Biolinguistics: Current State and Future Prospects

[Invited Article]

BIOLINGUISTICS: CURRENT STATE AND FUTURE PROSPECTS

Lyle Jenkins Biolinguistics Institute

The study of the biology of human language, biolinguistics, has been fruitfully investigated over the last sixty years. Many important insights have been gained into the questions of what language is (mechanisms and functions), how language develops (growth of language), and how language evolves in the species. Principles of symmetry have often helped to unify areas of the natural sciences such as physics, chemistry and biology. The application of symmetry to the kinship system of the Warlpiri aborigines of Australia is examined to demonstrate how symmetry illuminates the intersec- tion of language and other cognitive systems.*

Keywords: biolinguistics, development, evolution, unification, symmetry

1. Introduction: The Biolinguistic Program Biolinguistics, the study of the biology of human language, investigates the standard fields of inquiry common to all biological disciplines: form/ function, development (in the individual) and evolution (in the species). In the case of language biolinguists investigate the structure, function and use of language, the development of language in the individual and the evolution of language in the species. The following kinds of questions for language are studied:

* I have greatly profited from discussion of these issues over the years with my colleagues Allan Maxam, Anna Maria Di Sciullo and Noam Chomsky. I am grateful to Professor Yukio Otsu and Professor Koji Fujita for the opportunity to take part at both the Symposium “Language, Cognition, and Human Nature: Prospects of Linguistics” and at the Special Workshop on Biolinguistics, as well as to interact with all of the other participants. I would like to thank Secretary-General Nobuaki Nishioka of the English Linguistics Society of Japan very much for the opportunity to participate in the 30th an- niversary of the Society. Last, but not least, I want to express my deep appreciation for the unfailing help and hospitality of the Japanese people, who helped to make my visit a very pleasurable one.

(1) What is knowledge of language? (2) How does language develop in the child? (3) How does language evolve in the species? And, of course, the equivalent kinds of questions about mechanism, development and evolution can be asked of any biological system, whether it is egg-laying in Aplysia or the waggle dance of the honeybee. These questions for the biology of language were explicitly set out by Chomsky (1976) at a symposium in honor of Eric Lenneberg, one of the early pioneers of biolinguistics and was restated in early work on the minimalist program (see below) by Chomsky and Lasnik (1995). However, these interesting questions were the focus of discussion much earlier at the inception of modern biolinguistics; for some of this history, see Jenkins (2000), the seminal work on biology and language by Lenneberg (1967) and a recent insightful analysis of Lenneberg’s work by Boeckx and Longa (2011). Of course, Chomsky was only spelling out the research agenda for work on the biology of language (biolinguistics) in terms familiar to every bi- ologist. And this approach was implicitly and explicitly accepted by such biologists as the Nobel laureates, Salvador Luria, François Jacob and Niels Jerne in their discussions of aspects of the nascent biolinguistics program, to which they added their own interesting perspectives. Only in such fields as linguistics and philosophy did biolinguistics generate controversy, with end- less discussions of the so-called “Innateness Hypothesis,” etc. But biologists had difficulty understanding what these discussions were even about, since it was well-understood in that field that all biological systems have a genetic component, including language. Questions (1)–(3) are sometimes referred to as the what and how questions of biolinguistics. There is an additional question, the why question, which is perhaps more difficult to answer, which Chomsky (2004) notes is the question of why the principles of language are what they are. The study of this question is the basis for what has been called the minimalist program; see discussion in Chomsky (1995); Boeckx (2011); Di Sciullo et al. (2010); Di Sciullo and Boeckx (2011). One may also ask how the study of language might be integrated into the other natural sciences—what Chomsky (1994) has termed the “unification problem.” Chomsky (2005) has observed that properties of the attained language derive from three factors: BIOLINGUISTICS 487

