Introduction: The Optimal Argument?

In this paper, I examine the work of philosopher and neuroscientist Christopher Cherniak on optimization in the nervous systems of C. elegans, F. catus, and H. sapiens. I explicate several optimization mechanisms that Cherniak proposes, and explore their implications for evolutionary biology. Ultimately, I argue that brain-wiring optimization per se should not be seen as an adaptation, nor should it be seen as adaptive. Rather, (we can say with some degree of surety that) a minimal-level of nervous system organization is indeed necessary, and that biology gets this organization “for free, directly from physics” (Cherniak 1992; 2005, 105)—a sort of “non-genomic nativism” (Cherniak 2005). But, as Cherniak points out, this organization is not merely relatively optimized, but optimized to the absolute physical limits. While Cherniak entertains the possibility that such optimization may serve an important functional-physiological role, I argue that the “best-in-a-billion” organization actually seen in some parts of the nervous system is mostly supererogatory, that is, unnecessary for proper nervous system functioning. This claim points back to my anti-adaptationist thesis, viz., that optimization per se should be seen as neither (a) an evolutionary adaptation, nor (b) an adaptive nervous system trait.

Section 1: The Extraordinary Nematode

Caenorhabditis elegans is a 1.3mm long multicellular organism of the taxonomic phylum Nematoda that has recently served as a “model organism” in molecular and developmental biological research, as well as the neuroanatomical studies discussed in this paper. The C. elegans organism has two sexes, male and hermaphrodite, which exhibit some sexual dimorphism with respect to their nervous systems: the male contains 381 neurons and the hermaphrodite 302. Many of these neurons (91%) are clustered together in ganglia, of which there are a total of 10 in the hermaphroditic sex (Cherniak 1994, 2422; 2002, 76-77). These facts are known because, in the mid-1980s, a group of Cambridge scientists succeeded in mapping the entire nervous system of C. elegans, which they report “consists of about 5,000 chemical synapses, 2,000 neuromuscular junctions and 600 gap junctions” (J.G. White et al. 1986).

While the construction of a complete neuro-connectivity map of C. elegans’ 302 neurons was, no doubt, a momentous scientific achievement, a more astounding discovery came the following decade: the actual placement of nervous system components in C. elegans—including its primitive “brain,” ganglia, and individual neurons—is the optimal layout. To grasp the significance of this finding, which we owe to Cherniak and his colleagues, one must first have a rudimentary understanding of combinatorial network optimization theory, which I discuss in the next section. Then, in the sections following the next, I survey the literature on nervous system optimization in C. elegans, as well as in the cerebral cortices of higher mammals such as the cat and human. I also discuss a related, roughly inverse optimization problem, namely that of connecting “components” (e.g., synaptic loci) that are taken as fixed, in Steiner tree-like graphs or networks, with the aim of minimizing the volume of neuronal arbors.

Section 2: The Rudiments Of Combinatorial Network Optimization Theory

Problems of component placement optimization (CPO) involve optimally organizing x number of parts whose interconnects are known by placing them in discrete locations, which are given at the outset of the problem. (Note that ‘optimally’ may be defined in a number of ways, with respect to area, volume, length, and so on. In CPO problems, Cherniak takes optimization to be the minimization of nerve fiber length, whereas with the Steiner tree problems (next section) he takes it to be the minimization of neuronal arbor volume.) For example, let us say that parts a, b, and c must occupy loci along a single axis, and a must connect to b, and b to X at one end, while c must connect directly to X. Several arrangements are possible (see Figure 1). As should be obvious from even a quick glance, one of these possible arrangements is optimal, namely A, while the other is suboptimal, namely B. The complexity of CPO problems is a measure of the number of possible arrangements, which grows exponentially with the number of component parts; i.e., for x parts, there are x! different arrangements.

Figure 1: Component placement optimization (design idea from Cherniak 2002).

