Visual Illusions#1 : The Vanishing Head Illusion

I would try to get more systematic about my posts from now on. For every two non-technical posts I would keep two technical posts.

This post would also be the first in a series of posts that in which I intend to write about some Visual Illusions only.

Before getting into subject of this post, it would be helpful to have a quick recap of the background.

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The Blind Spot:

Consider a horizontal cross section of the human eye as shown below.

As seen in the above, the innermost membrane is the Retina, and it lines the walls of the posterior portion of the eye. When the eye is focused, light from the focused object is imaged onto the Retina. It thus acts as a screen. Pattern vision is caused by the distribution of discrete light receptors called rods and cones over the retinal surface.

Each eye has about 6-7 million cones, located primarily in the central portion of the Retina and they are highly sensitive to color. Humans can resolve fine details with cones as each cone is connected to its own nerve end. The vision due to cones is called Photopic or bright-light vision.

The number of rods is about 75-150 million andare distributed throughout the retina. The amount of details that can be resolved by rods is lesser as several of them are connected to the same nerve unlike in the cones. Vision due to rods is simply to give an overall picture of the field of view. Objects that seen in bright day light appear as color-less forms in moonlight as only the rods are stimulated. This type of vision is called Scotopic or dim-light vision.

As seen in the figure there is a portion on the retina which has no receptors (rods or cones), thus will not cause any sensation. This is called the blind spot.

Now because of the blind spot a certain field of vision is not perceived. We however do not notice it as the brain fills it with details from the surroundings or using information from the other eye.

The blind spots in both the eyes are arranged symmetrically so that the loss in field of vision in one eye will compensate for the other. This is shown by the figure below.

[Image Source]

If the brain would not fill the lost field of vision with surrounding details and information from the other eye, then the blind spot would appear something like the black dot on the image below.

[Image Source]

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Now that means, if you close one eye then you can indeed detect the presence of the blind spot as the brain would not have sufficient information about the lost field of vision (though it would be good enough for us to not notice it normally). The presence of the blind spot can be demonstrated by the simple figure below.

Click on the above image to enlarge

Now enlarge the above image and close your right eye and focus your left eye on the X only. Don’t try to look at the O on the left. You’d just notice it at the periphery. The object of interest should only be X.

Now move towards the screen, at a certain point you will not see O in the periphery. If you go ahead of this point or behind it you’ll see O again, this specific point (a range actually) where you can not see O indicates the presence of the blind spot.

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The Vanishing Head Illusion:

This leads to some interesting illusions, one of the most interesting being the so called vanishing head illusion.

As in the above figure. If the O is replaced by a head, the person would appear headless if the head falls on the blind spot.

Check the video below in full screen for best results.

View in Full Screen

We notice that Richard Wiseman on the left indeed appears headless and that field of view is filled up by the orange background when the blind spot falls.  Then he does something even more interesting. He uses a black bar and moves it up and down in front of his face.  Now instead of seeing the bar as discontinuous, the brain manages to show the bar as a continuous entity!

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The Emerging Mind

About two months back I came across a series of Reith lectures given by professor Vilayanur Ramachandran, Dr Ramachandran holds a MD from Stanley Medical College and a PhD from Trinity College, Cambridge University and is presently the director of the center for Brain and cognition at the University of California at San Diego and an adjunct professor of biology at the Salk Institute. Dr Ramachandran is known for his work on behavioral neurology, which promises to greatly enhance our understanding of the human brain, which could be the key in my opinion in making “truly intelligent” machines.

[Dr VS Ramachandran: Image Source- TED]

I heard these lectures two three times and really enjoyed them and was intrigued by the cases he presents. Though these are old lectures (they were given in 2003), they are new to me and I think they are worth sharing anyway.

