Category Archives: Bayesian

The Encounter

Over the last couple of years, Uta & I have been meeting with Simon McBurney, director of Complicite as he prepared for his one-man show, The Encounter. Simon hoped that we might be able to tell him what neuroscience can reveal about the nature of consciousness.

The Encounter dramatizes the experiences of Loren McIntyre, as described in Amazon Beaming by Petru Popescu. When Simon told us about this book it was long out of print, but we managed to find a second hand copy. As a result of Simon’s work it was republished in 2015.

Loren McIntyre was a National Geographic photographer, and this is the story about his experiences when he was lost in the remote Amazon rain forest. His survival depends on the leader of a small group of Mayoruna people who he has followed into the jungle and then become hopelessly lost. But there is no common language through which they can communicate. He feels utterly isolated with ‘a psychological distance of 20,000 years’ between him and the people who are his only hope finding a way back. Eventually he starts to experience ‘communication’ from the leader of the group when he sits near him. He begins to understand some puzzling behaviour, for example, why the group keep destroying their villages and moving on. Remarkably, this communication doesn’t depend on language.

McBurneyIn The Encounter everyone in the audience wears earphones, which helps Simon to recreate and share all the strangeness and terror of McIntyre’s experiences through the wonder of acoustic technology.

When we first talked to Simon about the work he was developing around Amazon Beaming, he asked us whether we thought it was possible for two people to communicate without words. We said, absolutely.

And here is why.

Continue reading The Encounter

Communication is not simply about the transfer of information. You can do that with a cash machine. When we communicate we know that we are communicating, and we know that our partner knows that she is communicating. We have a subjective, conscious experience of communicating. This experience, we hypothesise, predates language.

This is what I would have said in a discussion planned after a performance of The Encounter at the Barbican. Unfortunately I couldn’t be there because I had to have an operation for a detached retina.

What is conscious experience?

When I look out into the audience, I am aware of innumerable faces. I have the subjective experience of seeing many faces. But this is an illusion. I don’t mean that you are all figments of my imagination. I am confident you are all out there, but, even so, some of you at least are figments of my imagination.

The problem is that my contact with you all seems so direct, when it is really very slight. The only clues I have about you come from the sparse signals that my eyes and ears are sending to my brain. From these crude signals, and from years of experience, my brain can make quite a good model of what’s out there.

elephantYou will remember the story of the blind men who come across an elephant. One feels its trunk and thinks it is a snake, another feels its leg and thinks it is a tree.

A single sighted man who comes across an elephant is doing the same thing. The elephant is too big to see with a single fixation of the eye. We have to look all over it. If our eye lands on the trunk, then it’s a good bet that it’s a snake. But, then, as the eye moves along it a head or a tail should appear. When this doesn’t happen, then the model has to be changed. It isn’t a snake. Perhaps it’s an elephant. The more evidence our eyes take in the more plausible it becomes that the thing is an elephant. Our eyes move very fast (4 to 8 fixations per second). Within a few 100 msecs we see the elephant. We are entirely unaware of all the work our brain has done and, of course, what we are seeing is not the elephant, but the model that our brain has constructed. This model is often incomplete with several missing bits that are filled in with guesses. This is why some of you are figments of my imagination. There is a well known youtube video, showing that a gorilla can walk by some basketball players without being noticed, if you are too busy counting the basketball passes.

But what is the point of all this vivid subjective experience?

HuxleyCapTH Huxley believed that our conscious experience has no function: ’Consciousness [is]completely without any power of modifying the working [of the body] as the steam-whistle which accompanies the work of a locomotive engine is without influence upon its machinery.’ I believe that Huxley was wrong and we can see this from the metaphor he chose. This is because the steam-whistle does influence the behaviour of other engines.

Our conscious experience is very vivid, but also very private. There is no way I can have your experiences. It even is possible that the colour experience that I call red is actually the one you would call green if you were to experience it. How could we ever know? But there is a paradox here. Our conscious experience may be private, but it is also the only aspect of our mental life that we can share with others. I can’t tell you anything about what my brain is doing. And I certainly can’t tell you about all those mental processes that never reach my consciousness.