While the toy example above (Figure 1) contains only 3 parts, and thus yields an unimpressive total of 3! = 6 possibilities (only two of which are shown), the human cerebral cortex contains 52 distinct cytoarchitectonic/functional Brodmann areas, which gives 52! = 8.06581752 × 1067 possible layouts. As Cherniak notes, the process of solving CPO problems of this level of complexity would require far more than the 15 billion years that the universe has been around since the “Big Bang” cosmogonic event. Indeed, such problems fall under the category of NP-hard, which may be defined as being “at least as difficult as any NP-complete problem,” where NP-completeness designates a class of problems that are “strongly conjectured to be intrinsically computationally complex” (Cherniak 1994, 2426). In other words, “no efficient algorithm—that avoids the worst case exhaustive search of all possible solutions—is known” (Cherniak 1994, 2426).

Consequently, while some CPO problems are computationally tractable, i.e., the number of possible arrangements is not so astronomically large that a brute-force search would take several millennia or more, only the omniscient deity (assuming against all odds that He exists) can know whether the human cerebral cortex is in fact optimized. As we will see, Cherniak circumvents these computational problems by proposing heuristics, rules, and “laws” that allow one to estimate degrees of optimality. One can also reasonably extrapolate that, e.g., the human cortical sheet is optimized (or nearly optimized) with respect to the wire length of functional area interconnections based on prior observations of confirmed CPO at different organizational levels in the nervous system, such as at the level of ganglia in C. elegans.

A similar combinatorial optimization problem has as its paradigm case the “Traveling Salesman” problem, which asks: given x number of cities and a traveling salesman A, what is the cheapest round-trip that A can take such that A arrives and departs from each city only once? In this case, rather than the components being movable and the connections fixed, the components (points, vertices) are fixed and the connections movable. Along with CPO, such problems are considered to be NP-hard, requiring brute-force searches of all possible alternative solutions to find the connection pattern of cities that costs, in terms of distance, the least. When these cities are replaced by synaptic loci in the brain, the problem statement becomes: What is the optimal pattern of neuron interconnectivity that saves nerve fiber length? Rather than connecting each point to another, though, this combinatorial problem assumes a Steiner tree-like form. Steiner trees, unlike their distant cousins the minimum spanning trees, interconnect a set of fixed vertices by adding internodes or “Steiner points” to the graph. Steiner trees are roughly 4% shorter than minimum spanning trees (Cherniak 2002, 73).

For example, the optimal Steiner tree connecting three equidistant points adds a single internode at very the center of the graph, located where—if the three points were connected, thereby forming an equilateral triangle—three lines drawn inward, perpendicular to the triangle’s sides at their points of bisection would intersect. From this internode, three lines radiate, each connecting to one of the vertices (see Figure 2). Although I discuss Steiner trees in the context of local arbor optimization not until Section 4, note that the angle at which the Steiner tree branches in Figure 2 is 120 degrees. This is important to keep in mind, since one of the notable insights of Cherniak’s work is its explanation of why 120-degree bifurcations are not observed in the brain.

Figure 2: Steiner tree (from www.wikipedia.com).

Section 3: In Vivo Component Placement Optimization Problems

To recapitulate: the complexity of CPO problems increases at an exponential rate. Consequently, the difference between a combinatorial problem consisting of, say, 9 and 10 parts is 3,265,920 additional layouts. To further put this in perspective, the difference between a problem of 10 and 11 parts is 36,288,000—a total of 33,022,080 more possible layouts by adding just one more part! As mentioned above, the hermaphroditic C. elegans contains exactly 302 neurons, which renders the CPO problem of determining the optimal arrangement of neurons in this minim nematode a problem of computationally cosmic proportions. Like the human cerebral cortex, only the omni-Being can know whether the neurons in the C. elegans nervous system are in fact optimally placed.