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For those who are not aware, the Reith lectures were started by the British Broadcasting Corporation radio in 1948. Each year a person of high distinction gives these lectures. The first were given by mathematician Bertrand Russell. They were named so in the honor of the first director general of the BBC- Lord Reith. Like most other BBC presentations on science, politics and philosophy they are fantastic. Dr Ramachandran became the first from the medical profession to speak at Reith.

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The 2003 series named The Emerging Mind has five lectures, each being roughly about 28-30 minutes. Each are a trademark of Dr Ramachandran with funny anecdote, witty arguments, very intersting clinical cases, the best pronunciation of “billions” since Carl Sagan, and let me not mention the way he rolls the RRRRRRRs while talking. Below I don’t intend to write what the lectures are about, I think they should be allowed to talk for themselves.

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Lecture 1: Phantoms in the Brain

Listen to Lecture 1 | View Lecture Text

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Lecture 2: Synapses and the Self

Listen to Lecture 2 | View Lecture Text

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Lecture 3: The Artful Brain

Listen to Lecture 3 | View Lecture Text

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Lecture 4: Purple Numbers and Sharp Cheese

Listen to Lecture 4 | View Lecture Text

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Lecture 5: Neuroscience the new Philosophy

Listen to Lecture 5 | View Lecture Text

[Images above courtesy of the BBC]

Note: Real Player required to play the above.

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As a bonus to the above I would also advice to those who have not seen this to have a look at the following TED talk.

In a wide-ranging talk, Vilayanur Ramachandran explores how brain damage can reveal the connection between the internal structures of the brain and the corresponding functions of the mind. He talks about phantom limb pain, synesthesia (when people hear color or smell sounds), and the Capgras delusion, when brain-damaged people believe their closest friends and family have been replaced with imposters.

Again he talks about curious disorders. One that he talks about in the above video, the Capgras Delusion is only one among the many he talks about in the Reith lectures. Other things that he talks about here is the origin of language and synesthesia.

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Now look at the picture below and answer the following question: Which of the two figures is Kiki and which one is Bouba?

If you thought that the one with the jagged shape was Kiki and the one with the rounded one was Bouba then you belong to the majority. The exceptions need not worry.

These experiments were first conducted by the German gestalt psychologist Wolfgang Kohler and were repeated with the names “Kiki” and “Bouba” given to these shapes by VS Ramachandran and Edward Hubbard. In their experiments, they found a very strong inclination in their subjects to name the jagged shape Kiki and the rounded one Bouba. This happened with about 95-98 percent of the subjects. The experiments were repeated in Tamil speakers and then in babies of about 3 years of age. (who could not write) The results were similar. The only exceptions being in people having autistic disorders where the percentage reduced to only 60.

Dr Ramachandran and Dr Hubbard went on to suggest that this could have implications in our understanding of how language evolved as it suggests that naming of objects is not a random process as held by a number of views but depends on the appearance of the object under consideration. The strong “K” in Kiki had a direct correlation with the jagged shape of that object, thus suggesting a non-arbitrary mapping of objects with the sounds associated with them.

In the above talk and also the lectures, he talks about Synesthesia, a condition wherein the subject associates a color on seeing black and white numbers and letters with each.

His method of studying rare disorders to understand what in the brain does what is very interesting and is giving insights much needed to understand the organ that drives innovation and well, almost everything.

I highly recommend all the above lectures and the video above.

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Colony Cognitive Maps

Some posts back, i posted on Non-Human Art or Swarm Paintings, there I mentioned that those paintings were NOT random but were a Colony Cognitive Map.

This post will serve as the conceptual basis for the Swarm Paintings post, the next post and a few future posts on image segmentation.

Motivation: Some might wonder what is the point of writing about such a topic. And that it is totally unrelated to what i write about generally. No! That is not the case. Most of the stuff I write about is related in some sense. Well the motivation for reading thoroughly about this (and writing) maybe condensed into the following:

1. The idea of a colony cognitive map is used in SI/A-life experiments, areas that really interest me.

2. Understanding the idea of colony cognitive maps gives a much better understanding of the inherent self organization in insect swarms and gives a lead to understand self organization in general.

