Markov Blankets: The Boundaries That Make Things Things

Series: The Free Energy Principle | Part 3 of 10

A Markov blanket is the set of variables that, once you know them, makes a system statistically independent of everything outside it. In a Bayesian network, a node's blanket is its parents, its children and its children's other parents. Judea Pearl coined the term in 1988. Karl Friston's free energy principle uses blankets to say where an organism ends and its world begins, and critics argue that this stretches Pearl's tool into something it was never meant to be.

Where do you end and the world begins?

Point to your skin and you've already made assumptions. Skin cells flake off all the time. Your body carries about as many bacterial cells as human ones: roughly 38 trillion bacteria against 30 trillion human cells in a reference adult, which revises the old claim of ten bacteria for every human cell (Sender, Fuchs & Milo, 2016). The oxygen in your blood came from outside. So where, exactly, is the boundary that makes you one distinct thing?

The free energy principle answers with a concept borrowed from statistics. To see what it borrows, and what it adds, start with the original.

Pearl's blanket: a tool for inference

In a Bayesian network, variables are nodes and arrows show direct influence. Pearl's insight was that to predict one node you rarely need the whole network. You need a specific neighbourhood around it. That neighbourhood is the node's Markov blanket: the set of variables that renders it conditionally independent of all the others. In a Bayesian network, the minimal such set, which Pearl called the Markov boundary, consists of the node's parents, its children and the other parents of its children. Pearl coined both terms in 1988, in Probabilistic Reasoning in Intelligent Systems (Wikipedia).

A tiny example makes it concrete. Suppose a network has five variables:

• Season affects Rain
• Rain and Sprinkler both affect Wet grass
• Wet grass affects Slippery path

What is the blanket of Rain? Its parent is Season. Its child is Wet grass. Wet grass has one other parent, Sprinkler. So the blanket of Rain is {Season, Wet grass, Sprinkler}. Once you know those three, learning whether the path is slippery tells you nothing more about rain. The slippery path's only bearing on Rain runs through Wet grass, which you already know.

Why include the child's other parent? Because of what statisticians call explaining away. If the grass is wet, finding the sprinkler on makes rain less likely. Sprinkler and Rain are independent until you see their common effect, and then they aren't. A blanket has to include it.

In Pearl's use, the blanket is a property of a model. It tells you which variables you need to compute with. It says nothing about where things begin and end in the physical world.

Friston's blanket: sensory and active states

Friston's framework uses the same independence structure for a different purpose. It divides the states of a system and its surroundings into four kinds:

• Internal states: inside the system (a cell's chemistry, a brain's activity)
• External states: the rest of the world
• Sensory states: through which the world affects the inside
• Active states: through which the inside affects the world

Sensory and active states together form the blanket. Internal and external states never touch directly; given the blanket, they are conditionally independent. In this framework, the separation is what lets the inside carry a model of the outside: the internal states can be read as encoding beliefs about external causes they never contact. The Surprise Is the Enemy essay explains why that model has to keep surprise low, and Variational Inference for Humans shows how the inference works.

A cell is the textbook picture. Receptors in the membrane respond to the chemistry outside (sensory states); pumps and channels change it (active states). Inside are metabolic and genetic networks; outside, the extracellular world.

Blankets all the way down (and up)

The idea that made blankets famous outside statistics is nesting. Michael Kirchhoff and colleagues argued that living systems are "hierarchically composed of Markov blankets of Markov blankets", running "all the way down to individual cells, all the way up to you and me, and all the way out to include elements of the local environment" (Kirchhoff et al., 2018). They also argued that these boundaries "need not be co-extensive with the biophysical boundaries of a living organism".

On this reading, cells have blankets; organs built of cells have blankets of their own; an organism has one at a larger scale still. Some proponents extend the picture further, to groups and societies. That extension is more speculative, because the further you go from a membrane, the harder it is to say which variables are sensory and which are active.

Within a single body, the same logic suggests many overlapping blankets: the visual system, the gut, the immune system, each with its own inputs and outputs. One interpretation is that "you" are less a single unit than a coalition of subsystems coupled through shared signals. That's an interpretation, not a finding, but it is a natural one if you take the nesting seriously.

Pearl blankets versus Friston blankets

Here the critics come in, and the strongest critique is precise.

Jelle Bruineberg, Krzysztof Dołęga, Joe Dewhurst and Manuel Baltieri traced how Markov blankets moved from Bayesian networks, through variational inference, into the active-inference literature. They identified "a persistent confusion" between two uses: the formal, epistemic use of blankets as a tool for inference, and their "novel metaphysical use" in the free energy framework to mark the physical boundary between an agent and its environment. They proposed calling the first "Pearl blankets" and the second "Friston blankets" (Bruineberg et al., 2022).

The distinction matters because the two make very different claims. A Pearl blanket is relative to a model; change the model and the blanket changes. A Friston blanket is supposed to be a feature of the world, picking out real things. Bruineberg and colleagues distinguish "inference with a model" from "inference within a model", and argue that only the second can do metaphysical work with blankets, and that it "requires additional philosophical premises and cannot be justified by an appeal to the success of the mathematical framework alone" (2022).