To estimate the level of neuron placement optimization in C. elegans, Cherniak proposes the introversion rule or heuristic: “If neuron a connects to b, then a and b are placed near each other, in particular grouped together within the same ganglion, ceteris paribus” (Cherniak 1994, 2425). This rule, as a matter of fact, holds true in the case of C. elegans, whose neurons—nearly all of which have their somata located in ganglionic clusters—are much more likely to occupy the same ganglion if they are interconnected than if they are not. Indeed, empirical investigation reveals that all 10 C. elegans ganglia are introverted (Cherniak 1994). As Cherniak states: “If a pair of connected neurons is arbitrarily selected, they are in fact significantly more likely than chance to turn out to occupy the same ganglion” (Cherniak 1994, 2425). Furthermore, connections to extraganglionic loci, e.g., anterior to a given ganglion involve, to a high degree of statistical significance, neurons positioned in the anterior region of the ganglion, and vice versa. Thus, as Figure 3 delineates, neurons are apparently positioned within ganglia according to the “save wire” metaprinciple of nervous system micro-architecture.

Figure 3: Diagrammatic representation of introversion rule.

The evidence of CPO in C. elegans is irrefragable when one ascends to the next level of neural organization, namely that of the ganglia, which are arranged “roughly one-dimensional[ly]” in the nematode’s 0.065mm wide vermiform body (Cherniak 1994, 2422). While C. elegans contains only 10 total ganglia components, Cherniak counts the “ring of neuropil encircling the pharynx” —the location at which approximately 1/3 of the neural connections in C. elegans are made (Cherniak 1994, 2422; 2002a, 76-77)—as an 11th component. Thus, we have an 11-element NP-hard CPO problem that yields a total number of component placement layouts (11! = 39,916,800) that can be searched via brute-force. Cherniak uses eleven computers running in parallel for over 50 hours to determine that, quite astoundingly, the actual layout is the optimal, i.e., the ganglia of C. elegans are completely microoptimized.

Moving up yet another level of organization, to that of the Brodmann areas of the human cerebral cortex (Cherniak 1994, 2420), the philosopher-scientist once again encounters an intractable combinatorial problem. As Cherniak states: “Exact verification of an optimal layout for even a few dozen elements is not computationally feasible” (Cherniak 1993, 2420). Indeed, the number of possible arrangements of functional areas, as stated above, is an astronomical 8.06581752 × 1067. This would require far more than the age of the universe for the most powerful supercomputers, running in parallel, to exhaustively search. Consequently, the optimal arrangement of the 52 functional areas of the cerebral cortex is far beyond our epistemic reach. In light of this fact, Cherniak devises a stronger version of the introversion heuristic given above, namely the adjacency rule: “If areas a and b are connected, then a and b are contiguous,” ceteris paribus (Cherniak 1994, 2421). Interconnected networks of functional areas on the cortical sheet are likely optimized, the argument goes, if they follow this rule of component placement layout to a degree of statistical significance.

Cherniak applies the adjacency rule to the 18-element CPO problem of the Felis catus (i.e., the domesticated cat) visual system, which consists of 18 areas that make 178 interconnections and form a total of 70 (out of a possible 306) pairs or contiguities, according to the cortical maps of Alan Rosenquist (1985) (Cherniak 1994, 2421). The combinatorial optimization problem emerges from the fact that the visual area connectivities outnumber their contiguities, in this case by a factor of 25. Thus, each area must position itself so as to minimize nerve fiber length while competing with other areas for the best location on the cerebral cortex to achieve this goal. As it turns out, Cherniak discovers that “proportionally many more of the connected than nonconnected pairs [that are] contiguous, with a Fisher exact test of this difference showing it is highly significant, p < 0.0001” (Cherniak 1994, 2421), in the F. catus visual system. This provides strong evidence that the cat visual cortex is indeed optimized, just like the layout of ganglia in C. elegans.

The highest level on which to test for CPO also happens to be the simplest: a single component placement problem involving the brain. As I discuss below, the gradual concentration of nervous tissue toward the anterior region of the organism is an evolutionary phenomenon traceable from one end of the phylogenetic tree to the other. Indeed, while humans have highly organized central nervous systems located as far forward as possible, the primitive C. elegans has only clusters of neurons and ganglia scattered along its longitudinal axis. (Even more evolutionarily primitive organisms, such as jellyfish, have only a diffuse reticulum of interconnected neurons.) Nevertheless, a “low level” of cephalization is in fact appreciable in C. elegans, which has approximately 63% of its 302 neurons “located in the most anterior portion of [its] body, around and just behind the pharynx” (Cherniak 1994, 2419; Cherniak 1995).

