Determined, page 17
Because these two branches are narrower, the inner layers touch the outer layers after a length of only 2Z (below left), which splits the Growth Stuff into four pools, each with 1Z’s worth. And so on (below right).[*],[22]
The key to this “diffusion-based geometry” model is the speed of growth of the two layers differing. Conceptually, the outer layer is about growing, the inner about stopping growing. Numerous other models produce bifurcations just as emergently, with similar themes.[*] Wonderfully, two genes, coding for molecules with growth and stopping-growth properties, respectively, have been identified that are central to bifurcation in the developing lung.[*],[23]
And the intensely cool thing is that these very different physiological systems—neurons, blood vessels, the pulmonary system, and lymph nodes—use some of the same genes, coding for the same proteins in the construction process (a menagerie of proteins such as VEGF, ephrins, netrins, and semaphorins). These are not genes used for, say, generating the circulatory system. These are genes for generating bifurcating systems, applicable to one single neuron and to vascular and pulmonary systems using billions of cells.[24]
Aficionados will recognize that these bifurcating systems all form fractals, where the relative degree of complexity is constant, no matter at what scale of magnification you are considering the system (with the recognition that unlike the fractals of mathematics, fractals in the body don’t bifurcate forever—physical reality asserts itself at some point). We’re now in very strange terrain, having to consider the molecules of the sort mentioned in the previous paragraph being coded for by “fractal genes.” Which means that there must be fractal mutations, disrupting normal branching in everything from single neurons to entire organ systems; there are some hints of these out there.[25]
These principles apply to nonbiological complexity as well—for example, why rivers emptying into the sea bifurcate into river deltas. And it even applies to cultures. Let’s consider one last emergent bifurcating tree, one that shows either the deeply abstract ubiquity of the phenomenon or how I’m running too far with a metaphor.
Look at the intensely bifurcated diagram below; don’t worry about what the branch tips are—just note the branchings all over the place.
What is this tree? The perimeter represents the present. Each ring represents one hundred years back into the past, reaching the year 0 AD at the center, with a trunk going back millennia from there. And the branching pattern? The history of the emergence of earth’s religions—a mass of bifurcations, trifurcations, dead-end side branches, and so on. A partial magnification:[26]
One tiny piece of the history of religious branching
What constitutes the diameter of each “tube” in this emergent history of religions? Maybe measures of the intensity of religious belief—the number of adherents, their cultural homogeneity, their collective wealth or power. The wider the diameter, the longer the tube is likely to persist before destabilizing, but in a scale-free way.[*] Would this be adaptive, in the same sense as analyzing, say, bifurcating blood vessels? I think that right around now, I should recognize that I’m on thin speculative ice and call it a day.
What has this section provided us? The same themes as in the prior section about pathfinding ants, slime molds, and neurons—simple rules about how components of a system interact locally, repeated a huge number of times with huge numbers of those components, and out emerges optimized complexity. All without centralized authorities comparing the options and making freely chosen decisions.[*]
Let’s Design a Town
You’re on the planning board for a new town, and after endless meetings, you’ve collectively decided where it will be built, how big it will be. You’ve laid out a grid of the streets, decided on locations for the schools, hospitals, and bowling alleys. Time now to figure out where the stores will go.
The Stores Committee first proposes that stores be randomly scattered throughout town. Uh, that’s not ideal; people want stores conveniently clustered. Right, says the committee, and then proposes that all the stores be in a single cluster in the middle of town.
Uh, not quite right either. With this single cluster, there won’t be convenient parking, and the stores in the center of this megamall will be so inaccessible that they’ll go out of business—they’ll die from some commercial equivalent of insufficient oxygen.
Next plan—have six malls of the same size, set equal distances from each other. That’s good, but someone notices that all dozen coffee shops are in the same mall; these shops will drive each other out of business, while five malls will have no coffee shops.
Back to planning, paying attention now not just to “store-ness” but to the type of store. In each mall, one pharmacy, one market, two coffee shops. Consider interactions between different types of stores. Separate the candy shop and the dentist. The optometrist goes next to the bookstore. Get the correct ratio of places for sinning—a gelato shop, a bar—to those for repenting—a fitness center, a church. And whatever you do, don’t put the store selling “God Bless America” sweatshirts next to the store selling “God-Less America” ones.
Once that is implemented, there’s one last step, which is building major thoroughfares that connect the malls to each other.
At last, the commercial districts in your town are planned, after all these urban planning meetings filled with individuals with differing expertise, careerism, personal agendas, cooperation taking a hit because one person resents another for taking the last doughnut.
Take a beaker full of neurons. They’re newly born, so no axons or dendrites yet, just rounded-up little cells destined for glory. Pour the contents into a petri dish filled with a soup of nutrients that keep neurons happy. The cells are now randomly scattered everywhere. Go away for a few days, come back, look at those neurons under a microscope, and this is what you see:
A bunch of neurons in a mall, er, I mean clumped together; to the far right is the start of another cluster of cell bodies, with major thoroughfares of projections linking the two, as well as to distant clusters outside the picture.
