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Motion Perception
A first intuitional approach

Movement is a very old metaphysical problem that divided the great ancient Greek thinkers.
Zeno's paradoxes, as discussed by Plato, Aristotle and others, found their way in modern thinking in the form of calculus, relativity, and last but not least, in the neurological underpinnings of motion perception. I will confine myself in this thread to the latter aspect, with only brief remarks concerning the others. Both the physical and philosophical traditions are rich in debates that would take many volumes to treat properly. 

The idea that we are always looking at a stationary picture of reality (in which stationary objects remain in the same place relative to the visual scene they are part of), and that the sensation of movements comes from the differences between two consecutive images is, very often, the implicit assumption of the 'scientific" approach to motion perception. 
I need to be very clear on this point. In my view, it is not the calculation of these differences that gives rise to the sensation of movement. It fact, it is probably the reverse: the sensation of movement draws our attention to those differences. In the first case, we need neural circuits dedicated to those computations. In the second case, all we need to assume is an unavoidable fact: sensation (of movement). The effects and the circumstances in which those effects take place can then be investigated empirically.
I would like here to remind the reader of Carroll's satire (1894) about the Tortoise and Achilles. Any rational explanation we could give of why we have a sensation of movement would encounter the same fate as the foundation of logic, or, as is the case with consciousness, the fate of all neuronal correlates (see also Chalmer's objections in "The Conscious Mind: In Search of a Fundamental Theory"; 1995 ). 

This is contrary to the epiphenomenalism of certain authors (as in the case of Chalmers again, op.cit.), and also to the Helmhotzian conception of perception as an, unconscious, intellectual activity or inference. Once again, I will not endeavor a philosophical explanation, but will confine myself to the explicitation of my own assumptions: we would be as hard put to find a neural trace of motion as in the case of color or any other sensation. The assumption that the brain needs computations to explain such phenomena as motion only makes sense when we decide to ignore sensations as a whole. Then we seem to need rational explanations to explain what even the most primitive organisms is able to do. Those rational explanations need a home, and since connecting them to our own intellectual conceptions would turn them inevitably into subjective biases, we try to give them an objective raison d'être by localizing them in the brain itself, however primitive this brain is. Those explanations of how a biological brain is supposed to function is, so I am convinced, based on pure metaphysical assumptions that are still waiting for the first empirical proof of their validity. My own conceptions are not any better. They are also based on metaphysical assumptions that are certainly not easily proved... or disproved. The main difference being that I am not trying to construct an artificial brain to explain how real ones work. One only need to read Marr's "vision" ("Vision: A Computational Investigation into the Human Representation and Processing of Visual Information", 1982) to realize that his analysis, like Searle so justly remarked ("The Rediscovery of the Mind", 1992), only makes sense with a homunculus, and that it would be, as many articles have shown, much more useful in building an artificial vision module. Until now, brain scientists have tried to avoid the philosophical and methodological consequences of sensation even after the so-called cognitive revolution supposedly put behaviorism to rest. I am afraid it is still alive and kicking, even if it took another form. One where sensations, instead of being brutally and blindly ignored, are supposed to be replaced, or even better, displaced, by so-called scientific calculations.

[Marr's analysis is entirely based on retinal images, and is therefore, as far as I am concerned, intrinsically flawed. See my thread Retinal image and black spot .]

There is of course nothing wrong with those calculations. I am sure they will one day reveal themselves to be very useful for the creation of an artificial brain. There is after all no reason to doubt that whatever a human can do, a computer can do faster, if not better. Does that mean that a computer could, in principle, be as smart as a human, or can it be only as smart as humans will make it? Whatever philosophical choice we make, we should not lose out of sight the current situation. Even if computers will be able, somehow, to evolve to the point of equality with human brains, the vital question that remains now is. Can we consider biological brains as (biological) computers?
If they are, I am still waiting for someone to prove it.

What distinguishes Motion from other sensations is the fact that it seems, unlike all others, to have an objective character, amenable to the physical methods that have been so successful in interpreting and changing the world. Unlike sight (objects have no color), sound (no, a falling tree in a deserted forest does not make any), taste or touch, all of which obviously only make sense for living organisms, motion seems to be real enough to transcend any form of subjectivity. Who could, even in an extreme Berkeleyian perspective (and exception made of Plato's eternal forms), imagine a world without motion? 
Philosophers have no problem imagining zombies which (or who?) would therefore lack all the sensations motioned, but such zombies would apparently not need to do anything differently than living creatures when it comes to dealing with moving objects.

Is the physical concept of motion equivalent to the sense of motion? If not, do we really need such a sense to explain how living brains process motion?

I will make no attempt to define motion as a physical phenomenon, that is something way above my pay grade. I will try instead to describe it as a familiar, subjective sensation.