The optimal case, which we find in many higher mammals, is where the nervous system is as highly concentrated as far anterior (toward the sense organs) as is physically possible, assuming that the number of anterior connections exceeds the number of connections with the posterior end. This is to say: if there were even one more connection to the rear than to the front, the cephalized “brain” would fail to save wire, and thus the brain’s location would be suboptimal. As for humans, Cherniak reports that the ratio of antero-posterior connections exceeds 5, with the total number of sensory-motor fibers in the twelve cranial nerves being approximately 12,599,000, while the total number in the spinal cord is 2,400,000—a difference of 10,199,000 nerve fibers. This fact provides quantitative empirical evidence to support Cherniak’s hypothesis that the brain is positioned in the body to save as much neural “wiring” as possible.

Section 4: Variably-Weighted Steiner Tree Optimization Problems

So far, I have been discussing component placement optimization problems, in which the interconnections between component parts are given and the parts manipulable. The aim of such problems is to arrange the component parts so as to optimize their interconnections, where optimization is measured in terms of total nerve fiber length. The next combinatorial problem considered here measures optimization in terms not of total length, but of volume. Recall the Steiner tree problems discussed above. Recall that in the simple Y-shaped tree connecting three vertices, the branches intersect at a central internode, forming an angle of exactly 120 degrees. As Figure 4 illustrates, the angles at which most, e.g., secondary segments branch from primary dendritic segments is palpably less than 120 degrees. If neuronal arbors are optimized like Steiner trees, then why are the angles different?

Figure 4: Several < 120-degree dendritic branches (from www.ipmc.cnrs.fr).

The answer to this question is simple, although not obvious: the branches and trunks in Steiner tree graphs, as Euclidean lines of “breadth-less length,” have exactly the same costs, while the branches and trunks of neuronal arborizations are cost-differential. As a universal rule we may assert: “Trunks cost more than their branches.” The “cost” of the trunks and branches of neuronal arbors here is a measure of their cross-sectional area, and the optimization problem before us is one of volume-minimization (even if this means increasing total length). Thus, if we assume for a moment that neuronal arbors are in fact optimized with respect to volume, we may immediately infer that 120-degree trunk bifurcations are not volume minimizing, since such junction-angles are not observed in histological studies of the nervous system tissue, camera lucida drawings of neuronal arbors, etc. So, what angles are locally optimal?

Cherniak answers this question by formulating the “Local Tree Optimization Law,” which states that the minimization of Y-junction costs is expressible by the trigonometric equation: cos q = (t2 – b12 – b22) / 2b1b2, where q equals the angle at which two branches meet, t is the cost of the trunk per unit length, and b1 and b2 are branch costs per unit length (Cherniak 2007; Cherniak 1991, 504-505). In other words, when the two branches cost the exact same, the angle of bifurcation will be 60 degrees, which Cherniak dubs the “60-degree rule.” As one branch costs increasingly less (in terms of ontogeny, the exact opposite usually occurs), i.e., as the ratio of its own cross-sectional area to that of the other branch decreases, the angle at which the trunk bifurcates asymptotically approaches 90 degrees. Thus, 120-degree angles are not observed in the arbors of axons and dendrites (such as the pyramidal cell in Figure 5) because such arbors are optimizing over volume, and volume minimization favors angles that obey the Local Tree Optimization Law. Following Cherniak, we may call the resultant trees “variably-weighted” Steiner trees.

Figure 5: Pyramidal cell (from www.ipmc.cnrs.fr/…/neurophysiology/dtree.html).

Section 5: Possible Mechanisms Of Optimization, By Optimization, And For Optimization

Having established that optimization is present in the nervous systems of organisms spanning across the phylogenetic tree, the natural follow-up query is: How did the brain become optimized? What are the mechanisms of optimization? Are they biological or physical? And relatedly: What is the form-function relationship with respect to the layout of nervous system components and local arbor optimization? Is optimization in the brain an adaptation selected for because of the evolutionary advantage, if any, it confers to the organism? That is: Do organisms with optimized nervous systems have a better chance of surviving? Or is optimization a mere spandrel, an accident of physics serving no particular physiological function?

