Determined, page 65
*Neurobiologist Robin Hiesinger, whose work will be covered later in the chapter, gives a wonderful example of this idea. You’re learning a piece on the piano, and you make a mistake and grind to a halt. Rather than being able to resume two measures earlier, akin to resuming on the highway, most of us need to let the complexity unfold again—we go back to the beginning of the section.
*The early-twentieth-century essayist Lu Xun captured the essence of this, writing, “The world has no road at the beginning; once enough people walked on it, the road appeared” (Liqun Luo, personal communication).
*For example, suppose you share a sequence of ten items, nine of which are roughly similar. There is one glaring exception, and your overall assessment of the properties of this sequence can change depending on whether randomness resulted in the exception being the second example you see or the tenth.
*Crossing my t’s and dotting my i’s: As I noted, the traveling salesman problem is formally unsolvable, in that it is not possible mathematically to prove or disprove that a particular solution is the most optimal. This is closely related to what are called “minimal spanning tree problems,” where mathematical proofs are possible. The latter are relevant to things like telecommunication companies figuring out how to connect a bunch of transmission towers in a way that minimizes the total distance of cable needed.
*The worm, called Caenorhabditis elegans, is beloved because every worm has exactly 302 neurons, wired up in the same way in every worm. It’s a dream for studying how neuronal circuits form.
*This is a very abstract, dimensionless sort of “environment,” so that the likes of an ant leaving its nest to forage, a neuron extending a cable toward another one to form a connection, and someone doing an online search can be reduced to their similarities.
*The information contained in the waggle dance was first fully decoded by Karl von Frisch early in the twentieth century; the work was seminal to the founding of the field of ethology and won von Frisch a Nobel Prize in Physiology or Medicine, to the utter bafflement of most scientists—what do dancing bees have to do with physiology or medicine? A lot, as one point of this chapter.
*Thus, colonies differ as to how evolutionarily “fit” they are at getting self-organized swarm intelligence just right. One paper exploring this has an all-time best title in a science journal: “Honeybee Colonies Achieve Fitness through Dancing.” Presumably, this paper pops up regularly in Google searches for Zumba classes.
*This approach isn’t perfect and can produce the wrong consensus decision. Ants living on a plain want a really good lookout from the top of a hill. There are two nearby hills, one twice the height of the other. Two scouts go out, each heads up their hill, and the one on the shorter hill gets there and starts broadcasting in half the time that it takes the loftier hill ant to start. Meaning it starts the recruitment doubling earlier than the other ant, and soon the colony has chosen . . . the shorter hill. In this case, the problem arises because the strength of the recruitment signal is inversely correlated with the quality of the resource. Sometimes a process can be completely out of whack. There are all sorts of cases of machine-learning algorithms that come up with a bizarre solution to a problem because the programmer underspecified the instructions, not informing it of all the things it was not allowed to do, what information it was not supposed to pay attention to, and so on. For example, one AI seemingly learned to diagnose melanomas but learned instead that lesions photographed with a ruler next to them are likely to be malignant. In another case, an algorithm was designed to evolve a simulated organism that was very fast; the AI simply grew an organism that was incredibly tall and thus reached high velocities when it would fling itself over. In another, the AI was supposed to design a Roomba that could move around without bumping into things—as assessed by its bumper being hit—and learned instead to simply stagger around leading with its back, where there was no bumper. For more examples, see: “Specification Gaming Examples in AI—Master List: Sheet1,” docs.google.com/spreadsheets.
*Pheromones are chemical signals released into the air—odorants—that carry information; in the case of ants, they have glands for this particular pheromone in their rears, which they dip down to the ground, leaving a trail of droplets of the stuff. So these virtual ants are leaving virtual pheromones. If there is a constant amount of pheromone in the gland at the beginning, the shorter the total walk, the thicker the amount of pheromone that gets laid down per unit of distance.
*This search algorithm was first proposed by the AI researcher Marco Dorigo in 1992, giving rise to “ant colony optimization” strategies, with virtual ants, in computer science. This is such a beautiful example of quantity producing quality; when I first grasped it, I felt dizzy with its elegance. And as a result, the quality of this approach is reflected in the loudness of my broadcasting about it—I drone on about this more frequently in lectures than about less cool subjects, making it more likely that my students will grasp it and tell their parents about it at Thanksgiving, increasing the odds that parents will tell neighbors, clergy, and elected representatives about it, leading to the optimized emergent behavior of everyone naming their next child Dorigo.
Note that, as stated, this is an ideal way to get close to the optimal solution. If you require the optimal solution, you’re going to need to brute-force it with a slow and expensive centralized comparator. Moreover, ants and bees obviously don’t follow these algorithms precisely, as individual differences and chance creep in.
*As a dichotomy, in cellular slime mold species, the collective forms only temporarily; in plasmodial slime molds, it’s permanent.