Do we need more than one receptor to sense motion? 
Imagine all the receptors in the retina, but one, deactivated. Would we still sense an object, a dot, moving? Would we follow a moving dot with our eyes as it disappears from sight? The problem is of course that we would have no idea in which direction to look for it. Is that essential for a sense of motion?
Let us make it a little bit easier and replace the dot by a vertical bar. It will make detection much easier, but the distinction between flicker and motion will still be impossible to make. Or will it? Would the act of looking for it left and right, not contribute to our feeling that the dot/bar is moving? I honestly do not know. But that is surely something that would deserve a thorough investigation.
By the way, why demand that only one receptor be activated? We could be in a completely dark room looking at an illuminated object moving through the room. Since all the photoreceptors would be activated at the same time, with no intermediate images, the number of receptors, be it one or many, would not make any difference. Such a case would also make much more plausible the idea that we would have a sense of movement even if we have no way of comparing start and finish.

Let us add one active receptor. There still need not be any physical distinction  between flicker and motion, even though we can have a sense of motion if the timing is right. I do not think we need more than two receptors to get a sense of motion. What would a third or fourth receptor add that the second did not bring to the mix?
Here is a thing to ponder: images on a monitor never depict real motion. They are all, even when reproducing real movements, always flicker patterns. Even "old" techniques like cellular films, represent motion by a series of stills that pass briefly before a lamp, get illuminated, and disappear into the darkness again. The perfect description of flickering.
The brain does not, apparently, need real motion, properly timed flickering is sufficient to give us a sensation of motion.
This is quite a discovery if we think about it for a moment. Motion, just like any sensation, cannot be found out there in the real world. It is, after all, no so much different from other sensations which also have a physical or chemical substrate.
That can also mean that the phenomenon physicists talk about is not the same as the sense of motion. All their mathematical formula's only make sense under the assumption of real motion. Two flickering objects at a random distance of each other are, scientifically speaking, just that, and not what they appear to be for living brains. The concept of distance, for instance, would lose any signification. It would need to be replaced by another physical property, the frequency at which dots or objects are flickering.
This property would have to be limited by the speed at which chemical processes (the regeneration of rhodopsin in the photoreceptors, neuronal refraction period, etc.) can replenish themselves. But flicker is not motion, and we have then left the field of physics to enter not that of chemistry (in which both, motion and flicker, are indistinguishable), but of sensations, even if based on chemical processes.
This conclusion would definitely throw a veil of suspicion on any attempt to analyze motion perceptions as physical phenomena. So how are we supposed to interpret these scientific explanations? Are they wrong, or simply not relevant?

[A very ironic development is the vindication of the queen's conception in Alice in Wonderland by modern computer games. The main character is usually permanently situated in the center of the screen, never changing its position, even when it is supposed to be running. Instead, the rest of the screen, the world, is each time redrawn to give the impression of movement.]

Motion Perception
Remark: the example of the dark room would make much more sense if the object was turned off while moving, and only turned on at destination. This in such a way that there would be no after-image effect, or other visual artifacts. Also, very often the term 'movement' is used where 'motion' would be more appropriate. Even after all these years, the French language is still reaffirming its influence. 

Motion Perception
Methodological considerations
Since Gödel's "On Formally Undecidable Propositions of "Principia Mathematica" and Related Systems" (1931/1958), we know that you can deduce anything from an incorrect theory. It is the dilemma of completeness (deduce all true statements) and soundness (deduce only true statements).
When applied to neuroscience, it becomes hazardous, not to say impossible, to refute all the experimental results obtained on the basis of (putatively) false assumptions.
When those results concern retinal cells, the problem become even more acute. The retina is the front line in a war of competing theories aiming at explaining the fundamental principles of brain processes. It determines how we look at the rest of the brain and influences the way experiments are set up. Mistakes at this level can only be answered by better techniques and better analysis at the same level. 
Barlow&Hill "Selective sensitivity to direction of motion in ganglion cells of the rabbit's retina", 1963 [see also Barlow et al "Retinal Ganglion Cells responding Selectively to Direction and Speed of Image Motion in the Rabbit", 1964; Barlow&Levick "The Mechanism of Directionally Selective Units in Rabbit's retina", 1965]
illustrate this aspect very nicely when they "showed" that, contrary to what Hubel and Wiesel had advanced in "Receptive fields, binocular interaction and functional architecture in the cat's visual cortex" (1962), direction sensitivity was independent of receptive fields properties.