What I can tell you about is my model of the world. And, at the same time, you can be telling me about your model of the world. So if we are like steam locomotives, we are certainly hearing each other’s whistles.




Conscious experience is for interacting

And, because we are sharing the same world and because we also have very similar brains, our models are also likely to be very similar. But they will not be entirely similar. Our models will also depend on all our past experiences including our interactions with others. Our models of the world will be strongly influenced by our cultural background.

But what happens when two people interact? Interacting with another person is different from interacting with a rock. Unlike a rock, the person I am interacting with is creating a model of me at the same time as I am making a model of her. The model I create of you helps me to predict what you are going to do, which also helps me to communicate with you. My model of you will have many different aspects. I will try to discover what sort of person you are. But in my view the most important aspect of you that I am trying to model, is your model of the world. That is the model of the world we are currently sharing.

brainsBecause we are sharing the same world, any differences in our models will reflect our different experiences and cultural backgrounds. So, when I know something about your model, I know something about you. But, if I need to communicate with you, then I should try to make my model similar to yours. And, at the same time, you will be trying to make your model similar to mine. Some believe that, if two devices interact while making inferences about each other, then they will eventually converge on the same model.

Language is extremely useful for discovering something about other peoples’ models of the world, but it is not the only way. Simply by watching how someone moves you can learn about how they see and understand the world about them. The more you spend time with someone else, the better you will get at predicting how they are going to move. You won’t know how you do it. It just happens.

To make this prediction you have learned about their model of the world and, inevitably, this has changed your own model. At some point the two models will be in almost perfect synchrony. At this point you will have the conscious experience of what seems like, and, indeed is, wordless communication.

The last ferry from Esbjerg to Harwich: Why do we behave irrationally – or do we?

DSCF0114The Dana Sirena, the huge ferry, which has crossed the North Sea every day for uncountable years, will run no more. There is only one more journey and that will be to return from Harwich to Esbjerg – and that ‘s it. We don’t know who made the decision and we wonder what the arguments might have been. We are a bit sad and wonder whether this is a sign that our annual trips to Aarhus for the last ten years must come to an end sometime.

Waiting in the car to get on the ferry, we looked back at a lecture by Antonio Rangel, a few days before, which we much enjoyed. Rangel is a leading practitioner of neuro-economics, from Caltech, and he talked about some serious methodological issues in this field. It’s not about lack of replication, but about remoteness from real life. We have to face it, what people do in the lab just doesn’t transfer to the real world. Something crucial is being left out and not understood. People aren’t behaving as if they were optimal Bayesians. Continue reading The last ferry from Esbjerg to Harwich: Why do we behave irrationally – or do we?

UF: To be optimal our behaviour should be rational – no?

CDF: What economists and others mean by rational behaviour is that you choose the option that gives the highest benefit.

UF: This sounds okay, but people often seem not to choose what’s best for them.

CDF: Ah, this depends. Think of the famous Marshmallow experiment. You have to resist taking the one Marshmallow so that after a certain time you will receive two. But, is it always better to delay? Of course not. If the situation is unpredictable, then it is better to take the one Marshmallow than risk never getting any.

UF: So being impulsive is not always a bad idea.

CDF: You don’t choose a big reward option, if it is very unlikely to be achieved. To answer your question, people and other animals for that matter, don’t necessarily behave irrationally if they don’t do what is predicted by a formula to get them the highest value. The formula works in the lab where stakes are low and choices to be made occur with equal likelihood. Rangel argued that these situations are quite irrelevant to real life situations. What looks like weird behaviour from the theoretician’s point of view, turns out to be quite sensible when looked at in the right context. Maybe supposedly irrational people are maximising different variables compared to what the theoreticians think they ought to be maximising.

UF: So ‘crazy’ people aren’t irrational either?

CDF: Well, a very common idea is that everyone would behave like them if they had their bizarre experiences. Irrational behaviour means the model doesn’t fit.

UF: I see. The bizarre experiences are the proper context to explain the behaviour, which might be optimal. I like it, because once again we see how important it is to consider context. Do you have an example?