No committee, no planning, no experts, no choices freely taken. Just the same pattern as for the planned town, emerging from some simple rules:
—Each neuron that has been thrown randomly into the soup secretes a chemoattractant signal; they’re all trying to get the others to migrate to them. Two neurons happen to be closer than average to each other by chance, and they wind up being the first pair to be clumped together in their neighborhood. This doubles the power of the attractant signal emanating from there, making it more likely that they’ll attract a third neuron, then a fourth . . . Thus, through a rich-get-richer scenario, this forms a nidus, the starting point of a local cluster growing outward. Growing aggregates like these are scattered throughout the neighborhood.
—Each clump of neurons reaches a certain size, at which point the chemoattractant stops working. How would that work? Here’s one mechanism—as a ball of clumping neurons gets bigger, the ones in the center are getting less oxygen, triggering them to start secreting a molecule that inactivates chemoattractant molecules.
—All along, neurons have been secreting a second type of attractant signal in minuscule amounts. It’s only when enough neurons have migrated into an optimally sized cluster that there is collectively enough of the stuff to prompt the neurons in the cluster to start forming dendrites, axons, and synapses with each other.
—Once this local network is wired up (detectable by, say, a certain density of synapses), a chemorepellent is secreted, which now causes neurons to stop making connections to their neighbors, and to instead start sending long projections to other clusters, following a chemoattractant gradient to get there, forming the thoroughfares between clusters.[*]
This is a motif of how complex, adaptive systems, like neuronal shopping malls, can emerge thanks to control over space and time of attractant and repellent signals. This is the fundamental yin/yang polarity of chemistry and biology—magnets attracting or repelling each other, positively charged or negatively charged ions, amino acids attracted to or repelled by water.[*] Long strings of amino acids form proteins, each with a distinctive shape (and therefore function) that represents the most stable formation for balancing the various attraction and repulsion forces.[*]
As just shown, constructing neuronal shopping malls in the developing brain entailed two different types of attractant signals and one repellent one. And things get fancier: Have a variety of attractant and repellent signals that work individually or in combinations. Have emergent rules for which part of a neuron a growing neuron forms a connection with. Have growth cones with receptors that respond to only a subset of attractant or repellent signals. Have an attractant signal pulling a growth cone toward it; however, when it gets close, the attractant starts working as a repellent; as a result, the growth cone swoops past—it’s how neurons make long-distance projections, doing flybys of one signpost after another.[27]
Most neurobiologists spend their time figuring out minutiae like, say, the structure of a particular receptor for a particular attractant signal. And then there are those marching superbly to their own drummer, like Robin Hiesinger, quoted earlier, who studies how brains develop with simple, emergent informational rules like we’ve been looking at. Hiesinger, whose review papers have puckish section titles like “The Simple Rules That Can,” has shown things like the three simple rules needed for neurons in the eye of a fly to wire up correctly. Simple rules about the duality of attraction and repulsion, and no blueprints.[*] Time now for one last style of emergent patterning.[28]
Talk Locally, but Don’t Forget to Also Talk Globally Now and Then
Suppose you live in a thoroughly odd community. There is a total of 101 people in it, each in their own house. The houses are arranged in a straight line, say, along a river. You live in the first house of this 101-house-long line; how often do you interact with each of your 100 neighbors?
There are all sorts of potential ways. Maybe you talk only to your next-door neighbor (figure A). Maybe, as a contrarian, you interact only with the neighbor the farthest from you (figure B). Maybe the same amount with each person (figure C), maybe randomly (figure D). Maybe you interact the most with your immediate neighbor, X percent less with the neighbor after that, and X percent of that less with the neighbor after that, decreasing at a constant rate (figure E).
Then there’s a particularly interesting distribution where around 80 percent of your interactions occur with the twenty closest neighbors and the remainder spread out across everyone else, with interactions a little less likely with each step farther out (figure F).
This is the 80:20 rule—approximately 80 percent of interactions occur among approximately 20 percent of the population. In the commercial world, it’s sardonically stated as 80 percent of complaints come from 20 percent of the customers. Eighty percent of crime is caused by 20 percent of the criminals. Eighty percent of the company’s work is due to the efforts of 20 percent of the employees. In the early days of the pandemic, a large majority of COVID-19 infections were caused by the small subset of infected super-spreaders.[29]
The 80:20 descriptor captures the spirit of what is known as a Pareto distribution, of a type mathematicians call a “power law.” While it is formally defined by features of the curve, it’s easiest to understand in plain English: a power-law distribution is when the substantial majority of interactions are very local, with a steep drop-off after that, and as you go out further, interactions become rarer.