(A) Genetic endowment (B) Experience (or Environment) (C) Principles not specific to the faculty of language Factors (A) Genetic endowment and (B) Experience/Environment are familiar in the popular literature as “Nature” and “Nurture.” Palmer (2004) has illustrated how the above factors can interact in different ways. In the classical mode genotype precedes phenotype, whereas in another mode (genetic assimilation), phenotype precedes genotype. Feher et al. (2009) have also demonstrated how a phenotype can emerge as genetics and experience interact over multiple generations in the case of birdsong learning in the zebra finch. In a paper on the comparative approach to the study of biology and language, Hauser et al. (2002) note that it is useful to distinguish the faculty of language in the broad sense and the faculty of language in the narrow sense. When considering some property of language, such as recursion, one should not assume that it is uniquely human until one has looked for that property in a wide variety of species. An example of the application of the comparative method is the investigation of the computational abilities of nonhuman primates by Fitch and Hauser (2004), who tested the ability of cotton-top tamarins, a New World primate species, as well as human controls, to process different kinds of grammars. Furthermore, one should not restrict such studies to animal communication; one must entertain “the hypothesis that recursion evolved to solve other computational problems such as navigation, number quantification, or social relationships,” etc. And before we conclude that such a property is unique to human language, we should look for that property in other cognitive domains; e.g., we might examine and compare the property of recursion in mathematics. But if a module for recursion was co-opted from a navigation system for language or some other system, how would we determine that? One pos- sibility is what Shubin et al. (2009) coined “deep homology.” Shubin et al. (1997) argued that “major innovations (e.g. in appendages) are largely derived from pre-existing developmental systems” by modifications of genetic regulatory changes so that “… the evolution of successively derived limb types, from lobopods to insect wings, and from agnathan fins to tetrapod limbs appears to be due, in part, to the successive cooption and redeploy- ment of signals established in primitive metazoans.” Principles in (C) can be non-domain-specific or non-organism-specific principles. Chomsky (2005) suggested such principles as computational efficiency and data analysis. We want to suggest symmetry as a candidate 488 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013) for a principle (set of principles) that is both non-domain-specific and non- organism-specific. Similar questions can be asked about any biological system—icosahedral virus architecture, protein folding, chemotaxis, phyllotaxis, falling cats, cognitive functions, etc. In recent years there has been an explosion of research in a variety of fields (Boeckx and Grohmann (2013) and Hogan (2011)); e.g. studies of sound, structure and meaning in the languages of the world, including universal and comparative grammar, syntax, semantics, morphology, phonology and articulatory and acoustic phonetics, language acquisition and perception, language change (Radford et al. (2009)), studies of genes involved in human language (and other animal systems) (see below), agrammatism (Grodzinsky and Amunts (2006)), neurology of language, including expressive and recep- tive aphasias, imaging and the electrical activity of the brain (Stemmer and Whitaker (2008)), studies of split brain patients (Gazzaniga (2005)), sign language (Brentari (2010)), pidgin and creole languages (Hickey (2010)), language savants (Smith and Tsimpli (1995)), comparative ethology and evolution (Christiansen and Kirby (2003)), mathematical modeling and dynamical systems (see below), language and mathematics (Dehaene et al. (2007)), etc., to name only a handful. Biolinguistics also studies how the biology of human language relates to other human cognitive systems and to precursors in other species. During and after the Human Genome Project, a number of tools and techniques have been developed to accelerate research of entire genomes as well as to permit the comparative genomic study of human vs. nonhuman primates. These include; e.g. microarray techniques, next-generation sequencing, and Whole Genome Association studies. We are now able to examine and compare brain samples from human and nonhuman primates and ask questions like: what genes and what brain areas contribute to language and cognition? Already a number of genes have been identified that are associated with language and other cognitive functions. Other questions that are being studied are what genes associated with language/cognition are differentially expressed in the brain of humans and in nonhuman primates. The FOXP2 gene is the most extensively studied gene affecting language. Of course, it goes without saying that no one gene can determine such a complex brain mechanism as human language. We consider it here since it provides a useful illustration how one can proceed to unravel one thread of the intricate tapestry that makes up the genetics of language. One starts by asking what the phenotype is for the aberrant gene. In this BIOLINGUISTICS 489 case, Hurst et al. (1990) studied a family, later referred to as the KE family, and reported that the affected subjects exhibited a number of speech deficits in the areas of syntax, semantics and phonology as well as in other areas such as speech articulation. Moreover, they determined that the pattern of inheritance was autosomal dominant and that about half of the 30 family members were affected. Additional in depth studies of the phenotype followed. Gopnik and Crago (1991) investigated grammatical deficits in morphology. Vargha- Khadem et al. (1995) reported a “striking articulatory impairment,” as well as defects in “orofacial praxic function.” They state that the “evidence from this family thus provides no support for the existence of ‘grammar genes,’ ….” However, the notion of “grammar genes” was never seriously entertained among biologists, although the idea sometimes circulated in the media. Even the authors of this study conceded that the KE family’s “linguistic difficulties do constitute a prominent part of their phenotype. Inves- tigations of the neural and genetic correlates of their disorder could therefore uncover important clues to some of the bases of the primary human faculties of speech and language.” In parallel investigations, the locus of the gene, which was dubbed SPCH1, was localized on chromosome 7q31 and the gene was subsequently sequenced. The protein sequence was determined and found to contain a forkhead-box motif, so that the protein was named FOXP2; see Marcus and Fisher (2003). It was determined that FOXP2 belonged to a family of transcription factors and that it therefore was involved in regulating “down- stream” target genes; for a review, see Fisher and Marcus (2006). Enard et al. (2002) sequenced the DNA corresponding to FOXP in the chimpanzee, gorilla, orang-utan, rhesus macaque and mouse and found several amino-acid differences between chimpanzees and humans, which “strongly suggest that this gene has been the target of selection during recent human evolution.” Konopka et al. (2009) used whole-genome expression microarray data from human and chimpanzee brain to look for differences in gene regulation of the targets. They found that the targets were differentially regulated, indicating that they might play an important function in the language path- ways in humans; see Dominguez and Rakic (2009) for additional discussion. As these studies also show, FOXP2 is only one component of a larger genetic network underlying the human-specific language faculty. Many other genes affecting language are currently under investigation; see Graham and Fisher (2013) and Jenkins (2006). Warren et al. (2010) announced the sequencing of the zebra finch ge- 490 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013) nome, after which Hilliard et al. (2012) reported that they had “found 2,000 singing-regulated genes … in area X, the basal ganglia subregion dedicated to learned vocalizations. These contained known targets of human∼ FOXP2 and potential avian targets.” For discussion of some possible connections between bird song and language, see Bolhuis et al. (2010).