CDF: It always matters how something is framed. If someone says, “my glass is half-empty” this most likely means “please fill it up”. If someone says, “my glass is half-full” this means, “I’ve got enough for the moment”. So glass half-full and half-empty are not one and the same ‘value’. We find it incredibly easy to understand the meaning of utterances when we interact with others. We can calculate the value in a particular context quite fast.

UF: Isn’t it odd that when the questions are framed in a complex real life context, they become easy? It’s like a magic trick that shows us what the mind is really good at. It’s at home with complex computations that take into account what another person might know or not know. Strip the problems down to their logical essentials, and the computations become hard and result in errors.

CDF: The question is how does the mind do it? Models proposed by behavioural scientists and economists are extremely good at modelling very basic decision processes, but in social interactions other models are needed. Only if you have such models – and this will be after lots of behavioural experiments, – should you even begin to think of brain scanning. As Rangel said in his talk, brain scanning very rarely gives you any answers. You need a model first. It will not emerge from the data. If the data fit the model, then that means something.

UF: There is something else that I wish I understood better: What our ‘priors’ tell us, and what we pick up from current information are often at odds with each other. How do we deal with this?

CDF: There is a good example of how these two computations can be experimentally made to conflict, and in this case the priors win: In a trust game you learn over many rounds how people behave and this should give you a good idea of whether or not to trust that person. But you pay less attention to this learning process when the experimenter has planted in you some prior knowledge about the other person. For example, you read that Peter, the partner in your game, has recently been given a medal for rescuing a child from a fire, and has raised large amounts of money for charity. During the game, however, Peter behaves abominably and cheats. Yet, you remain trusting when all your unconscious processes want to tell you that you should distrust. Bad mistake.

UF: I can see how this relates to irrational behaviour: It is the personal and the subpersonal fighting it out with each other. But it is not always clear which type of knowledge you should use for the best: the prior knowledge that you have about the other person and their past deeds, or the information you currently extract from your interaction with them.

CDF: The prior knowledge you get from others will always come from a much larger database than your own direct experience. Perhaps that’s why we pay more attention to knowledge from others?

UF: Sometimes the priors can be too strong, and sometimes the bottom-up learning can exert too much influence. If there is a conflict that can’t be resolved, the decision is likely to be considered irrational.

CDF: Of course the priors are not fixed. They are constantly being altered by what happens in our real time interaction with the world and other people. Data from psychophysics tasks tell us that the decision you just made affects your next decision. How can I know what I like until I see what I have chosen? My behaviour tells me something – now I know what I should do next time.

UF: Is this similar to what happens when we follow the crowd and do what other people do? They may know something that we don’t know. We can benefit from their knowledge, as long as they have it. Like the traders on the stock exchange, who buy stocks that others buy. Perhaps they believe that the others have inside knowledge. This might sometimes even be true, but if it isn’t, stock market bubbles can be created. This certainly looks like irrational behaviour.

CDF: I think we have been talking about our favourite topic: Two systems and how they influence each other, System 1 and System 2, in Kahneman’s sense. Sub-personal and personal in Dennett’s sense. The influence of other people on us, and our influence on them occur both at the personal and the subpersonal level.

UF: But how does the influence of other people, say on the stockmarket, come about?

CDF: That’s what our book has to be about.

Meanwhile, after a long wait, we can drive onto the ferry. We spot a TV cameraman and a presenter in a long black coat, watching and commenting on the last journey of the old Dana Sirena from Denmark to England.

Our colleague from the Interacting Minds Centre at Aarhus University, Andreas Højlund Nielsen, told us about a 15 minute documentary film made by his sister-in-law, Mie Lorenzen. It is called ‘18 hours aboard the England ferry’. It will provide you with the tranquillity of a very calm transit.


