Scaling Familiarity With Self-Similarity

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Where we learn that those flocking birds of a feather may need to check themselves every now and then.

I love hearing new ideas. I love those moments when I’m in a group environment and someone says something that makes me – and you, and everyone else in the room – just P A U S E and replay the words in my head over and over. Much more often than not, that New Idea Person hasn’t been around that group for very long. And when that new idea is examined further and if it’s proven to be viable, well hell, that new idea energy can be totally invigorating. Maybe even feel a bit savior-like.

Now, once you get to the other side of this essay, I don’t want you to think that there’s only negativity when it comes to the presence of self-similarity IRL. There’s absolutely positive examples of it out there; I just had a really hard time coming up with any right now 🤷‍♀️. I seem to only be able to recall situations where I’ve wanted that dang group of birds to not flock – at least not blindly.

Perhaps because the hyphenated word self-similarity is the combo of two basic vocabulary words, you’d assume it’s like saying that this one thing over here is kinda-sorta a copy of this other thing over there. You might even think that one begat the other.

Self-similarity is an attribute often used in mathematics, usually as a visual descriptor in reference to something geometric like a fractal or an object in nature like the leaves of a fern. But when this self-similarity property is referenced in math, it’s not about comparing two static images. It’s actually focusing on the carbon-copy action that got it from point a (self) to point b (self-similar). It’s about the specifics of that action of repetitive behavior as it scaled up or scaled down, known as the scaling invariance. (You remember invariance, right?)

Though there seems to be a bazillion ways to define self-similarity, our fractal buddy Benoit Mandelbrot explained it a couple of ways:

Now, let’s all take one more step back to get an even broader scope of the action of self-similarity:

Self-similarity is symmetry across scale…it is a matter of looking at the whole… [It] is built into the technique of constructing the curves –the same transformation is repeated at smaller and smaller scales.

“Chaos: Making A New Science” by James Gleick
(pg. 103)

No surprise that I’m drawn to that word transformation, and its reiteration here that the similar repeating behavior is all about the movement itself in what the scaling up or down looks like. Self-similar properties are represented mathematically by simple power laws which dictate that as it grows or shrinks there’s an equal ratio of change at all points. Everything changes in proportion and, IRL, it becomes a remarkably systematic repetitive behavior.

But, here’s the rub for me.

At what point does the carbon-copy action start to have some fall-off, some detritus that’s flaking and causing increased instability the farther away we get from the original of this carbon-copy chainmail?What’s now happening may seem to be a self-similar action – but in actuality it has broken down because the conditions it’s existing in have changed.

Even more challenging and of perhaps greater urgency is the need to understand how to scale organizational structures of increasingly large and complex social organizations such as companies, corporations, cities, and governments, where the underlying principles are typically not well understood because these are continuously evolving complex adaptive systems.

“Scale: The Universal Laws of Life and Death in Organisms, Cities and Companies”
by Geoffrey West
(pg. 16)

In my experience of having become a member of groups where I am not let’s-call-it a founding member, I realized that we could/should apply the property of self-similarity to the human biases that have developed within.

I am looking at self-similarity as an analysis tool
for examining our own biases of groups of people.

The self-similarity principle states that, when you make network contacts, you tend to choose people who resemble you in terms of experience, training, worldview, and so on. We have found that executives, in particular, disproportionately use the self-similarity principle to build their networks. This initial comfort, though, offers diminishing returns – and can even become negative.

Harvard Business Review – “How To Build Your Network”
by Brian Uzzi and Shannon Dunlap

If you know anything about the basis for relationships and then, on a broader scope, the basis for larger groups (be it clubs, congregations, or fan bases), they can also emit a level of exclusivity when all the participants really start to mirror each other in not just the way they self-identify but also in the way that they think…leading to group think. The proverbial echo chamber.

One of the group hangovers of the self-similarity principle
are halo effects (in biases).

If you wanna talk about never even getting the chance to get up to bat, then let’s talk about that extra invisible bias, ye ol halo effect. This term was coined by the psychologist Edward Thorndike, and it “occurs when an initial positive impression of a person impacts how favorably the person is subsequently perceived.” It’s striking how deeply rooted this is in self-similar groups, where an opinion made by one person years or even decades ago, and all subsequent interaction with that individual – or the role or title associated with that individual – by other members in that group is not just preceded by that first person’s impression, but is expected to be subsumed by all subsequent members.

(Social network analysis is) a powerful way of exploring the structures of power that are inscribed within organisations by our habits of association. Just as people wear paths across lawns when they take short cuts between buildings, so they weave unseen connections across the formal organisation structure as they befriend each other, form allegiances or simply gravitate towards each other.

“The Value of Difference: Eliminating bias in organisations” by Binna Kandola
(pg. 91)

Mmmm. What to do, what to do.

Is…is that all it takes? Sure, the word effort is used, but it isn’t like you need superhuman strength effort or Mensa level intelligence effort. You just need to be conscious of those times where you may be in auto-mode when you’re participating with a long-staid group of people. Basically, check yourself.

The most important thing of it all. Be conscious to it.

Human cognitive biases aren’t generally a bad thing. Most of them developed because they are, or at least have been, of advantage to us. We are, for example, more likely to put forward opinions that we believe will be well received by others. This “social desirability bias” is a side effect of our need to fit into a group for survival. You don’t tell the tribal chief the tent stinks if behind you stand a dozen fellows with spears. How smart of you.

“Lost in Math” by Sabine Hossenfelder
(pg. 229)

So, yeah, birds of a feather flocking together. Sometimes it’s good, sometimes it’s bad, blah blah blah – I know I know you can say this about most things. My point is – please be conscious of what that bird in front of you is doing and know where they intend to fly to, and why. And even more importantly, every once in awhile, get your eyes on the bird that they are following, and their why and their intended destination. And occasionally, how about taking a hard left and seeing what happens? See what other birds you might meet and give a listen to their potential mind-blowing new bird ideas.

Allright. That’s quite enough of mashing-up a proverb with an analogy.

You know, Mandelbrot liked to quote the writer Jonathan Swift when he talked about self-similarity.

So, naturalists observe, a flea
Hath smaller fleas that on him prey;
And these have smaller still to bite ‘em
And so proceed ad infinitum.

Thanks math, you’re the best.