3. The parallel to colony cognitive maps, the cognitive maps follow from cognitive science and brain science. Again areas that really interest me as they hold the key for the REAL artificial intelligence evolution and development in the future.

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The term “Colony Cognitive Map” as i had pointed earlier is in a way a parallel to a Cognitive Map in brain science (i use the term brain science for a combination of fields like neuroscience, Behavioral psychology, cognitive sciences and the likes and will use it in this meaning in this post ) and also that the name is inspired from the same!

There is more than just a romantic resemblance between the self-organization of “simple” neurons into an intelligent brain like structure, producing behaviors well beyond the capabilities of an individual neuron and the self-organization of simple and un-intelligent insects into complex swarms and producing intelligent and very complex and also aesthetically pleasing behavior! I have written previously on such intelligent mass behavior. Consider another example, neurons are known to transmit neurotransmitters in the same way a social insect colony is marked by pheromone deposition and laying.

[Self Organization in Neurons (Left) and a bird swarm(Below).  Photo Credit >> Here and Here]

First let us try to revisit what swarm intelligence roughly is (yes i still am to write a post on a mathematical definition of the same!), Swarm Intelligence is basically a property of a system where the collective actions of unsophisticated agents, acting locally causes functional and sophisticated global patterns to emerge. Swarm intelligence gives a scheme to explore decentralized problem solving. An example that is also one of my favorites is that of a bird swarm, wherein the collective behaviors of birds each of which is very simple causes very complex global patterns to emerge. Over which I have written previously, don’t forget to look at the beautiful video there if you have not done so already!

Self Organization in the Brain: Over the last two months or so i had been reading Douglas Hofstadter’s magnum opus, Gödel, Escher, Bach: an Eternal Golden Braid (GEB). This great book makes a reference to the self organization in the brain and its comparison with the behavior of the ant colonies and the self organization in them as early as 1979.

[Photo Source: Wikipedia Commons]

A brain is often regarded as one of the most if not the most complex entity. However if we look at a rock it is very complex too, but then what makes a brain so special? What distinguishes the brain from something like a rock is the purposeful arrangement of all the elements in it. The massive parallelism and self organization that is observed in it too amongst other things makes it special. Research in Cybernetics in the 1950s and 1960s lead the “cyberneticians” to try to explain the complex reactions and actions of the brain without any external instruction in terms of self organization. Out of these investigations the idea of neural networks grew out (1943 – ), which are basically very simplified models of how neurons interact in our brains. Unlike the conventional approaches in AI there is no centralized control over a neural network. All the neurons are connected to each other in some way or the other but just like the case in an ant colony none is in control. However together they make possible very complex behaviors. Each neuron works on a simple principle. And combinations of many neurons can lead to complex behavior, an example believed to be due to self-organization. In order to help the animal survive in the environment the brain should be in tune with it too. One way the brain does it is by constantly learning and making predictions on that basis. Which means a constant change and evolution of connections.

Cognitive Maps: The concept of space and how humans perceive it has been a topic that has undergone a lot of discussion in academia and philosophy. A cognitive map is often called a mental map, a mind map, cognitive model etc.

The origin of the term Cognitive Map is largely attributed to Edward Chace Tolman, here cognition refers to mental models that people use to perceive, understand and react to seemingly complex information. To understand what a mental model means it would be favorable to consider an example I came across on wikipedia on the same. A mental model is an inherent explanation in somebody’s thought process on how something works in the spatial or external world in general. It is hypothesized that once a mental model for something or some representation is formed in the brain it can replace careful analysis and careful decision making to reduce the cognitive load. Coming back to the example consider a mental model in a person of perceiving the snake as dangerous. A person who holds this model will likely rapidly retreat as if is like a reflex without initial conscious logical analysis. And somebody who does not hold such a model might not react in the same way.