How to influence people and get approval from your Granny by Uri Hertz



Continue reading How to influence people and get approval from your Granny by Uri Hertz

The cartoon by Uri Hertz was sparked by a paper by Bayarri and DeGroot (1989) entitled “Optimal Reporting of Predictions”. Uri is part of Bahador Barami’s group on Crowd Cognition at UCL Institute of Cognitive Neuroscience. The last time I visited the ICN I asked Bahador if he or his colleagues might like to contribute to Socialminds. To my delight, he agreed, and he suggested that Uri draw a cartoon relating to a topic we were just discussing:  The importance of metacognition for social communication. How certain are you about what you want to communicate? What risk is there to your reputation if you get it wrong? There was a paper about this, Bahador said and the point the paper makes is that the advice depends on your current influence on the person you advise.

What does this mean? The cartoon makes it very clear. You and a number of other advisors report your belief in some variable (say the probability of a phone being a good buy, a stock going up). The advisee knows each of the advisors and she does not trust them all equally. This can be rephrased as follows: she has assigned a prior weight that represents the amount of influence each advisor has on her. These weights are updated when information about the variable comes to light (the phone is shown to break down easily; the stock did actually go up). The updating process takes into account not only whether the advisor was correct, but also how vigorously he reported his belief. If you stated high belief in some previously ignored stock going up, and it actually does go up, your influence will show an increase. It will get the highest increase if the other advisors expressed only weak belief about the stock going up (e.g. they overlooked or discarded the possibility). However, if you are wrong, and if you stated your belief very strongly, as opposed to the other advisors, then your influence will suffer a dramatic fall.

Bayarri and DeGroot show in their paper that in order to increase their influence (posterior weight) over time, advisors should adapt their belief reporting strategy, rather than faithfully stating their beliefs. If you happen to be an advisor, your optimal strategy depends on your current influence (or weight). When your influence is low, you should exaggerate your beliefs (vigorously give a definite yes or a definite no).

This is what the left side of the figure illustrates. It shows how you can take advantage of situations in which other advisers report low belief, and the outcome agrees with your belief. Optimal strategiesHowever, if you are a person who has high influence to begin with, the optimal strategy is to be conservative, understating your belief, as shown on the right side of the figure. This strategy keeps your influence rating from collapsing when your advice turns out to be wrong.

The cartoon highlights the real life implications. Optimal strategies really depend on your current influence! Any mistake that Max makes will cost him dear. But Moritz does not have to worry about such cost. His influence can hardly go down any further.

Is this a rare case? Far from it. The process of giving advice, and any transmission of privately held information, is the basis of communication and cooperation. It includes a first step of establishing the private beliefs, either from perception or experience, and a second step of communicating these beliefs. In the first stage you have identified a stimulus and assessed the probability of a reward – but it also involves metacognitive abilities. Bayarri and DeGroot’s study shows that your beliefs are transformed according to the social context even before they are communicated. So giving advice is not just a case of identifying a stimulus, and communicating it to another person. You have to assess not only how confident you are in your judgement but have to factor in the other person’s likely opinion about you. This is how deeply our social nature affects our judgment as well as our presentation. It makes sense: if we are highly trusted already we can easily fall from grace with injudiciously worded advice. Likewise, if we were previously ignored, we can suddenly gain status if we hit the bull’s eye. If we were wrong, no matter, – you can’t sink even further. As the hedge fund managers say “always remember the value of your investments can go down as well as up”.

So yes, metacognition is critical for social communication.

Where is the crack in the mind machine: some insights from Bayesian theory into mental disorders by Pavel Voinov & József Arató

Where is the crack in the mind machine? Some insights from Bayesian theory into mental disorders.

Pavel Voinov and József Arató are PhD students in the Cognitive Sciences Programme at the Central European University, Budapest.

As cognitive scientists we keep asking ourselves what knowledge society expects from us and what the implications of this knowledge are. “Mind as a machine” is a good metaphor, as we feel it captures those expectations: to describe the principles of how the mind works, and, furthermore, to explain its failures and suggest ways to fix it.