They were of course unaware of the fact that their own results put a serious damper on the credibility of the concepts involved. Receptive fields had become a random property of neurons and could not be blindly relied upon to understand neuronal processes. 
[Which Barlow's team certainly cannot be accused of: "it is easy to be misled into thinking a unit is directionally selective if one tests its responses to movement before mapping out the receptive field.", 1964]

What interests me are the methods used to arrive at a very peculiar conclusion: ganglion cells, without involving any non-retinal processes, are capable of detecting direction of movement and speed! (see Retina: Miscellanious, Direction Selectivity in the Retina).
Barlow and colleagues use the so-called "unopened-eye technique".
[A misnomer if there ever was one. In fact, the eye lids are removed! It was invented by Kuffler in 1952 and consisted in keeping the eye in its orbit instead of removing it. See for what prompted this technical innovation the series "Handbook of Sensory Physiology" edited by Autrum et al, the volume "Central Processing of Visual Information A: Integrative Functions and Comparative Data", 1973. p.576]

I will leave the way the animals were prepared out of the discussion. The objections the new technique was supposed to remedy certainly must make us aware of the great influence preparations can have on the results. In the absence of expertise, I can only take note of this fact.

We can distinguish between the methods of stimulation, and those of recordings. Just like preparations, they play a great role in the results, and must therefore be looked at critically.

as is usual in this kind of experiments, stimulation was directed to a retinal region, however small, and not to individual receptors. The use of stationary or moving (light or dark) spots or cards is itself secondary.

Let me give you some quotes from (1964) to sketch the general way in which that took place.
- "The sclera was then pierced and the electrode placed in position while observing the retina through a hand-held ophthalmoscope."
- "To reduce the degree of light adaptation caused during the search for a usable unit, a red filter was placed in the beam..."
- "The image of white or black spot could be moved over the retina around the electrode tip to assist the search for a unit."
- "It was usually only after several prods that the electrode yielded action potentials which were considered with reasonable certainty to come from a single neurone."
- "The receptive field always lay near the electrode tip"
Before I go on with more representative quotes, let us see if we can analyze what we already have. First, these remarks seem to concern 'stimulation' more than 'recording'. Which is quite understandable when we are dealing with elusive cells that have to be localized first. What we must not lose out of sight though is that we are not looking at the responses of specific neurons to well defined stimulations like the spots or the cards, but that the whole set up must be taken into consideration. That makes any interpretation of the results problematic to say the least.

Let us go on.
- "Having isolated a good unit the first step was always to map out its receptive field by
turning on and off an exploring spot."
- "The response to a moving spot was next tested, 
[-] first, to see if the responses 'made sense' in terms of the on and off zones of the receptive fields, 
[-] secondly, to see if the unit responded selectively to certain directions of motion, and
[-] thirdly, to find the velocity of motion that gave the maximum response."

This looks much more serious. The researchers are actively selecting for the desired properties. Something all researchers must do of course, but here the distinction between 'isolating' and 'creating' the desired responses seems to be lost. This impression (that is all it is until now), is reinforced by the following remarks made at the occasion of a second series of experiments:

"Difficulties arose in finding the receptive fields for two reasons. First, with tungsten electrodes we often made use of records from single fibres running over the retinal surface, and the electrode tip affords only a poor guide to the positions of the receptive fields of such units. The second more serious source of difficulty lay in the peculiar properties of the central units that can be isolated with these fine electrodes. They are strongly inhibited from the surround, hence they only respond to localized stimulation; furthermore, rapid motion, even if well localized in the receptive field, fails to arouse them. Thorough search with a small object moving slowly is obviously liable to take a long time."

Let me first say that these lines prove, if it ever was needed, the high degree of professionalism of Barlow and colleagues. They certainly do not try to hide the technical difficulties retinal cells present to scientific research. 
Unluckily, this does not change the fact that this kind of methods can be considered as highly invasive and unfocused. To repeat one of the first quotes: "It was usually only after several prods that the electrode yielded action potentials which were considered with reasonable certainty to come from a single neurone." 
Such a method, especially considering the importance that is given to 'receptive fields' would be considered as unacceptable if the aim had been the chemical analysis of the recorded cells. These "prods" very often create damages to the cells that can seriously hamper or change their functioning. In other words, the researchers are continuously changing those receptive fields that are so important to their interpretations!

The fact that there seem to be no alternatives possible to the techniques employed in the field is not enough to rely blindly on the validity of their results. Quite the contrary.
Even now, the techniques employed to study (visual) neurons are more likely to find what the researchers are looking for, and not necessarily because it is already out there. The methods employed cannot be considered separately from the theoretical (not to say the metaphysical) assumptions, and the results obtained have to be looked at under this perspective also.

The discussion of whether retinal cells can be, independently from any other supra-retinal processes, selective of direction and speed, will not be resolved (only) by looking at the methods employed. These methods are just the implementation of more fundamental assumptions. It is those assumptions that have to be put on trial.

Motion Perception
The Mystery of Memory
[Before I go back to the subject of this thread, let me, once again, try to understand the general principles which govern the creation of memories. The results will certainly be of use in the investigation of DS-cells.]