2. Unification in the Natural Sciences 2.1. Unification in Mathematics A simple example of what we mean by unification in mathematics is the field of analytic geometry, which some of us may have encountered in school. René Descartes (and others) took the classical subject of geometry and unified it with algebra to provide powerful tools. Another more modern example is the unification of geometry with group theory. Everyone is familiar with such systems as Euclidean geometry, which most of us were exposed to in school. But perhaps not many are as familiar with the term “group theory.” Group theory is the mathematical study of symmetry. For an intuitive definition of symmetry, let us state the informal definition by the physicist Weyl (1952) (as interpreted by Richard Feynman et al. (1965): “Professor Hermann Weyl has given this definition of symmetry: a thing is symmetrical if one can subject it to a certain operation and it appears exactly the same after the operation.” A simple example would be a flower vase with no external markings. If wee rotat the vase by 360° (or 90°, 13°, etc.) the starting configuration of the vase is indistinguishable from the initial configuration. We say that the vase is symmetrical under rotation. Note that “thing” should not be taken too literally, as we wish to consider not only concrete objects, like vases, but also abstract objects, like equations and physical laws. We also wish to apply the concept in many domains, such as mathematics, physics, and biology. At first glance it might appear that a concept with such general application might not be useful for specific applications. However, exactly the opposite is true. As we will see, symmetry also has the power to restrict. In his inaugural address at the University of Erlangen in 1872, Felix Klein proposed what became known as the Erlangen Program. In this theory, Klein showed that one could regard many of the classical and modern geometries, including Euclidean geometry (where parallel lines never meet), as well as non-Euclidean geometries and others, could be characterized by groups of transformations that left certain properties invariant. BIOLINGUISTICS 491

Another program for unification in mathematics is the so-called Langlands program, a series of conjectures, some of which have been shown to link seemingly unrelated subfields of mathematics, such as number theory and representation theory. An example of this comes from the recent much publicized proof by Wiles of “Fermat’s Last Theorem,” discussed in Singh (1998), which states that there are no non-trivial solutions x, y and z of the equation xn + yn = zn where n ≥ 3. Fermat had famously written in the margin of his copy of Diophantus’ Arithmetica around 1637 that “I have a truly marvelous demonstration of this proposition which this margin is too narrow to contain.” However, no one was able to construct a proof of this conjecture since then until Wiles found a proof around 1994. It turned out that the mathematical machinery used in the proof was of more interest than the proof itself. The key step was Wile’s proof of the Shimura-Taniyama-Weil conjecture, a simplified statement of which is: All elliptic curves are modular. Elliptic curves are curves described by an equation of the form y2 = x3 + ax + b (subject to an additional technical requirement). Modular forms are objects from the world of representation theory, a part of the theory of symmetry. For our purposes, it is enough to note that the Shimura- Taniyama-Weil conjecture (now called the Modularity Theorem) unifies what had been two separate domains in mathematics—elliptic curves and modular forms. This gives an idea of the flavor of the ongoing work under the um- brella of the Langlands program. Before moving on to physics, we would like to point out the central role of the theory of symmetry in several of these unifications—groups in the Erlangen program and the use of (Galois) representations and associated tools in the Langlands program.