A separate, technical critique found that the various definitions of a Markov blanket used across free energy papers are not even equivalent to one another (Biehl, Pollock & Kanai, 2021). Neither paper shows that Friston blankets are useless. Both show that the jump from a statistical boundary to a real one is an argument that still has to be made. The site's essay on critics and controversies covers the wider debate.

Blankets and the extended mind

If blankets are statistical rather than physical, their edges need not stop at the skin. This is one reading of blankets, and it connects them to the extended mind thesis that Andy Clark and David Chalmers proposed in 1998, the idea that objects in the environment, such as a notebook, can be part of a person's cognitive processes (Wikipedia).

Consider a blind person using a cane. Where does their sensory boundary end, at the fingertips or the cane tip? On the extended reading, the answer depends on coupling. If vibrations through the cane are woven into the person's predictions about the ground, the cane works as part of the sensory interface. The same reasoning would apply to a musician's instrument or a surgeon's scalpel: skill becomes a matter of extending and refining the boundary. Kirchhoff and colleagues' phrase "all the way out to include elements of the local environment" is this idea in the formal language (2018). The essay on extended cognition develops it.

The Pearl/Friston distinction applies here too. That you can draw a blanket around person-plus-cane in a model doesn't by itself show that the mind physically includes the cane. That takes extra premises.

Is a blanket an existence proof?

Friston's argument goes further still: on his view, to be a "thing" at all is to have a Markov blanket that persists over time. A system exists, as a system, to the degree that it maintains the statistical separation between its inside and its outside. A cell has a sharp blanket. A species or a nation, with porous and contested boundaries, would have a weaker one.

That is Friston's argument, not an established result, and it inherits every question above. If Friston blankets are just Pearl blankets drawn by a modeller, then existence-by-blanket says more about our models than about the world. If they are real features of physical dynamics, the claim is bold and interesting, and it still needs the philosophical premises the critics ask for.

The boundary question, honestly

Markov blankets give a precise, computable answer to a very old question: where does a thing end? In Pearl's hands that answer is modest and powerful, a rule about which variables matter for prediction. In Friston's, it is ambitious: a candidate definition of what it is to be a self. The mathematics is the same; the philosophy is the part still being argued.

The pebble: a boundary you can calculate is not yet a boundary that exists.

FAQ

What is a Markov blanket in simple terms?

It is the set of variables that, once known, make a target variable independent of everything else in a system. Knowing the blanket tells you everything the rest of the system could tell you about the target.

Who coined the term?

Judea Pearl, in 1988, in his book Probabilistic Reasoning in Intelligent Systems. He also coined the related term "Markov boundary" for the smallest such set.

Is a cell membrane a Markov blanket?

In the free energy framework, the membrane is the standard example: its receptors act as sensory states and its pumps and channels as active states. Whether the membrane is a Markov blanket in a strict, physical sense, rather than a convenient way to model a cell, is part of the debate.

What is the difference between Pearl's and Friston's Markov blankets?

Pearl's blankets are a property of a statistical model, used to simplify inference. Friston's are meant to mark real boundaries between an agent and its environment. Bruineberg and colleagues (2022) proposed the names "Pearl blankets" and "Friston blankets" to keep the two apart, and argued the second needs extra philosophical justification.

Why do Markov blankets matter for the free energy principle?

They define what the "system" is. The principle describes how internal states, shielded from the world by sensory and active states, come to model and act on external states. Without a blanket, there is no inside to do the modelling.

Further Reading

• Pearl, J. (1988). Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference. Morgan Kaufmann. (As credited in "Markov blanket," Wikipedia: https://en.wikipedia.org/wiki/Markov_blanket)
• Bruineberg, J., Dołęga, K., Dewhurst, J. & Baltieri, M. (2022). "The Emperor's New Markov Blankets." Behavioral and Brain Sciences. https://doi.org/10.1017/S0140525X21002351
• Kirchhoff, M., Parr, T., Palacios, E., Friston, K. & Kiverstein, J. (2018). "The Markov blankets of life: autonomy, active inference and the free energy principle." Journal of the Royal Society Interface. https://doi.org/10.1098/rsif.2017.0792
• Biehl, M., Pollock, F. A. & Kanai, R. (2021). "A technical critique of some parts of the free energy principle." Entropy 23(3), 293. https://doi.org/10.3390/e23030293
• Sender, R., Fuchs, S. & Milo, R. (2016). "Revised estimates for the number of human and bacteria cells in the body." PLoS Biology 14(8), e1002533. https://doi.org/10.1371/journal.pbio.1002533
• "Extended mind thesis." Wikipedia: https://en.wikipedia.org/wiki/Extended_mind_thesis

This is Part 3 of the Free Energy Principle series. Previous: Surprise Is the Enemy Next: Variational Inference for Humans: The Math Made Intuitive