As Cherniak notes, “the view of the worm neuroanatomists has been that [the C. elegans] ganglia or spatial clusterings of cell bodies may simply be brought about by extraneous mechanical factors and without functional significance” (Cherniak 1994, 2421). Interestingly, the neuroanatomists’ view departs from the “Panglossian paradigm” dominant in evolutionary biology since the Modern Synthesis in the early to mid-twentieth century, when biologists succeeded in integrating Darwinian evolution and Mendelian genetics. The hallmark feature of this “paradigm”—a programmatic approach to evolutionary biology—is the firm conviction that natural selection is the primary, preponderant mechanism responsible for evolutionary change over time and that most, if not all, organismic traits are adaptations selected for by nature; after Sterelny and Griffiths, let us call this view “empirical adaptationism” (Sterelny & Griffiths 1999, 226).

In a 1979 paper, Gould and Lewontin attack the empirical adaptationist position for their theoretical fixation on Darwinian selectionism to the exclusion of other possible factors that might influence and shape the phenotypes of species. Indeed, Gould emphasizes “the bauplan, or fundamental body plan,” of organisms (Sterelny & Griffiths 1999, 228), which relates to what Darwin called the “Unity of Type” law, i.e., that there is a “fundamental agreement in [organism] structure, which we see in organic beings of the same class, and which is quite independent of their habits of life” (Darwin 1964, 206). In a similar anti-adaptationist vein, process structuralists emphasize developmental and physical constraints on the design space of organisms, describing—in the language of chaos and complexity theory—“highly conserved traits [as] strong attractors for development” (Sterelny & Griffiths 1999, 232), thereby suggesting a classificatory approach to explanation in evolutionary biology, not unlike that found in, e.g., chemistry (Sterelny & Griffiths 1999, 229). The lesson to be learned here is nothing less than circumspection when designating a trait as an adaptation, or even as being adaptive, since it is quite possible that it (e.g., the tetrapod limb) might be neither.

We should be especially careful in attributing an adaptive value to optimization in the brain because of the mechanisms that Cherniak proposes as responsible for the placement of nervous system components and the volume-minimization of neuronal arbors. With respect to the latter, one notices an obvious isomorphism between the arborizations of axons and dendrites in the brain and the pattern of tree structures found in nature (such as in a forest). More interestingly, the Y-junctions in water drainage systems follow Cherniak’s Local Tree Optimization Law, bifurcating at 60 degrees when the “costs” of a trunk’s branches (orographic tributaries) are equal; as such, these purely physical systems exhibit the same sort of local optimization found in the brain. In addition, both neuronal arbors (a biological system) and water drainage systems (a physical system) exhibit certain peculiarities that further suggest a single underlying non-biological mechanism is responsible for their morphologies: (a) “branches of all observed types of natural tree-structures consistently bend inward,” including the “dendrite, axon; artery, vein, plant (root & branch); river fan-in, fan-out” (Cherniak 2007), and (b) rivers exhibit oxbow loop or meander—a wiggle, especially in the river’s lower course—an analogue of which can be found in neuronal processes (see Figure 6).

Figure 6: Analogue of oxbow loop in an axon (from www.faculty.washington.edu).

Cherniak suggests that the angle of Y-junctions in neuronal arbors, as well as the branch-branch and branch-trunk ratios of diameters, is the result of a “tug-of-war” between fluid dynamics, which “sets” the trunk and branch diameters, and fluid statics, which “sets” the junction angle according to the local optimization law above. Thus, local arbor optimization is the result of a purely physical, fluid mechanical mechanism, and as such is not, and cannot, be an adaptation per se, selected for by nature. This conclusion would explain why, unlike the phenomenon of cephalization, organisms at both ends of the phylogenetic tree, from C. elegans to H. sapiens, seem to exhibit local arbor optimization. Furthermore, selection by nature requires that the trait selected is heritable, as Darwin himself points out in Origin of Species (1859). This immediately disqualifies local optimization as a selectable trait, since (a) heritability is measured by taking the portion of a population with a trait and counting how many of its offspring have that same trait, thereby assigning a heritability value between 0 and 1 (Sterelny & Griffiths 1999), and (b) optimization at local arbor junctions is more or less pervasive among populations of most, if not all species.

