Determined, page 16
Informative Scouts Followed by Random Encounters
Many examples of emergence involve a motif that requires two simple phases. In the first, “scouts” in a population explore an environment; when they find some resource, they broadcast the news.[*] The broadcast must include information about the quality of the resource, such as better resources producing louder or longer signals. In the second phase, other individuals wander randomly in their environment with a simple rule regarding their response to the broadcast.
Back to honey bees as an example. Two bee scouts check out the neighborhood for possible food sources. They each find one, come back to the hive to report; they broadcast their news by way of the famed bee waggle dance, where the features of the dance communicate the direction and distance of the food. Crucially, the better the food source a scout found, the longer it carries out one part of the dance—this is how quality is being broadcast.[*] As the second phase, other bees wander about randomly in the hive, and if they bump into a dancing scout, they fly away to check out the food source the scout is broadcasting about . . . and then return to dance the news as well. And because a better potential site = longer dancing, it’s more likely that one of those random bees bumps into the great-news bee than the good-news one. Which increases the odds that soon there will be two great-news dancers, then four, then eight . . . until the entire colony converges on going to the optimal site. And the original good-news scout will have long since stopped dancing, bumped into a great-news dancer, and been recruited to the optimal solution. Note—there is no decision-making bee that gets information about both sites, compares the two options, picks the better one, and leads everyone to it. Instead, longer dancing recruits bees that will dance longer, and the comparison and optimal choice emerge implicitly; this is the essence of swarm intelligence.[10]
Similarly, suppose the two scout bees discover two potential sites that are equally good, but one is half as far from the hive as the other one. It will take the local-news bee half the time to get to and back from its food source that it takes the distant-news bee—meaning that the two, four, eight doubling starts sooner, exponentially swamping the signal of distant-news bee. Everyone soon heads to the closer source. Ants find the optimal site for a new colony this way. Scouts go out, and each finds a possible site; the better the site, the longer they stay there. Then the random wanderers spread out with the rule that if you bump into an ant standing at a possible site, maybe check the site out. Once again, better quality translates into a stronger recruitment signal, which becomes self-reinforcing. Work by my pioneering colleague Deborah Gordon shows an additional layer of adaptiveness. A system like this has various parameters—how far do ants wander, how much longer do you stay at a good site versus a mediocre one, and so on. She shows that these parameters vary in different ecosystems as a function of how abundant food sources are, how patchily they are distributed, and how costly foraging is (for example, foraging is more expensive, in terms of water loss, for desert ants than for forest ants); the better a colony has evolved to get these parameters just right for its particular environment, the more likely it is to survive and leave descendants.[*],[*],[11]
The two steps of scout broadcasters followed by recruitment of random wanderers explains virtual ant traveling-salesman optimization. Place a bunch of ants at each of the virtual foraging sites; each ant then picks a route at random that involves visiting each site once, and leaves a pheromone trail in the process.[*] How does better quality translate into a stronger broadcast? The shorter the route, the thicker the pheromone trail that is laid down by a scout; pheromones evaporate, and thus shorter, thicker pheromone trails last longer. A second generation of ants shows up; they wander randomly, with the rule that if they encounter a pheromone trail, they join it, adding their own pheromones. As a result, the thicker and therefore longer-lasting the trail, the more likely another ant is to join it and amplify its recruiting message. And soon the less efficient routes for connecting the sites evaporate away, leaving the optimized solution. No need to gather data about the length of every possible route and have a centralized authority compare them and then direct everyone to the best solution. Instead, something that comes close to the optimal solution emerges on its own.[*]
(Something worth pointing out: As we’ll see, these rich-get-richer recruitment algorithms explain optimized behavior in us as well, along with other species. But “optimal” is not meant in the value-laden sense of “good.” Just consider rich-get-richer scenarios where, thanks to the recruitment signaling of economic inequality, it’s literally the rich who get richer.)
Next we turn to how emergence helps slime molds solve problems.
Slime molds are these slimy, moldy, fungal, amoeboid, single-cell protists, just to make a bunch of taxonomic errors, that grow and spread like a carpet over surfaces, looking for microorganisms to eat.
In a slime mold, zillions of single-cell amoebas have joined forces by merging into a giant, cooperative single cell that oozes over surfaces in search of food, apparently an efficient food-hunting strategy[*] (and as a hint of the emergence pending, a single, independent slime mold cell can no more ooze than a molecule of water can be wet). What used to be the individual cells are interconnected by tubules that can stretch or contract, depending on the direction of oozing (see figure on the next page).
Out of these collectivities emerge problem-solving capabilities. Spritz a dollop of slime mold into a little plastic well that leads to two corridors, one with an oat flake at the end, the other with two oat flakes (beloved by slime molds). Rather than sending out scouts, the entire slime mold expands to fill both corridors, reaching both food sources. And within a few hours, the slime mold retracts from the one–oat flake corridor and accumulates around the two oats. Have two pathways of differing lengths leading to the same food source; the slime mold initially fills both paths but eventually takes only the shortest route. Same with a maze with multiple routes and dead ends.[*],[12]
Initially, the slime mold fills every path (panel a); it then begins retracting from superfluous paths (panel b), until eventually reaching the optimal solution (panel c). (Ignore the various markings.)
