You & Your Markov Blanket

1100 words, 5 minute read

Like Peanuts’ Linus, we all struggle to let go of our security blankets. If you are old enough to read this post, you have probably severed your textile tether…but what about that bottle of scotch you keep in your desk drawer? Truth to tell, we all have our security blankets but our childhood ‘blankies’ are nothing compared to the Markov Blankets we wrap around our adult selves.

Although the concept of a Markov Blanket was first proposed in 1988 by Judea Pearl, it was defined almost a century earlier (1910) by John Collins Brophery:

And this is good old Boston,

The home of the bean and the cod,

Where Lowells talk only to Cabots

And Cabots talk only to God.

The Cabots are a Markov Blanket separating…and connecting…the hapless Lowells with their God. If the Lowells wish to address ‘the maker of heaven and earth’ they have (only) to address their prayer through the Cabots who may, or may not, choose to pass on their entreaty.

Likewise, in Boston at least, if God wishes to communicate with the Lowells (or by extension, with any of us), he must filter his message though the Cabots and so we must depend on ‘the kindness of strangers’ to hear his voice. According to some ecclesiologists, the Christian Church is a ‘Boston Baked Blanket’. (Sorry, I couldn’t resist.)

Once identified, we begin to see Markov Blankets all around us. The famous Telephone Game is a perfect example. The final, often hilarious, message may, or may not, include a trace of the original. So it is with the Lowells, the Cabots, and God.

In earlier posts on this site, Masks and Masks Too,  I theorized that all of us communicate with ‘others’ through Markov Blankets. In this case we are indebted to Brophy’s British contemporary, T. S. Eliot, for the idea:

“Prepare a face to meet the faces that you meet.” (Prufrock)

Two recent articles by Callie Holterman in the New York Times detect ‘Markov’ hiding in the thicket known as Human Resources:

“If you haven’t applied for a job recently, you might be surprised by the new common procedure. At one end, job seekers use A.I. chatbots to churn out résumés and cover letters. At the other, employers use A.I. to sift through all of those applications.”

“Increasingly, our digital intermediaries will collide. We’ll talk to our bots, and our bots will talk to one another.” Holterman envisions a future in which our bots build an ever thicker ‘no-man’s-land’ (literally) between subjects. As we are pushed further and further apart by the bot-o-sphere, will we eventually lose touch with one another and become solipsistic appendages of process, unrelated kids accidentally sharing a see-saw?

Holterman calls bot-on-bot interactions ‘bot-loops’ and she warns that “they flip our conversational dynamic inside out, turning chatbots into the interlocutors and humans into their enablers.” We are becoming tools of our tools! We are becoming their accessories.

In every day life, we imagine that we interact with one another in a way that is reciprocal and commutative (A, B and C are interchangeable):

B

↗   ↖    

↙              ↘

A       ←  →      C

But if ‘B’ stands for ‘Blanket’, things change drastically:

B

↗   ↖    

↙            ↘

A                     C

This new world is anything but commutative; it is rigidly ordered with B playing a role entirely different from A and C.

The World we imagine is Archimedean and for the most part Euclidean. The insertion of a Markov Blanket changes that. Welcome to ‘UUU’ (the Unexpected Ultrametic Universe). You are far from Kansas now! This is Cloud Coocoo Land (Aristophanes and the Lego Movie); the rules of arithmetic do not apply here.

An Archimedean Universe consists of entities that can be measured using real numbers and whose measurements obey the laws of arithmetic. We can be forgiven for believing (for centuries) that the only possible world was Archimedean. But it turns out that an Archimedean universe is missing something pretty big: Infinity (a pretty big thing to miss), i.e. infinite numbers and, even more importantly, their infinitesimal reciprocals.

Astonishingly, there are an infinite number of discrete infinitesimal numbers smaller than the smallest real number but greater than zero. In fact, there are an infinite number of discrete infinitesimals between any two real numbers. Once you open your tent flaps to these ‘quantitative miscreants’, everything changes! May I offer you a mixed tape of Ultrametric’s Greatest Hits?

• All triangles are isosceles.

• Every point in a sphere is its center.

• Any two spheres are either entirely disjoint or one is contained completely within the other: no touching!

• If A and C are disjoint subsets of B…

  • The metric (A + C) can be greater than B, even infinitely greater.

  • A or C or both may be greater than B.

  • Even if A and C have ‘positive’ metrics, B’s metric may be ‘negative’.  

Roughly speaking, the whole is unrelated to the sum of its parts. Every discrete entity has its own independent metric. The Tardis in the long running British sci-fi series, Doctor Who, is an example of an ultrametricentity: its interior metric (an operations center) is larger, much larger, than its exterior (a phone booth). The ordinary concept of ‘containment’ no longer applies.

Apparently, Boston is another example of an ultrametric entity: if A and C are in B, then B, Cabot like, functions as their intermediary. A can communicate with B and C can communicate with B, but A and C cannot communicate with each other…except via the ‘voluntary’ (undetermined) intermediation of B.

Brophery’s Boston is an ultrametric city; so is Eliot’s London (The Waste Land):

Unreal City,

Under the brown fog of a winter dawn,

A crowd flowed over London Bridge, so many,

I had not thought death had undone so many.

Sighs, short and infrequent, were exhaled,

And each man fixed his eyes before his feet.

Flowed up the hill and down King William Street,

To where Saint Mary Woolnoth kept the hours

With a dead sound on the final stroke of nine.