*Raising the question of when the optimized behavior of those ex–individual cells constitute “intelligence,” in the same way that the optimized function of vast numbers of neurons can constitute an intelligent person.
*To vastly simplify things, the two growth cones have receptors on their surfaces for the attractant molecule. As those receptors fill up with the attractant, a different type of attractant molecule is released within the growth-cone branch, forming a gradient down to the trunk that pulls the tubules toward that branch. More extracellular attractant broadcasting, by way of more receptors filled, and more of an intracellular broadcast signal recruiting tubules. As one complexity in real nervous systems, different target neurons might be secreting different attractant molecules, making it possible to be broadcasting qualitative as well as quantitative information. As another complexity, sometimes a growth cone has a specific address in mind for the neuron it wants to connect with. In contrast, sometimes there’s relative positional coding, where neuron A wants to connect with the target neuron that is adjacent to the target neuron that has connected up with the neuron next to neuron A. Implicit in all this is that the growth cones are secreting signals that repulse each other, so that the scouts scout different areas. I thank my departmental colleagues Liqun Luo and Robin Hiesinger, two pioneer scouts in this field, for generous and helpful discussions about this topic.
*As an aside, there are also horizontal connections within the same layer between different mini columns. This produces a thoroughly cool piece of circuitry. Consider a cortical mini column responding to light stimulating a small patch of retina. As just noted, the mini columns surrounding it respond to light stimulating patches on either side of that first patch. As a great circuitry trick, when a mini column is being stimulated, it uses its horizontal projections to silence the surrounding mini columns. Result? An image that is sharper around its edges, a phenomenon called lateral inhibition. This stuff is the best.
*As each new neuron arrives at the scene, it forms its synapses in sequence, one at a time, which is a way for a neuron to keep track of whether it has made the desired number of synapses. Inevitably, among the various growth cones spreading outward, looking for dendritic targets to start forming a synapse, one growth cone will have more of a “seeding” growth factor than the others, just by chance. Lots of the seeding factor causes the growth cone to recruit even more of the seeding factor and to suppress the process in neighboring growth cones. This rich-get-richer scenario results in one synapse forming at a time.
*Lest we get overly familiar, that’s Georg Cantor, nineteenth-century German mathematician; Helge von Koch, turn-of-the-century Swedish mathematician; and Karl Menger, twentieth-century Austrian American mathematician.
*With it being likely that dendrites, blood vessels, and trees would differ as to how many multiples of the diameter branches grow before splitting.
*Lurking in here is the need for a fourth rule, namely to know when to stop the bifurcating. With neurons, or the circulatory or pulmonary systems, it’s when cells reach their targets. With growing, branching trees . . . I don’t know.
*Chapter 10 will cover where randomness comes into biology, in this case in the form of the Growth Stuff not splitting exactly in half (i.e., 50 percent of the molecules going each way) every time. Those small differences mean that there can be some variability tolerated in a bifurcating system; in other words, the real world is messier than these beautiful, clear models. As emphasized by Hungarian biologist Aristid Lindenmayer, this is why everyone’s brains (or neurons, or circulatory system . . .) look similar but are never identical (even in identical twins). This is symbolically represented by the asymmetry in the final drawing of the 1Z level (which wasn’t what I planned, but which I messed up while drawing it).
*One model is called a Turing mechanism, named after Alan Turing, one of the founders of computer science and the source of the Turing test and Turing machines. When he wasn’t busy accomplishing all that, Turing generated the math showing how patterns (e.g., bifurcations in neurons, spots in leopards, stripes in zebras, fingerprints in us) can be generated emergently with a small number of simple rules. He first theorized about this in 1952; it then took a mere sixty years for biologists to prove that his model was correct.
*A recent study has shown that two genes pretty much account for the branching pattern in Romanesco cauliflower. If you don’t know what one of those looks like, stop reading right now and go Google a picture of it.
*With historical events providing some of that instability. Think of Martin Luther getting fed up with the corruption of Rome, leading to the Catholic/Protestant schism; a disagreement as to whether Abu Bakr or Ali should be Muhammad’s successor, resulting in Sunnis and Shi’ites going their separate Islamic ways; Central European Jews being allowed to assimilate into Christian society, in contrast to Eastern European Jews, giving rise to the former’s more secular Reform Judaism.
*A reminder, once again, that the real world of cells and bodies isn’t as clean as these highly idealized models.
*And there’s an additional level of rules like these with different attractant and repellent signals that sculpt what types of neurons wind up in each cluster, rules like “Only two coffee shops per mall.”
*What are termed hydrophobic or hydrophilic amino acids—whether the amino acid is attracted to or repelled by water. I once heard a scientist mention in passing how she didn’t like to swim, referring to herself as being hydrophobic.
*Think biochemistry’s equivalent of domes being most stable for the smallest cost when geodesic.