The final, and most compelling reason for thinking that local arbor optimization was not naturally selected for as a nervous system trait, advantageous in the Malthusian “struggle for survival,” is that such combinatorial problems are, as previously noted, NP-hard. What does this really mean? Although paleobiologists generally agree that life emerged from the primordial soup some 3.6 billion years ago, it was not until the “Cambrian explosion” at the beginning of the Paleozoic era that “most of the major groups of animals appear for the first time” (Charlesworth & Charlesworth 2003, 47)—over 500 million years ago. The point is that, if such optimization were an adaptation, nature would have no choice—if only because of the problem’s NP-hardness—but to search brute-force style all the possible alternatives of a given combinatorial problem to find the optimal solution, and this would have taken many times longer than life has been here, on its sublunar abode.

Although it is clear at this point that nature did not select for such optimization, it is also clear, at least in several important cases, that nature has not selected against it. As Cherniak states, biology seems to have gotten a “free ride” from physics—order from chaos thanks to “dumb” fluid mechanical forces. Indeed, one finds it difficult to imagine what a histological slice of brain tissue would look like if neuron arborization patterns were completely random and haphazard: connections would be jumbled; organization would be compromised; the organism would be stupid. It may simply be a propitious coincidence of the universe that physics yields the optimal solution to variably-weighted Steiner tree problems, just as it yields the optimal solution to the problem of how to fit the most volume into a space with the least surrounding area: the balloon just assumes a spherical shape. And it may simply be that biology exploited this coincidence to create locally optimal axonal and dendritic arbors.

Thus, we can conjecture that while nature did not make a positive selection for local arbor optimization, it might have negatively selected against traits that would have compromised or interfered with optimization. With respect to the CPO problem of brain placement, if Cherniak’s claim that nerve fibers are “infinitely costly” is true, then any attempt by evolution to locate the brain more posteriorly than it is actually located—for the sake of, e.g., reducing the length of arteriovenous connections from the heart to the brain—would have been rejected by nature, and the organism would have died. While the argument for the single-component placement problem of the brain here seems plausible, I argue that it is problematic for other reasons. Nevertheless, we can say with some degree of certitude that: (a) local arbor optimization is the result of a physical (i.e., fluid mechanical), not biological, mechanism, and (b) if nature did indeed select against optimization-interfering traits, then it is likely that the arborization patterns of axons and dendrites do indeed have a functional value. If not, then the sentiment expressed by the neuroanatomists above is probably true.

Section 6: Possible Optimization Mechanisms Continued…

Let us turn to a small constellation of questions revolving around the CPO problem. The philosopher-scientist would like to know: Can we give a mechanistic explanation of cephalization? Of the placement of functional areas on the cortical sheet? Of the ganglia in C. elegans? Of individual neurons within ganglia and spread throughout C. elegan’s microscopic body? As noted above, Cherniak argues that nerve fibers must have an “infinite cost” because, if this weren’t the case, then one would not expect to find the brain as far forward in the organism as it is found. Indeed, the location of the brain not only puts a significant strain on the cardiovascular system, which must pump blood vertically through the neck (consider a giraffe, for example, or Brachiosaurus brancai), but it also places the brain in a position that makes it particularly vulnerable to mechanical trauma.

As the cliché in evolutionary biology goes, “Nature satisfices; it does not optimize.” This is because the best overall design often requires local systemic tradeoffs. Thus, one would expect to find the brain located more posterior than it is—somewhere in the region of the neck—for the sake of protecting delicate (and mostly amitotic) nerve cells, as well as saving arteriovenous pipes. Even in mathematical optimality models, which Maynard Smith admits do not test “the general proposition that nature optimizes” (Maynard Smith 1978), scientists begin by specifying a “phenotype set,” of which one phenotype will emerge as “optimal.” This sense of optimality, though, is only relative; the optimization that Cherniak discovered in the nervous system, on the other hand, is absolute. This is to say that organisms solve the NP-hard problem of where to place their components to save nerve fiber to a “best-in-a-billion” approximation (Cherniak et al. 2003). Thus, Cherniak infers that nervous tissue must be far more—maybe infinitely more—costly than any other bodily system, tissue, and so on.

