Netherlands Graduate School of Linguistics LOT Summer School 2006 Issues in the biology and evolution of language

1. Netherlands Graduate School of LinguisticsLOT Summer School 2006Issues in the biology and evolution of language Massimo Piattelli-Palmarini University of Arizona Session 4 (June 15) The return of the laws of form (The third factor in language design)

2. My line of argument today • The Minimalist Program can be on the right track or can be on a wrong track • (I think it’s on the right track) • However • The central importance of general principles of optimal design would not be the only instance we find in biology (pace Pinker and Jackendoff) The return of the laws of form

3. A basic datum: • About 30,000 genes in the human genome • Which, among other things, have to build: • Millions of specific varieties of antibodies • And • 1011 “situated” neurons • 1013 to 1014 synapses (some excitatory, some inhibitory) • The crazy neuro-anatomist: Identifies a different synapse every minute, nonstop • It will take him 10 million years to complete the job The return of the laws of form

4. Possible solutions: • A combinatorial process of gene assortments (the immune system) • Only the basic “guidelines” are genetically specified (Monod’s and Changeux’s notion of a genetic “envelope”) • Massive auto-organization (mass laws, diffusion phenomena, morphogenes, internal gradients, spontaneous inter-coordination via nearest neighbor contacts, cell-adhesion molecules etc.) • Physico-chemical laws acting from “above” and “below” • Natural maximization processes (densest packing, minimal distance, minimal computation, minimal memory, surface-to-volume ratio, etc.) • Other kinds of combinatorics (birdsongs, parameters, syntactic derivations - the infinite use of finite means) The return of the laws of form

5. A caveat: • Diehard neo-Darwinians would be OK with optimization as an outcome of random trials • But, has there been enough time? Enough generations? Is the search-space too vast? • Sometime it seems to be (Cherniak et al. optimization up to “best-in-a-billion”) • What about optimization without a “search”? • (Antonio Coutinho’s joke about the stones) • Can evolution (adaptation and selection) be “riding” the narrow channels of what is possible? • Steepest descent, narrow canalization • Necessity from “below” and from “above” The return of the laws of form

6. Natural selection • Can only select what can be selected • Stability and reproducibility are basic constraints • The Evo-Devo revolution • Resistance to (small) perturbations is another (Waddington’s chreods and homeorhesis) • A very important concept: nudging • Genes as “nudgers” towards one or another pre-fixed pathway of development, among the very few that are at all possible (given physical laws and the boundary conditions) • Natural selection as the fixation of just such nudges The return of the laws of form

7. A logical priority: • “The primary task of the biologist is to discover the set of forms that are likely to appear [for] only then is it worth asking which of them will be selected.” • ( P. T. Saunders, (ed.). (1992). Collected Works of A. M. Turing: Morphogenesis. London: North Holland:xii). The return of the laws of form

8. The grand unification: • “Unless we adopt a vitalistic and teleological conception of living organisms, or make extensive use of the plea that there are important physical laws as yet undiscovered relating to the activities of organic molecules, we must envisage a living organism as a special kind of system to which the general laws of physics and chemistry apply. And because of the prevalence of homologies of organization, we may well suppose, as D’Arcy Thompson has done, that certain physical processes are of very general occurrence. . . What is novel in [this diffusion reaction] theory is the demonstration that, under suitable conditions, many diffusion reaction systems will eventually give rise to stationary waves; in fact to a patterned distribution of metabolites”. (Turing and Wardlaw 1953/1992: 45) The return of the laws of form

9. A traditional debate: • The extremely low probability of every biological trait (Monod, Dawkins, Pinker, among others) • What is the probability baseline? • Of the aggregation of molecules whirling freely in a broth? • Or of complex spontaneous morphogenetic processes to start with? (Ilya Prigogine versus Monod; Hilary Putnam versus Daniel Dennett) • Is there a theory-free (absolute) metric of probabilities? • Probably not! The return of the laws of form

10. Order from chaos: The Belhusov-Zhabotinsky reaction • http://online.redwoods.cc.ca.us/instruct/darnold/DEProj/Sp98/Gabe/intro.htm • Boris P. Belousov, director of the Institute of Biophysics in the Soviet Union, submitted a paper to a scientific journal purporting to have discovered an oscillating chemical reaction in 1951, • it was roundly rejected with a critical note from the editor that it was clearly impossible. • His confidence in its impossibility was such that even though the paper was accompanied by the relatively simple procedure for performing the reaction, he could not be troubled. • If citric acid, acidified bromate and a ceric salt were mixed together the resulting solution oscillated periodically between yellow and clear. He had discovered a chemical oscillator. The return of the laws of form