2.2. Unification in Physics and Chemistry In physics there are numerous significant examples of unification; e.g. the unification of thermodynamics and mechanics into statistical mechanics, the unification of electricity and magnetism into the theory of electromagnetism, and the unification of atomic physics and chemistry and quantum mechanics. A further example would be the unification by Noether of the principles of physical symmetry with the conservation laws of physics. She showed that each continuous symmetry was associated with a conservation law: the symmetry of time with the conservation of energy, the symmetry of transla- tion in space with the conservation of linear momentum, the symmetry of 492 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013) rotation in space with the conservation of angular momentum, and so on. In addition, there are a number of “internal symmetries” in particle physics with their associated conservation laws. Another criterion that is sometimes put forth for scientific theories is that of, beauty often in connection with symmetry. For example, the physicist P. A. M. Dirac (1963) wrote that “it is more important to have beauty in one’s equations than to have them fit experiment.” The example he had in mind was Schrödinger’s wave equation in quantum mechanics. First Schrödinger tried to extend some ideas of De Broglie to quantum mechanics and came up with a beautiful equation, but did not pay close attention to recent experimental developments. When he attempted to apply his equation to the behavior of the electron in the hydrogen atom, his predictions did not agree completely with the experimental data. The reason for this was that he (and no one else) knew at the time that the electron had a spin. Schrödinger found that if he ignored the effects of relativity, an approximate form of his equation did agree with the data. It was this equation that he published. Later, when the effects of electron spin were understood, it was seen that the original (relativistic) version of his equation was the one that agreed with Nature. From this (and other cases), Dirac concluded that “It seems that if one is working from the point of view of getting beauty in one’s equations, and if one has really a sound insight, one is on a sure line of progress. If there is not complete agreement between the results of one’s work and experiment, one should not allow oneself to be too discouraged, because the discrepancy may well be due to minor fea- tures that are not properly taken into account and that will get cleared up with further developments of the theory.” Dirac himself proposed a famous equation one of whose predictions seemed not to be in accord with nature. In particular the equation pre- dicted the existence of what were later to be called anti-particles, and which were in fact discovered by Carl Anderson in cosmic rays a few years after the equation was proposed, as recounted in Quinn and Nir (2008). When discussing symmetry in physics it is important to distinguish between the symmetry of the solutions to an equation and the symmetry of the equation itself. For example, the ancient Greeks believed that the orbits of the planets had the “perfect” symmetry of the circle. Kepler then showed, on the basis of data from Brahe, that the orbits of the planets in our solar system were elliptical. Isaac Newton was able to derive Kepler’s laws ana- lytically. Newton (2000) notes that “the perfect rotational invariance origi- nally embodied in the shape of a circle instead becomes a property of the BIOLINGUISTICS 493 gravitational law, together with the absence of a preferred direction contained in the equations of motion.” However, due to “accidents of history” and “initial conditions,” a “symmetry of the underlying equation does not neces- sarily lead to the same symmetry in their solutions.” This results “in ‘ugly’ ellipses—a ‘spontaneously broken symmetry,’ as we would call it now.” Note that symmetry has the property of being “portable;” i.e., symmetry principles are operative in more complex systems, in chemistry, condensed matter physics, biology, etc. Let us consider a simple example from chemistry. Like the vase we considered earlier, a chemical molecule can also have rotational symmetry. For example, water molecules (H2O) consisting of an oxygen atom bonded to two hydrogen atoms has two indistinguishable configurations which we get by rotating the molecule so that the two hydrogen atoms are interchanged. We say that H2O has a symmetry number equal to 2. The molecule HCL, on the other hand, has no such rotational symmetry and we say that its symmetry number is equal to 1. The difference in symmetry between two isomers can have a significant effect on their melting point. For example, Heilbronner and Dunitz (1993) observe that the more symmetrical isomer, neopentane, melts at −16°C, whereas the less symmetrical isomer, n-pentane, melts at −130°C. Hargittai and Hargittai (2005) note that other areas that have been profitably studied with symmetry methods include molecular vibrations, electronic structure and chemical reactions. In his seminal essay, More Is Different, Anderson (1972) discusses the important role of symmetry in physics, saying that “it is only slightly over- stating the case to say that physics is the study of symmetry;” for more discussion of Anderson’s views, see Jenkins (2000). Anderson points out the central role of symmetry breaking in solid-state physics (“many-body” physics); e.g. in such phenomena as superconductivity, anti-ferromagnets, ferro- electrics, liquid crystals, etc. When symmetry breaking occurs in a system, the resulting system exhibits less symmetry. In addition, the lost symmetry may be hidden, although a trace of it may be left behind (e.g. sound wave vibrations). Anderson argues that one cannot simply “construct” solid-state physics from the science which underlies it; viz., elementary particle physics. Rather “entirely new laws, concepts, and generalizations are necessary” so that “the whole becomes not only more than but very different from the sum of its parts.” He views the sciences as a hierarchy (elementary particle physics > solid-state physics > chemistry > molecular biology > cell biology > … > psychology > social sciences), where ultimately the same 494 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013) set of fundamental laws underlie the sciences, a view he calls “reduction- ism.” However, he parts ways with many reductionists, in that he believes that one cannot “construct” one stage in the hierarchy from the preceding one. Instead one needs new laws and concepts like symmetry breaking. These ideas are well established in the sciences located lower in the hierarchy; however, Anderson predicts that the more complex sciences near the top of the hierarchy will exhibit the same behavior: “Surely there are more levels of organization between human ethology and DNA than there are between DNA and quantum electrodynamics, and each level can require a whole new conceptual structure.” Another example of understanding that arose from the unification of atomic physics and chemistry is that of Mendelev’s periodic table of the elements, familiar to many from high school. As observed by Icke (1995): “The presence of the shells, mandated by Pauli exclusion, is the cause of the different chemical behaviors of the elements, and of the periodic table of these elements.” So we have unification in mathematics, physics, and chemistry, with symmetry an important factor. What about biology?