As the tour de force of slime mold intelligence, Atsushi Tero at Hokkaido University plopped a slime mold down into a strangely shaped walled-off area with oat flakes at very specific locations. Initially, the mold expanded, forming tubules connecting all the food sources to each other in multiple ways. Eventually, most tubules retracted, leaving something close to the shortest total path length of tubules connecting food sources. The Traveling Slime Mold. Here’s the thing that makes the audience shout for more—the wall outlines the coastline around Tokyo; the slime was plopped onto where Tokyo would be, and the oat flakes corresponded to the suburban train stations situated around Tokyo. And out of the slime mold emerged a pattern of tubule linkages that was statistically similar to the actual train lines linking those stations. A slime mold without a neuron to its name, versus teams of urban planners.[13]
How do slime molds pull this off? A lot like ants and bees. Take the two corridors leading to either one or two oat flakes. The slime mold initially oozes into both corridors, and when food is found, tubules contract in the direction of the food, pulling the rest of the slime mold toward it. Crucially, the better the food source, the greater the contractile force generated on the tubules. Then the tubules a bit farther away dissipate the force by contracting in the same orientation, increasing the force of contraction, spreading outward until the whole slime mold has been pulled into the optimal pathway. No part of the slime mold compares the two options and makes a decision. Instead, the slime mold extensions into the two corridors act as scouts, with the better route broadcast in a way that causes rich-get-richer recruiting via mechanical forces.[14]
Now let’s consider a growing neuron. It extends a projection that has branched into two scout arms (“growth cones”) heading toward two neurons. Simplifying brain development to a single mechanism, each target neuron is attracting the growth cone by secreting a gradient of “attractant” molecules. One target is “better,” thus secreting more of the attractant, resulting in a growth cone reaching it first—which causes a tubule inside that growing neuron’s projection to bend in that direction, to be attracted to that direction. Which makes the parallel tubule adjacent to it more likely to do the same. Which increases the mechanical forces recruiting more and more of these tubules. The other scout arm is retracted, and our growing neuron has connected up with the better target.[*],[15]
Let’s look at our ant / bee / slime mold motif as applied to the developing brain forming the cortex, the fanciest, most recently evolved part of the brain.
The cortex is a six-layer-thick blanket over the surface of the brain, and cut into cross section, each layer consists of different types of neurons (see figure on the next page).
The multilayered architecture has lots to do with cortical function. In the picture, think of that slab of cortex as being divided into six vertical columns (best seen as the six dense clusters of neurons at the level of the arrow). The neurons within any of these mini columns send lots of vertical projections (i.e., axons) to each other, collectively working as a unit; for example, in the visual cortex, one mini column might decode the meaning of light falling on one spot of the retina, with the mini column next to it decoding light on an adjacent spot.[*]
It’s ants redux in building a cortex. The first step in cortical development is when a layer of cells at the bottom of each cross section of cortex sends long, straight projections to the surface, serving as vertical scaffolding. These are our ant scouts, called radial glia (ignore the letters in the diagram on the next page). There is initially an excess of them, and the ones that have blazed the less optimal, less direct paths are eliminated (through a controlled type of cell death). As such, we have our first generation of explorers, with the ones with the more optimal solution to cortex building persisting longer.[16]
Radial glia radiating outward from the center of a cross section
You know what’s coming next. Newly born neurons wander randomly at the base of the cortex until they bump into a radial glia. They then migrate upward along the glial guide rail, leaving behind chemoattractant signals that recruit more newbies to join the soon-to-be mini column.[*],[17]
Scouts, quality-dependent broadcasting, and rich-get-richer recruiting, from insects and slime molds to your brain. All without a master plan, or constituent parts knowing anything beyond their immediate neighborhood, or any component comparing options and choosing the best one. With remarkable prescience about these ideas in 1874, the biologist Thomas Huxley wrote about the mechanistic nature of organisms, such that they “only simulate intelligence as a bee simulates a mathematician.”[18]
Time for another motif in emergent systems.
Fitting Infinitely Large Things into Infinitely Small Spaces
Consider the figure below. The top row consists of a single straight line. Remove its middle third, producing the two lines that constitute the second row; the length of those two together is two thirds the length of the original line. Remove the middle third from each of those, producing four lines that, collectively, are four ninths the total length of the original line. Do this forever, and you generate something that seems impossible—an infinitely large number of specks that have an infinitely short cumulative length.
Let’s do the same thing in two dimensions (below). Take an equilateral triangle (#1). Generate another equilateral triangle on each face, using the middle third as the base for the new triangle, resulting in a six-pointed star (#2). Do the same to each of those points, producing an eighteen-pointed star (#3), then a fifty-four-pointed star (#4), over and over. Do this forever and you’ll generate a two-dimensional version of the same impossibility, namely a shape whose increase in area from one iteration to the next is infinitely small, while its perimeter is infinitely long:
Now three dimensions. Take a cube. Each of its faces can be thought of as being a three-by-three grid of nine boxes. Take out the middle-most of those nine boxes, leaving eight:
Now think of each of those remaining eight as a three-by-three grid, and take out the middle-most box. Repeat that process forever, on all six faces of the cube. And the impossibility achieved when you reach infinity is a cube with infinitely small volume but infinitely large surface area (see figure on the next page).
