a property of a pumpkin experience, a property that helps makes this experience the kind of experience it is, how does one become aware that e is P ? Is this achieved by an awareness of e and P or is it, instead, indirect--mediated by an awareness of some other object and (or) property ?

There is a long tradition stemming from Descartes that conceives of the mind's awareness of itself as direct. We become f -aware that a visual experience is P by means of o -awareness of the experience, e , and p -awareness of P . According to some philosophers, all fact-awareness begins here. 11 Thus, awareness of facts about a pumpkin, that the pumpkin is P , are reached via inference from o -awareness of e and p -awareness of one or more of its properties. We become fact-aware of what is going on outside the mind in something like the way we become f -aware of what is happening outside a room in which we watch TV. The only objects we are aware of are in the room (e.g., the television set) the only properties we are aware of are properties of those objects (patterns on the screen). Only f -awareness--awareness of what is happening on the playing field, concert hall, or the broadcast studio--is capable of taking us outside the room.

I will not discuss such theories (basically sense-data theories). I set them aside, without argument, because they all deny thesis (2), and my purpose here is to understand the mind's awareness of itself in a way compatible with (1) and (2). Contrary to (2) sense-data theories affirm that there is something in a person's head that has the properties the person is aware of when he sees or hallucinates an orange pumpkin. Sense-data are inside, and sense-data actually have the properties one is aware of when one sees or hallucinates a pumpkin. The sense-datum is orange. It is bulgy and shaped like a pumpkin. It moves--at least it does so relative to other sense-data. In having a visual experience of a pumpkin it is the bulgy orange sense-datum, an internal object, one is o -aware of, and it is the properties of this internal object one is p -aware of. Awareness of pumpkins is, at best, indirect. It is the same type of awareness (i.e., fact -awareness) that one has of Boris Yeltsin when one "sees" him on TV.

Armed, as we now are with the distinction between object, property, and fact awareness, though, we are in a position to understand what goes wrong in traditional arguments for indirect realism. We are in a position to understand--and, thus, resist--arguments against (2). The mistake in traditional arguments lies in failing to distinguish between f -awareness of experience, that it has phenomenal character P , on the one hand, and, on the other, p -awareness of the qualities (e.g., P ) that give it this character. Failing to distinguish these forms of awareness, one concludes, mistakenly, that awareness of what it is like to see (experience) pumpkins must be awareness of the properties (i.e., P ) of these experiences. That is the first mistake--the mistake of inferring p -awareness of the properties of experience from f -awareness of the fact that experience has those properties. The second mistake (this is optional the major damage has already been done) is inferring o -awareness from p -awareness--that is, inferring that one must be o -aware of e in order to be p -aware of e 's properties. The conclusion? To be aware of what it is like to experience pumpkins, one must be aware of one's own pumpkin experiences in something like the way one is aware of pumpkins.

The fact that we don't have to be p -aware of an object's properties to be f -aware that it has those properties does not mean that we are not aware of our own experiences and their properties. It only shows that an awareness--even a privileged awareness--of what it is like to have a given experience is not, by itself, a good reason to think we are aware of either the experience or its properties. Once the distinctions between kinds of awareness are in place, our privileged awareness of what it is like to have these experiences may simply be a form of fact-awareness, an indirect awareness of a fact about an experience that is psychologically immediate and epistemically privileged.

But how is this possible? How is it possible to be aware in both a privileged and (or so it seems) direct way of facts about one's experiences without being aware of either the experiences or t heir properties? If one's f -awareness of one's own experience is supposed to be indirect like becoming aware, by looking at X-ray photographs, that one's arm is broken, what objects and properties is it an awareness of that is supposed to give one this awareness? I can become (indirectly) aware that my arm is broken by having the doctor tell me it is or by looking at the photographs for myself, but what could possibly bring about an indirect fact-awareness of the quality of one's own experience that would preserve the immediacy and privileged character of this awareness? No one tells us--indeed, no one can tell us--what our own experiences are like in the way a doctor can tell us about our broken bones. X-rays are not of much help in telling what it is like to be a bat or what it is like to see orange pumpkins. What, then, is supposed to tell us what qualities our experiences have if we are not, in having them, p -aware of them ? There must be something (other than the experience) that tells us this since, in accordance with (1) and (2), we are now assuming that the properties we are aware of in having the experience are not properties of the experience. If we are to be made f -aware of what our experiences are like--that they are P for some value of " P "--then, we must be made f -aware of this fact by an awareness of properties and objects other than those of the experience itself. What are these other objects and properties?

They are--what else?-- the objects and properties our experiences make us aware of. One is made aware of what a pumpkin experience is like (that it is P ) not by an awareness of the experience, but by an awareness of the pumpkin and an awareness of its (the pumpkin's) properties. When the perception is veridical, the qualities one becomes p -aware of in having a perceptual experience are qualities of external objects (the pumpkins) that one experiences, not qualities of the pumpkin-experience. One becomes f -aware of experience--that it is P --by p -awareness of P --the pumpkin's properties. The reason p -awareness of P can make one f -aware that one's experience is P is that P is the property of being an experience, in fact a p -awareness, of P . P tells one what specific kind of experience e is: it is an e of the P kind--i.e., an awareness of P kind. Even when there are no pumpkins, even when hallucinating, it is nonetheless true that what (properties) one is p -aware of in having the pumpkin experience are color, shape, texture, distance, and movement--properties that pumpkins normally have.

The key to this account is the relation between P , the property we are p -aware of in having experience e , and the property of the experience ( P ) that we thereby become f -aware that e has. If P is the pumpkin's movement, a property that one becomes aware of in observing a moving pumpkin, then P is the property of being an experience (a p -awareness)-of-movement . P is not the property: is moving . P is the property that a possibly stationary experience has that makes this experience a p -awareness of movement. 12 P , therefore, helps fix the kind of experience e is--an experience of movement. Though P is not a property one is p -aware of, it is nonetheless a property that (helps) make that experience the kind of experience it is--an experience, specifically, of a moving pumpkin.

What this means is that if we follow philosophical convention and take qualia to be properties of one's experiences (and not the properties one experiences), then it is P , not P , that is the quale. Nonetheless, it is P (i.e., movement) not P (an awareness of movement) that one is p -aware of. One is (or can be--see §4 below) aware of the quale P , to be sure, but this is fact , not property -awareness. One's experiences of movement do not (or need not) have the properties one is p -aware of in having these experiences. The experiences don't move. Nonetheless, when experiencing movement, the property the experience has is P , the property of being a p -awareness of movement.

This account of the mind's awareness of itself gives a neat and, I think, satisfying account of both the psychological immediacy (i.e., the seeming directness) of introspective knowledge and the epistemically privileged character of self awareness. F -awareness of the fact that one's experience (of P ) is P is psychologically immediate because, although it is indirect (one is not p -aware of P ), one cannot have an experience of this sort without thereby being aware of P , a property (usually) of external objects that reveals (to the person having the experience) exactly what property it is that his or her experience has--namely, P (= an awareness of P ). Technically speaking (given my earlier definitions) this is indirect fact-awareness, yes, but the fact one is indirectly aware of is so directly given by the properties (of external objects) one is aware of that the process (from p -awareness of P to f -awareness that one's experience is P ), when it occurs, seems direct and immediate. It can be made to seem even more direct, of course, if one confuses the properties one is aware of in having the experience with the properties of the experience. F -awareness that e is P is also privileged because only the person having the experience is necessarily (in virtue of having it) aware of a property, P , that reveals what kind of experience (viz., P ) he is having. Other people might also be experiencing P , of course, but unless they know you are, they can only guess about the quale (viz., P ) of your experience.

Before leaving this discussion of perceptual experience, it may be useful to see how a familiar (to philosophers) scenario plays out on this account. What Jackson's (1986) Mary does not have before she emerges from her colorless room is an awareness of red (or of any other color). Assuming that colors are objective properties (if they aren't, we don't need Jackson's argument to refute materialism (1) and (2) will do the job), Mary knows all about tomatoes--that they are red ( P )--and she knows all about what goes on in other people's heads when they see red objects (there is something in their brain that has the property P ), but she does not herself have internal states of this sort. If she did, she would, contrary to hypothesis, be p-aware of (she would actually experience) the color red. Once she walks outside the room, objects ( e s) in her head acquire P --she becomes p -aware of red. She is now aware of things (i.e., p -aware of colors) she was not previously aware of. Using our present distinctions to express Jackson's point, the question posed is not whether Mary is now aware of something she was not previously aware of (of course she is she is now p -aware of colors), but whether Mary is now f -aware of things that she was not previously f -aware of. The answer, on the present account of things, is No. 13 Mary always knew that ripe tomatoes were red ( P ) and that ripe tomato experiences were P --viz., awarenesses of red. There are no other relevant facts for her to become aware of. 14 Emerging from the color-free room gives her an awareness of properties ( P ) that figure in the facts (that o is P ) she was already aware of, but it doesn't give her an awareness of any new facts.

We have now taken the first step in this account of the mind's awareness of itself. In a way that is consistent with both (1) and (2) and in a way that preserves the essential features of the mind's awareness of itself (the psychological immediacy and epistemically privileged character of this awareness) we have an account--at least the broad outlines of one--of how we are aware of our own experiences of the world. What remains to be done is to see whether this account can be generalized to all mental states. My efforts at generalization (§3) will be feeble. I can, at this point, do little more than gesture in what I take to be the appropriate directions. I close (in §4) with a mildly interesting implication of this account of self-awareness.

3. Pains, Feelings, Emotions, and Moods.

Up to this point I have focused exclusively on conscious perceptual experiences, mental episodes that are of things--whatever objects and properties we are, in having the experience, made aware of. Perceptual experiences are being identified with internal states having properties (e.g., P ) that make them p -awarenesses, experiences, of the properties (e.g., P ) that external objects have. Something, e , in my head having the property P (a property that is not movement) constitutes my awareness of movement ( P ). I can become f -aware that something in me has P by an awareness of P . If e 's having P is caused by a pumpkin having P (i.e., by the movement of a pumpkin), then I am aware of a pumpkin's movement. I see it move. If there is no such object, I am aware of movement without being aware of any moving object and, thus, without being aware of any object's movement. I hallucinate or imagine something moving.

This account works nicely enough for phenomenal experiences that are, in some ordinary sense, of or about things (mental states the having of which makes us perceptually aware of things). For this reason it is tempting to try extending the account to mental states that are, in some related (but, perhaps, different) sense, also of or about things: beliefs, desires, intentions, hopes, and, in general, the propositional attitudes. Just as my experience of movement has a property that makes it a p -awareness of movement, perhaps my belief (i.e., my f -awareness) that some object, o , is moving is, likewise, an internal state having a property, B (not itself movement), a property the having of which makes an internal state into a conceptual representation or depiction (i.e., an f -awareness) of movement. Just as the English word "movement" need not itself be moving in order to figure in a representation of something as moving (e.g., a sentence), so too, perhaps, there are symbols (concepts?) in the head that do not (or need not) have the properties they represent objects as having. If this were so, then thoughts, just as experiences, would be mental states that would not (or need not) have the properties we become f -aware of in having these thoughts.

If this were so, then we could tell the same story about awareness of these states that we told about our f -awareness of perceptual experiences. We become f -aware that we are having thoughts about movement (internal states with B ) by actually thinking about movement. It is the movement we think about --the content of our thought--that (when we introspect) "tells us" what we are thinking about and, hence, if we understand what thinking amounts to, that we are thinking about movement (not color or shape). Just as I reach the f -awareness that I am experiencing movement from a p -awareness of movement, so too I reach an f -awareness that I am thinking that o moves from an f -awareness that o is moving. 15

I will not pursue this line of thought any further here since it seems like a more or less obvious extension of the present theory, and there are much more difficult problems to face. This treatment of belief, judgment, and thought is, I think, merely a version of the view that Tyler Burge has promoted about the introspective accessibility of externally grounded belief content. Burge's idea is that my second order belief (the content of which is that I believe o moves) inherits the conceptual content MOVES from the content (that o moves) of my first order belief. Hence, if I really do believe (1st level) that o moves, I must be right in thinking (2nd level) that that (viz., that o moves ) is what I think. The present theory is a version of this idea since a (2nd level) f -awareness that I am aware (at the first level) that o moves is privileged because the property (viz., movement) I am (1st level) f -aware of (= believe something has) "tells me" more or less infallibly what content-property my 1st level belief has--viz., M , a conceptual awareness that something is moving.

Unlike the propositional attitudes, though, there are a great many mental states (emotions, moods, and so forth) that, unlike experiences and thoughts (both of which seem representational at some level), do not, at least not on the surface, make us aware of anything (either of objects, properties, or facts). And it is these states that pose the real problem for the present account. When I am hungry, have a splitting headache, or am depressed, for instance, I seem to be aware of mental objects (the hunger, the ache, the depression) and their properties (the headache is splitting , the hunger gnawing , the depression constant) . Surely in such cases I am aware not only of the fact that I have certain feelings or am in a certain mood, but also aware of the feelings and moods themselves--the pain, the hunger, the depression.

This, I concede, is a natural way to talk about feelings, emotions, and moods. What I think worth questioning, though, is whether this way of talking doesn't embody a confusion between awareness of something (an act) and the something of which we are aware (the object of that act)--a confusion that is fostered by a failure to distinguish between the different things we can be aware of. Why suppose, for instance, that feelings of hunger are internal mental objects (i.e., conditions, states) we are o -aware of and not awarenesses (i.e., experiences) of certain internal (non-mental) objects--a chemical state of the blood, say? Just as we conceived of visual experiences as internal states having the property of being awarenesses of P (for some P of an external o ), why can't hunger be similarly conceived of as an internal experience (a p -awareness) of the properties of an internal o ? Why can't an itch in one's arm be thought of not as something in the arm (brain?) one is o -aware of, but an o -awareness (in the head) of a physical state of the arm? Why can't we, following Damasio (1994), conceive of emotions, feelings, and moods as perception of chemical, hormonal, visceral, and muscuoskeletal states of the body?

This way of thinking about pains, itches, tickles, and other bodily sensations puts them in exactly the same category as the experiences we have when we are made perceptually aware of our environment. The only difference is that bodily sensations are the experiences we have of objects in the body (the stomach, the head, the joints, etc.), not objects outside the body. What gives these sensations their phenomenal character, the qualities we use, subjectively, to individuate them, are the properties these experiences are experiences of, the properties (of various parts of the body) that these experiences make us p -aware of (irritation, inflammation, time of onset, injury, strain, distension, intensity, chemical imbalance, and so on). What gives a (veridical) visual experience of an orange pumpkin its particular quality ( P ) are the qualities of the pumpkin (viz., P ) that this experience (in virtue of being P ) is an experience of. Likewise, what gives headaches their particular quality (what distinguishes them from pains in the back, itches, thirst, anger or fear) are the properties (and these include locational properties) that these experiences are p -awarenesses of. Just as one becomes aware of external objects in having visual and olfactory experiences, so one becomes aware of various parts of the body (and the properties of these parts) in having bodily sensations--e.g., pain. Having a headache is not an awareness--certainly not an o -awareness--of a mental entity: a pain in the head. The only awareness one has of pain is an f -awareness that one has it. In saying that one feels pain what one is really saying is not that one is o -aware of something mental (viz., a pain)--but that one feels (is aware of) a part of the body the feeling (awareness) of which is painful (is pain). Once again, the phenomenal qualities (= qualia) of these mental states are not the properties of those parts of the body one becomes p -aware of in occupying these states. They are, instead, awarenesses (= S) of these properties ( P ). We do not have to be aware of the state ( e ) itself (or its properties S ) to be aware--authoritatively aware--that we occupy a state of that phenomenal kind. P gives our conscious awareness its phenomenal character and tells us what kind of experience we are having.

But can such an account possibly work for all experiences--for love and hatred, joy and depression, ennui and anxiety? Even if such feelings are not all properly classified as "experiences," they all seem to have an associated phenomenology that calls out for explanation. Can what-it-is-like to have these feelings or experiences always be interpreted (using the model of perceptual experiences) not as internal objects we are o -aware of, but as awarenesses of the properties of internal objects? Can the entire phenomenology of the conscious mind be boiled down to the properties (of bodily parts and external objects) that we are p -aware of in having these experiences?