2.3. Unification in Biology There has been skepticism in some quarters about the idea of “laws,” “laws of nature,” “laws of form,” etc. in biology. For example, the ge- neticist Dover expressed the following view at a conference on mind and language (see Piattelli-Palmarini et al. (2009)): “I want to point out that the whole thrust of modern-day genetics is going against such ideas of laws of form and principles of natural law.” By “laws of form” he seems to have in mind reaction-diffusion models such as Turing (1952) proposed and the laws of growth that D’Arcy Thompson (1992; 1st edition, 1917) discussed in his On Growth and Form., However both reaction-diffusion models and Thompsonian laws of growth are currently very much under discussion in mainstream biology. The case that Dover discusses concerns positional information in segmen- tation of the larva of Drosophila melanogaster. But no one has claimed that the Turing reaction-diffusion model should account for every biological mechanism. There are other cases in the literature where the Turing model has been applied in interesting ways; e.g. to fish pigment pattern (Kondo et al. (2009)), to hair follicle spacing (Sick et al. (2006)), to glycolosis (Strier and Ponce Dawson (2007)), and to cell division (Howard et al. (2001)). For example, Strier and Ponce Dawson (2007) conclude of their proposal BIOLINGUISTICS 495 for a mechanism for glycolysis as follows that “to the best of our knowledge, this is the first closed example of Turing pattern formation in a model ofl a vita step of the cell metabolism, with a built-in mechanism for chang- ing the diffusion length of the reactants, and with parameter values that are compatible with experiments. Turing patterns inside cells could provide a check-point that combines mechanical and biochemical information to trig- ger events during the cell division process.” Another path of research is to consider a larger class of systems of which Turing structures are a special instance, as is the case with “flow and diffusion-distributed structures” studied by Satnoianu et al. (2001). In fact, Cartwright et al. (2004) proposed a model for the embryonic development of left-right asymmetry in vertebrates based on fluid dynamics and suggest the model could possibly be accounted for by the mechanism discussed by Satnoianu et al. For a review of brain asymmetries, see Toga and Thompson (2003). Returning to the discussion of Thompson’s laws of growth, Dover’s criticism of laws of form (and principles of natural law) are also directed at current work on the biology of language. He seems worried that linguists may subscribe to the idea of laws of form “out of reach of the genes” or “beyond the genes.” But as we saw above, current work on language is based on the uncontroversial assumption that properties of language come from the interaction of (at least) three factors—genetic endowment, experience and principles not specific to the faculty of language. And in the discussion at hand, Chomsky states only that “[laws of form] … emerge from the principles of physics and chemistry, which say that these are the ways in which molecules can work, and not a lot of other ways.” Ander- son noted above that, as the field of solid state physics (many-body physics) developed, “entirely new laws, concepts, and generalizations” proved necessary.e W will demonstrate below that even such ideas as symmetry breaking that proved of great value in solid state physics also carry over into a number of areas of biology. Keller (2007) has questioned the nature of the “laws of biology,” in an essay, A Clash of Two Cultures. The two cultures she is speaking of are those of physics and biology. She asks: “does biology have laws of its own that are universally applicable?” She thinks not. She argues that biology is based on historical contingency. In a reply, Enquist and Stark (2007) note that Kant raised similar concerns about the “science” of chemistry, saying that it had not risen to the status of a Science (with a capital S). They point out that D’Arcy 496 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013)