It is a well-known truism of neurobiology that nerve cells are extremely costly in terms of metabolism. Indeed, the brain consumes approximately 30% of the oxygen absorbed into the bloodstream irrespective of physical activity, and it requires huge quantities of glucose to function. The fact that over 50% of body heat is lost through the head indicates the brain’s tremendous metabolic activity. And as Cherniak points out, with the exception of insect flight muscle cells, neurons are more costly than any other cell-type known (Cherniak 2007). But would these facts explain cephalization, the gradual reduction of total wire length in the body? To what extent do they support the claim that nerve fibers are infinitely costly? Might there be another explanation for cephalization, one that does not interpret this phenomenon as an adaptation, but rather accounts for this phenomenon via purely physical mechanisms similar to those described above?

Cherniak suggests that one might “picture each sensory and motor fiber behaving in effect over generations like a micro-spring stretching from sensory or muscle locations to the brain” (Cherniak 1994, 2426). Cherniak explicitly states that this “hypothesis” is nothing more than a conceptual model for understanding the cephalization phenomenon, where the microspring nerve fibers can be seen as “pulling” on the brain according to “non-Hooke’s Law.” Nevertheless, the microspring model resembles Van Essen’s (1997) “tension-based” theory, which purports to explain the gross anatomical features of brain topology (e.g., species-specific invaginations and convolutions) by pointing to actual mechanical tension along axons in the white matter during morphogenesis. Recall that there are 10,199,000 more nerve fibers in the cranial nerves than in the spinal cord, and perhaps there are many more that might actually “tug” at the brain during the early morphogenetic stages—nerve fibers that later perish via the apoptotic phenomenon of programmed cell death. Indeed, one can imagine how sensory-motor nerve fibers might mechanically “pull” the brain toward the sense organs at the anterior region of the body during embryonic morphogenesis in the womb. Over evolutionary time, nature would then select those organisms with anterior extremities (i.e., a head) that can accommodate an increasingly centralized and forwardly located concentration of nervous tissues. Whether or not this is the case, of course, is an empirical matter; I leave it to further research to determine if these incipient conjectures are correct.

Note that the difference of antero-posterior nerve fibers is at least partly the result, as far as I know, of the fact that there exist quasi-autonomous, local “nervous systems,” most notably in the heart and intestines. With respect to the heart, while it is extrinsically innervated to by sympathetic and parasympathetic fibers (the latter of which send to the heart constant inhibitory signals), its systolic contractions are under the control of specialized autorhythmic cells located in the sinoatrial node (SA) (i.e., in the sinus of the right atrium). These SA node cells send, in temporal patterns, signals (indirectly) to Purkinje fibers, which stimulate the myocardial syncytium to contract. Similarly, the intestines are regulated by the enteric nervous system, a highly complex “second brain” in the body. This system operates via visceral reflex arcs that consist of sensory, motor, and inter-neurons; as such, the enteric nervous system is largely autonomous. Even the human stomach has pacemaker cells located in its smooth muscle that produce its “basic electrical rhythm,” which results in roughly three “peristaltic waves” per minute (Marieb 2004, 906).

One might at first wonder how these quasi-autonomous systems “fit” with cephalization, i.e., Why doesn’t the enteric nervous system migrate north like the rest of the nervous system? First of all, to reiterate, the enteric nervous system consists of reflex arcs; second, such local neuro-regulatory systems might in fact represent yet another instance of optimization, following the new tentative rule: “If neural system N regulates some bodily system S (e.g., the gastrointestinal system), and only S, then N will move as close to S as possible.” Thus, the brain migrates towards the sensory organs, while the enteric nervous system migrates towards the lower alimentary canal. Another possibility is that “saving wire” is not an important principle of nervous system organization, and thus cephalization is not an adaptation per se. Maybe the brain moves forward because of actual mechanical, Van Essen-like forces during morphogenesis—forces that can’t, for whatever reasons, be counteracted, viz., the arteriovenous pipes that extend from the heart to the brain simply cannot “tug” back on the brain. Once again, I leave these empirical questions open for future research.