Whether it can or not, this is clearly the direction suggested by our analysis of perceptual experience. It may turn out, of course, that even if our account of perceptual experience is on target, perceptual experiences are unique. Other feelings, moods, and emotions--itches, pains, hunger, anger, jealousy, pleasure, and anxiety--may have a phenomenal character that they get from other sources. If the story I have told about perceptual experience is plausible, though, it is tempting to try extending it to other qualia-laden mental states along similar lines. I leave the argument that it can be so extended to another time.

4. Prerequisites of Self-Awareness

Fact -awareness, unlike p -awareness and o -awareness, requires an understanding of what one is aware of. 16 One cannot be f -aware that o is an apple without understanding, at some conceptual level, what an apple is. If a child (or an animal) doesn't know what an apple is, this does not prevent it from being o -aware of apples or p -aware of their properties (this presumably happens when the child is a few months old), but it prevents it from being f -aware that the apples (she is o -aware of) are apples.

Since the account developed in §2 and §3 identifies our awareness of our own (not to mention everyone else's) experiences with f -awareness, it requires of anyone aware of the P quality of her own experience an understanding, a conceptual grasp, of the property P (and, thus, of P which e 's having P is an awareness of). If S doesn't know what it is to be P , then even if S has a P -experience (i.e., an experience of P ), S cannot be aware of this. S will be "blind" to it. Since the mind's awareness of itself is always (according to this account) f -awareness, there is no way one can be aware of one's mental states without a mastery of the relevant concepts. The senses make you aware (i.e., o -aware and p -aware) of the world (and, if we can generalize, your own body) before you have developed the concepts needed for understanding what you are aware of, but, lacking a "mental sense" (a sense that allows us to become o -aware of the mind and p -aware of its properties) we must first develop the required concepts before we can be made conscious of what transpires in our own minds.

This result may seem mildly paradoxical so let me take a moment to soften the mystery. Imagine a naive (about numbers and shapes) child shown brightly colored geometrical shapes. The child, possessing normal eyesight, sees the difference between these figures in the sense that the pentagons look (phenomenally) different from the triangles and squares. How else explain why we could teach her to say "pentagon" when (and only when) she saw a pentagon? In the terminology we have already introduced for describing these facts, the child (before learning) is o -aware of circles, squares, and pentagons, and p -aware of their shapes. The child hasn't yet been taught what a circle, a square, or a pentagon is, so it isn't (yet) f -aware of what these figures are, but that doesn't prevent it from being aware of the figures themselves and p -aware of their (different) shapes.

Is the child also aware--in any sense--of what its experience of these shapes is like, of what it is like to see a pentagon? No. 17 Lacking the concept of a pentagon (not to mention the concept of awareness) the only awareness a child has when it sees a pentagon is an awareness of the pentagon and its shape. It cannot be made aware of its experience of the pentagon until it develops the resources for understanding what pentagons are and what it means to be aware of (experience) them. Only then can it become aware of its awareness of pentagons. In having an experience of a pentagon, the child is, to be sure, aware (i.e., o -aware) of a pentagon and p -aware of its distinctive shape. What the child lacks is not a visual awareness (experience) of pentagons, but an awareness of pentagon experiences. Awareness of experience awaits development of the understanding, an understanding of what property one is p -aware of in having the experience. If you lack this understanding, you can still be aware of pentagons, but you cannot be aware of your pentagon experiences. It is like awareness of neutrinos. Being what they are (i.e., unobservable: we do not have a sense organ that make us o -aware of them), neutrinos are objects one cannot be aware of until one learns physics. Unlike pentagons, you have to know what they are to be aware of them.

The mind becomes aware of itself, of its own conscious experiences, by a developmental process in which concepts needed for such awareness are acquired. You don't need the concepts of PENTAGON or EXPERIENCE to experience (e.g., see or feel) pentagons, but you do need these concepts to become aware of pentagon experiences. As psychologists are learning (in the case of such concepts as EXPERIENCE), this doesn't happen with children until around the ages of 4-5 years. In most animals it never happens. The mind is the first--indeed, the only --thing we are aware with, but it is among the last things we are aware of.

REFERENCES

Chisholm, R. 1957. Perceiving . Ithaca, NY Cornell University Press

Damasio, A. R. 1994. Descartes' Error: Emotion, Reason, and the Human Brain . New York: Avon Books.

Dretske, F. 1995. Naturalizing the Mind . Cambridge, MA MIT Press/A Bradford Book.

Frisby, J. P. 1980. Seeing: Illusion, Brain and Mind . Oxford: Oxford University press.

Hardcastle, V. G. 1994. Psychology's Binding Problem and Possible Neurobiological Solutions. Journal of Consciousness Studies , 1:1, pp. 66-90.

Jackson, F. 1986. What Mary Didn't Know. The Journal of Philosophy LXXXIII, 291-95.


Static Motion After Effects?

I really do love illusions of all sorts, in large part because they fit nicely into my narrative about the fallibility of human thought, but illusions are also great as windows into the ordinary working of our brains. For example, color afterimages provide direct evidence for opponent-processing theories of color vision, and when we find aftereffects for a particular class of stimuli, we can be pretty certain that class of stimuli has particular neurons or populations of neurons that encode it. And speaking of aftereffects, there's a really cool paper in the March issue of the journal Psychological Science that uses motion aftereffects to test an interesting hypothesis about the processing of static images that I thought I'd tell you about.

The classic example of the motion aftereffect is the waterfall illusion, an example of which you can see here. Exactly what's causing motion aftereffects is still a matter of some debate, but the basic story is probably something like this. There are populations of cells in your visual cortex that respond to motion in particular directions and orientations (e.g., straight down ). These neurons are always competing with cells that respond to motion in the opposite direction. Basically, these cells are firing a little bit all the time, but only when they receive some sort of push (e.g., through the input they happen to respond to) do they fire enough to out pace their competing cells and create the perception of their preferred motion. When you stare at motion in a particular direction and at a particular orientation for a while, the cells that respond to that sort of motion adapt -- get worn out, in essence -- and when you take the stimulus away, their firing rate drops below their resting rate. This allows the competing cells to create an imbalance, and suddenly, they cause you to perceive motion in the opposite direction. The effect can be so strong that it can make for some really trippy visuals (see this, for example).

Anyway, an interesting question which, at first glance, seems to have nothing to do with motion aftereffects is, how do we infer motion from static images? How does your brain process the implied motion? For example, how does your brain figure out not only that the horses in the picture below are moving, but in what direction they're moving?

Presumably all of you can tell that the horses are moving, and more specifically, moving from left to right. There is some evidence from neuroimaging studies that this implied motion is processed in the same brain area, the medial temporal area (or V5, or MT, or if we're being specific, hMT+), that processes actual motion(1). Unfortunately, as is generally the case, the imaging studies don't really tell us what's going on in MT. Most importantly, it doesn't tell us whether implied and actual motion are processed by the same cells and in the same way. To determine that, you have to use behavioral data, just as you have to use behavioral data to learn just about anything except that something happens in the brain.

Enter the motion aftereffect. In their Psych Science paper, Winawer et al.(2 presented participants with a series of static images like this one (from their Figure 1a, p. 277):

They then tested them for a motion aftereffect using moving dot configurations. When a motion after effect is present, it will warp people's perception of moving displays of randomly configured dots. So, if the cells in the brain that are responding to actual motion also respond to implied motion, then viewing a bunch of photos, one after the other, that imply motion in the same direction, should cause those cells to adapt, resulting in a motion aftereffect, and thus distort the participants' perception of the moving dot displays.

Since I'm writing this post, you already know that's what they found. In their first experiment, participants viewed static images implying motion in the same direction for sixty seconds, and immediately afterwards saw the moving dot images. In their second experiment, they observed a 60 second series of displays containing two images that appeared to be either moving toward each other or away from each other, and thus toward or away from a point in between the two implicitly moving objects. In both these cases, Winawer et al. were able to observe the motion aftereffect in the random dot displays. In another experiment, they showed participants the series of images for 60 seconds, and then placed a three second delay between the image series and the moving dot display. In this condition, they didn't observe the motion aftereffect, indicating that the aftereffect for implied motion decays much as the aftereffect for real motion.


Author Contributions

Authors contributed according to their competences and interests. AC and AG conceived the main idea of the article. AC collected all data and carried out statistical analyses. LC and FF conceived and developed the technical setup. AC wrote the first draft of the manuscript, while AG, FF, and LC contributed to the final writing of the manuscript by giving suggestions regarding the issues related to the rhetoric and to the literature. AG supervised the entire work. All authors contributed to the manuscript, read, and approved the final version.


Author Contributions

Authors contributed according to their competences and interests. AC and AG conceived the main idea of the article. AC collected all data and carried out statistical analyses. LC and FF conceived and developed the technical setup. AC wrote the first draft of the manuscript, while AG, FF, and LC contributed to the final writing of the manuscript by giving suggestions regarding the issues related to the rhetoric and to the literature. AG supervised the entire work. All authors contributed to the manuscript, read, and approved the final version.


Essay on Perception | Psychology

After reading this essay you will learn about:- 1. Introduction to Perception 2. Phenomenological and Gestalt View on Perception 3. Perceptual Organisation 4. Transactional Approach 5. Depth Perception 6. Constancy 7. Perception of Movement 8. Development 9. Errors 10. Studies.

  1. Essay on the Introduction to Perception
  2. Essay on the Phenomenological and Gestalt View on Perception
  3. Essay on the Perceptual Organisation
  4. Essay on the Transactional Approach to Perception
  5. Essay on the Depth Perception
  6. Essay on the Constancy of Perception
  7. Essay on the Perception of Movement
  8. Essay on the Development of Perception
  9. Essay on the Errors of Perception
  10. Essay on the Studies on Perception

Essay # 1. Introduction to Perception:

Perception involves arriving at meanings often leading to action. In addition to the nature of the stimuli, and past knowledge, perception is influenced by many other factors. In this article, an attempt is made to present to the student a discussion of the various factors involved in attention and perception.

How exactly are we able to relate to discrete sensory experiences in order to see them as meaningful? In other words, how exactly does perception occur? At any time we are attending to a number of stimuli. For example even when we are listening to the teacher we are conscious of his voice, his movement, his appearance etc., but at the same time we respond to him as a single person. This shows that our response is integrated and organised to become meaningful. This process of organising and integrating discrete stimuli and responding to them meaningfully is known as perception.

In the early part of this century the structuralist view of perception was dominant. It held that just as consciousness could be neatly dissected into its component parts, so also could perceptual experiences. Thus, the phenomenon of perception was, for the structuralists, the sum of mere sensations and the meaning associated with it through experience.

Without the benefits of experience there can be no meaning attached to stimuli or to sensations, and thus, there can be no ‘perception’. The infant, therefore, is able only to receive sensory input it is not able to ‘perceive’ anything meaningful. William James described the infant’s perceptual world as a “booming, buzzing confusion.”

However, what does this actually mean in terms of the process of perception? It means that the infant has to learn to differentiate between different sensory experiences. It has to learn to construct perceptual categories through which it can perceive the differences between various sights, sounds, smells and feelings.

The infant’s visual world is formless, shapeless and chaotic. The real physical categories that exist in the world like forms, sounds and colours have to be repeated a sufficient number of times to be perceived as distinct and separate impressions by the infant. In this way the infant learns to perceive forms and objects and associates them with various meanings in their context.

Essay # 2. Phenomenological and Gestalt View on Perception:

A view totally different from the one given above emerged from the writings of phenomenologists. Even in the earlier days, German writers and philosophers had differed on the concept of perception as resulting from a combination of discrete sensory stimulations compounded by experience. They had tended to take the view that perception is a total act not necessarily bearing total resemblance to external stimulus characteristics.

The process of perception is not totally logical but it is, to a large extent, phenomenological. The German philosophers made a distinction between physical reality and experienced reality or phenomenal reality. One’ fact of experience is that perceived objects are always perceived as one and not as assemblages or discrete pieces of sensory information.

The phenomenological writers tended to lay emphasis on the inner processes rather than just experience and stimulus characteristics. The phenomenological view gained popularity through the writings of Husserel Brentano and Carl Stumpf. The real landmark in phenomenology was the work of Ehrenfels on tonal qualities.

He emphasised the totality of experience in melodies. The total experience is something more than some of the individual elements and he gave the name Gestalt Qualitat to this. An example of the phenomenological process in perception can be clearly seen in our experience of illusions. This line of explanation and experimentation was further developed by gestalt psychologists.

The ‘gestalt psychologists’ experiments on animals and birds showed that even at birth there are certain perceptual categories and abilities already present. Riesen showed that chicks brought up in total darkness could immediately distinguish the shape of a grain on the floor when brought into the light.

More recently, experiments by Lipsitt and Siquel have shown that even- a few hours old human infants can distinguish between the sound of a buzzer and that of a bell. Thus the infant’s world is neither a confusion nor a chaos as it was earlier made out to be.

Of course, the infant cannot perceive all objects with the same depth of meaning and understanding as adults can. But certain fundamental perceptual and discriminatory abilities – called perceptual organisations-are built into animals and human beings from birth.

Furthermore, the gestaltists challenged the view that perceptions can be divided into component elements. According to the structuralists, perceiving a chair means dissecting it into the elements of shape, size and angles of the parts of the chair, bound together by meanings from previous experience.

To the gestaltists, this molecular view of the subject destroyed one’s understanding of the phenomenon of perception as a whole. They demonstrated how perceptual phenomena often could not be reduced to elements. The experience of watching a movie on a screen cannot be explained by analysing the series of still pictures that go to make it up.

Listening to a tune- or a particular tune- in one key still gives the experience of the same tune when listening to it in another key, although the elements in both cases are entirely different. This lead to their famous dictum that the whole is greater than the sum of its parts – Gestalt Qualitat. – a unique quality of wholeness.

Essay # 3. Perceptual Organisation:

Animals and human beings are endowed with the capacity to organise and group stimuli which are ambiguous, confusing and novel, thus making them meaningful or sensible. Gestalt psychologists have demonstrated the principles which affect and direct the organisation in order to make the stimulus a meaningful whole within the perceptual field.

Some of the well recognised principles which contribute to perceptual organisation are as follows:

Figure and Ground Relationship:

The basic principle behind perceptual organisation is known as figure and ground organisation. This phenomenon was originally demonstrated by Rubin. One of the most fundamental principles of organisation in the field of perception is distinguishing between the figure and the ground, i.e. the figure which appears against a background.

Gestalt psychologists claim that even in the simplest form of perception, the figure and ground factor operates. For instance, when one is reading these sentences the black letters are perceived against the white background. A flying aero plane, for example, stands out as a figure against the sky or the clouds around it which form its background.

Stimuli which are outstanding and striking in terms of colour, shape etc. come to the foreground to form the figure and the less important or less significant ones recede to the background. However, when there are several objects in the general field of awareness which have equally balancing qualities there may be a conflict and two or more figures may be formed. In such a case there will be a shifting of ground and figure. One part may become the figure at one moment and at the next moment the same may become the ground (see Fig.7.1).

Essay # 4. Transactional Approach to Perception:

The traditional watertight distinctions among different kinds of behaviour like learning perception, motivation are also being given up resulting in a tendency to look at human actions as involving an entire organism totally integrated and directed towards adjusting or adopting to certain environmental requirements.

This emerging view has led to a perspective called the transactional perspective or transactional approach. One of the pioneers in promoting this approach was Ames whose experiments on perception and perceptual illusions are well known.

The transactional approach to perception basically holds that any act of perception at any time is influenced by the past learning experience of the individual and looks at any perception as a transaction or an act of dealing with the environment and other stimulus situations and tries to structure one’s perception in a manner that is maximally approximate to the world of reality.

Some of the basic postulates of the transactional approach to perception are:

(A) Basically those who support this view hold that perception involves an active interaction between the perceiver and the environment, and in this, the past experience and learning of the individual plays a crucial role. Further they also hold that every new perception results in new learning.