Even if there was something like a neural trace, we would still be confronted with the retrieval problem. How does the brain know how to look for a specific memory? Does it have an internal index somewhere that it can look through?
[The homunculus is nonchalantly looking at its finger nails, pretending to clean them while whistling.]
Let us go back to the idea that I had expressed very briefly in another thread: the (inter)neuron itself is the memory. (Neurons, Action Potential and the Brain)
I know, that sounds exactly like the kind of genetic memory I reproached Hubel and Wiesel to make use of in their work. In other words, a stimulus will not change the nature of what a neuron represents or refers to. The neuron does not need a neural code because itself is the code.
Let us take a sensation of red. It does not just pop up in our brain, buts need a specific photoreceptor to create it, or at least activate it. This specific photoreceptor, via its own path through all the retinal layers, will activate a specific ganglion cell, which in turn will project to the LGN, and from there to V1. 

Let us stop there for a minute before it becomes too complex for us to handle.
From the LGN, we have to assume that the same ganglion cell will project to other parts of the brain and that somehow the sensation of red will be produced. So far, just the average brain mysteries.

Let us go back to V1. Our neuron will become a specific memory of red, and not simply a sensation, through the links that will be created with other neurons. In computer terms, we would consider all neurons (and interneurons) a baby is born with as its Read only Memory (ROM), while the new connections that are made between rom-neurons will be the Random Access Memory or RAM.[The use of computer terms must be understood purely as an analogy, didactic as it were.]
 The relationship needs not of course be absolutely static, but details are at this point irrelevant.

Therefore, we could, in a way, say that visual stimuli do nothing else but activate the dormant representation carried by each neuron. Nonetheless, that would only work, however improbable, if a single neuron is activated without creating any new (ram) memory. When researchers show an animal images of bars, spots or gratings, their are certainly creating new memories, which, unsurprisingly, they can find back in the way the neurons react later on

Sensory neurons will therefore either be activated directly by sensory stimulation, or by their interneurons representing the (visual) experiences the brain had.
[This of course does not apply to the optic nerve and all other sensory neurons directly linked to the external or internal environment.]
This definitely sounds like a vindication of Kandel's results.
Also, it might explain some of the results that have prompted many researchers to put all their money on so-called DS-cells.

Motion Perception
Why not DS cells at the retina level? 
After all, we have no trouble believing that photoreceptors convey color sensations. Assuming that motion can also be considered as a sensation, having cells respond to it would not be a far fetched idea.
Let us analyze this assumption in more details.
Direction is a specific form of motion, one that physicists like to express in vectorial terms. For us, the different directions would be different modulations of a ur-sensation. Again, just like different colors could be considered as a variation of the same principle, we can sense movement in every possible direction. Just like we can see different colors and hear different sounds we can also hear the direction from which a sound is coming from, or going to. We can feel in which direction a hand is moving on our skin.
Are those different sensations, or do they denote one and the same ability: a spatial sense?
A comparative study of the different senses in this respect would certainly be interesting.
I will confine myself to vision.
A remark by Maturana and Frenk in "Directional Movement and Horizontal Edge Detectors in the Pigeon Retina", 1963, sums up quite clearly my main objection against the idea of DS cells in the retina:
"[...]each ganglion cell, to respond to a particular kind of visual stimulus, needs to take into account what happens at any moment in its whole receptive field and surroundings [...]"
They assume a degree of "intelligence" that I find hard to attribute to single cells. 
The question is, can the logical mechanism of (1965) devised by Barlow and Levick take away this objection?
[A mechanism which I thought quite ingenious, the whole article being a tribute to Barlow's greatness as a researcher.] 