All sorts of weird things turn out to have power-law distributions, as demonstrated by work pioneered by network scientist Albert-László Barabási of Northeastern University. Of the hundred most common Anglo-Saxon last names in the U.S., roughly 80 percent of people with those names possess the twenty most common. Twenty percent of people’s texting relationships account for about 80 percent of the texting. Twenty percent of websites account for 80 percent of searches. About 80 percent of earthquakes are of the lowest 20 percent of magnitude. Of fifty-four thousand violent attacks throughout eight different insurgent wars, 80 percent of the fatalities arose from 20 percent of the attacks. Another study analyzed the lives of 150,000 notable intellectuals over the last two millennia, determining how far each individual died from their birthplace—80 percent of the individuals fell within 20 percent of the maximal distance.[*] Twenty percent of words in a language account for 80 percent of the usage. Eighty percent of craters on the Moon are in the smallest twentieth percentile of size. Actors get a Bacon number, where if you were in a movie with the prolific Kevin Bacon (1,600 people), your Bacon number is 1; if you were in a movie with someone who was in a movie with him, yours is 2; in a movie with someone who was in a movie with someone who was in a movie with Bacon, 3 (the most common Bacon number, held by ~350,000 actors), and so on. And starting with that modal number and increasing the Bacon number from there, there is a power-law distribution to the smaller and smaller number of actors.[*],[30]
I’d be hard-pressed to see something adaptive about power-law distributions in Bacon numbers or the size of lunar craters. However, power-law distributions in the biological world display can be highly adaptive.[*],[31]
For example, when there’s lots of food in an ecosystem, various species forage randomly, but when food is spare, roughly 80 percent of foraging forays (i.e., moving in one direction looking for food, before trying a different direction) are within 20 percent of the maximal distance ever searched—this turns out to optimize the energy spent searching relative to the likelihood of finding food; cells of the immune system show the same when searching for a rare pathogen. Dolphins show an 80:20 distribution of within-family and between-family social interactions; the 80-ness means that family groups remain stable even after an individual dies, while the 20-ness allows for the flow of foraging information between families. Most proteins in our bodies are specialists, interacting with only a handful of other types of proteins, forming small, functional units. Meanwhile, a small percentage are generalists, interacting with scores of other proteins (generalists are switch points between protein networks—for example, if one source of energy is rare, a generalist protein switches to using a different energy source).[*],[32]
Then there are adaptive power-law relationships in the brain. What counts as adaptive or useful in how neuronal networks are wired? It depends on what kind of brain you want. Maybe one where every neuron synapses onto the maximal possible number of other neurons while minimizing the miles of axons needed. Maybe one that optimizes solving familiar, easy problems quickly or being creative in solving rare, difficult ones. Or maybe one that loses the minimal amount of function when the brain is damaged.
You can’t optimize more than one of those attributes. For example, if your brain cares only about solving familiar problems quickly, thanks to neurons being wired up in small, highly interconnected modules of similar neurons, you’re screwed the first time something unpredictable demands some creativity.
While you can’t optimize more than one attribute, you can optimize how differing demands are balanced, what trade-offs are made, to come up with the network that is ideal for the balance between predictability and novelty in a particular environment.[*] And this often turns out to have a power-law distribution where, say, the vast majority of neurons in cortical mini columns interact only with immediate neighbors, with an increasingly rare subset wandering out increasingly longer distances.[*] Writ large, this explains “brain-ness,” a place where the vast majority of neurons form a tight, local network—the “brain”—with a small percentage projecting all the way out to places like your toes.[33]
Thus, on scales ranging from single neurons to far-flung networks, brains have evolved patterns that balance local networks solving familiar problems with far-flung ones being creative, all the while keeping down the costs of construction and the space needed. And, as usual, without a central planning committee.[*],[34]
Emergence Deluxe
We’ve now seen a number of motifs that come into play in emergent systems—rich-get-richer phenomena where higher-quality solutions give off stronger recruiting signals, iterative bifurcation that inserts near-infinity into finite places, spatiotemporal control of attraction and repulsion rules, mathematical optimizing of the balance between different wiring needs—and there are many more.[*],[35]
Here are two last examples of emergence that incorporate a number of these motifs. One is startling in its implications; one is so charming that I can’t omit it.
Charm first. Consider a toenail that is a perfect Platonic rectangle X units in height (after ignoring the curvature of a nail) (diagram A). Savage the perfection with some scissors, cutting off a triangle of toenail (diagram B). If the toenail universe did not involve emergent complexity, the toenail would now regrow as in diagram C. Instead, you get diagram D.
How? The top of a toenail thickens from bearing the brunt of contacting the outside world (e.g., the inside of your sock; a boulder; that damn coffee table, why don’t we get rid of it, all we do is pile up junk on it), and once it thickens, it stops growing. After the cutting, only point a, at the original length (next diagram), retains the thickening. And as point b’s regrowth brings it to the same height as point a, it now bears the brunt of the outside worlds and thickens (its further growth is probably also constrained by the thickness of point a adjacent to it). The same process occurs when point c arrives. . . . There’s no comparative information involved; point c doesn’t have to choose between emulating point b or emulating point d. Instead, the optimal solution emerges from the nature of toenail regrowth.