(B) The final perception results from a process of active interaction, in which the individual operates on the environment. Thus interaction serves our adaptive function and in view of this they often use the term transactional functionalism.

(C) Such interactions are often unconscious and unknown to the individual resulting in sudden and spontaneous inferences – the role of the conscious process being insignificant.

(D) Transactions not only reflect the past and help us in drawing inferences about the past of the persons, but are also future orientations and the overall life orientations of people. Thus, it may be seen that the past .influence and the present, both are integrated and oriented towards the future.

Ames says that people perceive things, objects, persons and the environment not always as the latter are, but in such a way as to make them compatible with one’s own assumptions and beliefs already acquired, thus very often necessitating distortion of objective reality.

Ames designed a number of experiments using a variety of perceptual situations designed by him like the well-known rotating trapezoid and also what are well known as Ames room experiments. Some of the other postulates of this approach are, that perception follows a certain trend of development during childhood.

It is further claimed that perceptual illusions can be overcome through learning. Though far from being advocates of the typical learning theory approach, those who support the transactional view express the view that even space perception and depth perception are very much products of learning. Thus, they do not support a mechanical view.

What happens in perception is a projection of the perceiver’s own constructs about the stimulus situation with the intention of achieving one’s purpose in action. Thus there is a give and take relationship between perceiver and the perceived situation involving a compromise with the actual reality and one’s own propensity or desire to keep certain assumptions and beliefs constant. The transactional approach is still a loosely formulated approach on the basis of a variety of experiments carried out by different investigators.

One can clearly see the impact of other earlier views on human behaviour like psychodynamics, influences of past experiences, tendency to maintain equilibrium and constancy (dynamic-homeostasis) and phenomenology. The transactional approach in a way makes use of all these assumptions and integrates them. One may not call it a theory, but it certainly is an approach.

Essay # 5. Depth Perception:

One important aspect in perception is the perception of depth, the third dimension or distance we are able to perceive objects as being near or far off. The basic psychological mechanism cannot explain this. The question has been a perplexing one. One view holds that this ability is innate while the other holds that this is an acquired ability. We perceive one rupee coin as one with a depth. This is called the third dimension.

Empiricistic and Nativistic Views:

To have a better understanding of the phenomenon of depth one ought to consider the philosophies of empiricism and nativism. Their views emerged as a consequence of the certainties and uncertainties about human nature. Their key concepts regarding the mind contradict each other and yet remain as the supporting pillars of these views to this day. Empiricism claims that the mind at birth is like a ‘blank slate’ while nativism claims that it is like a ‘veined marble’.

John Locke was the first philosopher who suggested that the mind was initially a ‘tabula rasa’,i.e. it is like a smooth wax table upon which impressions of external events print themselves. This is the crux of empiricism.

Processes like perception and thought reflect the particular structure and dynamics of the world in which we happen to live. However, the basic mechanism through which printing or imprinting operates is by the principles of association, similarity, contiguity, etc. According to the empiricists impressions arrange and rearrange themselves to form the core of our perceptions.

We can see that this idea has shaped many modem systems of psychology. Wundt’s theory of introspectionism is bolstered by empiricism. Pavlov’s work on conditioning, Guthrie’s theory of contiguity, and Broadbent’s account of mental functioning in terms of information processing are all built on the philosophy of empiricism.

Other theorists like Leibnitz proclaimed that the mind is like a slab of marble with veins or streaks. His theory of knowledge was aimed against sensualism and empiricism. To Locke’s postulate “there is nothing in the mind which has not been in the senses” Leibnitz added except the intellect itself.

According to him intellect is present at birth and only gets shaped by experiences. It becomes obvious that nativism as a doctrine boldly proclaims the importance of innate factors in the development of an organism rather than the environmental or experiential ones. A lot of research findings of recent years are heading towards nativism.

Andrey’s books “The African Genesis” “The Territorial Imperative” have popularized a nativistic interpretation of man’s aggression and of his alleged tendency to defend his territory. Audrey believes that many of the modem man’s aggressive tendencies can be traced back to his meat-eating, weapon using ancestors.

Jung’s concept of archetypes leans heavily on nativism. Ethnologists like Lorenz and Tinbergen have shown a strong evidence for innate determination of species-specific behaviour. Another piece of nativistic evidence comes from the field of perception. T.G.R. Bower has found a striking evidence that form constancy, through the visual cliff experiment, is innate in human infants.

A circle seen at an angle is responded to as a circle and not as an ellipse. Gibson and others have provided evidence indicating that depth perception is innate in many species. Immense support to this doctrine is lent from oriental philosophy which has recently been invading the western scientific world. The oriental philosophers support nativism to the core. In the following discussion we see a clear swing towards nativism.

In Gibson’s experiment, the visual cliff consists of a wide sheet of transparent glass placed over a drop on the floor. Gibson and Walk showed that by the time infants could crawl, they would not crawl over the deep side of a visual cliff under any circumstances (see Fig.7.7). This is also true of most new-born animals, which refuse to cross over the cliff.

By the time they start crawling, however, human infants have had ample time to learn depth cues. White tested infant perception of depth prior to the crawling stage by noting eye-blink responses to a falling object in a transparent cylinder positioned over the infant’s face.

If the infants blinked it was assumed that they were responding to the change in distance rather than just the change in retinal size of the falling object which did not otherwise elicit a blink. White also observed that the eye-blink response and, therefore, distance perception-occurred only after eight weeks in the human infant.

Bower put even younger infants in an upright position in a chair and found that infants even as young as two-week old adopted defensive behaviour when seeing an object approach their faces. Eye-blinking, which in this case would not have served to protect them, did not occur, but there was clear eye widening, head retraction and the interposition of the hands between the face and the object.

Bower, thus, demonstrated a clear functional response to visual cues of distance alone, which, in a one-week old infant can be assumed to be unlearned.

Feature Analysis:

Our analysis of the perceptual process has indicated that in any instance the act of perception is influenced by two types of processes. On the one hand we have high level central and also psychological factors like expectations and motivations which do not originate from lower order sense impressions, even though they may be triggered off by them.This type of involvement of high level process is known as top-down processing.

On the other hand processes which originate from lower level physiological and stimulation information are known as bottom-up processing. In this context, psychologists refer to a term called ‘feature analysis’, explaining how these two types of processes operate.

Some psychologists hold the view that perceptual recognition is made possible because a particular set of neurons in the brain are activated, as and when they find an appropriate matter in the field of perception. This is like the phenomenon where only one tuning fork from among a row goes into vibration, when its corroborating match is set in motion.

This is the hierarchical feature detection model. But the difficulty with this model is that this would require a specific set of neurons or feature detection in our brain .Every corresponding sound or light stimulus should have such detectors.

Though it is now known that there are specific set of neurons for certain specific stimulus characteristics, the possibility of having an endless number of specific detectors is yet to be proved. Thus the correctness of this view depends on further achievements in neurology regarding the neuronal functions.

A different and perhaps more widely accepted view is that there occurs what may be called feature analysis. According to this view, the specific detection neurons are of such a type that they can operate in different combinations. For example, they may be recognised as a pair of vertical lines which are parallel with a horizontal line connecting the two in the middle.

Feature analysis involves the brain analysing experiences or perceptual contents into such sets and whenever such set or combination, is available for retrieval from neurons, then recognition occurs. This concept of feature analysis explains how people recognise stimuli and in addition, also provides a clue as to how different stimuli can be given a common interpretation.

For example, when we see different flowers, though we see them as different, we see them all as flowers. But what happens when a. combination of such detections stored in memory do not match with what is actually present? For example, it is very difficult for us or at least some of us to recognise cauliflower as a flower, though many stimulus characteristics resemble that of many other flowers.

It is here that the concept of feature analysis cannot explain, what happens, when the stimuli are ambiguous and are both similar and dissimilar to stored up combinations. It is here that one sees the limitations of bottom up processing theory. It is in this context that the top down processing comes into operation.

Top down processing is influenced by the context of stimuli which creates certain expectations or “expectancies.” We expect certain things to occur, under certain situations or contexts. These expectations based on past experiences and contextual factors, set in motion certain perceptual sets.

The role of expectancy in perceptual recognition was clearly demonstrated in an experiment by Palmer. Palmer showed his subject a scene of a kitchen. Then they were given a very brief exposure to two objects, one resembling a loaf of bread (context relevant) and another a mail box (context irrelevant). The two objects were of the same size and shape. But the subject recognised the loaf of bread more than the mail box, thus showing the influence of centrally aroused expectancy.

Motivation is another factor. The importance of needs in influencing process of perceptions has already been examined. The classical experiments of Brownes and others have already demonstrated the role of motivational factors and needs in the process of perception.

Normally in most acts of perception both top down and bottom up processes work together, each supplementing and complementing the other. Top down processing plays a more crucial role where the stimulus situations are ambiguous, or relatively unfamiliar.

The importance of top down processing will become clearer to the reader later when we discuss the role of “personality factors in perception”. A number of experiments have shown that our perception is very much influenced by the totality of our personality, and personalities have been classified even on the basis of perceptual styles or modes.

Essay # 6. Constancy in Perception:

When we think about perceptual experiences they seem to be incredibly paradoxical. We realise that we see mobility in stationary objects, immobility in moving objects, and see things which are incomplete as complete. The cues which are said to facilitate perception of distance can, at times, corrupt and distort the same.

Similarly, we are able to respond to a stimulus appropriately even with a distorted, wrong or absent retinal image. This contradicts the view that the retinal image is a true reproduction of the object being sensed and considered as a basic mechanism which provokes an appropriate action or reaction. All these make us wonder if we are in a world of illusions or whether perception, by itself, is a big illusion.

One such paradoxical phenomenon discussed here is perceptual constancy. The phenomenon of constancy refers to our perceptual experiences wherein perception remains constant, in spite of the fact that stimulating conditions stipulate a change. Thus, the human being is perceived to be of the same height whether he is seen from a distance of two feet, five feet or fifteen feet.

The phenomenon of constancy is seen in relation to several attributes of the objects like shape and size. To a certain extent the phenomenon of constancy also results in errors of perception, though its advantages far outweigh its disadvantages.

If we accept that the infant does not have to learn entirely to distinguish between forms, shapes and sounds in his environment, but possesses a congenital capacity to do so, there is yet another problem which has aroused a lot of controversy. When we talk of visual perception in particular, how do infants – or even adults – actually make sense of visual objects? The obvious answer seems to be that objects in the external world appear as images on the retina and the individual then responds to these images as objects.

However, the answer is not quite so simple. The retina receives images which vary drastically depending on the particular lighting conditions, the viewing angle and the distance of the object at any given time. If one were to perceive objects merely on the basis of retinal images, one would see a different object at each angle and at each distance from which the same object was viewed. This obviously, does not happen.

When we see a plate at an angle its retinal image is an ellipse. If we see it head on then the retinal image is a complete circle. Yet, we know that both the greatly differing images are of the same object. When we see a chair from a foot away, the retinal image we receive is much larger than that received when the chair is two yards away from us. Yet we know that it is the same object. How do we come to know this?

The controversy that has surrounded the answer to this question has been again one of the opposition between the view that the child is born with the complete ability to see the world as the adult sees it, and the view that the child has to learn to see stable objects. For a long time the latter view held sway-namely, that the individual has to learn to compensate for the differences in angle, colour and distance presented by the same objects.

Recently, however, this view has been challenged and it has been shown that infants of six to eight weeks possess the ability to compensate for changes in the size and shape of retinal images. T.G.S. Bower’s experiments suggest that this ability is innate. Very young infants were conditioned to a cube of a certain size shown at a distance of one metre. Different-size cubes were then shown at a distance of three metres from the infant.

The conditioned response was always given, not to the larger cube which would have presented the same size of retinal image as did the correct cube at one metre, but to the correct cube despite its smaller retinal image size. Size constancy, however, does not occur in the absence of information or cues regarding the distance of the object. Holway and Boring showed that the judged size of cardboard disks became more and more inaccurate as more distance cues were eliminated.

Similar constancies occur regarding colour. A familiar object is always perceived as having the same colour even under different lighting conditions. For example, a piece of white paper is perceived as white whether seen under the yellowish glow of candle light, the stark whiteness of a tube light or under any other coloured lights.

Perceptual constancy, then, seems to be partly due to some innate mechanism and partly due to the influence of past experience and knowledge. The role of past experience in perception and the human being’s tendency to perceive on the basis of assumptions constructed from this past experience was clearly brought out by Ames.

In his famous ‘distorted room’ experiment Ames presented to his subjects an apparent perceptual contradiction between a specially constructed room (which looked normal from the subjects viewing angle when the room alone was seen) and known normal-sized objects seen in windows of the room.

Ames showed that whether the room or the object was suddenly seen as distorted, depended on the subject’s assumptions, i.e. whether the subject ‘assumed’ the room to be truly rectangular. He believed that our perceptions of the objects and people in our environment are subjective. In other words, they are based upon the assumptions we have built up about various objects and people. The organism, therefore, creates its phenomenal world.

Essay # 7. Perception of Movement:

Perception of movement is essential not only to human beings but also to animals. Movement is closely linked to the instinct of self-preservation because moving objects sometimes mean danger. However, the perception of movement involves both the visual messages from the eye as an image moves across the retina and the kinesthetic messages from the muscles around the eye as they shift the eye to follow a moving object.

But at times our perceptual processes play tricks on us and we think we perceive movement when the objects we are looking at are actually not moving at all. Thus, perceived movements can be divided into two types: real movement and illusory movement.

Real movement means the actual physical displacement of an object from one position to another. When we see a car being driven we perceive only the car in motion and the other things around it like trees, buildings etc. are stationary.

Illusory movement is that when an individual perceives objects as moving although they are stationary as is shown in Fig.7.12. One perceives this figure as moving black waves. Another example to illustrate this phenomena is an experience that you must have often felt while sitting in a stationary train if another train moves by you feel that your own train is moving.

Another form of illusory movement is stroboscopic motion-the apparent motion created by a rapid movement of a series of images of stationary objects. A motion picture, for example, is not actually in motion at all. The film consists of a series of still pictures each one showing persons or objects in slightly different positions.

When these separate images are projected in a sequence on to the screen at a specified speed, the persons or objects seem to be moving because of the rapid change from one still picture to the next. The same illusion occurs when two lights are set apart at a suitable distance from each other and when they are switched on and off at an interval of one sixteenth of a second.

As a consequence the perceptual effect created is that of one light moving back and forth. This phenomenon of apparent motion is called the phi-phenomenon. Wertheiner’s experiments on phi- phenomenon formed the foundation for gestalt psychology.

Essay # 8. Development of Perception:

The infant’s perceptual world is different from the adult’s. Perception develops gradually as the individual grows and develops. It has also been shown that it is influenced to a great extent by the biological needs, maturation, learning, culture etc. Thus, qualitative and quantitative changes in perception take place in the course of an individual’s development.

The experiments of Gibson and Bowers show that depth and object perceptions are inborn, i.e. they are not dependent on learning, although they develop and shape at different rates. Goldstein emphasised the gradual development of perception from concrete to abstract.

However, Goldstein does not make a direct reference to perception but refers to it as the development of thinking or attitude. Witkin emphasises that perception which in the early years is field dependent gradually transforms itself into field independent.

Thus, stability and abstraction become possible as the individual develops. Von Senden presented a very interesting data regarding the patients who were born blind but have gained their vision as the result of operations. Their perceptual processes were studied carefully because their situation was considered analogous to a new-born infant’s who sees the world for the first time. Von Senden found that these patients did not experience normal perception immediately after they gained vision.

When an object was shown to them they could see something against a background but could not identify it, its shape and its distance from them. Colour discriminations were learned immediately. However learning to identify forms and objects in different contexts was a long and difficult process.

One patient learned to identify an egg, a potato and sugar in normal light on a table after many repetitions although he failed to recognise the same objects in colour light or when they were suspended by a thread with a change of background.

He could point correctly to the source of a sound but could not say from which direction it was coming. One can know from the above studies that perception does not develop overnight perceptual capacity may be inborn but the ability develops gradually along with the development of other processes.