*How do those various neurons know, say, which attractant or repellent signals to secrete and when to do it? Thanks to other emergent rules that came earlier, and earlier before that, and . . . turtles.
*The study was fascinating. Some places were net exporters of intellectuals, places that they were more likely to move away from than move to—Liverpool, Glasgow, Odessa, Ireland, the Russian Empire, and my simple village of Brooklyn. This is the “please get me out of here” scenario. And then there are the net importers, magnets like Manhattan, Paris, Los Angeles, London, Rome. One of those magnets where intellectuals clustered, living out the rest of their (short) lives, was Auschwitz.
*Bacon numbers show what the long tail of unlikelihood looks like in a power-law distribution. There are approximately one hundred thousand actors with a Bacon number of 4 (84,615), about ten thousand with 5 (6,718), about one thousand with 6 (788), about one hundred with 7 (107), and eleven with a Bacon number of 8—with each step further out in the distribution, the event becomes roughly ten times rarer.
Mathematicians have “Erdös numbers,” named for the brilliant, eccentric mathematician Paul Erdös, who published 1,500+ papers with 504 collaborators; a low Erdös number is a point of pride among mathematicians. There is, of course, only one person with an Erdös number of 0 (i.e., Erdös); the most common Erdös number is 5 (with 87,760 mathematicians), with the frequency declining with a power-law distribution after that.
Get this—there are people with both a low Bacon number and a low Erdös number. The record, 3, is shared by two people. There’s Daniel Kleitman (who published with Erdös and appeared in the movie Good Will Hunting as an MIT mathematician, which is, well, what he is; Minnie Driver, with a Bacon number of 1, costarred). And there’s mathematician Bruce Reznick (also a 1-Erdös-er who, oddly, was an extra in what was apparently an appallingly bad movie, with a Rotten Tomatoes score of 8 percent, called Pretty Maids All in A Row, which included 1-Bacon-ist Roddy McDowall). As long as we’re at it, MIT mathematician John Urschel has a combined Flacco/Erdös number of 5, due to an Erdös number of 4 and a Flacco number of 1; Urschel played in the NFL alongside quarterback Joe Flacco, who apparently is/was extremely important.
*Most, but not all, show this property. The exceptions are important, showing that cases with the distribution were selected for, evolutionarily, rather than being just inevitable features of networks.
*As an example of a generalist, the mutation in Huntington’s disease produces an abnormal version of a particular protein. How does this explain the symptoms of the disease? Who knows. The protein interacts with more than one hundred other types of protein.
*A contrast that has been framed as choosing between maximizing strength versus robustness, or maximizing evolvability versus flexibility, or maximizing stability versus maneuverability.
*The brain contains “small-world networks,” a particular type of power-law distribution that emphasizes the balance between optimizing the interconnected nature of clusters of functionally related nodes, on one hand, and optimizing the fewest average number of steps linking any given node to another.
*Due diligence footnote: Not everyone is thrilled with the notion of the brain being chock-full of power-law distributions. For one thing, as some techniques improve for detecting thin axonal projections, many of the scant long-distance projections turn out to be less scant than expected. Next, there is a difference between power-law distributions and “truncated” power-law distributions. And mathematically, other “heavy-tailed” distributions are incorrectly labeled as power-law ones in many cases. This is where I gave up on reading this stuff.
*“Many more” including an emergent phenomenon called stigmergy, which, among other things, explains how termites move more than a quarter ton of soil to build thirty-foot-high mounds that do gas exchange like your lungs do; back-propagating neural networks that computer scientists copy in order to make machines that learn; wisdom-of-the-crowd emergence where a group of individuals with average expertise about something outperforms a single extreme expert; and bottom-up curation systems that, when utilized by Wikipedia, generate accuracy on the scale of the Encyclopedia Britannica (Wikipedia has become the major source of medical information used by doctors).
*Which seems important, as the differences in patterns of genes expressed in these cells when comparing human brain organoids with those of other apes are really dramatic.
*A number of labs now are making human brain organoids with neurons containing Neanderthal genes. Other research allows cortical organoids to communicate with organoids of muscle cells, making them contract. And another group has been making organoid/robot interfaces, each communicating with the other.
Okay, is it time to freak out? Are these things on their way to consciousness, feeling pain, dreams, aspirations, and love/hate feelings about us, their creators? As framed in the title of one relevant paper, time for a “reality check.” These are model systems of brains, rather than brains themselves (useful for understanding, say, why Zika virus causes massive structural abnormalities in human fetal brains); to give a sense of scale, organoids consist of a few thousand neurons, while insect brains range in the hundreds of thousands. Nonetheless, all this must give one pause (“Can Lab-Grown Brains Become Conscious?” asks another paper as its title), and legal scholars and bioethicists are starting to weigh in about what kinds of organoids might not be okay to make.