Conclusion: Is Optimization Necessary For Brain Functioning?

There is some prima facie evidence that nerve fibers are not, in fact, “infinitely costly,” which thereby implies that cephalization, as well as other CPO problems such as ganglion and neuron layout, is not an adaptation, but the mere accidental byproduct of, say, physical forces. For example, the human body contains numerous contralateral ascending and descending spinal cord tracts that decussate at the medulla oblongata or in the spinal cord itself. Furthermore, the special senses project fibers to the contralateral side of the brain, e.g., optic nerve fibers from the nasal hemiretina cross over at the optic chiasma, synapsing at the thalamus and then the primary visual cortex (V1). Two points could here be made: first, if nerve fibers do have an “infinite cost,” then why is ipsilaterality not universal? And second, given the adjacency rule, why does the optic nerve project to the dorsal portion of the brain? Why not, say, the frontal lobes instead, for the sake of “saving wire”?

This suggests, I think, that nerve fibers might not have an infinite cost after all. Rather, the optimization of component placement layouts in the body might be nothing more than a Gouldian spandrel-like accident of physical forces, just like the sphericity of a fluid-filled balloon results from the way the universe just happens to be. Thus, one might look to other possible mechanisms to explain, e.g., why the brain is in the head, and not in the neck. As mentioned above, it is conceivable that the cardiovascular system is simply unable to “tug” back on the brain, and therefore, over evolutionary time, the brain moves forward, like chromosomes during anaphase. Optimization-interfering traits, then, on the present anti-adaptationist view, are not of great concern; indeed, nature has, as a matter of neuroanatomical fact, selected organisms with contralateral connections, eyes that project as far back as possible, and so on. Thus, rather than viewing optimization as adaptive, we might see it as nothing more than an accidental byproduct of physics.

This is not to say, of course, that if physics were different, then organisms would survive just as well as they do. Instead, it is only to propound the modest thesis that organisms might not need absolute optimization to survive, but that some level of nervous system organization might indeed be a necessary condition. Thus, if biology weren’t getting structure “for free, directly from physics” (Cherniak 1992; 2005, 105), nature might have to “manually” select organisms via evolutionary mechanisms with some basic level of neural systemic organization (reminiscent, most likely, of what is actually seen). This would probably not be easy, especially since information concerning the architecture and organization of the brain—“the most complex structure known in [the] Universe” (Cherniak 2007)—must pass through a genomic bottleneck (Cherniak 2005, 7). In other words, only about 3% of human DNA is not “junk,” an amount that is not nearly enough to specify in all its involute detail the complex neurostructural features found in the brain. Thus, without physics, biology would be confronted by an insurmountable evolutionary obstacle, namely the problem of creating an unfathomable amount of order from a relatively small number of information-encoding DNA molecules.

This leads Cherniak to suggest an extension of the anthropic principle: “Any model of the Universe must meet the adequacy condition that it permits the development of life and intelligence—as has in fact occurred” (Cherniak, forthcoming). Cherniak continues: “If such neural network optimization is in fact somehow prerequisite for brain functioning (Cherniak 2002), we can now contemplate a possible further set of brain-enabling conditions of the Universe” (Cherniak, forthcoming; emphasis added). I would urge that optimization per se is not a necessary condition for brain functioning, but that there is a requisite minimal level of nervous system organization, a level that cannot be provided solely by the organism’s genotype (non-junk DNA). Thanks to physics, though—the “deaf, dumb, and blind” watchmaker—the nervous system has the maximum level possible, i.e., absolute optimization. Indeed, optimization to spare.

© 2008 Phil Torres. Do not reproduce or cite without permission.