Essay # 9. Errors of Perception:

The perceptual processes enable an individual to perceive things around him accurately and facilitate his smooth functioning. However, some errors creep into this process, under certain circumstances, leading to wrong or impaired perceptions.

Two well-documented errors of perceptions are illusions and hallucinations:

1. Illusions:

A mistaken perception or distortion in perception is called an illusion. Generally perception involves the integration of sensory experiences and present psychological and organismic conditions. When the interpretation of a particular stimulus goes wrong, it gives rise to a wrong perception. For example, a rope in the dark is perceived as a snake a dry leaf moving along the ground in the dark is perceived as a moving insect. Similarly, in the phi-phenomenon, although there is no physical movement of the lights, they are still perceived as moving.

Some illusions which occur commonly in the perception of geometrical figures are discussed in this article. These illusions are popularly known as ‘geometrical optical illusions’ a term coined by Oppel, a German scientist. He used this term to explain the over-estimation of an interrupted spatial extent compared to an uninterrupted one. Later, the term was used for any illusion seen in line drawings.

a. Mueller – Lyer Illusion:

In Figure 7.13 one line is bounded by ‘arrowheads’ and the other by ‘shaft heads’. Though these two lines are equal in length, invariably the line with closed heads is perceived as shorter than the line with open heads. Similarly, lines bounded by closed curves or brackets and circles are underestimated with respect to their length and vice versa.

b. Horizontal-Vertical Illusion:

In Fig.7.14 one line is horizontal and the other is vertical. Though both are equal in length, the vertical line is perceived as longer than the horizontal line. To test this you can make someone stand straight stretching both arms out to their full length.

Ask your friend whether the height of this person is the same as the length of his arms, i.e. the length from the right fingertips to the left fingertips. If your friend is not aware that these two lengths are equal, then he will invariably report that the height is greater than the length of the arms.

c. Poggendorff’s Illusion:

In Fig.7.15 a straight line appears to become slightly displaced as it passes through two parallel rectangles. Poggendorffs’ illusion is demonstrated in this figure.

In Fig.7.16 when two parallel lines are intersected by numerous short diagonal lines slanting in the opposite direction then the parallel lines are perceived as diverging, i, e. slanting backwards slightly instead of being straight.

The Mueller-Lyer Illusion, the Poggendorff’s Illusion and the Zollner’s Illusion are named after the scientists who discovered these phenomena. Illusions are not totally caused by subjective conditions. Sometimes the environment or the context within which a particular stimulus is perceived is responsible for illusions. For instance, the perception of a rope as a snake or a leaf as an insect, may have occurred due to darkness which is an environmental condition.

It has been suggested by scientists that geometrical illusions like the ones mentioned above are the natural outcome of a certain kind of nerve structure, functioning under a given set of physical conditions. The reader may raise the question as to why only visual illusions are elaborated in this article.

This is because so far scientists have been attracted by the problem of vision and consequently the maximum amount of research has been done in this particular area. However, researchers today are busy exploring and experimenting with illusions arising out of other sensory experiences like audition, gustation and so on.

2. Hallucinations:

Hallucinations are identified as one of the major errors of perception. While an illusion is considered as an inaccuracy, a distorted perception of existing stimuli, hallucinations are considered as false perceptions. Hallucinations are sensory perceptions in the absence of any corresponding external sensory stimuli.

For example, if a person claims that he has seen a ghost or a goddess when there is practically no stimulus either in the form of a human skeleton or a live human figure or at least anything resembling it, this will be conceived by scientific minds as a hallucination.

Strictly speaking, dreams are hallucinations since the persons and things perceived while one is asleep have no factual basis. But for all practical purposes the use of the term hallucination is restricted to imaginary perceptions experienced in the waking state. Thus, when a person hallucinates he hears, sees and feels non-existent objects or stimuli.

Like illusions, hallucinations sometimes depend on needs, mental states like fear, anxiety, culture, etc. Hallucinations are not necessarily indicative of abnormality. For example, normal individuals reared in certain cultures are encouraged to hallucinate as part of their religious experiences. They may claim to have seen or heard from their deity and this is considered a normal phenomenon.

Similarly, in our present society, it is not an uncommon sight, if a lover waiting anxiously says he heard the telephone ringing or a knock on the door and other such experiences in the absence of stimuli. These experiences which occur specially in moments of anxiety or fear or keen expectation are taken as natural and normal phenomena.

However, hallucinations verge on abnormality when they become chronic, intense and problematic to the perceiver and others around him and begin to hamper the normal and smooth functioning of his day-to-day activities.

Auditory Hallucination:

Mr. S, an agricultural worker, around 30 years of age, complained to his psychiatrist that voices bother him day and night. He can hear them cursing his mother and father Sometimes they command him to hit himself sometimes they say obscene things. These voices are feminine and sometimes masculine at times he hears his own voice commanding him.

Hallucinations are caused by psychological factors like conflict, guilt, fear, anxiety etc. They can also occur due to cerebral injuries, intake of alcohol, drugs like L.S.D. or heroin and the presence of certain toxic substances in the body.

Figural After – Effects:

The term figural after-effect is used to denote certain phenomena observed by Gibson in a series of interesting experiments. In one of his experiments subjects saw a distorted line passing through a prism. After 10 minutes, the apparent ‘curvature’ of the line was perceived as very much decreased.

The line tended to straighten out and when the prism was removed, the line was perceived as being curved in the opposite direction. In another experiment, by Kohler & Wallach, one figure (known as l or inspection figure) is observed for several minutes with total fixation.

Then this figure is replaced by a Test stimuls card T1 and the subjects are required to report its characteristics. It may be seen that objectively the two figures, the one inside T1 and T2 are identical in size, brightness and the distance from P. But both are smaller than the 1 square.

The square T1 falls in line with the contours of the inspection square and a little nearer its right hand contours. The phenomenal reports indicated that T1 was perceived as smaller and more distant from point P and further, its margins appeared paler. It is not necessary that all these characteristics should appear in the case of a given person at any time.

Kohler & Wallach offer an explanation for this, based on certain electrical field processes in the brain. According to them, there are some unspecified regions, of the central visual area through which current keeps on flowing. The currents flow according to the principle of least resistance.

When the 1 figure is presented, this flow is interrupted and the current flow is set up along the contours of this figure. The flow of the current however, increases the resistance in the tissues, thus forcing the current to flow into the neighbouring regions which in turn results in a gradient of resistance satiation about the contour of fig. Satiation present after the – removal of the 1 figure, lead to distortions in the T figures. There has been a lot of criticism against this view, particularly from the neurophysiological angle. It is also argued that the phenomenon of figural after-effect can be explained without having to take recourse to ‘electrical fields.’

Essay # 10. Studies on Perception:

Findings arrived at by studies of perception are not as dramatic as the findings of experiments in learning. Nevertheless their value has been recognised increasingly to serve mankind in many significant ways. An understanding of the subtleties and complexities of perception as a process gives an impression that human behaviour can be reduced to an interplay of the perceptions of self, the world, people, objects and events. As a matter of fact, various activities like science, art, religion etc., are nothing more than the outcome of human perceptions.

Turning to more concrete contributions, one of the major areas of investigation is in the field of colour perception. This brought out interesting findings as to why and how certain psychological factors determine colour perception. The impact of these findings can be seen on the walls of living rooms, bedrooms, showrooms, in the market for selling automobiles, textiles and even fruits and flowers.

Colour technologists involved in manufacturing dyes, textiles, and those who are involved in agencies of mass media like the cinema, television, magazines, photography and interior decorators invest large amounts of money to find out, create, and impress human perception, captivate their interests, moods and money through colours. They try to demonstrate how different and pleasant it is living and working with certain colours around you, rather than being in colourless, or lifeless surroundings.

Another area in which the findings of perception studies are being used is communication. Communication devices ranging from satellites to telephones are devised to facilitate the audio-visual perceptions of human beings. The utmost care has to be taken in designing transmission devices and equipping them to counter­balance phenomena like illusions, constancies etc. which arise in perception especially regarding sounds and figures.

They take care to make the communication of the speaker and the listener clear and intelligible, eliminate non-essential stimuli and aim at presenting synchronized and simultaneous transmission. Transport system such as airways, seaways and roadways have realised the importance of perception because the individuals who steer these vehicles make use of processes like sensation, attention and perception to the maximum extent.

If these processes fail or do not function adequately for one reason or the other, the consequence is human error or accident. Scientists working in the area of prevention of accidents, especially on highways, realised that accidents occur due to certain visual and auditory illusions.

Over-estimation or under-estimation of curves, distortion of cues due to excess of light, fog, or snow, and illusions of sound created by moving stimuli, all these sometimes can produce disasters. Thus, measures are being taken to provide information, instructions and clues which are specially devised and placed at convenient heights, angles and directions so that the driver can perceive from his fast-moving vehicle and avert disasters. The importance of such findings can be well understood by this illustration.

On December 4, 1965, a TWA Boeing 707 and an Eastern Airline Lockheed 1049 were enroute to John F. Kennedy International Airport and to Newark Airport, respectively. Both were converging on the New York area, the Boeing 707 at its assigned altitude of 11,000 feet and the Lockheed at its assigned altitude of 10,000 feet.

At the time, the area was overcast and the cloud tops protruded above a height of 10,000 feet. The clouds were generally higher in the north than in the south and seemed to form an upward, sloping bar of white against the blue background of the sky. Within a few moments of each other, the crew of both the aircraft perceived what appeared to be an imminent collision between the two planes.

They rapidly began evasive manoeuvres. The Lockheed aircraft pulled up and the Boeing rolled first to the right then to the left. The two aircrafts collided at approximately 11,000 feet. The structural damage to the Lockheed was sufficient to force it to land in an open field, where it was destroyed by impact and friction.

There were four fatalities and forty-nine non-fatal injuries. The U.S. Civil Aeronautics Board attributed the collision to misjudgment of altitude separation by the crew of the Lockheed aircraft because of an ‘optical illusion’ created by the upward sloping contours of the cloud tops.

Four persons died and 49 were injured through the operation of the simple effect that we mimic on paper with simple lines and call the ‘Poggendorff illusion’. Perhaps, the idea that visual illusions are interesting but relatively unimportant oddities of perceptions itself is merely another illusion, which can prove costly.

Similar precautions are being taken in certain accident-prone heavy industries, like mining and manufacturing of volatile substances like explosives, chemicals and “so on where individuals have to attend to and comprehend several stimuli accurately within a short time.

Contributions to clinical psychology of the findings on hallucinations are immense. It has become one of the most important tools in diagnosing psychotic disorders. The seriousness of a psychosis is determined to a great extent by the degree, intensity and number of hallucinations experienced by the individual.

Researchers working on the problem of subliminal perception are trying to contribute their share of findings through work done on advertisements, unconscious processes etc. The advertising agencies are realising that they can capture their audience and customers by making their messages less obvious and more subtle. This is one way to induce curiosity and attract them to their products and thus, increase their sales.

The role of the unconscious in the area of subliminal perception is quite significant. Unconscious processes and their allied phenomena, for all practical purposes, can be considered synonymous with subliminal perceptions, because they operate from a level of consciousness which is less than normal.

One may wonder whether findings on ESP have any value to the present computer world which is capable of anything right from brushing one’s teeth to singing a lullaby. But ESP seems to offer so much that the world is beginning to develop an impression that parapsychology is no more a mere intellectual adventure. If individuals could be taught and made to develop this capacity we could go to the moon and other planets, eat and live comfortably and chat with friends across the seas and continents for hours together.

Imagine, all this could be done without spending a paisa and then money would lose its importance. However, to achieve this stage, sciences have to travel a long and difficult way like Christian in ‘A Pilgrim’s Progress’. Today, such fantastic activities may appear to be distant probabilities but we may soon see them as distinct possibilities.

The one area where research findings on perception and the perceptual processes have been found extremely useful is in advertising. Very innovative advertisements are designed today based on their knowledge of the perceptual processes.


Contents

Chaos theory concerns deterministic systems whose behavior can, in principle, be predicted. Chaotic systems are predictable for a while and then 'appear' to become random. The amount of time that the behavior of a chaotic system can be effectively predicted depends on three things: how much uncertainty can be tolerated in the forecast, how accurately its current state can be measured, and a time scale depending on the dynamics of the system, called the Lyapunov time. Some examples of Lyapunov times are: chaotic electrical circuits, about 1 millisecond weather systems, a few days (unproven) the inner solar system, 4 to 5 million years. [19] In chaotic systems, the uncertainty in a forecast increases exponentially with elapsed time. Hence, mathematically, doubling the forecast time more than squares the proportional uncertainty in the forecast. This means, in practice, a meaningful prediction cannot be made over an interval of more than two or three times the Lyapunov time. When meaningful predictions cannot be made, the system appears random. [20]

In common usage, "chaos" means "a state of disorder". [21] [22] However, in chaos theory, the term is defined more precisely. Although no universally accepted mathematical definition of chaos exists, a commonly used definition, originally formulated by Robert L. Devaney, says that to classify a dynamical system as chaotic, it must have these properties: [23]

In some cases, the last two properties above have been shown to actually imply sensitivity to initial conditions. [24] [25] In the discrete-time case, this is true for all continuous maps on metric spaces. [26] In these cases, while it is often the most practically significant property, "sensitivity to initial conditions" need not be stated in the definition.

If attention is restricted to intervals, the second property implies the other two. [27] An alternative and a generally weaker definition of chaos uses only the first two properties in the above list. [28]

Chaos as a spontaneous breakdown of topological supersymmetry Edit

In continuous time dynamical systems, chaos is the phenomenon of the spontaneous breakdown of topological supersymmetry, which is an intrinsic property of evolution operators of all stochastic and deterministic (partial) differential equations. [29] [30] This picture of dynamical chaos works not only for deterministic models, but also for models with external noise which is an important generalization from the physical point of view, since in reality, all dynamical systems experience influence from their stochastic environments. Within this picture, the long-range dynamical behavior associated with chaotic dynamics (e.g., the butterfly effect) is a consequence of Goldstone's theorem—in the application to the spontaneous topological supersymmetry breaking.

Sensitivity to initial conditions Edit

Sensitivity to initial conditions means that each point in a chaotic system is arbitrarily closely approximated by other points that have significantly different future paths or trajectories. Thus, an arbitrarily small change or perturbation of the current trajectory may lead to significantly different future behavior. [3]

Sensitivity to initial conditions is popularly known as the "butterfly effect", so-called because of the title of a paper given by Edward Lorenz in 1972 to the American Association for the Advancement of Science in Washington, D.C., entitled Predictability: Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?. [31] The flapping wing represents a small change in the initial condition of the system, which causes a chain of events that prevents the predictability of large-scale phenomena. Had the butterfly not flapped its wings, the trajectory of the overall system could have been vastly different.

A consequence of sensitivity to initial conditions is that if we start with a limited amount of information about the system (as is usually the case in practice), then beyond a certain time, the system would no longer be predictable. This is most prevalent in the case of weather, which is generally predictable only about a week ahead. [32] This does not mean that one cannot assert anything about events far in the future—only that some restrictions on the system are present. For example, we do know with weather that the temperature will not naturally reach 100 °C or fall to −130 °C on earth (during the current geologic era), but that does not mean that we can predict exactly which day will have the hottest temperature of the year.

In more mathematical terms, the Lyapunov exponent measures the sensitivity to initial conditions, in the form of rate of exponential divergence from the perturbed initial conditions. [33] More specifically, given two starting trajectories in the phase space that are infinitesimally close, with initial separation δ Z 0 _<0>> , the two trajectories end up diverging at a rate given by

In addition to the above property, other properties related to sensitivity of initial conditions also exist. These include, for example, measure-theoretical mixing (as discussed in ergodic theory) and properties of a K-system. [10]

Non-periodicity Edit

A chaotic system may have sequences of values for the evolving variable that exactly repeat themselves, giving periodic behavior starting from any point in that sequence. However, such periodic sequences are repelling rather than attracting, meaning that if the evolving variable is outside the sequence, however close, it will not enter the sequence and in fact, will diverge from it. Thus for almost all initial conditions, the variable evolves chaotically with non-periodic behavior.