Thompson argued that chemistry had evolved into a Science and that biology was about to become a quantitative Science as well. The authors also note that the question of historical contingency is also present in other quantitative sciences, such as cosmology, geology and economics. The authors conclude that “the future of biology belongs to those who follow Thompson’s roadmap.” We note that the question that Keller asks is misphrased, as there is no reason to insist that the laws be “universal.” As Anderson noted above, in more complex systems like condensed matter physics—and we would include biology—“entirely new laws, concepts, and generalizations are necessary” so that “the whole becomes not only more than but very different from the sum of its parts.” For example, in condensed matter physics, we have the Landau theory of symmetry breaking which explains such phenomena as superconductivity. This is an emergent property that arises when we study the interaction of many atoms. In biology, there is the well-studied phenomenon of the falling cat which, if it falls upside-down, rotates in mid-air in an (optimal) way so as not to violate the law of the conservation of angular momentum (as it cannot). Marsden (1992) notes that “it turns out that the solution of the falling cat problem is closely related to Wong’s equations that describe the motion of a colored particle in a Yang-Mills field.” Is this a “law of biology?” It would seem to make more sense to say that the cat’s nervous system has evolved in such a way as to elegantly solve the problem of controlling its fall under the constraint of the universal law of conservation of angular momentum. It is certainly not a universal law of biology, in the sense that it is not genetically programmed into all animals (apart from some mi- croorganisms that swim at low Reynolds number studied by Shapere and Wilczek (1987)), although human divers and astronauts are able learn to use the principle. We think that this perspective should be compatible with Keller’s concerns—as she herself notes, “of course, the laws of physics and chemistry are crucial” (in biology). Klopper (2011) elaborates on this theme by noting that “when D’Arcy Thompson penned his 1917 book On Growth and Form he boldly declared that the morphologist—devoted to understanding the structure of organ- isms—is ipso facto a student of physical science. His meaning was clear: the growth of complex structures mediating specific biological function is underpinned by an intrinsic mechanics, an appreciation of which is crucial to a broader understanding of both form and function.” This observation is part of a commentary on a recent article by Savin et BIOLINGUISTICS 497 al. (2011) in Nature. In this work the morphology in question is the verte- brate gut tube and the mechanics involved is the differential strain between the gut tube and the adjacent dorsal mesentery tissue. The authors show that the looping morphology of the gut tube can be explained by this mechanism. She notes that this work is a “timely nod to Thompson’s century- old ideas, given the recent surge of physicists and mathematicians into the biological sciences …” Savin and colleagues note that what they call the “metaphoric approach to biological shape” is “epitomized in D’Arcy Thompson’s On Growth and Form,” which emphasizes “the role of differential growth in determining form.” However, recent work has shown that “to understand morphogenesis in three dimensions, it is necessary to combine molecular insights (genes and morphogens) with knowledge of physical processes.” The contribution of the research of Savin et al. is to “bring a quantitative bio- mechanical perspective to the mostly metaphoric arguments in On Growth and Form.” Evidence drawn from animal diets and gut residence times supports the idea that the “diversity in gut looping patterns” can be simply explained by mechanical origin and “because it is sufficient to modulate the uniform tissue growth rates, tissue geometry and elasticity of the gut-mesentery system to change these patterns, this is the minimal set of properties on which selection has acted to achieve the looping patterns found in nature.” Li and Bowerman (2010) review many applications of symmetry breaking in a number of areas, including cell division, cell polarization, asymmetric division of stem cells, the generation of left-right asymmetry of the body axis in mammals, movement, generation of cells with different fates, etc. Palmer (2004) has studied examples of symmetry breaking in biological systems where “developmental plasticity” is the operative mechanism where (as he puts it), “phenotype precedes genotype,” where the phenotype is “direction of asymmetry.” Stewart et al. (2003) have suggested a symmetry breaking analysis of origin of species for the case of sympatric speciation; e.g., when there is no geographical or other barrier present between subpopulations. Accord- ing to Darwin (On the Origin of Species), 13 species of finch evolved on the Galápagos Islands from a common ancestor by gradual changes (e.g. in beak length) brought about by natural selection. The authors propose a symmetry-breaking bifurcation to be the mechanism for sympatric speciation, which predicts a sudden speciation event when the system becomes unstable; i.e., “bifurcations occur when the state of the system changes from being stable to being unstable; the system then seeks a new stable state, 498 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013) which may mean a big change …. Symmetry breaking is a particular type of bifurcation behavior, found in symmetric systems.” If, for example, “a species of birds with medium-sized beaks splits into two, then one group has shorter beaks, the other has longer ones, and suddenly there are very few birds occupying the old middle ground, which then get selected out” (if, for example, the medium size seeds are no longer available in sufficient quantity). Trevisan et al. (2007) model neural behavior with symmetry breaking, which has also proven useful in investigating systems such as singing in songbirds, for example, canaries, although the syrinx, used for song-produc- tion, does not exhibit any obvious asymmetries. Fee et al. (1998) studied the song system of the zebra finch and were able to demonstrate “that the isolated syrinx behaves as a classic nonlinear dynamical system,” with such properties as period-doubling and transitions from “periodic to chaotic.” Trevisan et al. modeled the neural circuits that control the muscles as a set of non-linear equations, which are underlyingly symmetric, in accordance with the fact that the neural circuitry and the vocal organ are perfectly symmetric. However, the solutions to the equations reflect spontaneous symmetry breaking bifurcations, which they suggest is “another example of how nature can achieve complex solutions with minimal physical requirements.” Let us recall a final application of symmetry considerations in biology; viz. the “falling cat” problem, discussed earlier. For a number of years, the ability of a cat to rotate from an upside-down orientation and land on its feet presented a puzzle. Some thought that this rotation violated an iron-clad principle of physics, the law of conservation of angular momentum. For if the cat began upside-down with angular momentum = 0, then it should not be able to generate any more angular momentum to flip over into an upright position. This became known in the literature as the “falling cat” problem. The problem was finally solved with the help of some deep mathematics from differential geometry, where it was shown that by altering its shape during the fall, as it rotated, conservation of angular momentum was not violated by the cat. This result became enshrined as a mathematical theorem, the “falling cat” theorem. It was also shown that the falling cat’s motion corresponded to the motion of a colored particle in Wong’s equation(s) in gauge theory and that this solution was in some sense optimal, as discussed in Marsden (1992). This is an elegant application of the “Galilean method.” This analysis abstracts away from the details of brain architecture and circuits. Nor does BIOLINGUISTICS 499 it depend on any understanding of the underlying genetics, or the evolutionary origin of the ability of the cat to perform this feat. As far as I know, nothing relevant is yet known in these areas. But the “falling cat” theorem sheds light on what the underlying brain circuits and algorithms do, as well as on what they cannot do. For example, minimally, no algorithm for flips and rotations of the cat can operate such that it would cause a violation of angular momentum. This provides us with an illustration of how symmetry and optimality can guide us in biological investigations as well.

