Combinatimics: exploring better rhythms for better lives

Chaos & Trauma

We live in a chaotic & traumatized world.

Given the ambient chaos, it’s natural to think about things like phase transitions and bifurcations. Likewise it is natural to think about diversity.

America’s diversity is often cited as a strength, and it is. But there are unhelpful forms of diversity. And these unhelpful forms have a habit sometimes of persisting themselves through regulatory capture, addiction, and other malignant means.

What is important to keep in mind is that at the end of the day diversity affects ecosystems. Whatever solutions we develop to work with our challenges must carefully account for the ecosystems in which those solutions are expected to perform.

One ecosystem that is particularly delicate right now is the internet.

To an extent this delicacy is unavoidable. Networks & supply chains are multidirectional. They can carry fear & hate just as readily as they can carry hope & love.

Nowhere is the nuance of networks more apparent than in the conversations people are having about diversity of opinion vs intentional disinformation & hate speech.

We’re gonna come back to that in a moment. Let’s first talk about rhythm.


In The Geometry of Musical Rhythm, author Godfried Toussaint begins with a discussion of rhythm vs melody. Rhythm, he notes, “is associated with time and the horizontal direction in a typical Western music score. Melody, on the other hand, is associated with pitch and the vertical direction. Rhythm can do very well without melody, but melody cannot exist without rhythm” (emphasis added).

There have been thousands of attitudes towards rhythm over the years. A few of my favorites:

  • Baccheios the Elder: rhythm is “a measuring of time by means of some kind of movement.
  • S. Hollos and J.R. Hollos: “In its most general form rhythm is simply a recurring sequence of events
  • A.C. Lewis: “Rhythm is the language of time.”

Syncronization & space

If rhythm is the language of time, what does rhythm relate to? And what does it ultimately have to say to us or anyone else? How is this language useful?

One incredibly interesting area of research right now concerns the mathematics of synchronization & Euclidian rhythms.

Natural sync refers to such phenomena as when fireflies synchronize their blinking with one another. Another fascinating example are the so called chimera states, in which phase-locked oscillators couple with drifting ones and cause problems (among other things, Chimeras have been linked to the Parkinson’s disease, epileptic seizures, schizophrenia, and other degenerative diseases).

Euclidian rhythms, meanwhile, occur when you spread N beats across M slots in such a way that each beat is equally spaced from every other beat.

What I think is especially fascinating about Euclidian rhythms is that they allow you to take a series of rapid fire pulses & spread them out over time so that each of them has the same amount of space.

I am not a doctor, but given this ability to spread pulses evenly across a measure, I believe Euclidian rhythms may prove useful for unwinding chimera states and potentially preventing seizures, for example, or strokes. It’s an incredibly fascinating research area, with a great deal of promise.

Basketcases of time

One incredibly fascinating thing to me about time is that we often talk about it as if it were experienced the same way by everyone everywhere moving at the same speed and in the same direction.

In other words, we like to pretend that time is well-behaved.

If you’ve ever worked with distributed systems and had to debug clock drift, you know for a fact that time is many things, but none of them are well-behaved. That’s precisely why CAP is a thing.

But if you combine the notion of natural rhythm with the fact that information is a physical phenomenon, I think it makes sense to consider how different combinations of timing of physical events might be used to help heal bodies & brains.

Healing the fractures

Back to the the internet and the delicacy of that ecosystem.

Across the world, we are all struggling to cope with a rapidly changing world that is often made scarier because of the networks we have built.

There are talks of passing laws to control the spread of misinformation (Singapore did actually). Different countries are responding in different ways. Many consumers feel it is the tech companies’ jobs to clean up the fakeness & make it apparent to everyone what is really true.

Your body is a distributed database

Setting aside what to do about fake news on our networks, I’d encourage you to consider another question:

Does it make sense to teach software engineering in ballet class, or to send seniors to yoga to learn about beat poetry & TikTok?

I think, in fact, that it does.

One thing that we know about trauma is that the memories of it are stored in the body. We also know that longitude is not measurable without time, which means that where you are & where you are going cannot be measured instantaneously. This is actually super useful.

Your body, in a way, is a distributed database, kinda like a blockchain. So it stands to reason if we can recover virtual databases on the internet and make them eventually consistent (which we are very good at doing), it makes sense that we could also recover bodies & brains by experimenting with different combinations of exercise, both physical & mental, and spacing them out over time in ways that support healing and regeneration.

I think this is a compelling idea because the amount of collective trauma is very high right now, and can be expected to grow more. The evidence of these traumas is apparent in the many physical, mental, and societal wounds that have become inflamed in recent memory, and are likely to become more so given the lack of safety on our networks & supply chains.

We have, though, if we choose to use it, an incredibly large reserve of national trauma from which we might be able to draw energy to create a better future.

But if we are to do that, I think we must revisit notion of “time” and how we relate to it, and how others relations differ from our own (perhaps there is a mathematics of empathy somewhere that we might recover).


I’ll leave it here for now, but I would suggest that our tendency to think about “NOW NOW NOW WE’RE ALMOST THERE OMG IF WE CAN JUST DO THIS ONE MORE THING” is probably not the healthiest of all rhythms for our societies & economies to follow, or the most stable. I doubt it’s much good for anybody’s physical or mental health either.

Give it some thought, and hit me up if you have any thoughts. More in a bit.

Photo by Lee Pigott on Unsplash

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