Topological mixing Edit

Topological mixing (or the weaker condition of topological transitivity) means that the system evolves over time so that any given region or open set of its phase space eventually overlaps with any other given region. This mathematical concept of "mixing" corresponds to the standard intuition, and the mixing of colored dyes or fluids is an example of a chaotic system.

Topological mixing is often omitted from popular accounts of chaos, which equate chaos with only sensitivity to initial conditions. However, sensitive dependence on initial conditions alone does not give chaos. For example, consider the simple dynamical system produced by repeatedly doubling an initial value. This system has sensitive dependence on initial conditions everywhere, since any pair of nearby points eventually becomes widely separated. However, this example has no topological mixing, and therefore has no chaos. Indeed, it has extremely simple behavior: all points except 0 tend to positive or negative infinity.

Topological transitivity Edit

A map f : X → X is said to be topologically transitive if for any pair of non-empty open sets U , V ⊂ X , there exists k > 0 such that f k ( U ) ∩ V ≠ ∅ (U)cap V eq emptyset > . Topological transitivity is a weaker version of topological mixing. Intuitively, if a map is topologically transitive then given a point x and a region V, there exists a point y near x whose orbit passes through V. This implies that is impossible to decompose the system into two open sets. [34]

An important related theorem is the Birkhoff Transitivity Theorem. It is easy to see that the existence of a dense orbit implies in topological transitivity. The Birkhoff Transitivity Theorem states that if X is a second countable, complete metric space, then topological transitivity implies the existence of a dense set of points in X that have dense orbits. [35]

Density of periodic orbits Edit

Sharkovskii's theorem is the basis of the Li and Yorke [37] (1975) proof that any continuous one-dimensional system that exhibits a regular cycle of period three will also display regular cycles of every other length, as well as completely chaotic orbits.

Strange attractors Edit

Some dynamical systems, like the one-dimensional logistic map defined by x → 4 x (1 – x), are chaotic everywhere, but in many cases chaotic behavior is found only in a subset of phase space. The cases of most interest arise when the chaotic behavior takes place on an attractor, since then a large set of initial conditions leads to orbits that converge to this chaotic region. [38]

An easy way to visualize a chaotic attractor is to start with a point in the basin of attraction of the attractor, and then simply plot its subsequent orbit. Because of the topological transitivity condition, this is likely to produce a picture of the entire final attractor, and indeed both orbits shown in the figure on the right give a picture of the general shape of the Lorenz attractor. This attractor results from a simple three-dimensional model of the Lorenz weather system. The Lorenz attractor is perhaps one of the best-known chaotic system diagrams, probably because it is not only one of the first, but it is also one of the most complex, and as such gives rise to a very interesting pattern that, with a little imagination, looks like the wings of a butterfly.

Unlike fixed-point attractors and limit cycles, the attractors that arise from chaotic systems, known as strange attractors, have great detail and complexity. Strange attractors occur in both continuous dynamical systems (such as the Lorenz system) and in some discrete systems (such as the Hénon map). Other discrete dynamical systems have a repelling structure called a Julia set, which forms at the boundary between basins of attraction of fixed points. Julia sets can be thought of as strange repellers. Both strange attractors and Julia sets typically have a fractal structure, and the fractal dimension can be calculated for them.

Minimum complexity of a chaotic system Edit

Discrete chaotic systems, such as the logistic map, can exhibit strange attractors whatever their dimensionality. Universality of one-dimensional maps with parabolic maxima and Feigenbaum constants δ = 4.669201. , α = 2.502907. [39] [40] is well visible with map proposed as a toy model for discrete laser dynamics: x → G x ( 1 − t a n h ( x ) ) (x))> , where x stands for electric field amplitude, G [41] is laser gain as bifurcation parameter. The gradual increase of G at interval [ 0 , ∞ ) changes dynamics from regular to chaotic one [42] with qualitatively the same bifurcation diagram as those for logistic map.

In contrast, for continuous dynamical systems, the Poincaré–Bendixson theorem shows that a strange attractor can only arise in three or more dimensions. Finite-dimensional linear systems are never chaotic for a dynamical system to display chaotic behavior, it must be either nonlinear or infinite-dimensional.

The Poincaré–Bendixson theorem states that a two-dimensional differential equation has very regular behavior. The Lorenz attractor discussed below is generated by a system of three differential equations such as:

where x , y , and z make up the system state, t is time, and σ , ρ , β are the system parameters. Five of the terms on the right hand side are linear, while two are quadratic a total of seven terms. Another well-known chaotic attractor is generated by the Rössler equations, which have only one nonlinear term out of seven. Sprott [43] found a three-dimensional system with just five terms, that had only one nonlinear term, which exhibits chaos for certain parameter values. Zhang and Heidel [44] [45] showed that, at least for dissipative and conservative quadratic systems, three-dimensional quadratic systems with only three or four terms on the right-hand side cannot exhibit chaotic behavior. The reason is, simply put, that solutions to such systems are asymptotic to a two-dimensional surface and therefore solutions are well behaved.

While the Poincaré–Bendixson theorem shows that a continuous dynamical system on the Euclidean plane cannot be chaotic, two-dimensional continuous systems with non-Euclidean geometry can exhibit chaotic behavior. [46] [ self-published source? ] Perhaps surprisingly, chaos may occur also in linear systems, provided they are infinite dimensional. [47] A theory of linear chaos is being developed in a branch of mathematical analysis known as functional analysis.

Infinite dimensional maps Edit

The straightforward generalization of coupled discrete maps [48] is based upon convolution integral which mediates interaction between spatially distributed maps: ψ n + 1 ( r → , t ) = ∫ K ( r → − r → , , t ) f [ ψ n ( r → , , t ) ] d r → , (>,t)=int K(>->^<,>,t)f[psi _(>^<,>,t)]d>^<,>> ,

Jerk systems Edit

In physics, jerk is the third derivative of position, with respect to time. As such, differential equations of the form

are sometimes called jerk equations. It has been shown that a jerk equation, which is equivalent to a system of three first order, ordinary, non-linear differential equations, is in a certain sense the minimal setting for solutions showing chaotic behaviour. This motivates mathematical interest in jerk systems. Systems involving a fourth or higher derivative are called accordingly hyperjerk systems. [52]

A jerk system's behavior is described by a jerk equation, and for certain jerk equations, simple electronic circuits can model solutions. These circuits are known as jerk circuits.

One of the most interesting properties of jerk circuits is the possibility of chaotic behavior. In fact, certain well-known chaotic systems, such as the Lorenz attractor and the Rössler map, are conventionally described as a system of three first-order differential equations that can combine into a single (although rather complicated) jerk equation. Another example of a jerk equation with nonlinearity in the magnitude of x is:

Here, A is an adjustable parameter. This equation has a chaotic solution for A=3/5 and can be implemented with the following jerk circuit the required nonlinearity is brought about by the two diodes:

In the above circuit, all resistors are of equal value, except R A = R / A = 5 R / 3 , and all capacitors are of equal size. The dominant frequency is 1 / 2 π R C . The output of op amp 0 will correspond to the x variable, the output of 1 corresponds to the first derivative of x and the output of 2 corresponds to the second derivative.

Similar circuits only require one diode [53] or no diodes at all. [54]

See also the well-known Chua's circuit, one basis for chaotic true random number generators. [55] The ease of construction of the circuit has made it a ubiquitous real-world example of a chaotic system.

Under the right conditions, chaos spontaneously evolves into a lockstep pattern. In the Kuramoto model, four conditions suffice to produce synchronization in a chaotic system. Examples include the coupled oscillation of Christiaan Huygens' pendulums, fireflies, neurons, the London Millennium Bridge resonance, and large arrays of Josephson junctions. [56]

An early proponent of chaos theory was Henri Poincaré. In the 1880s, while studying the three-body problem, he found that there can be orbits that are nonperiodic, and yet not forever increasing nor approaching a fixed point. [57] [58] [59] In 1898, Jacques Hadamard published an influential study of the chaotic motion of a free particle gliding frictionlessly on a surface of constant negative curvature, called "Hadamard's billiards". [60] Hadamard was able to show that all trajectories are unstable, in that all particle trajectories diverge exponentially from one another, with a positive Lyapunov exponent.

Chaos theory began in the field of ergodic theory. Later studies, also on the topic of nonlinear differential equations, were carried out by George David Birkhoff, [61] Andrey Nikolaevich Kolmogorov, [62] [63] [64] Mary Lucy Cartwright and John Edensor Littlewood, [65] and Stephen Smale. [66] Except for Smale, these studies were all directly inspired by physics: the three-body problem in the case of Birkhoff, turbulence and astronomical problems in the case of Kolmogorov, and radio engineering in the case of Cartwright and Littlewood. [ citation needed ] Although chaotic planetary motion had not been observed, experimentalists had encountered turbulence in fluid motion and nonperiodic oscillation in radio circuits without the benefit of a theory to explain what they were seeing.

Despite initial insights in the first half of the twentieth century, chaos theory became formalized as such only after mid-century, when it first became evident to some scientists that linear theory, the prevailing system theory at that time, simply could not explain the observed behavior of certain experiments like that of the logistic map. What had been attributed to measure imprecision and simple "noise" was considered by chaos theorists as a full component of the studied systems.

The main catalyst for the development of chaos theory was the electronic computer. Much of the mathematics of chaos theory involves the repeated iteration of simple mathematical formulas, which would be impractical to do by hand. Electronic computers made these repeated calculations practical, while figures and images made it possible to visualize these systems. As a graduate student in Chihiro Hayashi's laboratory at Kyoto University, Yoshisuke Ueda was experimenting with analog computers and noticed, on November 27, 1961, what he called "randomly transitional phenomena". Yet his advisor did not agree with his conclusions at the time, and did not allow him to report his findings until 1970. [67] [68]

Edward Lorenz was an early pioneer of the theory. His interest in chaos came about accidentally through his work on weather prediction in 1961. [12] Lorenz was using a simple digital computer, a Royal McBee LGP-30, to run his weather simulation. He wanted to see a sequence of data again, and to save time he started the simulation in the middle of its course. He did this by entering a printout of the data that corresponded to conditions in the middle of the original simulation. To his surprise, the weather the machine began to predict was completely different from the previous calculation. Lorenz tracked this down to the computer printout. The computer worked with 6-digit precision, but the printout rounded variables off to a 3-digit number, so a value like 0.506127 printed as 0.506. This difference is tiny, and the consensus at the time would have been that it should have no practical effect. However, Lorenz discovered that small changes in initial conditions produced large changes in long-term outcome. [69] Lorenz's discovery, which gave its name to Lorenz attractors, showed that even detailed atmospheric modelling cannot, in general, make precise long-term weather predictions.

In 1963, Benoit Mandelbrot found recurring patterns at every scale in data on cotton prices. [70] Beforehand he had studied information theory and concluded noise was patterned like a Cantor set: on any scale the proportion of noise-containing periods to error-free periods was a constant – thus errors were inevitable and must be planned for by incorporating redundancy. [71] Mandelbrot described both the "Noah effect" (in which sudden discontinuous changes can occur) and the "Joseph effect" (in which persistence of a value can occur for a while, yet suddenly change afterwards). [72] [73] This challenged the idea that changes in price were normally distributed. In 1967, he published "How long is the coast of Britain? Statistical self-similarity and fractional dimension", showing that a coastline's length varies with the scale of the measuring instrument, resembles itself at all scales, and is infinite in length for an infinitesimally small measuring device. [74] Arguing that a ball of twine appears as a point when viewed from far away (0-dimensional), a ball when viewed from fairly near (3-dimensional), or a curved strand (1-dimensional), he argued that the dimensions of an object are relative to the observer and may be fractional. An object whose irregularity is constant over different scales ("self-similarity") is a fractal (examples include the Menger sponge, the Sierpiński gasket, and the Koch curve or snowflake, which is infinitely long yet encloses a finite space and has a fractal dimension of circa 1.2619). In 1982, Mandelbrot published The Fractal Geometry of Nature, which became a classic of chaos theory. [75] Biological systems such as the branching of the circulatory and bronchial systems proved to fit a fractal model. [76]

In December 1977, the New York Academy of Sciences organized the first symposium on chaos, attended by David Ruelle, Robert May, James A. Yorke (coiner of the term "chaos" as used in mathematics), Robert Shaw, and the meteorologist Edward Lorenz. The following year Pierre Coullet and Charles Tresser published "Itérations d'endomorphismes et groupe de renormalisation", and Mitchell Feigenbaum's article "Quantitative Universality for a Class of Nonlinear Transformations" finally appeared in a journal, after 3 years of referee rejections. [40] [77] Thus Feigenbaum (1975) and Coullet & Tresser (1978) discovered the universality in chaos, permitting the application of chaos theory to many different phenomena.

In 1979, Albert J. Libchaber, during a symposium organized in Aspen by Pierre Hohenberg, presented his experimental observation of the bifurcation cascade that leads to chaos and turbulence in Rayleigh–Bénard convection systems. He was awarded the Wolf Prize in Physics in 1986 along with Mitchell J. Feigenbaum for their inspiring achievements. [78]

In 1986, the New York Academy of Sciences co-organized with the National Institute of Mental Health and the Office of Naval Research the first important conference on chaos in biology and medicine. There, Bernardo Huberman presented a mathematical model of the eye tracking disorder among schizophrenics. [79] This led to a renewal of physiology in the 1980s through the application of chaos theory, for example, in the study of pathological cardiac cycles.

In 1987, Per Bak, Chao Tang and Kurt Wiesenfeld published a paper in Physical Review Letters [80] describing for the first time self-organized criticality (SOC), considered one of the mechanisms by which complexity arises in nature.

Alongside largely lab-based approaches such as the Bak–Tang–Wiesenfeld sandpile, many other investigations have focused on large-scale natural or social systems that are known (or suspected) to display scale-invariant behavior. Although these approaches were not always welcomed (at least initially) by specialists in the subjects examined, SOC has nevertheless become established as a strong candidate for explaining a number of natural phenomena, including earthquakes, (which, long before SOC was discovered, were known as a source of scale-invariant behavior such as the Gutenberg–Richter law describing the statistical distribution of earthquake sizes, and the Omori law [81] describing the frequency of aftershocks), solar flares, fluctuations in economic systems such as financial markets (references to SOC are common in econophysics), landscape formation, forest fires, landslides, epidemics, and biological evolution (where SOC has been invoked, for example, as the dynamical mechanism behind the theory of "punctuated equilibria" put forward by Niles Eldredge and Stephen Jay Gould). Given the implications of a scale-free distribution of event sizes, some researchers have suggested that another phenomenon that should be considered an example of SOC is the occurrence of wars. These investigations of SOC have included both attempts at modelling (either developing new models or adapting existing ones to the specifics of a given natural system), and extensive data analysis to determine the existence and/or characteristics of natural scaling laws.

In the same year, James Gleick published Chaos: Making a New Science, which became a best-seller and introduced the general principles of chaos theory as well as its history to the broad public, though his history under-emphasized important Soviet contributions. [ citation needed ] [82] Initially the domain of a few, isolated individuals, chaos theory progressively emerged as a transdisciplinary and institutional discipline, mainly under the name of nonlinear systems analysis. Alluding to Thomas Kuhn's concept of a paradigm shift exposed in The Structure of Scientific Revolutions (1962), many "chaologists" (as some described themselves) claimed that this new theory was an example of such a shift, a thesis upheld by Gleick.

The availability of cheaper, more powerful computers broadens the applicability of chaos theory. Currently, chaos theory remains an active area of research, [83] involving many different disciplines such as mathematics, topology, physics, [84] social systems, [85] population modeling, biology, meteorology, astrophysics, information theory, computational neuroscience, pandemic crisis management, [17] [18] etc.

Although chaos theory was born from observing weather patterns, it has become applicable to a variety of other situations. Some areas benefiting from chaos theory today are geology, mathematics, biology, computer science, economics, [87] [88] [89] engineering, [90] [91] finance, [92] [93] algorithmic trading, [94] [95] [96] meteorology, philosophy, anthropology, [15] physics, [97] [98] [99] politics, [100] [101] population dynamics, [102] psychology, [14] and robotics. A few categories are listed below with examples, but this is by no means a comprehensive list as new applications are appearing.