These are, respectively, called a Cantor set, a Koch snowflake, and a Menger sponge. These are mainstays of fractal geometry, where you iterate the same operation over and over, eventually producing something impossible in traditional geometry.[19]
Which helps explain something about your circulatory system. Each cell in your body is at most only a few cells away from a capillary, and the circulatory system accomplishes this by growing around forty-eight thousand miles of capillaries in an adult. Yet that ridiculously large number of miles takes up only about 3 percent of the volume of your body. From the perspective of real bodies in the real world, this begins to approach the circulatory system being everywhere, infinitely present, while taking up an infinitely small amount of space.[20]
Branching patterns in capillary beds
A neuron has a similar challenge, in that it wants to send out a tangle of dendritic branches that can accommodate inputs at ten thousand to fifty thousand synapses, all with the dendritic “tree” taking up as little space as possible and costing as little as possible to construct:
A classic textbook drawing of an actual neuron
And of course, there are trees, forming real branches to generate the maximal amount of surface area for foliage to absorb sunlight, while minimizing the costs of growing it all.
The similarities and underlying mechanisms would be obvious to Cantor, Koch, or Menger,[*] namely iterative bifurcation—something grows a distance and splits in two; those two branches grow some distance and each splits in two; those four branches . . . over and over, going from the aorta down to forty-eight thousand miles of capillaries, from the first dendritic branch in a neuron to two hundred thousand dendritic spines, from a tree trunk to something like fifty thousand leafy branch tips.
How are bifurcating structures like these generated in biological systems, on scales ranging from a single cell to a massive tree? Well, I’ll tell you one way it doesn’t happen, which is to have specific instructions for each bifurcation. In order to generate a bifurcating tree with 16 branch tips, you have to generate 15 separate branching events. For 64 tips, 63 branchings. For 10,000 dendritic spines in a neuron, 9,999 branchings. You can’t have one gene dedicated to overseeing each of those branching events, because you’ll run out of genes (we only have about twenty thousand). Moreover, as pointed out by Hiesinger, building a structure this way requires a blueprint as complicated as the structure itself, raising the turtles question: How is the blueprint generated, and how is the blueprint that generated that blueprint generated . . . ? And it’s these sorts of problems writ large and larger for the circulatory system and for actual trees.
Instead, you need instructions that work the same way at every scale of magnification. Scale-free instructions like this:
Step #1. Start with a tube of diameter Z (a tube because geometrically, a blood vessel branch, a dendritic branch, and a tree branch can all be thought of that way).
Step #2. Extend that tube until it is, to pull a number out of a hat, four times longer than its diameter (i.e., 4Z).
Step #3. At that point, the tube bifurcates, splits in two. Repeat.
This produces two tubes, each with a diameter of 1/2Z. And when those two tubes are four times longer than that diameter (i.e., 2Z), they split in two, producing four branches, each 1/4Z diameter, which will split in two when each is 1Z (see figure on the following page).
While a mature tree sure seems immensely complex, the idealized coding for it can be compressed into three instructions requiring only a handful of genes to pull this off, rather than half your genome.[*] You can even have the effects of those genes interact with the environment. Say you’re a fetus inside someone living at high altitude, with low levels of oxygen in the air and thus in your fetal circulation. This triggers an epigenetic change (back to chapter 3) so that tubes in your circulation grow only 3.9 times the width, instead of 4.0, before splitting. This will produce a bushier spread of capillaries (I’m not sure if that would solve the high-altitude problem—I’m making this up).[*]
So you can do this with just a handful of genes that can even interact with the environment. But let’s turn this into the reality of real biological tubes and what genes actually do. How can your genes code for something abstract like “grow four times the diameter and then split, regardless of scale”?
Various models have been proposed; here’s a totally beautiful one. Let’s consider a fetal neuron that is about to generate a bifurcating tree of dendrites (although this could be any of the other bifurcating systems we’ve been covering). We start with a stretch of the neuron’s surface membrane that is destined to be where the tree starts growing (see figure below, left). Note that in this very artificial version, the membrane is made of two layers, and in between the layers is some Growth Stuff (hatched), coded for by a gene. The Growth Stuff triggers the area of the neuron just below to start constructing a trunk that will rise from there (right):[21]
How much Growth Stuff was there at the beginning? 4Zs’ worth, which will make the trunk grow 4Z in length before stopping. Why does it stop? Critically, the inner layer of the growing front of the neuron grows a little faster than the outer layer, such that right around a length of 4Z, the inner layer touches the outer layer, splitting the pool of Growth Stuff in half. No more Growth Stuff in the tip; things stop at 4Z. But crucially, there’s now 2Zs’ worth of Growth Stuff pooled on each side of the tip of the trunk (left). Which triggers the area underneath to start growing (right):