In this post we will take the perspective of reverse mind-engineers. We will use one of the most prominent computational theories in contemporary cognitive science –  Continue reading Where is the crack in the mind machine: some insights from Bayesian theory into mental disorders by Pavel Voinov & József Arató

the Bayesian perspective, and show how it contributed to our understanding of two prevalent mental disorders – schizophrenia and autism. A distinctive feature of Bayesian theories of cognition is that they provide a formal description of the mind: it can be grasped with mathematical expressions, and thus be computationally modelled.Fig 1

Bayesian models of cognition can explain how people handle the uncertainty that is constantly present in the world. As we can never be sure what the true state of the world actually is, perception works by hypothesis testing. We continuously guess what we might expect to happen in the world. For these guesses we can use the accumulated knowledge we have acquired through past experience.

In other words, we evaluate newly incoming sensory information in the light of prior experience, and this is how we constantly make fresh predictions of what it is that we are seeing, hearing and feeling. What we actually perceive is not what is out there. Instead we perceive the most likely event out there. The most likely event is what we hypothesise given the new sensory signal (evidence) evaluated on the basis of the probabilities of past events (priors). We continuously update our expectations based on the differences between the predicted and experienced sensory stimuli (prediction error). The same model applies to belief formation: we update our beliefs based on the differences between expected and experienced events (Figure based on Van Boxtel & Lu).

Here’s an example how this works. ImagiFig 2ne you need to read a signboard at a distance. Even if you can’t discriminate individual letters, the context will help you, and you are likely to identify common words like “caution”, “danger”, “exit” etc., just by matching approximate length of a word or its salient features. Even if you can’t see any details at all, you may make a guess: this will be a case of relying solely on your priors. But when the context is not informative, and there are many probable alternatives, you will have to rely more on what your eyes deliver to the brain. Now you can’t guess the word and you need to distinguish the individual letters.

The Bayesian approach has been impressively powerful in modelling various aspects of human cognition: let’s see whether it has been useful for explaining malfunctions of the mind.


The most distinctive features of the schizophrenic mind are the so-called positive symptoms: delusions (abnormal beliefs) and hallucinations (false perceptions). Hence, a Bayesian framework is a promising tool for exploring these features.  After all, it was developed to deal with belief formation and perception – and these are precisely the cognitive functions that are most affected in schizophrenia.

Various experiments have shown that something goes wrong in the combination of prior knowledge and iFig 4ncoming sensory evidence. For example a weaker reliance on prior expectations can explain why schizophrenics are less susceptible to some visual illusion. Not being tricked by an illusion means, that in some situations, they perceive the world more veridically. So why does this not happen in healthy people? Healthy perception is optimally adapted to the environment, with the brain inferring the most likely patterns from raw sensory inputs. In contrast, schizophrenic patients are more influenced by what their eyes see, and less by the higher-level expectations their brain has derived from past experience. Look at the picture with two masks (image from: Grosjean et al., 2012). Our strong perceptual bias (or ‘prior’) for natural convex faces overrides competing information (such as shadows) and makes a concave hollow mask (bottom) perceived as a convex face (top). Schizophrenic patients are generally less susceptible to this illusion.

A weaker influence from higher-level expectations is also shown in tasks which involve uncertainty – for example in playing stone-paper-scissors game. Here schizophrenic patients take less account of the past history of their contestant’s decisions and as a result follow strategies based on only the most recent evidence. Patients were also more confident about their decisions, and raised the stakes after smaller number of sequential winnings than healthy players (Joyce et al, 2013).

Another important feature of decision-making under uncertainty in schizophrenic patients is their reduced sensitivity to negative feedback once they have formed their belief. In Bayesian terms they do not use the prediction error correctly to update their models of the world.

These findings are especially intriguing when linked to our knowledge about the neurotransmitter dopamine. Dopamine plays the key role in learning based on the prediction error. Abnormally high levels of dopamine found in the brains of schizophrenic patients may underlie their failures to integrate sensory (and higher order) error signals appropriately.  We are not surprised by outcomes of our actions because our brain foresees them. But absence or distortion of this prediction in the brain of schizophrenic patients may create strange experience and give rise to delusional beliefs about it (Fletcher  & Frith, 2009).