Cryptography Edit

Chaos theory has been used for many years in cryptography. In the past few decades, chaos and nonlinear dynamics have been used in the design of hundreds of cryptographic primitives. These algorithms include image encryption algorithms, hash functions, secure pseudo-random number generators, stream ciphers, watermarking and steganography. [103] The majority of these algorithms are based on uni-modal chaotic maps and a big portion of these algorithms use the control parameters and the initial condition of the chaotic maps as their keys. [104] From a wider perspective, without loss of generality, the similarities between the chaotic maps and the cryptographic systems is the main motivation for the design of chaos based cryptographic algorithms. [103] One type of encryption, secret key or symmetric key, relies on diffusion and confusion, which is modeled well by chaos theory. [105] Another type of computing, DNA computing, when paired with chaos theory, offers a way to encrypt images and other information. [106] Many of the DNA-Chaos cryptographic algorithms are proven to be either not secure, or the technique applied is suggested to be not efficient. [107] [108] [109]

Robotics Edit

Robotics is another area that has recently benefited from chaos theory. Instead of robots acting in a trial-and-error type of refinement to interact with their environment, chaos theory has been used to build a predictive model. [110] Chaotic dynamics have been exhibited by passive walking biped robots. [111]

Biology Edit

For over a hundred years, biologists have been keeping track of populations of different species with population models. Most models are continuous, but recently scientists have been able to implement chaotic models in certain populations. [112] For example, a study on models of Canadian lynx showed there was chaotic behavior in the population growth. [113] Chaos can also be found in ecological systems, such as hydrology. While a chaotic model for hydrology has its shortcomings, there is still much to learn from looking at the data through the lens of chaos theory. [114] Another biological application is found in cardiotocography. Fetal surveillance is a delicate balance of obtaining accurate information while being as noninvasive as possible. Better models of warning signs of fetal hypoxia can be obtained through chaotic modeling. [115]

Economics Edit

It is possible that economic models can also be improved through an application of chaos theory, but predicting the health of an economic system and what factors influence it most is an extremely complex task. [116] Economic and financial systems are fundamentally different from those in the classical natural sciences since the former are inherently stochastic in nature, as they result from the interactions of people, and thus pure deterministic models are unlikely to provide accurate representations of the data. The empirical literature that tests for chaos in economics and finance presents very mixed results, in part due to confusion between specific tests for chaos and more general tests for non-linear relationships. [117]

Chaos could be found in economics by the means of recurrence quantification analysis. In fact, Orlando et al. [118] by the means of the so-called recurrence quantification correlation index were able detect hidden changes in time series. Then, the same technique was employed to detect transitions from laminar (i.e. regular) to turbulent (i.e. chaotic) phases as well as differences between macroeconomic variables and highlight hidden features of economic dynamics. [119] Finally, chaos could help in modeling how economy operate as well as in embedding shocks due to external events such as COVID-19. [120]

Other areas Edit

In chemistry, predicting gas solubility is essential to manufacturing polymers, but models using particle swarm optimization (PSO) tend to converge to the wrong points. An improved version of PSO has been created by introducing chaos, which keeps the simulations from getting stuck. [121] In celestial mechanics, especially when observing asteroids, applying chaos theory leads to better predictions about when these objects will approach Earth and other planets. [122] Four of the five moons of Pluto rotate chaotically. In quantum physics and electrical engineering, the study of large arrays of Josephson junctions benefitted greatly from chaos theory. [123] Closer to home, coal mines have always been dangerous places where frequent natural gas leaks cause many deaths. Until recently, there was no reliable way to predict when they would occur. But these gas leaks have chaotic tendencies that, when properly modeled, can be predicted fairly accurately. [124]

Chaos theory can be applied outside of the natural sciences, but historically nearly all such studies have suffered from lack of reproducibility poor external validity and/or inattention to cross-validation, resulting in poor predictive accuracy (if out-of-sample prediction has even been attempted). Glass [125] and Mandell and Selz [126] have found that no EEG study has as yet indicated the presence of strange attractors or other signs of chaotic behavior.

Researchers have continued to apply chaos theory to psychology. For example, in modeling group behavior in which heterogeneous members may behave as if sharing to different degrees what in Wilfred Bion's theory is a basic assumption, researchers have found that the group dynamic is the result of the individual dynamics of the members: each individual reproduces the group dynamics in a different scale, and the chaotic behavior of the group is reflected in each member. [127]

Redington and Reidbord (1992) attempted to demonstrate that the human heart could display chaotic traits. They monitored the changes in between-heartbeat intervals for a single psychotherapy patient as she moved through periods of varying emotional intensity during a therapy session. Results were admittedly inconclusive. Not only were there ambiguities in the various plots the authors produced to purportedly show evidence of chaotic dynamics (spectral analysis, phase trajectory, and autocorrelation plots), but also when they attempted to compute a Lyapunov exponent as more definitive confirmation of chaotic behavior, the authors found they could not reliably do so. [128]

In their 1995 paper, Metcalf and Allen [129] maintained that they uncovered in animal behavior a pattern of period doubling leading to chaos. The authors examined a well-known response called schedule-induced polydipsia, by which an animal deprived of food for certain lengths of time will drink unusual amounts of water when the food is at last presented. The control parameter (r) operating here was the length of the interval between feedings, once resumed. The authors were careful to test a large number of animals and to include many replications, and they designed their experiment so as to rule out the likelihood that changes in response patterns were caused by different starting places for r.

Time series and first delay plots provide the best support for the claims made, showing a fairly clear march from periodicity to irregularity as the feeding times were increased. The various phase trajectory plots and spectral analyses, on the other hand, do not match up well enough with the other graphs or with the overall theory to lead inexorably to a chaotic diagnosis. For example, the phase trajectories do not show a definite progression towards greater and greater complexity (and away from periodicity) the process seems quite muddied. Also, where Metcalf and Allen saw periods of two and six in their spectral plots, there is room for alternative interpretations. All of this ambiguity necessitate some serpentine, post-hoc explanation to show that results fit a chaotic model.

By adapting a model of career counseling to include a chaotic interpretation of the relationship between employees and the job market, Amundson and Bright found that better suggestions can be made to people struggling with career decisions. [130] Modern organizations are increasingly seen as open complex adaptive systems with fundamental natural nonlinear structures, subject to internal and external forces that may contribute chaos. For instance, team building and group development is increasingly being researched as an inherently unpredictable system, as the uncertainty of different individuals meeting for the first time makes the trajectory of the team unknowable. [131]

Some say the chaos metaphor—used in verbal theories—grounded on mathematical models and psychological aspects of human behavior provides helpful insights to describing the complexity of small work groups, that go beyond the metaphor itself. [132]


Traffic forecasting may benefit from applications of chaos theory. Better predictions of when traffic will occur would allow measures to be taken to disperse it before it would have occurred. Combining chaos theory principles with a few other methods has led to a more accurate short-term prediction model (see the plot of the BML traffic model at right). [133]

Chaos theory has been applied to environmental water cycle data (aka hydrological data), such as rainfall and streamflow. [134] These studies have yielded controversial results, because the methods for detecting a chaotic signature are often relatively subjective. Early studies tended to "succeed" in finding chaos, whereas subsequent studies and meta-analyses called those studies into question and provided explanations for why these datasets are not likely to have low-dimension chaotic dynamics. [135]


Static Motion After Effects?

I really do love illusions of all sorts, in large part because they fit nicely into my narrative about the fallibility of human thought, but illusions are also great as windows into the ordinary working of our brains. For example, color afterimages provide direct evidence for opponent-processing theories of color vision, and when we find aftereffects for a particular class of stimuli, we can be pretty certain that class of stimuli has particular neurons or populations of neurons that encode it. And speaking of aftereffects, there's a really cool paper in the March issue of the journal Psychological Science that uses motion aftereffects to test an interesting hypothesis about the processing of static images that I thought I'd tell you about.

The classic example of the motion aftereffect is the waterfall illusion, an example of which you can see here. Exactly what's causing motion aftereffects is still a matter of some debate, but the basic story is probably something like this. There are populations of cells in your visual cortex that respond to motion in particular directions and orientations (e.g., straight down ). These neurons are always competing with cells that respond to motion in the opposite direction. Basically, these cells are firing a little bit all the time, but only when they receive some sort of push (e.g., through the input they happen to respond to) do they fire enough to out pace their competing cells and create the perception of their preferred motion. When you stare at motion in a particular direction and at a particular orientation for a while, the cells that respond to that sort of motion adapt -- get worn out, in essence -- and when you take the stimulus away, their firing rate drops below their resting rate. This allows the competing cells to create an imbalance, and suddenly, they cause you to perceive motion in the opposite direction. The effect can be so strong that it can make for some really trippy visuals (see this, for example).

Anyway, an interesting question which, at first glance, seems to have nothing to do with motion aftereffects is, how do we infer motion from static images? How does your brain process the implied motion? For example, how does your brain figure out not only that the horses in the picture below are moving, but in what direction they're moving?

Presumably all of you can tell that the horses are moving, and more specifically, moving from left to right. There is some evidence from neuroimaging studies that this implied motion is processed in the same brain area, the medial temporal area (or V5, or MT, or if we're being specific, hMT+), that processes actual motion(1). Unfortunately, as is generally the case, the imaging studies don't really tell us what's going on in MT. Most importantly, it doesn't tell us whether implied and actual motion are processed by the same cells and in the same way. To determine that, you have to use behavioral data, just as you have to use behavioral data to learn just about anything except that something happens in the brain.

Enter the motion aftereffect. In their Psych Science paper, Winawer et al.(2 presented participants with a series of static images like this one (from their Figure 1a, p. 277):

They then tested them for a motion aftereffect using moving dot configurations. When a motion after effect is present, it will warp people's perception of moving displays of randomly configured dots. So, if the cells in the brain that are responding to actual motion also respond to implied motion, then viewing a bunch of photos, one after the other, that imply motion in the same direction, should cause those cells to adapt, resulting in a motion aftereffect, and thus distort the participants' perception of the moving dot displays.

Since I'm writing this post, you already know that's what they found. In their first experiment, participants viewed static images implying motion in the same direction for sixty seconds, and immediately afterwards saw the moving dot images. In their second experiment, they observed a 60 second series of displays containing two images that appeared to be either moving toward each other or away from each other, and thus toward or away from a point in between the two implicitly moving objects. In both these cases, Winawer et al. were able to observe the motion aftereffect in the random dot displays. In another experiment, they showed participants the series of images for 60 seconds, and then placed a three second delay between the image series and the moving dot display. In this condition, they didn't observe the motion aftereffect, indicating that the aftereffect for implied motion decays much as the aftereffect for real motion.


Is there a waterfall visual after-effect with discrete inputs? - Psychology

The hard problem of consciousness--the nature of phenomenal experience--is especially hard for people who believe that:

(1) Conscious perceptual experiences exist inside a person (probably somewhere in the brain) 1

(2) Nothing existing inside a person has (or needs to have 2 ) the properties one is aware in having these experiences.

The experience I have when I see (dream of, hallucinate) a large orange pumpkin is certainly inside me. Why else would it cease to exist when I close my eyes, awaken, or sober up? Yet, nothing inside me--certainly nothing in my brain--has the properties I am aware of when I have this experience. There is nothing orange and pumpkin shaped in my head. How, then, can I be aware of what my perceptual experiences are like--presumably a matter of knowing what qualities they have--if none of the properties I am aware of when I have these experiences are properties of the experience?

Surely, though, we are, in some sense, aware of our own conscious experiences. We have, if not infallible, then privileged, access to their phenomenal character. I may not know what it is like to be a bat, but I certainly know what it is like to be me, and what it is like to be me is primarily--some would say it is exclusively--a matter of the phenomenal qualities of my perceptual (including proprioceptive) experience. I am aware--directly aware--of what it is like to see (dream of, hallucinate) orange pumpkins. If such awareness is incompatible with (1) and (2), so much the worse for (1) and (2).

This is a problem that some philosophers have given up trying to solve. Others spend time tinkering with (2). The problem is real enough, but (2) is not the culprit. The solution lies in distinguishing between the fundamentally different sorts of things we are aware of and, as a result, the different forms that awareness (or consciousness 3 ) of things can take. Once these distinctions are in place, we can see why (1) and (2) are compatible with privileged awareness of one's own experience. We can have our cake and eat it too.

By way of previewing the argument for this conclusion, let o be an object (or event, condition, state--i.e., a spatio-temporal particular), P a property of o . We speak of being aware of o , of P , and of the fact that o is P . These differences in the ontological kinds we are aware of are reflected in differences in the corresponding mental acts of awareness. Awareness of P is a much different mental state from awareness of the o which is P , and both differ from an awareness of the fact that o is P .

In thinking about the mind's awareness of itself, these differences are important. For if e is some mental particular and P a property of e 4 , we must not confuse awareness that e is P with awareness of either e or P . For one can be aware of the former--aware, that is, that one's experience is P --without being aware of either the experience ( e ) itself or the quality ( P ) that helps make it that kind of experience.

Therein lies an answer to the puzzle generated by (1) and (2), the puzzle of how one can be aware of internal affairs--aware of what one's experiences are like--without being aware of these experiences themselves or the properties that give them their phenomenal character. The mind's awareness of itself is an awareness of facts about itself, an awareness that internal experience, e , is P . It is not an awareness of the internal object e or the property P out of which such facts are composed. The facts we are aware of in knowing what it is like to experience orange pumpkins are, to be sure, facts about internal affairs--thus the truth of (1)--but the properties we are aware of in achieving this awareness (being universals 5 ) exist nowhere. They aren't in the head. Thus the truth of (2).

1. Objects, Properties, and Facts

When an object is moving, I can be aware of: (A) the moving object (B) the fact that it is moving (C) the movement (D) all of the above (E) none of the above. Consider:

Case A: I study the minute hand of a clock. The hand is moving so the object I see, the object I am aware of, is a moving object. I do not, however, sense, I am not aware of, its movement. Nor (thinking the clock is broken) am I aware of the fact that it is moving . I am aware (I see) the moving hand, o , but I am aware of neither its movement, M , nor the fact that it is moving: that o is M .

Case B: I observe the minute hand on the clock for several minutes. I see that the hand is in a different position now than it was a moment ago. I thus become aware that it is moving. Nonetheless, I still do not perceive the movement. The minute hand moves too slowly for that. I know it is moving. but I cannot see it move. I am aware of o and that o is M but not M .

Case C: I observe the movement of a nearby vehicle and mistakenly take it to be my own movement. I stomp on the brakes. Nothing happens. In this case I was aware of both the neighboring vehicle and its movement without at the time being aware that it (the adjacent vehicle) was moving. I thought I was moving. Awareness of o and M , but not of the fact that o is M .

Case D: I observe the second-hand of another clock. Unlike the minute hand of the first clock, the movement of this object is plainly visible. I am aware of the moving hand, its movement, and also the fact that it is moving. When one becomes aware of the fact that o is M by awareness of both o and the M of o I call it direct fact-awareness. I am directly aware that the second hand is moving, but indirectly aware that the minute hand is moving.

Case E: I am aware of neither the object, its properties, nor the fact that it has those properties. There are unobservable objects (e.g., electrons) that have properties (e.g., spin) I am not conscious of. I am, to be sure, aware of the fact that electrons have this property (I read about it in a book), but there was a time I was not. There was a time, in other words, when I was unaware of o , the property S , and the fact that o was S (not to mention the fact that there were o 's).