Extending this idea we can look at cognitive maps as a method to structure, organize and store spatial information in the brain which can reduce the cognitive load using mental models and and enhance quick learning and recall of information.

In a new locality for example, human way-finding involves recognition and appreciation of common representations of information such as maps, signs and images so to say. The human brain tries to integrate and connect this information into a representation which is consistent with the environment and is a sort of a “map”. Such spatial (not necessarily spatial) internal representations formed in the brain can be called a cognitive map. As the familiarity of a person with an area increases then the reliance on these external representations of information gradually reduces. And the common landmarks become a tool to localize within a cognitive map.

Cognitive maps store conscious perceptions of the sense of position and direction and also the subconscious automatic interconnections formed as a result of acquiring spatial information while traveling through the environment. Thus they (cognitive maps) help to determine the position of a person, the positioning of objects and places and the idea of how to get from one place unto another. Thus a cognitive map may also be said to be an internal cognitive collage.

Though metaphorically similar the idea of a cognitive map is not really similar to a cartographic map.

Colony Cognitive Maps: With the above general background it would be much easier to think of a colony cognitive map. As it is basically a analogy to the above. As described in my post on adaptive routing, social insects such as ants construct trails and networks of regular traffic via a process of pheromone deposition, positive feedback and amplification by the trail following. These are very similar to cognitive maps. However one obvious difference lies in the fact that cognitive maps lie inside the brain and social insects such as ants write their spatial memories in the external environment.

Let us try to picture this in terms of ants, i HAVE written about how a colony cognitive map is formed in this post without mentioning the term.

A rather indispensable aspect of such mass communication as in insect swarms is Stigmergy. Stigmergy refers to communication indirectly, by using markers such as pheromones in ants. Two distinct types of stigmergy are observed. One is called sematectonic stigmergy, it involves a change in the physical environment characteristics.An example of sematectonic stigmergy is nest building wherein an ant observes a structure developing and adds its ball of mud to the top of it. Another form of stigmergy is sign-based and hence indirect. Here something is deposited in the environment that makes no direct contribution to the task being undertaken but is used to influence the subsequent behavior that is task related. Sign based stigmergy is very highly developed in ants. Ants use chemicals called as pheromones to develop a very sophisticated signaling system. Ants foraging for food lay down some pheromone which marks the path that they follow. An isolated ant moves at random but an ant encountering a previously laid trail will detect it and decide to follow it with a high probability and thereby reinforce it with a further quantity of pheromone. Since the pheromone will evaporate the lesser used paths will gradually vanish. We see that this is a collective behavior.

Now we assume that in an environment the actors (say for example ants) emit pheromone at a set rate. Also there is a constant rate at which the pheromone evaporates. We also assume that the ants themselves have no memory of previous paths taken and act ONLY on the basis of the local interactions with pheromone concentrations in the vicinity. Now if we consider the “field” or “map” that is the overall result and formed in the environment as a result of the movements of the individual ants over a fixed period of time. Then this “pheromonal” field contains information about past movements and decisions of the individual ants.

The pheromonal field (cognitive map) as i just mentioned contains information about past movements and decisions of the organisms, but not arbitrarily far in the past since the field “forgets” its distant history due to evaporation in time. Now this is exactly a parallel to a cognitive map, with the difference that for a colony the spatial information is written in the environment unlike inside the brain in the case of a human cognitive map. Another major similarity is that neurons release a number of neurotransmitters which can be considered to  be a parallel to the pheromones released as described above! The similarities are striking!

Now if i look back at the post on swarm paintings, then we can see that the we can make such paintings, with the help of a swarm of robots. More pheromone concentration on a path means more paint. And hence the painting is NOT random but is EMERGENT. I hope i could make the idea clear.

How Swarms Build Colony Cognitive Maps: Now it would be worthwhile to look at a simple model of how ants construct cognitive maps, that I read about in a wonderful paper by Mark Millonas and Dante Chialvo. Though i have already mentioned, I’ll still sum up the basic assumptions.

