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The Inevitability Of Structure- Nancy Hillis MD & Bruce Sawhill PhD

The Inevitability Of Structure- Nancy Hillis MD & Bruce Sawhill PhD


Randomness and order is in the eye of the beholder.

Last time we talked about entropy, a measure of disorder in a system. But “disorder” is a slippery concept.

Imagine we roll a dozen dice at once.

After we get the one that went under the sofa, we look at the result. Usually it would be “something like” this:  132463422154. We would not expect this: 666666666666.

We think of the first result as “random” and the second one as “not random.”

The first number feels less unique because it feels like one of a class of possible outcomes that mixes all of the possible dice roll outcomes with no detectable pattern. 

But “random” and “not random” is a blunt instrument of classification. It reminds me of the quote by Ulysses S. Grant, Union leader in the American Civil War, who was not a music connoisseur:


I know only two tunes: one of them is ‘Yankee Doodle’, and the other isn’t.

Ulysses S. Grant




Our old friend combinatorics tells us that there are millions of ways to get a number “like” the first one, but only one way to get one like the second, so the second one is more “ordered” by virtue of its uniqueness, though both numbers are generated by the same process of rolling twelve dice!

There are asterisks under the concept of randomness.  If we start considering the process by which “random” results are created, the plot thickens.

Insights come from both math and physics but have implications for art.

We all remember the constant Pi from math classes from long ago, the ratio of the circumference of a circle to its diameter, an endless number. 

The first few hundred digits are:


3.141592653589793238462643383279502884197169399375105820974944592307816406286 208998628034825342117067982148086513282306647093844609550582231725359408128481 117450284102701938521105559644622948954930381964428810975665933446128475648233 786783165271201909145648566923460348610454326648213393607260249141273724587006


The last ten digits of those are 3724587006. 

If you weren’t told they came from a “deterministic”  (you get the same result every time) calculation you might think they look random. But a great deal of computation went into getting them!


Context Matters


Knowing something about the process affects our interpretation of the outcome.

So context matters.

Those random looking numbers in the calculation of Pi aren’t random at all, but they satisfy most statistical measures of randomness!

Last week we brought up Ludwig Boltzmann and his application of statistics to the motion of very large numbers of particles, such as the behavior of gases made of huge numbers of identical atoms or molecules.

Ludwig used the idea of likeliness to claim that some behaviors were likely whereas others were so unlikely that we could safely ignore them. 

This tells us, among other things, why heat flows towards cold, but not the other way around. In a word, it’s (way) more likely.


The Nature Of Time


And, ultimately, statistics is implicated in the nature of time itself.

Even though the laws of physics are the same forwards as backwards on a microscopic scale, if you get lots of particles together an extremely likely direction emerges, the so called “Arrow of Time.”

The whole is different than the sum of the parts.

Including laws of physics into our consideration of likeliness and randomness can have surprising results, even artistic ones!


Randomness & Structure


Imagine a vast expanse of interstellar space, far from any stars or other large celestial bodies. In this space, imagine a cloud of gas, very diffuse, occupying an enormous volume. We would call this “disordered,” meaning that there is no information telling you where you are in the cloud, it’s the same everywhere.

It turns out that such a random looking starting point can end up looking very structured after a (usually very long) time. The only thing that is extremely improbable is for it to stay like it started!


A Thought Experiment


Consider the following thought experiment:  Place three objects of equal mass in a line, separated by two identical intervals, standing completely still, floating in space. At first blush, this seems like one of the most boring experiments in the Universe.

But this simple system is unstable! 

Because, according to Newton, gravitational attraction gets stronger the closer two objects get, any tiny motion of any of the three masses will cause at least two of the objects to clump together at some future time with the third one being left out, at least for a while.

If we consider scads (that’s a technical term) of particles, clumping begets clumping because clumps have more gravitational attraction than individual masses, and eventually remarkable and beautiful things happen: The cloud of diffuse gas coalesces like nebulae, planets, and stars. 



Lagoon Nebula


Jeans Instability


This phenomenon was first identified by Sir James Jeans in 1902, and is known as the “Jeans Instability,” a name any psychiatrist would be proud of and that has nothing to do with pants.

The rich structure of the observed Universe, which can appear highly unlikely, is actually almost inevitable.

The explanation above is highly simplified, as it does not include other considerations like temperature, the expansion of the Universe, electricity, or magnetism, but it delivers the gist of the idea.


Fractal Patterns: Structure & Variations


Perhaps a little closer to home, consider erosion patterns on a shallow beach with a receding tide. Beautiful fractal patterns of erosion appear and are washed away by the next high tide.

These patterns appear highly “structured,” many little rivulets joining and rejoining to form a main stream, but no two of them are exactly the same. There is variation within a framework of structure.



Fractal ephemeral beach erosion patterns, Humboldt County, California



The patterns are very likely in the sense that most water molecules draining a beach to the sea both create and pass through such a form.

Structure is inseparable from dynamics.


Jackson Pollock: Underlying Structure In Seeming Randomness


Jackson Pollock painted his drip paintings on a flat surface and applied paint in such a way (at a particular angle near the canvas and at a certain velocity- all of which he discovered by continually experimenting) as to take advantage of its viscosity (thickness) to create patterns.

The structure and the process of his paintings are intertwined and governed by the physical laws of fluid flow, and the result was seeming randomness with a strong statistical regularity underlying it. 



Jackson Pollock (1912-1956), Art Institute of Chicago





What other seemingly unlikely things are actually highly probable?

Life seems to be very non-random. It does not seem to obey the Second Law of Thermodynamics which says that disorder tends to a maximum.

Life seems to be amazingly ordered and “anti-entropic,” persisting with regularity and cohesion over time and space.



Marine ecosystem



Nobody has convincingly figured out how to get creatures out of lots of different atoms and molecules in some primordial soup, though hypotheses abound. I’m perfectly happy to add to the growing pile, for as the science fiction writer Arthur C. Clarke said, 


Give me an ounce of fact at breakfast and I’ll have you a ton of theory by teatime.

-Arthur C. Clarke


Our intuition says that life is remarkably unlikely, perhaps supernaturally so. We might be all there is, in the entire Universe!

But what if life is as inevitable as the fractal patterns on beaches or the creation of solar systems?

Perhaps it is everywhere, but no two versions of it are remotely similar, perhaps so dissimilar we wouldn’t see it if it were right in front of us or even part of us.


Not only is the world stranger than we imagine, it is stranger than we can imagine. 

-J.B.S. Haldane


Next week we will dig into the concept of context as it relates to structure.

Note: In the Masterclass this week, we’re studying the concept of shape and shape relationships. One of the interesting phenomena is that when shapes overlap, new shapes and forms emerge in the process. 


With gratitude from our studio to yours,

Nancy & Bruce

Click on arrow to see Book Trailer for our newest book: The Adjacent Possible: Guidebook & Stories Of Artistic Transformation

P.S. NOW is the perfect time to create.

This is the existential moment- this is the time where we see what our life is about. We notice what is meaningful and alive for us.

You might be thinking…I’m just too blocked, too down, too scared or frozen….or even just shy….

You may be feeling that you can’t create now….

But I say to you that you’re a creator…you’re an artist and artists create.

And there are many ways to create and be creative….

Pair your explorations in your art studio with our Art of the Possible Book Series!




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The Inevitability Of Structure- Nancy Hillis MD & Bruce Sawhill PhD

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