Yes it could. Were it not for the multitasking Barlow's analysis presupposes. 
I could certainly accept the existence of excitatory and inhibitory chemical processes in the intermediate layers of the retina that would explain the phenomenon of direction sensitivity. 
The problem is that a ganglion cell is, in this perspective, supposed not only to convey the direction and speed of the stimulus, but also its brightness, color and contrast. After all, it reacts like any visual cell to visual stimulation. Let us not forget that one of the main methods used to emphasize the existence of DS was the use of stationary spots on two units, where they responded "normally", in contrast with the direction selectivity they exhibited when they were activated consecutively. 
This multi-functional character of ganglion cells cannot, I think, be justified by any electrical or chemical analysis of the signals sent by optic fibers to the rest of the brain. So, unless ones chooses to abandon one function in favor of the other, I can only express my admiration for the strength of Barlow's argumentation against all odds.
I find particularly baffling the following argument that comes back all through the article in many disguises: cells react to stimuli moving in one direction, but not in the other.
Any objection against Barlow's view would have to deal with this "fact". I have tried to criticize the methods used in general, but I am also painfully aware that my arguments can certainly not be considered as being decisive. I choose not to put in question Barlow's integrity as a researcher, which I am convinced is beyond any reproach, but to hope that one day, better methods will show this error for what it is.
A possible direction of research which, as far as I know, has been insufficiently explored is the possibility that the so-called DSG's (Direction Selective Ganglions) are in fact not visual neurons but cells linked to various muscular reflexes of the eye.
Yoshoda et al ("A Key Role of Starburst Amacrine Cells in Originating Retinal Directional Selectivity and Optokinetic Eye Movement", 2001) researched the effects of the ablation of starburst cells on DS ganglion cells. They found out that ablation of starburst cells abolished not only direction selectivity, but also an "optokinetic reflex derived by stimulus movement". Their conclusion was the same as Barlow's: the discrimination of stimulus movement and the potential use of DS cells in pattern recognition.
I found the link with the optokinetic reflex much more promising. If it can be proven that ganglion cells that are directly connected to eye reflexes can show the kind of responses analyzed by Barlow and others, then we would have definitely buried the idea that DS is a pure retinal process.
What also gives me some hope is that, again as far as I know, no in vitro experiments have been done to show the existence of DS phenomena at the cellular level, independently of the rest of the brain. Even fish were kept alive during the trials (Damjanovic et al "Receptive field sizes of direction-selective units in the fish tectum", 2009). Also, a review by Borst and Euler ("Seeing Things in Motion: Models, Circuits, and Mechanisms", 2011) made no mention of such experiments.
[Here, the unopened eye technique, which was supposed to guarantee more natural responses of the retinal cells,  would seem to work against the researchers.]
Furthermore, many so-called DS cells have been found to project to the superior colliculus and the accessory optic system (AOS). Only the dominant view of computational processes in the retina seems to prevent researchers from giving this fact its due. The leading idea remains that of DS cells, instead of cells that can show DS properties because of supra-retinal processes in the brain.
Which are certainly as interesting.

Motion Perception

"Principles of Gestalt Psychology" by Koffka (1935/1963) is one of the most influential works in the 20th century. I do not have the pretension to be able to analyze in details all the concepts of Gestalt and the way they are used in current works, but will glean some remarks here and there to make my own points, however biased that may seem.
Let me first start with a quote that I find quite interesting in light of my own remarks in "Seeing Darkness" (Retina: Miscellanious):
 "Even in complete darkness [our perceptual field] has an above and a below, right and left, near and far...] (p.281). Koffka does not consider the case of a single stimulus the way I do for the simple (in fact very complicated) reason that the considers the subject experiencing the sensation ("the ego") as also a stimulation point, or at least as a spatial point.The situation of someone experiencing two light dots must be analyzed as the relationship between 3 dots located and moving in space. Like I said, very complicated.
More interesting is his treatment of apparent and/or stroboscopic motion in an objective, scientific manner. [He is making use of the work of other researchers that will remain unnamed. I will just refer to Koffka all the time.]
Taking the sensations of motion in human subjects, experiments are devised to measure objectively the distance that would have been crossed if the movement had been a real one. That means of course taking into considerations all the known psychological effects like the fact that object moving in the dark are experienced as moving with a different velocity as the same objects (with the same objective velocity) in a light environment. Details are, here also, quite irrelevant.
What is important is the signification of such calculations. What do they tell us about motion sensation? Is it really possible to treat sensation just like a variable susceptible to all scientific tools that we could apply to any physical phenomenon?
That seems certainly to be the conviction behind all this. Just like their disciple Gibson, Gestaltists seem to believe that one can find "organizational principles" of perception with objective measuring procedures.
But what is really happening when the sensations of a subject are turned into a set of variables?
The first thing that jumps to mind is that the subject of these sensations has been quite elegantly eliminated from the equation. The scientist can now look at those variables as if they concerned natural phenomena in another planet with laws slightly different from our own.
Let us think this through for a moment. Suppose that our scientist meets an alien colleague from another galaxy and they start comparing notes. I dare predict that their conclusions would not be much different from the results obtained from eliminating the subject altogether. But could they each say that they have now explained what motion sensation is?
It is obvious that both know intimately what it feels like to see an object moving. We are in another galaxy, not in a Chinese Room.
Still, I suppose that they would no longer be satisfied with comparing formula's, because it would then be evident that different circumstances would give rise to different calculations. They could easily imagine another colleague from a third galaxy where the natural laws would differ from both their planet, where the apparent laws of motion for one are the objective laws for another.
Would they reinstate the sensing subject, or would they keep looking for the ultimate galaxy where all calculations come beautifully together?