The Bayesian approach is also promising in modelling how this lower-level prediction error could give rise to false beliefs at higher – ’more cognitive’ – levels. In this case corrupted output from lower levels would feed into higher cognitive functions leading to faulty beliefs of a higher order. Altogether, within a Bayesian picture of the mind one can build a coherent story, which would explain positive symptoms of schizophrenia with strong links between neural, cognitive, and behavioural levels.


Autism spectrum disorder has a clinical picture distinctively different from schizophrenia. The characteristic symptoms of this condition are repetitive behaviours and problems in social interaction and communication. Furthermore, autism is usually accompanied by a range of sensory peculiarities. The origin of these differences and its relation to the core symptoms of autism is still a mystery for psychologists. Atypical features of autistic perception include hyper-sensitivity to ordinary incoming stimuli, enhanced focus on details, and more fragmented perception. On the picture with kiwi fruits people with autism would likely see three separate objects rather than a triangle.Fig 3

Recently, Pellicano and Burr (2012) have proposed a Bayesian account of abnormal perception in autism. According to this account, perception in autism is shaped by weak priors. As we remember, a prior basically means accumulated information about the environment, and a weak prior means that less account is taken of this accumulated information. Hence we can say that the brain is not tuned appropriately to the environment. As a consequence, the perceived reality would be dominated by new incoming stimuli, and would be less influenced by internal information (priors). This would explain why autistic children are less susceptible to visual illusions and are often better at accurate copying of unusual images.

On the other hand, weak priors would also explain the phenomenon of sensory overload, that is hyper-sensitivity to ordinary sensory stimuli, like human voices or lamplight. While our sensitivity is modulated by the context, – we would be surprised if we heard a human voice in the middle of a forest, but not in the street. This contextual information does not seem to work for people living with autism. For ordinary people the brain would filter out most of incoming information. For autistic people everything from the sensory stream would be preserved, and this might lead to blurring of the figure with the background in their perception.

However, a theory has low scientific value if it can only incorporate already known facts, but can’t make predictions for new findings. What empirical prediction can the Bayesian theory make? The weak priors hypothesis can be tested against the sensory enhancement hypothesis: while the former suggests reduced influence of contextual information on perception, the latter predicts less noise in the sensory input for autistics. Joshua Skewes and colleagues (2014) tested this prediction in an experiment probing acuity of visual perception in ordinary people. The experiment demonstrated that people with higher scores on a scale measuring autistic traits, the AQ,  were less sensitive to the context information, but were as sensitive to the noise in stimuli as the control group. This result favours the weak priors hypothesis. However, it has not yet been tested with autistic individuals.

Conclusion. If you read the two stories carefully you can see surprising similarities between them: faulty functioning of prior knowledge is suggested as an explanatory cause for both conditions, and this cause is described in almost identical words. This is the weak part of the story: the theory seems to be so unspecified at the moment that it apparently fails to account for qualitative differences between two conditions, which a clinician would never confuse. We seem to be at the stage of trying to embed things in vague and extensively general principles, but small pieces of the big puzzle are yet to be defined. Perhaps this would sound disappointing if you expected a story like “There is a function in the normal brain which checks whether or not our beliefs are realistic. The part of the brain responsible for this function is broken in schizophrenics and that’s why you believe I’m an alien”. Unfortunately, we are not even close to the mechanical description of the “Mind as a machine”. But our first steps indicate that we’re on the right path…






Under the Markov Blanket

I mentioned Markov blankets to Uta and she immediately was intrigued, as was my intention. We talked about it again when we were having lunch on a sunny Saturday in the Angelica Café next to St. Anna church.

Over a nourishing beef broth and a chicken salad, we were sitting under a tree that was just bursting into leaf. We could look across the Danube. Opposite us, in filigree splendour, was the Parliament building. In the distance, to the left, we could see the island in the river that is connected to both sides of the town via Margit bridge. Yellow trams were constantly moving along it in both directions. Toylike.


Continue reading Under the Markov Blanket

Uta felt despondent despite the glittering river view, despite the magnificent scenic backdrop, despite the delicious beef broth. She was complaining about people not liking boundaries in diagnostic categories, like autism and dyslexia. They were forever talking about grey areas and one thing shading into another.