11. Order from chaos: The Belhusov-Zhabotinsky reaction • Another Russian biophysicist, Anatol M. Zhabotinsky, refined the reaction, replacing citric acid with malonic acid • and discovering that when a thin, homogenous layer of the solution is left undisturbed, fascinating geometric patterns such as concentric circles and Archimedian spirals propagate across the medium. • Therefore, the reaction oscillates both in space and time, a so-called spatio-temporal oscillator. The return of the laws of form

12. The Belouzov-Zhabotinsky patterns in a Petri dish The return of the laws of form

13. Bautiful animations are to be found in: http://online.redwoods.cc.ca.us/instruct/darnold/DEProj/Sp98/Gabe/intro.htm Oscillations in time and space (spontaneous morphogenesis) The return of the laws of form

14. Bautiful animations are to be found in: http://online.redwoods.cc.ca.us/instruct/darnold/DEProj/Sp98/Gabe/intro.htm The recipe 10ml 0.48M malonic acid 10ml saturated KBrO3 20ml 0.6M H2SO4 10ml 0.005M ferrion 0.15 g Ce(NH4)2(NO3)6 Oscillations in time and space (spontaneous morphogenesis) The return of the laws of form

15. Beautiful animations are to be found in: http://online.redwoods.cc.ca.us/instruct/darnold/DEProj/Sp98/Gabe/intro.htm Oscillations in time and space (spontaneous morphogenesis) The system is not at equilibrium: No violation of the 2nd Law of Thermodynamics. The return of the laws of form

16. http://hermetic.nofadz.com/pca/bz.htm A computer simulation (cellular automaton) of the B-Z reaction can be run on the website The return of the laws of form

17. The return of the laws of form

18. Ilya Prigogine (1917-2003) • Nobel Prize in Chemistry 1977 • “For his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures” • “Non-equilibrium may be a source of order. Irreversible processes may lead to a new type of dynamic states of matter which I have called “dissipative structures””. • “…a formulation of theoretical methods in which time appears with its full meaning associated with irreversibility or even with “history”, and not merely as a geometrical parameter associated with motion”. The return of the laws of form

19. a single solution for the value 1, but multiple solutions for the value 2. From Prigogine’s Nobel Lecture The return of the laws of form

20. In this way we introduce in physics and chemistry an “historical”element, which until now seemed to be reserved only for sciences dealing with biological, social, and cultural phenomena. a single solution for the value 1, but multiple solutions for the value 2. From Prigogine’s Nobel Lecture The return of the laws of form

21. A central consideration • “Every description of a system which has bifurcations will imply both deterministic and probabilistic elements…., the system obeys deterministic laws, such as the laws of chemical kinetics, between two bifurcations points, while in the neighborhood of the bifurcation points fluctuations play an essential role and determine the “branch” that the system will follow.” • The theory of bifurcations (catastrophe theory) is due to René Thom (see infra) • “The development of the theory permits us to distinguish various levels of time: time as associated with classical or quantum dynamics, time associated with irreversibility through a Lyapounov function and time associated with "history" through bifurcations. I believe that this diversification of the concept of time permits a better integration of theoretical physics and chemistry with disciplines dealing with other aspects of nature”. The return of the laws of form

22. Some historical landmarks

23. D’Arcy Wentworth Thompson (1860-1948) on “The Laws of Form” (1917) • Biologists have overemphasized the role of evolution, and underemphasized the roles of physical and mathematical laws in shaping the form and structure of living organisms. • The Miraldi angle, the Fibonacci series, the golden ratio and the logarithmic spiral. • “Beyond this stage of perfection in architecture, natural selection could not lead; for the comb of the hive-bee, as far as we can see, is absolutely perfect in economising labour and wax”. (Darwin, 1958:249) • ”….the beautiful regularity of the bee's architecture is due to some automatic play of the physical forces.” (D’Arcy Thompson) The return of the laws of form

24. http://au.geocities.com/psyberplasm/ch5.html The music of the spheres The return of the laws of form

25. The snowflake The return of the laws of form

26. D’Arcy Thompson’s famous grids A simple mathematical transformation converts one form into the other The return of the laws of form

27. The return of the laws of form

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29. The return of the laws of form

30. The central ideas: • You only have to specify 2 or 3 parameters for the grid • And you generate all the superficially “different” forms • Different rates of chemical diffusion may be the key • Same forces, same physical laws, only slightly different lines of minimal resistance • Or directions of a gradient • Or axes of maximal diffusion • (in my terminology) just a little bit of nudging The return of the laws of form

31. A straightforward inference • If the action of a gene, or a genetic network, consists in specifying the values of a few parameters for chemical diffusion • And/or activating a few genes at the right time in the right cells • Even the most elaborate forms of life can be explained • As we will see in a moment: in some cases, the “solutions” for a given parametric space can be extremely limited, with sharp discontinuities between them. • Minor quantitative variations can give rise to major qualitative differences. The return of the laws of form