Motion Perception
Retinal image and motion sensation
Without the existence of projective devices and later of ophthalmologist instruments like an ophtalmoscope, researchers would still be in the position of our Renaissance painter trying to explain perception. The question is whether the new inventions have brought any progress in insight at all.
The existence of a retinal image has given rise to so many contradictory conclusions that that its use as a concept must be seriously put in question.
Let us start with one of founding fathers of Psychology, Helmhotz.
This great intellectual is the perfect illustration of how easy it is to see our own prejudices generously reflected by our own experiments and experiences.
All the cases I will be dealing with will concern non-voluntary stimulations and eye movements. In the case of Helmholz, it consists simply in pushing or pulling  the eye slightly out of position with familiar gestures anybody could perform on themselves. 
The result is the same: the image on the retina is moved in the same way that it would have been moved if we had "willed" such a movement. But the consequences could not be any more different. While we clearly see a movement of even stationary objects in the first case, moving our eyes or head while fixating a stationary object never makes it move in the second case.
Here is Helmholtz' conclusion: "These phenomena prove conclusively that our judgments as to the direction of the visual axis are simply the result of the effort of will involved in trying to alter the adjustment of the eyes." Which is of course the perfect illustration of his conception of perception as a form of unconscious inference. (par.29 of the third volume of his "Treatise on Physiological Optics", 1910/1925). (my emphasis)

Let us now look at Gibson (1950) again. Here is how he formulates the problem:
"Anyone who pushes on the outer side of his open eye [...] can see the visual world being displaced, and anyone who has ever been dizzy knows that it can move. Why does this kind of perception not occur during normal exploratory eye movements?" (p.146).
As you can see, it is based exactly on the same "experiment" as by Helmholz. 
But here is how it is explained by Gibson. First he presents a plausible theory that was accepted in his lifetime by most, Helmholz included: "when the eye actively rotates to the right the scene should appear to be displaced to the left, but that it is not displaced because there is a compensatory shift to the right which cancels it... If the eyeball is mechanically rotated toward the right the scene should appear to move to the left and will do so, according to the theory, because the compensating shift is absent." That does not explain, according to him, the fact that the retinal image seems to be unchanged by its movement across the retina. The only explanation he can think of is given by projective geometry that explains how an object can retain its form during translational movements. And that is the object that we are in fact seeing free of deformations. (p.153-155).

The approach of Raymond and colleagues ("The Cerebellum: A Neuronal Learning Machine?", 1996; "Neural Learning Rules for the Vestibulo-Ocular Reflex" [VOR], 1998) is much more elaborated. We are now dealing with a lab-animal, and there is a complicated device that moves it around while keeping its head fixed. That makes it possible to investigate the effects of involuntary movements on the retinal image, and on the learning capacity of the animal.
Apparently all those years have not changed anything to the fundamental problem, except giving rise to different ways of looking at it. Let us see if this new way of seeing things is of any help.
The problem is still how to explain the lack of deformation experienced even though the retinal image is moved across the retina, undergoing inevitable geometric transformations.
Here is the new formulation of a very old problem: "When it is working well, the VOR causes an eye rotation opposite in direction to each head turn and of an appropriate amplitude to keep visual images from slipping across the retina. If the VOR fails to stabilize visual images, it is adjusted by motor learning."
We can see that the focus has shifted from the movement itself to the end-phase: a VOR is terminated when the image on the retina is stable, that is not moving anymore. This is obviously a different case from saccades (the word is not mentioned once) where the eye is supposed to focus on the object to get a clear image. I have no idea what the relationship is supposed to be between those two physiological processes which in my mind seem inseparable.
Anyway, we are dealing with the movements of the head, the eye and a stimulus, and trying to find correlations between the three. By varying the direction and duration of the involuntary body movements, and those of the visual stimuli, the researchers could conclude to the existence of learning mechanisms concerning the VOR.
The question how the animal can see if the image is still moving, and thus, how it can decide (unconsciously of course) when to stop the VOR is never asked. Neither are we supposed to doubt that it can do that at all. In a very recent article Raymond and colleagues (Shin et al "Signals and learning rules guiding oculomotor plasticity", 2014; see also Katoh et al "Purkinje cell responses during visually and vestibularly driven smooth eye movements in mice", 2015) said the following: "The learning of motor skills is thought to occur largely through trial and error; however, the error signals and rules controlling the induction of motor learning have not been fully elucidated."
This is a confirmation of their view that the VOR is, or can be, considered as a voluntary reflex. After all, how else could we explain the fact that it can be changed by learning?
Well, that may be true, but consider this.
Suppose the VOR is really a reflex just like the scratch reflex, and the saccades as I understand them. That certainly does not mean that it could not be changed through learning.
The authors give themselves the example of "spectacles that double the size of the visual scene" and their effects on the VOR. Imagine a similar device whereby the movements of the dog would be changed so as to make it impossible to scratch the itch without somehow adapting to the device. We would still be speaking of trials and errors, only this time we would know exactly when such a trial would be very close to the target, and when not. We would be able as it were to follow the learning process as it happens. My question now is: how long do we need the stimulus? A tactile stimulation in one case, a visual one in the other. 
The effect of the first is an itch, a localized stimulation of the skin. Suppose that the visual stimulation, in the complex form of visual motion of a stimulus and an involuntary body movement, also created something like an itch? Why introduce the extra necessity of a stable image which can never be answered by a simple motor reflex?
These considerations would go a long way in bringing closer to each other such, apparently, disparate concepts as VOR and saccades. The learning process could also certainly more easily be followed and explained by the use of retina locators.

