Of Minds and Language (20 page)

Just one final thing: about the myth of the unique relationship between a specific gene and its very specific effect. First let us set aside the confounding property of rampant pleiotropy of most genes – that is, each and every gene having widely diverse effects at one and the same time – and let's just concentrate on one gene and one of its effects. Some of the best characterized of all molecular genetic diseases are the hemoglobin thalassemias. Now if you talk to David Weatherall and all those guys who have been working several decades on these genes,
⁹
they tell you the following. If you take a number of individuals, each of which has the identical mutation in say the beta-globin gene, which in turn is embedded in thirty kilobases of identical surrounding DNA (presumably with identical epigenetic patterns of chromatin condensation and methylation), you can then ask the question, what is the phenotype of all these individuals sharing the identical mutation in the same sequence neighborhood? Will they all have beta-thalassemia as part of their phenotype? And the surprising answer is “No.” The disease phenotype is not just a specific effect of a specific mutation in a specific gene. They all have the specific mutant beta-globin allele but their phenotypes range from no clinical manifestations through to a requirement for life-long blood transfusions. This spectrum of effects arises because the rest of each individual's genetic background – all those other interactive genes (proteins) and metabolites, whether directly involved with blood metabolism or not, plus of course the internal and external environmental milieu – is absolutely crucial for the extent to which an individual goes down with beta-thalassemia. And the same story is emerging from the etiology of the majority of human diseases, once thought to be a specific consequence of single mutant genes. I think that in biology the pursuit of genetic subdivision, hierarchy, and specificity is not necessarily the appropriate approach to the seemingly indivisible, whether of legs or language. A recipe for despair or an exhilarating challenge?

F
ODOR
: At the end of the presentation (I think this is perhaps especially Massimo's department), you had some speculations about the biological encoding of
parameters. I wondered if we could relate this somehow to some of the thinking we have been doing at CUNY about that huge grammar lattice of ours.
¹⁰
We worry about the biological status of this huge amount of information. I want to divide it into two aspects. One is that there is this huge amount of information, all those thousands of subsets of relationships; and then there is also the apparent specificity of the information. It codes for very particular relationships. This grammar is a subset of this one, but not this one of this other one, something like that. Now, wondering how that information got there, we should consider the possibility that it isn't really so specific at all, that in fact there are many, many other relationships equally coded but that they are invisible to us as linguists, as psychologists. We don't know about them because those languages aren't learnable, so imagine just for a moment you had two grammars in the lattice, so to speak the wrong way up, so that the superset came before the subset. Then we would never know of the existence of the subset language because nobody would ever learn it. It would be unlearnable. So you can imagine that behind the lattice that is visible to us as scientists there is a whole lot of other stuff just like it that we know nothing about because it is arranged the wrong way to be put to use by humans in learning. So: unlearnable languages. It may be that the specificity of the particular parameters that we know about is actually illusory.

P
IATTELLI
-P
ALMARINI
: Well, this is really the core of the matter. I think that in the evo-devo approach to the evolution of language you have to take into account not just how we once got to the adult state; you have to take into account the whole process of getting there – how that evolved. And of course a very, very old puzzle is why we don't really have only one language. Since genetically we are predisposed to learn any language that there is, there is no specific inclination of a baby coming into this world in China to learn Chinese, nothing of the sort. So we have on the one hand the puzzle as to why we don't all literally speak the same language, and also on the other, why we don't have infinite variation beyond any limit, beyond any constraint. So the suggestion is that maybe what we have is a
minimax
solution, where you minimize the amount of genetic information and at the same time you optimize the amount of learning that there has to be in an acquisition somehow. Mark Baker (2001, 2003) has this hypothesis that the reason we don't all speak the same language is because we want to be understood by our immediate neighbors, but we don't want to be understood by people in the next tribe; which is a cute idea, but it really doesn't explain much, because you can only do that if you
already have an organ that is predisposed to have a large but finite set of possible languages. We could invent some codes that are different from having this parametric variation. So I think the consideration is in fact how complex the acquisition process is versus how much burden you have on the genetic or biological machinery. The guiding (and interesting) idea, in which Noam concurs, if I understand him correctly, is that you have a minimax, you have something close to the perfect compromise between loading the biology, loading the genetics, and having a reasonably complex acquisition process. You know, the things that you are doing and that Charles Yang is doing are closely related to this reflection.
¹¹
We will have to learn from you how exactly these things developed, how much work has to be done there and then continue possibly with some data on other functions, on other species, to see if we can get a grasp on how much genetic information is needed for this or for that, and whether this hypothesis of a minimax solution can be tested.

F
ODOR
: I guess I was trying to suggest that maybe there isn't as much biological design work to be done as we tend to think from our perspective, studying the particular cases, the particular languages that we observe, because in the case of language, if the design isn't optimal, we don't know about it, nobody is going to learn the language, nobody
has
to learn any particular language, so those languages just sort of disappear from view. So I am just wondering whether in fact there is so much specific biological design work going into what I still call universal grammar, and so the pattern of UG, as we tend to think.