3. Language and Other Cognitive Systems 3.1. Symmetry in Linguistics Note that symmetry considerations play a role in a number of areas of linguistics, including the faculty of language (syntax, morphology, semantics, speech systems), language change, language learning, and language evolution to name a few. In the present context, we are considering symmetry as a candidate for a “principle not specific to the faculty of language” (see discussion above) within the framework of Minimalism, as discussed in Boeckx (2011), but similar considerations apply in other approaches as well. Some work on properties of (a)symmetry in language include the huge body of Minimalist work just mentioned as well as in theories that preceded Minimalism and, as just mentioned, in theories based on other perspectives. However, we also note work that highlight questions of symmetry, asymmetry or antisymmetry, such as Kayne (1994), Di Sciullo (2005, 2011), Citko (2011), Haider (2013) and Liao (2011), among others. Some of the work on language change, language acquisition and evolution of language has taken place within the framework of dynamical systems. In this context Nowak and Komarova (2001) have derived a set of equations, which they call the “language dynamics equations” which give the population dynamics of grammar evolution. They run computer simula- tions which vary assumptions about the search space of Universal Grammar, the learning mechanism, population size, etc. Here too symmetry has played a useful role. For example, Niyogi (2004) (and Niyogi (2006)) has used symmetric and asymmetric nonlinear dynamical models to study lexical and syntactic change, the study of which he calls the “emerging field of population linguistics.” Such concepts as symmetry and stability (stable and unstable equilibria) are used in the study of the language dynamics equations. Similarly, Mitchener (2003) also uses bifurcation theory with the language dynamical equation to study problems 500 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013) of language change such as the transition from Old to Middle English under the influence of Scandinavian invaders. Cucker et al. (2004) and Cucker and Smale (2007) investigate the language evolution problem based on a model for emergent flocking behavior of birds. In the case of flocking, they investigate the conditions required for the convergence of the flock to a common velocity. This is a particular case of the more general problem of “reaching of consensus without a central direction.” They demonstrate how their model might find application in the study of the “emergence of common languages in primitive societies, or the dawn of vowel systems.” For another study examining the emergence of speech systems from the perspective of self-organization and symmetry breaking, see Oudeyer (2006).

3.2. Symmetry in the Warlpiri Kinship System The mathematician André Weil contributed an appendix entitled “On the Algebraic Study of Certain Types of Marriage Laws (Murngin System)” to a book on kinship systems by the anthropologist Lévi-Strauss (1971). Weil devised an analysis of the Murngin kinship system in terms of group theory. Later on Mary Laughren (1982) analyzed the kinship system of the Warlpiri aborigine tribe in terms of the symmetries of the dihedral group of order 8. Every Warlpiri belongs to a “skin group.” Warlpiri has eight skin groups in all. The names of the skin groups for males begin with “J” and the names for females with “N.” The skin determines one’s obligations toward all other members of Warlpiri society, and even toward outsiders. It determines, for example, which marriages are considered “preferred.”

Male Female JANGALA NANGALA JUNGARRAYI NUNGARRAYI JAPALJARRI NAPALJARRI JAKAMARRA NAKAMARRA JUPURRURLA NAPURRURLA JAPANANGKA NAPANANGKA JAPANGARDI NAPANGARDI JAMPIJINPA NAMPIJINPA Kinship system in Warlpiri—8 Skins BIOLINGUISTICS 501

We have 8 × 8 = 64 possible skin group combinations for marriage. However, the actual preferred marriages are much more restricted than that, even if we exclude marriages within the same skin group. There are only a total of 8 preferred marriages. The skin groups for the father, mother and child are always different from one another (but fixed).

Father Mother Child JANGALA NUNGARRAYI J(N)AMPIJINPA JUNGARRAYI NANGALA J(N)APALJARRI JAPALJARRI NAKAMARRA J(N)UNGARRAYI JAKAMARRA NAPALJARRI JU(NA)PURRURLA JUPURRURLA NAPANANGKA J(N)AKAMARRA JAPANANGKA NAPURRURLA J(N)APANGARDI JAPANGARDI NAMPIJINPA J(N)APANANGKA JAMPIJINPA NAPANGARDI J(N)ANGALA Warlpiri Preferred Marriages and Children’s SKIN GROUP

Note that if you start with a female (mother) in generation 1, say a NUN- GARRAYI mother, she will have a NAMPIJINPA daughter, etc. … until wee cycl back to the NUNGARRAYI skin. Similarly, if we begin with a NANGALA mother and trace her progeny through 4 generations, we will cycle back to the NANGALA skin. Let’s take a closer look. Since the lineage is determined by mother-daughter, this is called a matrilineal system. It has two distinct (in fact, disjoint) matrimoieties.