I will call these three forms of awareness o -awareness (for object -awareness 6 ), f -awareness (for fact -awareness) and p -awareness ( property -awareness). When the kind of awareness is clear from context--when, for example, I am talking about an awareness (and, thus, a p -awareness) of properties--I will generally drop the distracting prefixes. There are times, though, when it is important to specify exactly which form of awareness is at issue, and on these occasions the prefixes will appear. Though I use movement (a relational property) to illustrate these distinctions, I could as well have used any other property. I can, for instance, be f -aware that the wine is dry (someone told me it was or I read the label) without being aware of the wine or its dryness (I do not taste the wine for myself). One sees a fabric in normal light--thus experiencing (becoming p -aware of) its color (blue, say)--without realizing, without being f -aware, that it is blue. One thinks, mistakenly, that the illumination is abnormal. The fabric, one thinks, only looks blue. And one can be aware of the color of Tim's tie--that particular shade of blue--without being o -aware of his tie or the fact that it is blue. One sees another object of exactly the same color. If it sounds odd to speak of being aware of an object's color without actually seeing the object, imagine someone pointing at another object (a color sample perhaps) and saying, " That is the color of his tie." 7 What you are made p -aware of when you see the color sample is the color of his tie. One might also be p -aware of the color of his tie while being aware of no object at all. Imagine hallucinating a homogeneous expanse of color that exactly matches the blue of his tie.

This last claim may sound false--at least controversial. When a person hallucinates pink rats, isn't the person aware of colored images (shaped like rats)? Isn't awareness of properties (colors, shapes, sizes, orientations, etc.) always (and necessarily) awareness of objects having these properties? To insist on this point is a way of denying (2). It is a way of denying that there is nothing in one's head that has the properties one is aware of in having experience. Since I am here exploring the possibility of understanding conscious experience given the truth of both (1) and (2), I assume, to the contrary, that hallucinations are experiences in which one is aware of properties (shapes, colors, movements, etc.) without being o -conscious of objects having these properties. To suppose that awareness of property P must always be an awareness of an object (an appearance? a sense-datum?) having property P is what Roderick Chisholm (1957) called the Sense-Datum Fallacy. Following Chisholm, and in accordance with (2), I will take this to be a genuine fallacy. Hallucinating pumpkins is not to be understood as an awareness of orange pumpkin-shaped objects. It is rather to be understood as p-awareness of the kind of properties that o -awareness of pumpkins is usually accompanied by.

Awareness (i.e., p-awareness) of properties without awareness ( o -awareness) of objects having these properties may still strike some readers as bizarre. Can we really be aware of (uninstantiated) universals? Yes we can and, yes, we sometimes are. It is well documented that the brain processes visual information in segregated cortical areas (see Hardcastle 1994 for references and discussion). One region computes the orientation of lines and edges, another responds to color, still another to movement. 8 As a result of this specialization it is possible, by suitable manipulation, to experience one property without experiencing others with which it normally co-occurs. In the after-effect called the waterfall phenomenon , for instance, one becomes aware of movement without the movement being of any thing. There is no colored shape that moves. To obtain this effect one stares for several minutes at something (e.g., a waterfall) that moves steadily in one direction. In transferring one's gaze to a stationary scene one then experiences movement in the opposite direction. Remarkably, though, this movement does not "attach" itself to objects. None of the objects one sees appears to be moving. Yet, one experiences movement. As a psychologist (Frisby, 1980, p. 101) puts it, "although the after-effect gives a very clear illusion of movement, the apparently moving features nevertheless seem to stay still!" One becomes, he says, "aware of features remaining in their 'proper' locations even though they are seen as moving." This may seem paradoxical (Frisby describes it as contradictory), but it is nothing more than a p -awareness of one property (movement) without this movement being instantiated (as it normally is) in or by some object. One's movement detectors are active, but they are not made active by any object possessing the normal array of sensory properties (shape, color, texture, etc.).

Everyday perception is generally a mixture of object, property, and fact awareness. Usually we become aware of facts by becoming aware of the objects and properties that constitute these facts. I become aware that his tie is blue by seeing his tie and its color. I become aware that gas is escaping by smelling the escaping gas. Perceptual modalities being what they are, though, we are often made aware of facts by being made aware of properties altogether different from those involved in these facts. We become f -aware that the metal is hot by seeing it change color, not by feeling its temperature. Instruments, gauges, and natural signs (tree rings, tracks in the snow, cloud formations, etc.) have familiarized us with the various ways awareness of facts is mediated by awareness of objects and properties quite different from those involved in the fact. I see that the water is 92o by an awareness not of the water, but of a thermometer and the height of its mercury column. Use of language in communication is another source of f -awareness in which there is little or no connection between the objects (sounds and marks) and properties (spatial and temporal arrangement of symbols) we perceive and the facts (reported on) that communication makes one f -aware of. When f -awareness is achieved by awareness of properties and/or objects other than those involved in the fact, the f -awareness is indirect . Thus, awareness that your daughter has a fever is indirect when you use a thermometer, direct when you feel her forehead.

There is, then, a virtual 9 independence (conceptual, not causal) between f -awareness, o -awareness, and p -awareness when the awareness is perceptual. We can, and we often do, have one without the others. If this is also true--and why shouldn't it be?--of our awareness of mental affairs, this tells us something important about awareness of our own conscious states. I begin by describing what it tells us about a special class of conscious experiences-- perceptual experiences.

2. Perceptual Experience

Perceptual experiences are phenomenally rich in a way that beliefs are not. It is like something to have them. Unlike a belief or judgment (an f -awareness) that a pumpkin is moving toward you (something you can have without awareness of either the pumpkin or its movement), seeing a pumpkin move involves an experience that is phenomenally quite different from experiencing a green bean move toward you, a red tomato moving to the left, a ripe banana rotating in place, etc. The experience of a moving pumpkin, though it is caused by a pumpkin (and, according to causal theorists, must be so caused in order to be rightly classified as an experience of a pumpkin) is detachable from external causes in the sense that the very same kind of experience--an experience having the same phenomenal character--could occur (and in pumpkin hallucinations does occur) without a pumpkin.

This much, I hope, is philosophical (not to mention psychological) common sense. Disagreement arises when we turn to questions about our awareness not of pumpkins, their properties 10 , and facts about them, but of our experience ( e ) of a pumpkin, its properties, and facts about it . Letting P stand for a property of a pumpkin experience, a property that helps makes this experience the kind of experience it is, how does one become aware that e is P ? Is this achieved by an awareness of e and P or is it, instead, indirect--mediated by an awareness of some other object and (or) property ?

There is a long tradition stemming from Descartes that conceives of the mind's awareness of itself as direct. We become f -aware that a visual experience is P by means of o -awareness of the experience, e , and p -awareness of P . According to some philosophers, all fact-awareness begins here. 11 Thus, awareness of facts about a pumpkin, that the pumpkin is P , are reached via inference from o -awareness of e and p -awareness of one or more of its properties. We become fact-aware of what is going on outside the mind in something like the way we become f -aware of what is happening outside a room in which we watch TV. The only objects we are aware of are in the room (e.g., the television set) the only properties we are aware of are properties of those objects (patterns on the screen). Only f -awareness--awareness of what is happening on the playing field, concert hall, or the broadcast studio--is capable of taking us outside the room.

I will not discuss such theories (basically sense-data theories). I set them aside, without argument, because they all deny thesis (2), and my purpose here is to understand the mind's awareness of itself in a way compatible with (1) and (2). Contrary to (2) sense-data theories affirm that there is something in a person's head that has the properties the person is aware of when he sees or hallucinates an orange pumpkin. Sense-data are inside, and sense-data actually have the properties one is aware of when one sees or hallucinates a pumpkin. The sense-datum is orange. It is bulgy and shaped like a pumpkin. It moves--at least it does so relative to other sense-data. In having a visual experience of a pumpkin it is the bulgy orange sense-datum, an internal object, one is o -aware of, and it is the properties of this internal object one is p -aware of. Awareness of pumpkins is, at best, indirect. It is the same type of awareness (i.e., fact -awareness) that one has of Boris Yeltsin when one "sees" him on TV.

Armed, as we now are with the distinction between object, property, and fact awareness, though, we are in a position to understand what goes wrong in traditional arguments for indirect realism. We are in a position to understand--and, thus, resist--arguments against (2). The mistake in traditional arguments lies in failing to distinguish between f -awareness of experience, that it has phenomenal character P , on the one hand, and, on the other, p -awareness of the qualities (e.g., P ) that give it this character. Failing to distinguish these forms of awareness, one concludes, mistakenly, that awareness of what it is like to see (experience) pumpkins must be awareness of the properties (i.e., P ) of these experiences. That is the first mistake--the mistake of inferring p -awareness of the properties of experience from f -awareness of the fact that experience has those properties. The second mistake (this is optional the major damage has already been done) is inferring o -awareness from p -awareness--that is, inferring that one must be o -aware of e in order to be p -aware of e 's properties. The conclusion? To be aware of what it is like to experience pumpkins, one must be aware of one's own pumpkin experiences in something like the way one is aware of pumpkins.

The fact that we don't have to be p -aware of an object's properties to be f -aware that it has those properties does not mean that we are not aware of our own experiences and their properties. It only shows that an awareness--even a privileged awareness--of what it is like to have a given experience is not, by itself, a good reason to think we are aware of either the experience or its properties. Once the distinctions between kinds of awareness are in place, our privileged awareness of what it is like to have these experiences may simply be a form of fact-awareness, an indirect awareness of a fact about an experience that is psychologically immediate and epistemically privileged.

But how is this possible? How is it possible to be aware in both a privileged and (or so it seems) direct way of facts about one's experiences without being aware of either the experiences or t heir properties? If one's f -awareness of one's own experience is supposed to be indirect like becoming aware, by looking at X-ray photographs, that one's arm is broken, what objects and properties is it an awareness of that is supposed to give one this awareness? I can become (indirectly) aware that my arm is broken by having the doctor tell me it is or by looking at the photographs for myself, but what could possibly bring about an indirect fact-awareness of the quality of one's own experience that would preserve the immediacy and privileged character of this awareness? No one tells us--indeed, no one can tell us--what our own experiences are like in the way a doctor can tell us about our broken bones. X-rays are not of much help in telling what it is like to be a bat or what it is like to see orange pumpkins. What, then, is supposed to tell us what qualities our experiences have if we are not, in having them, p -aware of them ? There must be something (other than the experience) that tells us this since, in accordance with (1) and (2), we are now assuming that the properties we are aware of in having the experience are not properties of the experience. If we are to be made f -aware of what our experiences are like--that they are P for some value of " P "--then, we must be made f -aware of this fact by an awareness of properties and objects other than those of the experience itself. What are these other objects and properties?

They are--what else?-- the objects and properties our experiences make us aware of. One is made aware of what a pumpkin experience is like (that it is P ) not by an awareness of the experience, but by an awareness of the pumpkin and an awareness of its (the pumpkin's) properties. When the perception is veridical, the qualities one becomes p -aware of in having a perceptual experience are qualities of external objects (the pumpkins) that one experiences, not qualities of the pumpkin-experience. One becomes f -aware of experience--that it is P --by p -awareness of P --the pumpkin's properties. The reason p -awareness of P can make one f -aware that one's experience is P is that P is the property of being an experience, in fact a p -awareness, of P . P tells one what specific kind of experience e is: it is an e of the P kind--i.e., an awareness of P kind. Even when there are no pumpkins, even when hallucinating, it is nonetheless true that what (properties) one is p -aware of in having the pumpkin experience are color, shape, texture, distance, and movement--properties that pumpkins normally have.

The key to this account is the relation between P , the property we are p -aware of in having experience e , and the property of the experience ( P ) that we thereby become f -aware that e has. If P is the pumpkin's movement, a property that one becomes aware of in observing a moving pumpkin, then P is the property of being an experience (a p -awareness)-of-movement . P is not the property: is moving . P is the property that a possibly stationary experience has that makes this experience a p -awareness of movement. 12 P , therefore, helps fix the kind of experience e is--an experience of movement. Though P is not a property one is p -aware of, it is nonetheless a property that (helps) make that experience the kind of experience it is--an experience, specifically, of a moving pumpkin.

What this means is that if we follow philosophical convention and take qualia to be properties of one's experiences (and not the properties one experiences), then it is P , not P , that is the quale. Nonetheless, it is P (i.e., movement) not P (an awareness of movement) that one is p -aware of. One is (or can be--see §4 below) aware of the quale P , to be sure, but this is fact , not property -awareness. One's experiences of movement do not (or need not) have the properties one is p -aware of in having these experiences. The experiences don't move. Nonetheless, when experiencing movement, the property the experience has is P , the property of being a p -awareness of movement.

This account of the mind's awareness of itself gives a neat and, I think, satisfying account of both the psychological immediacy (i.e., the seeming directness) of introspective knowledge and the epistemically privileged character of self awareness. F -awareness of the fact that one's experience (of P ) is P is psychologically immediate because, although it is indirect (one is not p -aware of P ), one cannot have an experience of this sort without thereby being aware of P , a property (usually) of external objects that reveals (to the person having the experience) exactly what property it is that his or her experience has--namely, P (= an awareness of P ). Technically speaking (given my earlier definitions) this is indirect fact-awareness, yes, but the fact one is indirectly aware of is so directly given by the properties (of external objects) one is aware of that the process (from p -awareness of P to f -awareness that one's experience is P ), when it occurs, seems direct and immediate. It can be made to seem even more direct, of course, if one confuses the properties one is aware of in having the experience with the properties of the experience. F -awareness that e is P is also privileged because only the person having the experience is necessarily (in virtue of having it) aware of a property, P , that reveals what kind of experience (viz., P ) he is having. Other people might also be experiencing P , of course, but unless they know you are, they can only guess about the quale (viz., P ) of your experience.

Before leaving this discussion of perceptual experience, it may be useful to see how a familiar (to philosophers) scenario plays out on this account. What Jackson's (1986) Mary does not have before she emerges from her colorless room is an awareness of red (or of any other color). Assuming that colors are objective properties (if they aren't, we don't need Jackson's argument to refute materialism (1) and (2) will do the job), Mary knows all about tomatoes--that they are red ( P )--and she knows all about what goes on in other people's heads when they see red objects (there is something in their brain that has the property P ), but she does not herself have internal states of this sort. If she did, she would, contrary to hypothesis, be p-aware of (she would actually experience) the color red. Once she walks outside the room, objects ( e s) in her head acquire P --she becomes p -aware of red. She is now aware of things (i.e., p -aware of colors) she was not previously aware of. Using our present distinctions to express Jackson's point, the question posed is not whether Mary is now aware of something she was not previously aware of (of course she is she is now p -aware of colors), but whether Mary is now f -aware of things that she was not previously f -aware of. The answer, on the present account of things, is No. 13 Mary always knew that ripe tomatoes were red ( P ) and that ripe tomato experiences were P --viz., awarenesses of red. There are no other relevant facts for her to become aware of. 14 Emerging from the color-free room gives her an awareness of properties ( P ) that figure in the facts (that o is P ) she was already aware of, but it doesn't give her an awareness of any new facts.

We have now taken the first step in this account of the mind's awareness of itself. In a way that is consistent with both (1) and (2) and in a way that preserves the essential features of the mind's awareness of itself (the psychological immediacy and epistemically privileged character of this awareness) we have an account--at least the broad outlines of one--of how we are aware of our own experiences of the world. What remains to be done is to see whether this account can be generalized to all mental states. My efforts at generalization (§3) will be feeble. I can, at this point, do little more than gesture in what I take to be the appropriate directions. I close (in §4) with a mildly interesting implication of this account of self-awareness.

3. Pains, Feelings, Emotions, and Moods.

Up to this point I have focused exclusively on conscious perceptual experiences, mental episodes that are of things--whatever objects and properties we are, in having the experience, made aware of. Perceptual experiences are being identified with internal states having properties (e.g., P ) that make them p -awarenesses, experiences, of the properties (e.g., P ) that external objects have. Something, e , in my head having the property P (a property that is not movement) constitutes my awareness of movement ( P ). I can become f -aware that something in me has P by an awareness of P . If e 's having P is caused by a pumpkin having P (i.e., by the movement of a pumpkin), then I am aware of a pumpkin's movement. I see it move. If there is no such object, I am aware of movement without being aware of any moving object and, thus, without being aware of any object's movement. I hallucinate or imagine something moving.