But that is not all. Remember Gödel?
It really does not matter what the authors think how those reflexes are constituted, they could always use the same results whatever their original assumptions. In fact, I see no reason, if I were a researcher, not to use their results for my own purposes. I could assume that I am dealing with something similar to a scratch reflex, and still make sense of their work. Which is not to say that their results are correct. I honestly would not know.
Maybe that could be a signal to keep in mind: if your assumptions have no effect on the results, except on how to interpret those, then maybe it is time to look at them very critically.

Last but not least, this special, camouflaged, view of the retinal image shows just how traitorous the concept is. It can literally make you believe anything.

Motion Perception
The principle of correlation
[Hassenstein "Wie sehen Insekten Bewegungen?", 1961;
 Reichardt "Autocorrelation, a principle for the evaluation of sensory information by the central nervous system" 1961.]

There is nothing strange in the idea that the bodily reactions of an animal are one way or the other related with his perceptual experiences. Intuitively we are inclined to think that those perceptions must somehow have meaning for the animal. That is an intuition that we must definitely put aside when looking at the experiments of Hassenstein and Reichardt with beetles. The ingenious apparatus they have built leaves no room for such an intuition. The visual stimuli the animal gets are all of an abstract nature and meant to facilitate mathematical analysis more than answer to any biological imperative.
The main idea behind the device is that the animal only sees changes in brightness through very narrow gaps from within a stationary circle. These gaps show either a black or a white background on an also stationary outer circular wall, and between those two stationary circles, a moving circular panel with gray patterns moves around, changing the scenery along the way. To be clear, the different panels, the gaps, and the visual stimuli are such that the beetle is incapable to perceive anything else but a change in brightness. It therefore cannot see the movements of the middle panel. 
(There is no data concerning the trilling or the noise produced by the electro-motor.)

The results they obtained were so convincing that almost 50 years later Haag et al could declare "Fly motion vision is based on Reichardt detectors regardless of the signal-to-noise ratio" (2004)! It is the perfect illustration of what neuroscience aims to be: a biological/neuronal behavior is reduced to a strict mathematical pattern with as a bonus, a transistor-like schema that can be used as a motion detector! See how biology meets cybernetics and they both lived happily ever after! [Hassenstein "Kybernetik und biologische Forschung", 1966.]

I am afraid I do not share the enthusiasm of Haag and others, so allow me to tell you of (some of) my misgivings:

Reichardt-Hassenstein Motion Detectors
Here are some critical remarks:
1) The beetle finds itself in an unnatural position from which it tries to escape. Which is of course too bad, but more importantly...
2) The bug is shown patterns that appear and disappear in different places. Those places are not random. They are either to its left or to its right. It only needs to have one experience of appearing/disappearing patterns to know what to expect.
3) The animal is an adult insect, or at least no neonate. It already has experienced moving objects.
4) The beetle does not react when a new pattern appears further away than one or two ommatidias. Why? Why would it not react to a changing environment that is within its visual field? Why would it only react to an apparent motion? Maybe, just like the frog, it only reacts to moving objects? [I could not find any information on this point.]
6) why would the beetle react more strongly to different visual stimuli if they do not have any biological significance? [The difference in intensity of the reactions is a fundamental parameter in the analysis.] Unless maybe its expectations are not met? Babies are known to react to strange events by sucking harder on their pacifier.
7) The experiment is such that the beetle does not see any movements, only changing patterns in different positions.
 How then can it experience motion? Apparently, the theory is built on the unspoken assumption that the beetle moves right or left before the second stimulation happens. Otherwise, it would be nothing else but the reaction to a change in the visual environment.
It is therefore either a case of smooth pursuit, whereby the animal is in fact anticipating the object's future location before its appearance, or it is a saccade.
How could it be a case of smooth pursuit if the beetle is not allowed to sense movement? If it does anyway, then there is something in the animal's past that makes it associate the stimulus with a moving object. This past can be the very near past: after any stimulus, there will be something new at the left or at the right. (see point 2)
8) The beetle reacts up to 10 seconds after the first stimulus to a second stimulus. This has nothing to do with motion anymore, and all with a normal reaction to a change in the environment. But then, why the limit of 10 seconds? Where does it come from?  And why would it react to this stimulus and not to (4)?
9) Why does it look in the opposite direction when two opposite colors follow each other? And how does it know in which direction to look? If white is followed by white, the beetle looks in the same direction as the stimulus. If white is followed by black, in the opposite direction. Nothing in the first stimulus contains a clue about the stimulus that is to follow. It also does not make any difference whether white follows black or vice versa.