Generation Mother Daughter 1 NUNGARRAYI NAMPIJINPA 2 NAMPIJINPA NAPANANGKA 3 NAPANANGKA NAKAMARRA 4 NAKAMARRA NUNGARRAYI

Generation Mother Daughter 1 NANGALA NAPALJARRI 2 NAPALJARRI NAPURRURLA 3 NAPURRURLA NAPANGARDI 4 NAPANGARDI NANGALA

Warlpiri matrimoieties—matrilineal system 502 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013)

Ascher (1994) notes that among the Warlpiri the matrimoiety determines interpersonal relationships, while the patriomoiety determines “inheritance rights, religious rituals, and activities in the politico-religious domain.” A depiction of the Warlpiri skin system from the point of view of the native Warlpiri may be found at http://mttheo.org/home/warlpiri-skin-system/. Summing up, we can revisit the table above Warlpiri Preferred Mar- riages and Children’s SKIN GROUP, to follow the changes in skin groups through the generations (numbering of skin groups is from Ascher (1994)):

Father Mother Child JANGALA - 1 NUNGARRAYI - 5 J(N)AMPIJINPA - 7 JUNGARRAYI - 5 NANGALA - 1 J(N)APALJARRI - 4 JAPALJARRI - 4 NAKAMARRA - 8 J(N)UNGARRAYI - 5 JAKAMARRA - 8 NAPALJARRI - 4 JU(NA)PURRURLA - 2 JUPURRURLA - 2 NAPANANGKA - 6 J(N)AKAMARRA - 8 JAPANANGKA - 6 NAPURRURLA - 2 J(N)APANGARDI - 3 JAPANGARDI - 3 NAMPIJINPA - 7 J(N)APANANGKA - 6 JAMPIJINPA - 7 NAPANGARDI - 3 J(N)ANGALA - 1 ‌ Warlpiri Preferred Marriages and Children’s SKIN GROUP (REVIS- ITED)

Laughren (1982) demonstrated the Warlpiri kinship system can be analyzed as having the same structure as the dihedral group of order 8; that is, the symmetries of the kinship system are the same as the symmetries of the square. Note that once one has established the underlying group-theoretical structure of the skin system one can prove theorems about the kinship group (Cooper (2013)). Theorem 1—A woman is always in the same group as her maternal great-great grandmother. By way of illustration, assume the woman is in group 1. Then her mother is in group 3, her grandmother is in group 2, and her great grandmother is in group 4. Finally, her great great grandmother is in group 1, the same group as the woman we started with. Theorem 2—A man is always in the same group as his paternal grandfather. Again, assume the man is in group 1. Then his mother is group 3. That means his father must be in group 7. Then his grandmother must be BIOLINGUISTICS 503 in group 5. Finally, his grandfather must be in group 1, the same group he is in. Theorem 3—A woman’s mother-in-law is in the same group as her daughter-in-law. Assume the woman is in group 5. Then her husband is in group 1. This means his mother (her mother-in-law) is in group 3. Her son is in group 7. Finally, his wife (her daughter-in-law) is in group 3. That is to say, this woman’s mother-in-law is in the same group as her daughter-in- law. Here is an application of symmetry at the interface of language and cognition using the same tools of group theory as are utilized in physics, chemistry and other areas of biology. We have seen that one can approach language and cognition from the top-down, from behavior to neural circuits, and from the bottom-up, by studying genetic networks.

4. Conclusion In nearly every subfield of biolinguistics, there is a wealth of data available—unanalyzed (or only superficially analyzed) human languages, imaging, gene research. There is no danger of running out of data any time soon.e W are fortunate that we don’t have to build giant particle accelera- tors to get more data to study. In conclusion, we stress again that symmetry is only one of many factors in design—we mentioned a few others—probabilistic or stochastic factors, computational efficiency, etc., as well as many other kinds of genetic and developmental constraints, including deep homology, developmental plasticity, combinatorial gene control and so on. But it seems safe to say that the continued study of properties of symmetry in the design of language should turn out to be both important and fruitful, as it has in many other areas. This is in part because of the useful properties that symmetry possesses: it unifies, it restricts, it guides, it predicts, it is non-domain specific, and it is often covert. The physicist Roger Newton (2000) has speculated on the nature of a “theory of everything” for physics: “The ideal ‘theory of everything’ might thus not be directly embodied in a set of equations, but in an all-encompassing symmetry principle from which the fields, the particles, and the dynamics would follow.” It would be too much to hope for an all-encompassing symmetry design 504 ENGLISH LINGUISTICS, VOL. 30, NO. 2 (2013) principle in such a complex system as the faculty of language, but we would agree with David Gross (1996), who was speaking of modern physics at the time, that symmetry should serve as a “guiding principle in the search for further unification and progress.”

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[received April 29, 2013, revised and accepted July 19, 2013]

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