Assumptions:

1. The individual agent (or ant) is memoryless.

2. There is no direct communication between the organisms.

3. There is no spatial diffusion of the pheromone deposited. It remains fixed at a point where it was deposited.

4. Each agent emits pheromone at a constant rate say .

Stochastic Transition Probabilities:

Now the state of each agent can be described by a phase variable which contains its position and orientation . Since the response at any given time is dependent solely on the present and not the previous history, it would be sufficient to specify the transition probability from one location to another place and orientation an instant later. Thus the movement of each individual agent can be considered roughly to be a continuous markov process whose probabilities at each and every instance of time are decided by the pheromone concentration .

By using theoretical considerations, generalizations from observations in ant colonies the response function can be effectively summed up into a two parameter pheromone weight function.

This weight function measures the relative probabilities in moving to a site with the pheromone density .

Another parameter may be considered. This parameter measures the degree of randomness by which an agent can follow a pheromone trail. For low values of the pheromone concentration does not largely impact its choice but higher values do.

At this point we can define another factor . This signifies the sensory capability. It describes the fact that the ants ability to sense pheromone decreases somewhat at higher concentrations. Something like a saturation scenario.

Pheromone Evolution: It is essential to describe how the pheromone evolves. According to an assumption already made, each agent emits pheromone at a constant rate with no spatial diffusion. If the pheromone at a location is not replenished then it will gradually evaporate. The pheromonal field so formed does contain a memory of the past movements of the agents in space, however because of the evaporation process it does not have a very distant memory.

Analysis: Another important parameter is the regarding the number of ants present, the density of ants . Thus using all these parameters we can define a single parameter, the average pheromonal field . Where is what i mentioned above, the rate of scent decay.

Further detailed analysis can be studied out here. With the above background it is just a matter of understanding.

[Evolution of distribution of ants : Source]

Click to Enlarge

Now after continuing with the mathematical analysis in the hyperlink above, we fix the values of the parameters.

Then a large number of ants are placed at random positions, the movement of each ant is determined by the probability .

Another assumption is that the pheromone density at each point at is zero. Each ant deposits pheromone at a decided rate and also the pheromone evaporates at a fixed rate .

In the above beautiful picture we the evolution of a distribution of ants on a 32×32 lattice. A pattern begins to emerge as early as the 100th time step. Weak pheromonal paths are completely evaporated and we finally get a emergent ant distribution pattern as shown in the final image.

The Conclusion that Chialvo and Millonas note is that scent following of the very fundamental type described above (assumptions) is sufficient to produce an evolution (emergence) of complex pattern of organized flow of social insect traffic all by itself. Detailed conclusion can be read in this wonderful paper!

References and Suggested for Further Reading:

1. Cognitive Maps, click here >>

2. Remembrance of places past: A History of Theories of Space. click here >>

3. The Science of Self Organization and Adaptivity, Francis Heylighen, Free University of Brussels, Belgium. Click here >>

4.   The Hippocampus as a Cognitive Map, John O’ Keefe and Lynn Nadel, Clarendon Press, Oxford. To access the pdf version of this book click here >>

5. The Self-Organization in the Brain, Christoph von der Malsburg, Depts for Computer Science, Biology and Physics, University of Southern California.

5. How Swarms Build Cognitive Maps, Dante R. Chialvo and Mark M. Millonas, The Santa Fe Institute of Complexity. Click here >>

6. Social Cognitive Maps, Swarm Collective Perception and Distributed Search on Dynamic Landscapes, Vitorino Ramos, Carlos Fernandes, Agostinho C. Rosa.

Related Posts:

1. Swarm Paintings: Non-Human Art

2. The Working of a Bird Swarm

3. Adaptive Routing taking Cues from Stigmergy in Ants

Possibly Related:

Gödel, Escher, Bach: A Mental Space Odyssey

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