“Actually, it’s just the point of Markov blankets that there must be boundaries” – I said to cheer her up.

“Please say more.”

From this point on she couldn’t get a word in edgeways.

How I discovered Markov blankets

I went to a lecture by Pierre Jacob the other day, where I learned that people who believe in embodied and extended cognition hate boundaries. So there is no boundary between the brain and the body – hence embodied cognition – and there is no boundary between the brain and sophisticated tools such as iPhones – hence extended cognition.

Boundaries play such a critical role in biological systems, that it was strange for me to find that some people should hate them. Take for example the cell membrane.

The cell membrane surrounds the cytoplasm of living cells. Very complicated transmembrane proteins span from one side of a membrane the other. These function as gateways to control what enters and exits the cell. Without the membrane, the cell ceases to exist and its components are absorbed back into the environment.

In mammals, the skin acts as a protective barrier. The outermost layer of the skin, the epidermis, forms a protective barrier over the body’s surface, responsible for keeping water in the body and preventing pathogens from entering. Here again complicated mechanical devices are found, such as the ears, mouth and anus, which function as gateways to control what enters and exits the body.

So I started wondering, ‘Is there a cognitive boundary defending and defining that bundle of psychological abilities that we call the mind’?

Fortunately, I had just been reading Karl Friston’s paper on ‘Life as we know it’. This paper introduced me to the concept of the Markov Blanket.

“So, at last – what is a Markov blanket?” Uta asked, looking up from her plate expectantly.

Markov blanketA Markov blanket separates states in a Bayesian network into internal states and external states that are hidden (insulated) from the internal states. In other words, the external states can only be seen indirectly by the internal states, through the Markov blanket.

In response to Uta’s frown, I said,

“The blanket is like a cognitive version of a cell membrane, shielding states inside the blanket from states outside.”

I just had an e-mail exchange with Karl Friston to find out more about these cognitive membranes, I told her, opening my laptop.

CDF: Boundaries play such a critical role in biological systems, that it was strange to find that some philosophers hate them.

KJF: This is interesting – I got an e-mail from Jakob Hohwy a few days ago – he just got a paper accepted in “Noûs”. He was also addressing these strange philosophers by talking about “evidential boundaries”. He framed the issue in terms of radical embodiment but clearly wanted to use Markov blankets to bring the boundaries centre stage.

CDF: In cognitive terms, the brain/mind is shielded by a Markov blanket with sensory inputs and motor outputs as the only way of interacting with external states. Does this provide us with a cognitive definition of the mind?

KJF: To my mind (sic) yes. This is because (being completely ignorant of philosophy) I can equate consciousness with inference. Inference is only defined in relation to (sensory) evidence – that necessarily induces a Markov blanket (that separates the stuff that is being inferred from the stuff that is doing the inferencing)

CDF: 3. Are iPhones, laptops, &c. protected by their own Markov blankets? If so, this is an argument against the extended mind.

KJF: Yes it is – this would be Jakob’s position. As I understand it, we still have an internal representation of an iPhone and make active inferences about how we expect ourselves to use it. (But the iPhone itself is outside the blanket and may be making inferences about us.)

CDF: Can Markov blankets form and dissolve over a short time (e.g. during selective attention or joint attention)?

KJF: Yes – I have not thought about this but the Markov blanket is itself an dynamic process and, over time, will visit many different states. I can imagine the sleep-wake cycle being an example of formation and dissolution of a Markov blanket through sensory gating. I will have to think about attention!

Uta has cheered up. “Now we have defined the mind. Next time we can use a Markov blanket to define dyslexia and autism.”

Some more technical stuff

The Markov blanket for a node A in a Bayesian network is the set of nodes composed of A’s parents, its children, and its children’s other parents. The Markov blanket of a node contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behaviour of that node. The term was coined by Pearl in 1988. (Pearl, J (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Representation and Reasoning Series. San Mateo CA: Morgan Kaufmann.


There can be hierarchies of Markov blankets. For example, the Markov blanket of an animal encloses the Markov blankets of its organs, which enclose Markov blankets of cells, which enclose Markov blankets of nuclei and so on.