32. Enter mathematical biology • Differential equations for growth, extinction and stable oscillations Alfred J. Lotka 1880-1946 Vito Volterra 1860-1940 The return of the laws of form

33. A forerunner: the Belgian Pierre François Verhulst (1804-1849) The return of the laws of form

34. Solutions to Verhulst’s logistic equation The return of the laws of form

35. Carrying capa- city of the medium Solutions to Verhulst’s logistic equation The return of the laws of form

36. Alfred J. Lotka and “physical biology” (1924) • “… a viewpoint, a perspective, a method of approach, … a habit of thought…which has hitherto received its principal development and application outside the boundaries of biological science….. Namely: the study of fundamental equations whereby evolution is conceived as redistribution of matter.” (pp. 41-42). (my emphasis) • sustainable rates of growth, birth and mortality rates, equilibria between species, biochemical cycles and rates of energy transformations, the evolution of human means of transportation. The return of the laws of form

37. The Lotka-Volterra equations y = n. of predators x = n. of prey , ,  population parameters The return of the laws of form

38. The Lotka-Volterra equations y = n. of predators x = n. of prey , ,  population parameters The ratios between the parameters decide whether there is extinction, stable oscillations, transients etc. The return of the laws of form

39. An attractor: a dynamically stable state (mimicry is another application) The return of the laws of form

40. Limit cycles The return of the laws of form

41. One limit cycle and one attractor The return of the laws of form

42. The central ideas: • Extremely complex dynamic patterns • Closed orbits, limit cycles • Qualitatively different regimes determined by slight variations in parametric values • Discontinuous transitions in spite of a continuum of parameters’ change • Attractors • Critical and super-critical bifurcations • A lot of nudging in these systems The return of the laws of form

43. Limits of all these approaches • Poaverty of the mathematical tools (see René Thom 1975) • The “age of specificity” was yet to come • The microscopic determinants were unknown • Diffusion and catalysis were the only available concepts • No “real” genetics • No idea of a genetic blueprint • No idea of gene regulation • No idea of genes as switches • No idea of gene networks The return of the laws of form

44. Enter the mighty Turing • The Chemical Basis of Morphogenesis (1952) • Reaction-diffusion processes • “A system of chemical substances, called morphogens, reacting together and diffusing trough a tissue, is adequate to account for the main phenomena of morphogenesis” • Th[is] investigation is chiefly concerned with the onset of instability”. • A sphere and then gastrulation • An isolated ring of cells and then stationary waves • A two-dimensional field and then dappling The return of the laws of form

45. The purpose of Turing’s paper: • “Is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism” • “The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts.” (my emph.) • ..morphogens (Waddington’s evocators) diffusing into a tissue somehow persuade it[sic] to develop along different lines than would have been followed in its absence.” The return of the laws of form

46. A most revealing statement: • “The genes themselves may also be considered to be morphogens. But they certainly form rather a special class. They are quite indiffusible. Moreover, it is only by courtesy that genes can be regarded as separate molecules.It would be more accurate (at any rate at mitosis) to regard them as radicals of the giant molecules known as chromosomes. • “The function of genes is presumed to be purely catalytic. They catalyze the production of other morphogens, which in turn may only be catalysts.” The return of the laws of form

47. A vicious circle? • “Eventually, presumably, the chain leads to some morphogens whose duties are not purely catalytic”. • (a breakdown into smaller molecules that increase the osmotic pressure in the cell) • “The genes might thus be said to influence the anatomical form of the organism by determining the rates of those reactions which they catalyze. • … the genes themselves may [thus] be eliminated from the discussion.” • Hormones and skin pigments are other kinds of morphogens The return of the laws of form

48. In essence • The physics and the chemistry of the reaction-diffusion processes is all we need • The genes speed up certain processes, and that’s all. • We can ignore them in the model. • A “leg-evocator morphogen” may be present in a certain region of the embryo, or diffuse into it. • The distribution of that evocator in space and time can be regarded as fixed • We then pay attention only to the reactions “set in train by it.” • That’s how a leg will develop in that region. The return of the laws of form

49. The toolkit: • Standard equations of diffusion, and of periodical oscillations • The law of mass action • Standard catalytic reactions • Rates of diffusion of the morphogenes (the cell walls being a screen, with pores) The return of the laws of form

50. A puzzle: spherical symmetry • How do we “break” that symmetry (to get a horse) • Casual symmetry-breaks can become permanent and be amplified • Noise and instability can produce differences in the rate of migration of morphogens • Standing waves can be generated • A ring of N cells with only two morphogens • There is a “chemical wave-length” that does not depend on the dimension of the ring • It will be attained “whenever possible” but there will be constraints and approximations. The return of the laws of form