This account works nicely enough for phenomenal experiences that are, in some ordinary sense, of or about things (mental states the having of which makes us perceptually aware of things). For this reason it is tempting to try extending the account to mental states that are, in some related (but, perhaps, different) sense, also of or about things: beliefs, desires, intentions, hopes, and, in general, the propositional attitudes. Just as my experience of movement has a property that makes it a p -awareness of movement, perhaps my belief (i.e., my f -awareness) that some object, o , is moving is, likewise, an internal state having a property, B (not itself movement), a property the having of which makes an internal state into a conceptual representation or depiction (i.e., an f -awareness) of movement. Just as the English word "movement" need not itself be moving in order to figure in a representation of something as moving (e.g., a sentence), so too, perhaps, there are symbols (concepts?) in the head that do not (or need not) have the properties they represent objects as having. If this were so, then thoughts, just as experiences, would be mental states that would not (or need not) have the properties we become f -aware of in having these thoughts.

If this were so, then we could tell the same story about awareness of these states that we told about our f -awareness of perceptual experiences. We become f -aware that we are having thoughts about movement (internal states with B ) by actually thinking about movement. It is the movement we think about --the content of our thought--that (when we introspect) "tells us" what we are thinking about and, hence, if we understand what thinking amounts to, that we are thinking about movement (not color or shape). Just as I reach the f -awareness that I am experiencing movement from a p -awareness of movement, so too I reach an f -awareness that I am thinking that o moves from an f -awareness that o is moving. 15

I will not pursue this line of thought any further here since it seems like a more or less obvious extension of the present theory, and there are much more difficult problems to face. This treatment of belief, judgment, and thought is, I think, merely a version of the view that Tyler Burge has promoted about the introspective accessibility of externally grounded belief content. Burge's idea is that my second order belief (the content of which is that I believe o moves) inherits the conceptual content MOVES from the content (that o moves) of my first order belief. Hence, if I really do believe (1st level) that o moves, I must be right in thinking (2nd level) that that (viz., that o moves ) is what I think. The present theory is a version of this idea since a (2nd level) f -awareness that I am aware (at the first level) that o moves is privileged because the property (viz., movement) I am (1st level) f -aware of (= believe something has) "tells me" more or less infallibly what content-property my 1st level belief has--viz., M , a conceptual awareness that something is moving.

Unlike the propositional attitudes, though, there are a great many mental states (emotions, moods, and so forth) that, unlike experiences and thoughts (both of which seem representational at some level), do not, at least not on the surface, make us aware of anything (either of objects, properties, or facts). And it is these states that pose the real problem for the present account. When I am hungry, have a splitting headache, or am depressed, for instance, I seem to be aware of mental objects (the hunger, the ache, the depression) and their properties (the headache is splitting , the hunger gnawing , the depression constant) . Surely in such cases I am aware not only of the fact that I have certain feelings or am in a certain mood, but also aware of the feelings and moods themselves--the pain, the hunger, the depression.

This, I concede, is a natural way to talk about feelings, emotions, and moods. What I think worth questioning, though, is whether this way of talking doesn't embody a confusion between awareness of something (an act) and the something of which we are aware (the object of that act)--a confusion that is fostered by a failure to distinguish between the different things we can be aware of. Why suppose, for instance, that feelings of hunger are internal mental objects (i.e., conditions, states) we are o -aware of and not awarenesses (i.e., experiences) of certain internal (non-mental) objects--a chemical state of the blood, say? Just as we conceived of visual experiences as internal states having the property of being awarenesses of P (for some P of an external o ), why can't hunger be similarly conceived of as an internal experience (a p -awareness) of the properties of an internal o ? Why can't an itch in one's arm be thought of not as something in the arm (brain?) one is o -aware of, but an o -awareness (in the head) of a physical state of the arm? Why can't we, following Damasio (1994), conceive of emotions, feelings, and moods as perception of chemical, hormonal, visceral, and muscuoskeletal states of the body?

This way of thinking about pains, itches, tickles, and other bodily sensations puts them in exactly the same category as the experiences we have when we are made perceptually aware of our environment. The only difference is that bodily sensations are the experiences we have of objects in the body (the stomach, the head, the joints, etc.), not objects outside the body. What gives these sensations their phenomenal character, the qualities we use, subjectively, to individuate them, are the properties these experiences are experiences of, the properties (of various parts of the body) that these experiences make us p -aware of (irritation, inflammation, time of onset, injury, strain, distension, intensity, chemical imbalance, and so on). What gives a (veridical) visual experience of an orange pumpkin its particular quality ( P ) are the qualities of the pumpkin (viz., P ) that this experience (in virtue of being P ) is an experience of. Likewise, what gives headaches their particular quality (what distinguishes them from pains in the back, itches, thirst, anger or fear) are the properties (and these include locational properties) that these experiences are p -awarenesses of. Just as one becomes aware of external objects in having visual and olfactory experiences, so one becomes aware of various parts of the body (and the properties of these parts) in having bodily sensations--e.g., pain. Having a headache is not an awareness--certainly not an o -awareness--of a mental entity: a pain in the head. The only awareness one has of pain is an f -awareness that one has it. In saying that one feels pain what one is really saying is not that one is o -aware of something mental (viz., a pain)--but that one feels (is aware of) a part of the body the feeling (awareness) of which is painful (is pain). Once again, the phenomenal qualities (= qualia) of these mental states are not the properties of those parts of the body one becomes p -aware of in occupying these states. They are, instead, awarenesses (= S) of these properties ( P ). We do not have to be aware of the state ( e ) itself (or its properties S ) to be aware--authoritatively aware--that we occupy a state of that phenomenal kind. P gives our conscious awareness its phenomenal character and tells us what kind of experience we are having.

But can such an account possibly work for all experiences--for love and hatred, joy and depression, ennui and anxiety? Even if such feelings are not all properly classified as "experiences," they all seem to have an associated phenomenology that calls out for explanation. Can what-it-is-like to have these feelings or experiences always be interpreted (using the model of perceptual experiences) not as internal objects we are o -aware of, but as awarenesses of the properties of internal objects? Can the entire phenomenology of the conscious mind be boiled down to the properties (of bodily parts and external objects) that we are p -aware of in having these experiences?

Whether it can or not, this is clearly the direction suggested by our analysis of perceptual experience. It may turn out, of course, that even if our account of perceptual experience is on target, perceptual experiences are unique. Other feelings, moods, and emotions--itches, pains, hunger, anger, jealousy, pleasure, and anxiety--may have a phenomenal character that they get from other sources. If the story I have told about perceptual experience is plausible, though, it is tempting to try extending it to other qualia-laden mental states along similar lines. I leave the argument that it can be so extended to another time.

4. Prerequisites of Self-Awareness

Fact -awareness, unlike p -awareness and o -awareness, requires an understanding of what one is aware of. 16 One cannot be f -aware that o is an apple without understanding, at some conceptual level, what an apple is. If a child (or an animal) doesn't know what an apple is, this does not prevent it from being o -aware of apples or p -aware of their properties (this presumably happens when the child is a few months old), but it prevents it from being f -aware that the apples (she is o -aware of) are apples.

Since the account developed in §2 and §3 identifies our awareness of our own (not to mention everyone else's) experiences with f -awareness, it requires of anyone aware of the P quality of her own experience an understanding, a conceptual grasp, of the property P (and, thus, of P which e 's having P is an awareness of). If S doesn't know what it is to be P , then even if S has a P -experience (i.e., an experience of P ), S cannot be aware of this. S will be "blind" to it. Since the mind's awareness of itself is always (according to this account) f -awareness, there is no way one can be aware of one's mental states without a mastery of the relevant concepts. The senses make you aware (i.e., o -aware and p -aware) of the world (and, if we can generalize, your own body) before you have developed the concepts needed for understanding what you are aware of, but, lacking a "mental sense" (a sense that allows us to become o -aware of the mind and p -aware of its properties) we must first develop the required concepts before we can be made conscious of what transpires in our own minds.

This result may seem mildly paradoxical so let me take a moment to soften the mystery. Imagine a naive (about numbers and shapes) child shown brightly colored geometrical shapes. The child, possessing normal eyesight, sees the difference between these figures in the sense that the pentagons look (phenomenally) different from the triangles and squares. How else explain why we could teach her to say "pentagon" when (and only when) she saw a pentagon? In the terminology we have already introduced for describing these facts, the child (before learning) is o -aware of circles, squares, and pentagons, and p -aware of their shapes. The child hasn't yet been taught what a circle, a square, or a pentagon is, so it isn't (yet) f -aware of what these figures are, but that doesn't prevent it from being aware of the figures themselves and p -aware of their (different) shapes.

Is the child also aware--in any sense--of what its experience of these shapes is like, of what it is like to see a pentagon? No. 17 Lacking the concept of a pentagon (not to mention the concept of awareness) the only awareness a child has when it sees a pentagon is an awareness of the pentagon and its shape. It cannot be made aware of its experience of the pentagon until it develops the resources for understanding what pentagons are and what it means to be aware of (experience) them. Only then can it become aware of its awareness of pentagons. In having an experience of a pentagon, the child is, to be sure, aware (i.e., o -aware) of a pentagon and p -aware of its distinctive shape. What the child lacks is not a visual awareness (experience) of pentagons, but an awareness of pentagon experiences. Awareness of experience awaits development of the understanding, an understanding of what property one is p -aware of in having the experience. If you lack this understanding, you can still be aware of pentagons, but you cannot be aware of your pentagon experiences. It is like awareness of neutrinos. Being what they are (i.e., unobservable: we do not have a sense organ that make us o -aware of them), neutrinos are objects one cannot be aware of until one learns physics. Unlike pentagons, you have to know what they are to be aware of them.

The mind becomes aware of itself, of its own conscious experiences, by a developmental process in which concepts needed for such awareness are acquired. You don't need the concepts of PENTAGON or EXPERIENCE to experience (e.g., see or feel) pentagons, but you do need these concepts to become aware of pentagon experiences. As psychologists are learning (in the case of such concepts as EXPERIENCE), this doesn't happen with children until around the ages of 4-5 years. In most animals it never happens. The mind is the first--indeed, the only --thing we are aware with, but it is among the last things we are aware of.

REFERENCES

Chisholm, R. 1957. Perceiving . Ithaca, NY Cornell University Press

Damasio, A. R. 1994. Descartes' Error: Emotion, Reason, and the Human Brain . New York: Avon Books.

Dretske, F. 1995. Naturalizing the Mind . Cambridge, MA MIT Press/A Bradford Book.

Frisby, J. P. 1980. Seeing: Illusion, Brain and Mind . Oxford: Oxford University press.

Hardcastle, V. G. 1994. Psychology's Binding Problem and Possible Neurobiological Solutions. Journal of Consciousness Studies , 1:1, pp. 66-90.

Jackson, F. 1986. What Mary Didn't Know. The Journal of Philosophy LXXXIII, 291-95.


Possible explanations

attention focus — One suggestion for the cause of MIB has to do with the focus of attention.2 Perhaps the brain is simply distracted by the changing image and fails to pay attention to static portions of the visual field. In this respect, MIB may be similar to an effect produced when two different images are seen by the two eyes (binocular rivalry). In that case, the brain tends to focus on the image in one (dominant) eye, to the exclusion of the image in the other eye.

suppression of eye movements — There is some evidence that some eye movements are partially suppressed in the presence of background motion.3 In that case, the reduced eye motion may allow desensitization to occur, as it does in Cheshire Cat Illusions. However, more recent studies of eye movements in MIB experiments4 claim that eye movement suppression is not adequate to allow significant desensitization.

filling in the gaps — Some research has suggested that MIB might be related to a known effect called "perceptual filling-in",5 which explains why we don't see the blind spots in our eyes. In the absence of sensory input for portions of the visual field, the brain fills in the missing parts with information from surrounding areas. (See our lesson on Blind Spot for activities to explore the blind spot.)

contrary to logic — It has also been suggested6 that if a static image is inconsistent with the motion of its background, the brain may discount the static image as contrary to the logic of the scene, perhaps akin to how it ignores the blind spot in the eye.

streak suppression — The eye and brain integrate the visual image over time. For images that are moving, this integration produces streaking in visual perception, like the streaking in a long exposure photograph of fast motion. The brain actively suppresses the streaking in order to make better sense of the image. This suppression may account for some or all of the MIB effect. Research has demonstrated7 that MIB is enhanced at the trailing edge of motion, which supports this idea.


The Lie algebra of visual perception

The familiar perceptual constancies of image location in the field of view, image orientation, size constancy, shape constancy, binocular distortion, and motion, have their natural mathematical expression in terms of Lie groups of transformations over the visual manifold. If Lie's three fundamental theorems are to be satisfied, three additional perceptual invariances must also be present: time, efferent binocularity, and what apparently constitutes some sort of circulating memory in space-time. This Lie algebra of visual perception admits ready explanations for the following visual phenomena: the developmental sequence of infant vision orthogonal after-images after-effects of seen movement the spiral after-effect and the spiral images sometimes evoked under flicker reading reversals and the visual analogue of the Fitzgerald contration. The theory also predicts certain new complementary (orthogonal) after-images, the existence of which have been verified experimentally.

Work done at Boeing Scientific Research Laboratories.


2 Answers 2

This is a more detailed answer about conceptual mechanisms from the same author as AliceD is citing:

The first row represents the sensors (for instance photoreceptors) while the second row represents higher order responses (for instance of MT neurons). The latter's response is their resting level response plus the difference of the corresponding channel minus the opponent channel's response (so yes, the assumption is that there is an opponent mechanism). As you can see, there is no response beyond baseline before adaptation as the difference between the sensor's responses is zero. During adaptation, when subjects are seeing an upward motion, the corresponding response is higher, too.

Now after adaptation, the opposed system shows an above baseline response as now the up sensors display some form of adaptation, hence shifting the response difference of the sensors in the favour of the opponent motion direction:

I am not familiar with the underlying biophysical mechanisms, this model possibly suggests, however, decreased feedforward inhibition after adaptation.

The motion after-effect (MAE) is believed to be primarily due to adaptation of direction sensitive cells in the middle temporal area (MT) (Fig. 1.). The directional cells in this area of the cortex are selectively sensitive to motion in one direction. Hence, looking at a waterfall will selectively cause adaptation in those cells tuned to the direction of the waterfall. When one looks away, the MT cells responsive to opposite directions will become dominant, as their counterparts are momentarily shut down and one will see the waterfall running in opposite direction.

Adaptation thus apparently weakens the opponent input to the adapted MT cells, enabling an enhanced response to motion balanced stimuli. However, the possibility of adaptation occurring in MT neurons themselves cannot be ruled out (Mather et al., 2008).

The MT area is one of the principal visual cortical areas devoted to motion sensing and hence a likely culprit for MAE. However, fMRI studies have indicated that a lot more visual areas in the brain may be involved, either directly, or indirectly, including V1, V2, V3, VP, V3A, V4, and also MT (Mather et al., 2008).


Fig. 1. Two visual streams dominate vision: the dorsal 'where" pathway (containing the direction-sensitive MT area), and the ventral 'what' pathway. source: InTech Open


The surface and deep structure of the waterfall illusion

The surface structure of the waterfall illusion or motion aftereffect (MAE) is its phenomenal visibility. Its deep structure will be examined in the context of a model of space and motion perception. The MAE can be observed following protracted observation of a pattern that is translating, rotating, or expanding/contracting, a static pattern appears to move in the opposite direction. The phenomenon has long been known, and it continues to present novel properties. One of the novel features of MAEs is that they can provide an ideal visual assay for distinguishing local from global processes. Motion during adaptation can be induced in a static central grating by moving surround gratings the MAE is observed in the static central grating but not in static surrounds. The adaptation phase is local and the test phase is global. That is, localised adaptation can be expressed in different ways depending on the structure of the test display. These aspects of MAEs can be exploited to determine a variety of local/global interactions. Six experiments on MAEs are reported. The results indicated that relational motion is required to induce an MAE the region adapted extends beyond that stimulated storage can be complete when the MAE is not seen during the storage period interocular transfer (IOT) is around 30% of monocular MAEs with phase alternation large field spiral patterns yield MAEs with characteristic monocular and binocular interactions.

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