Could it no be that the beetle considers the second stimulus as unrelated to the first one, and therefore looks in the opposite direction where it is expecting to see the same stimulus to appear?

In all cases, it would seem that the beetle does not start moving before it has seen both stimuli.
In fact, the drawing of the Hassenstein-Reichardt detector shows it explicitly: there are two sensitive elements, representing the ommatidia, and the first stimulation is delayed (in the beetle we have to think about it as being retained in memory) until the second stimulation takes place.
The whole analysis is based on the deceiving suggestion that we are looking at reactions to motion perceptions (and therefore at anticipating behavior) even though everything was done to exclude any motion sense. If there was some kind of motion perception, it came exclusively from the beetle. That would be the real cause of its reactions, the properties of these reactions being nothing else but mechanistic consequences of these perceptions. 
What is then the value of the correlations discovered by the authors? I would say it would depend on what you need the data for. If you want to use it to predict the natural behavior of the animal in a natural setting, then this data is utterly unusable. In fact, it will only be of use in comparable experimental settings, like the one used by Haag and colleagues. Where it can reinforce the idea that neuronal processes can be reduced to mathematical calculations.

Motion Perception
A clearer conception of what memory consists in would help you here considerably.

Motion Perception
Could you be more specific as to what you are missing exactly?

Motion Perception
The thread memory as mystery is insufficiently specified.  Memory is an experience that is mediated by neural activity in large part, but it is not simply reducible in any coherent way to trains of neural spikes.

to do so is to adoptithe simplistic tactics of contemporary neuroscience --i.e., avoidance of the the phenomenon.  That is, reduce memory  it out of existence by whittling the experience to a tiny twig of itself so it can be fitted into available scientific method (rather than adapting method to phenomenon). 

All this speaks to the rather sad state of the psychological (and some aspects of the philosophical) research.

There is a rather important and persistent (@300-400 BC -- today) set of issues about memory, in its various forms, and I cannot go into that detail here.  Check out my paper on this site "What memory is" (s. Klein) and you will get a taste for the issues.  You may not agree with my particular "solutions" but the problems I identify are reasonably clear.

Motion Perception
I have the strong impression that you are criticizing a view which is not mine. Maybe your special interest in memory processes has made you pick out this particular entry to the exclusion of all the others. I certainly am looking for the neurological basis of "memory" as a general process. I would be the last to identify any experiential memory with its neural correlate. I do find it extremely important to understand how experience is stored and retrieved. I certainly do not pretend to have a clear view of what "memory" as a brain process entails exactly, except that , and here we shall I think meet, that it is not a function one can isolate from the different experiences an organism or individual has in his life. I am still looking for a model which would not be too speculative while at the same time accepting the fact that pure neurological processes are not enough to explain experience.

Motion Perception
E.g, "Even if there was something like a neural trace, we would still be confronted with the retrieval problem. How does the brain know how to look for a specific memory"

there is NO specific memory.  this is known since ancient times and empirically demonstrated by psychological research as early as 1909.

This is a neuroscience a-conceptual treatment of its subject matter.

ONE example of what I picked up in your thread on memory.  But I am sorry. Should have let it be.

Motion Perception
One more, then I promise to leave you alone.

"looking for the neurological basis of "memory" as a general process"

How does one find a neural (or the neural) correlate(s) of X when X is conceptually unspecified?  One should be clear what he or she is looking for if one hopes to locate it?

Again -- see the "What memory is" paper.  Too long rehash these things in this forum.  My bad.

Motion Perception
You keep referring to your paper instead of expliciting your position on one hand. On the other hand you seem eager to deny that there is something we call memory even if you, I suppose, do not deny the existence of "memories". You may consider it as unconceptualized, but these memories, as everything that happens to an organism, have somehow to be present at the neural level. You also seem bent on attributing to me a conception I do not share. It is easy to take expressions out of context and then hang your own ideas on to them. If you had read my threads you would have realized that I am all the time trying to show the sterility of a pure neurological approach and reinstating what I call with a generic terms, "sensations" in neuroscience. I also do not feel like rehashing my arguments as set forth in the different threads, but please do not use me as a cheap ride for your own merry-go-round.I am very grateful that you took the time to read whatever you felt like reading, just like I took the time to read the article you referred to. Your approach might be very different from mine, but I think that on this point we stand much closer to each other than you seem to realize.

Motion Perception
I tried to alert you to the strong possibility that your application terminology (i.e., memory)  is neither conceptually well-considered or empirically sanctioned.  If you have justifiable reason to disagree, then that's fine with me.  I am pretty certain that my "contribution" to discussion has gone way past "far enough".