V
ERCELLI
: I can answer Janet's question only indirectly, using an intriguing analogy – that between the problem of encoding what there is in language, and the central problem my own field, immunology, faced for years. Our problem was to figure out how a large but finite genome could harbor a huge amount of information without clogging up. As you know, that problem was solved by an atomization of the encoding process, whereby the final molecular repertoire results from rearrangements of multiple, smaller units. That allows for a relatively limited core – then the information is rearranged and used, switched on and off. Systems of this level of complexity run into this kind of problem: how do you build information capacity effectively but not at the expense of everything else in a genome which is finite? The idea that you make space by erasing is a little hard for me to picture, because somehow you have to encode what you erase as well as what you don't. Thus, the encoding problem remains. I would argue a better way to solve it is, as Massimo was saying, by minimizing what you encode and then being very plastic in the way you use what you encode.

Christopher Cherniak
^*

I will talk about combinatorial network optimization – that is, minimization of connection costs among interconnected components in a system. The picture will be that such wiring minimization can be observed at various levels of nervous systems, invertebrate and vertebrate, from placement of the entire brain in the body down to the sub-cellular level of neuron arbor geometry. In some cases, the minimization appears either perfect, or as good as can be detected with current methods – a predictive success story. In addition, these instances of optimized neuroanatomy include candidates for some of the most complex biological structures known to be derivable “for free, directly from physics” – that is, purely from simple physical energy minimization processes. Such a “physics suffices” picture for some biological self-organization directs attention to innate structure via non-genomic mechanisms, an underlying leitmotif of this Conference.

The innateness hypothesis is typically expressed in the DNA era as a thesis that some cognitive structure is encoded in the genome. In contrast, an idea of “non-genomic nativism” (Cherniak 2005) can be explored, that some biological structure is inborn, yet not genome-dependent; instead, it arises directly from simple physical processes. Not only, then, is the organism's
tabula rasa
in fact not blank, it is “pre-formatted” by the natural order: a significant proportion of structural information is pre-inscribed via physical and mathematical law.

In his opening remarks, Noam Chomsky described a strong minimalist thesis, that “a principled account” of language is possible: “If that thesis were true, language would be something like a snowflake, taking the form it does by virtue of natural law” (Chomsky “General Introductory Remarks,” this volume; see also 1965: 59). Of course, the snowflake reference calls to mind D'Arcy Went-worth Thompson's
On Growth and Form
(1917), where the paradigmatic example of mathematical form in nature was the hexagonal packing array, of which snow crystals are an instance. However, even the thousand pages of the unabridged 1917 edition of Thompson's opus contained few neural examples. Similarly, Alan Turing's study (1952) of biological morphogenesis via chemical diffusion processes opens a conversation that needs to be continued. In effect, we examine here how far this type of idea presently can be seen to extend for biological structure at the concrete hardware level of neuroanatomy. The key concept linking the physics and the anatomy is optimization of brain wiring.

Long-range connections in the brain are a critically constrained resource, hence there seems strong selective pressure to optimize finely their deployment. The “formalism of scarcity” of interconnections is network optimization theory, which characterizes efficient use of limited connection resources. The field matured in the 1970s for microcircuit design, typically to minimize the total length of wire needed to make a given set of connections among components. When this simple “save wire” idea is treated as a generative principle for nervous system organization, it turns out to have applicability: to an extent, “instant brain structure – just add wire-minimization.” The main caveat is that in general network optimization problems are easy to state, but enormously computationally costly to solve exactly. The ones reviewed here are “NP-hard,” each conjectured to require computation time on the order of brute-force search of all possible solutions, hence often intractable. The discussion here focuses upon the Steiner tree concept and upon component placement optimization. (For a full set of illustrations, see Cherniak and Mokhtarzada 2006.) The
locus classicus
today for neuroanatomy remains Ramón y Cajal (1909).

The basic concept of an optimal tree is: given a set of loci in 3-space, find the minimum-cost tree that interconnects them, for example the set of interconnections of least total volume. If branches are permitted to join at internodal junctions (sites other than the given terminal loci, the “leaves” and “root”), the minimum tree is of the cheapest type, a Steiner tree. If synapse sites and origin of a dendrite or axon are viewed in this way, optimization of the dendrite
or axon then can be evaluated. (Such an analysis applies despite the “intrinsically” driven character of typical dendrites, where leaf node loci are in fact not targets fixed in advance.) Approximately planar arbors in 2-space are easier to study. The most salient feature of naturally occurring arbors - neuronal, vascular, plant, water drainage networks, etc. - is that, unlike much manufactured circuitry, for each internodal junction, trunk costs (e.g., diameter) are higher than the two branch costs. The relation of branch diameters to trunk diameter fits a simple fluid-dynamical model for minimization of wall drag of internal laminar flow. Furthermore, when such micron-scale “Y-junctions” are examined in isolation, positioning of the junction sites shows minimization of total volume cost to within about 5 percent of optimal, via simple vector-mechanical processes (Cherniak 1992) (see
Fig. 8.1
).

Fig. 8.1. Neuron arbor junction (cat retina ganglion cell dendrite). (a) Branch and trunk diameters conform to
a fluid-dynamic model for minimum internal wall drag of pumped flow (laminar regime). (b) In turn, angle 0 conforms to the “triangle of forces” law, a cosine function of the diameters:
This yields the minimum volume for a Y-tree junction (Cherniak et al. 1999). So, “Neuron arbor junctions act like flowing water.”