Transcript University of Amsterdam LOT Summer School 2006 Issues in

Netherlands Graduate School of Linguistics
LOT Summer School 2006
Issues 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)
My line of argument today
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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)
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A basic datum:
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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
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Possible solutions:
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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)
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A caveat:
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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”
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Natural selection
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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
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A logical priority:
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“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).
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The grand unification:
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“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)
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A traditional debate:
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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!
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Order from chaos: The BelhusovZhabotinsky reaction
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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.
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Order from chaos: The BelhusovZhabotinsky reaction
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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.
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The Belouzov-Zhabotinsky patterns in a Petri dish
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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)
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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)
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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.
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http://hermetic.nofadz.com/pca/bz.htm
A computer simulation (cellular automaton) of the B-Z reaction
can be run on the website
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Ilya Prigogine (1917-2003)
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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”.
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a single solution for the value 1, but multiple solutions
for the value 2.
From Prigogine’s Nobel Lecture
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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
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A central consideration
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“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”.
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Some historical landmarks
D’Arcy Wentworth Thompson (18601948) on “The Laws of Form” (1917)
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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)
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http://au.geocities.com/psyberplasm/ch5.html
The music of the spheres
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The snowflake
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D’Arcy Thompson’s famous grids
A simple mathematical transformation converts one form into
the other
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The central ideas:
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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
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A straightforward inference
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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.
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Enter mathematical biology
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Differential equations for growth, extinction and
stable oscillations
Alfred J. Lotka 1880-1946
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Vito Volterra 1860-1940
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A forerunner: the Belgian Pierre François Verhulst (1804-1849)
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Solutions to Verhulst’s logistic equation
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Carrying capacity of the
medium
Solutions to Verhulst’s logistic equation
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Alfred J. Lotka and “physical biology”
(1924)
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“… 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.
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The Lotka-Volterra equations
y = n. of predators x = n. of prey , ,  population parameters
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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.
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An attractor: a dynamically stable state
(mimicry is another application)
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Limit cycles
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One limit cycle and one attractor
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The central ideas:
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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
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Limits of all these approaches
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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
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Enter the mighty Turing
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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
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The purpose of Turing’s paper:
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“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.”
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A most revealing statement:
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“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.”
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A vicious circle?
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“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
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In essence
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The physics and the chemistry of the reactiondiffusion 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.
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The toolkit:
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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)
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A puzzle: spherical symmetry
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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.
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Stationary waves of finite wavelength
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The truly interesting case.
Stable morphogenetic processes
Disturbances near the time when instability is
zero are the only ones which have any
appreciable definitive effect.
Under certain conditions, the most quickly
growing component may get a lead over its
closest competitor.
If a homogeneous one-morphogen system first
undergoes random disturbances without
diffusion, then undergoes diffusion without
disturbance, then we have dappling
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Dappling in 2D as the result of one morphogen
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Concentration of one morphogen (Y) in a ring of cells
“Variety with quick cooking”
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Concentration of one morphogen (Y) in a ring of cells
with two morphogens
final
Initial
Transient
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Spots and Stripes
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Activator and inhibitor
factors with different
diffusion rates can
interact to produce
regular spots/stripes
(Turing 1952).
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Biological instances
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The case of the sea-anemone Hydra and of the
leaves of the woodruff (Asperula odorata)
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Spherical harmonics: gastrulation
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Spherical Laplacian operator (vibrating strings
in three dimensions) with two morphogens
The concentrations of the two morphogens are
proportional, both being surface harmonics of
the same degree n
The skeletons of radolaria are instances
As the size of the sphere (the blastula)
increases, the wavelength of the concentration
is constant
If there is a perturbation, a pattern of
breakdown of homogeneity is created
It is axially symmetric around the perturbation
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Gastrulation
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The blastula grows with axial symmetry, but
At a greater rate at one end of the axis than at
the other end.
Chemical instability combines with mechanical
instability (elasticity of the tissue)
Gastrulation ensues
The axis is random in this theory, but biological
processes may well determine a privileged
direction (the animal pole)
Turing anticipates the use of digital computers
to simulate some model situations
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The ur-morphoge_
netic event in the
development of
the embryo
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Summing up: The third factor view
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The primary “engine” are physical and chemical
processes of a perfectly canonical kind
Biology only adds something like privileged
axes, selective catalysts, morphogens
The universal “basis” of morphogenesis is
genuinely universal.
Biology adds a “nudging” (in my terminology)
Maybe what natural selection does is selecting
those “nudges”
30,000 genes can do a lot of nudging of the
basic processes involved
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Where are we
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“Mighty” equations and all-covering laws of
physics and chemistry
But no specificity
1953 the double helix
1960 genes as switches
1960 the structure of myoglobin (Kendrew) and
hemoglobin (Perutz)
1961 the genetic code (Niremberg and
Matthaei, Crick and Brenner)
1970 Monod: what is true of E. coli is true of the
elephant
1977 Jacob: Evolution and tinkering
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A strange maverick: René Thom
(1923-2002) (Fields medal 1958)
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Originated by the French mathematician Rene Thom in the
1960s, catastrophe theory is a special branch of
dynamical systems theory. It studies and classifies
phenomena characterized by sudden shifts in behavior
arising from small changes in circumstances.
Catastrophes are bifurcations between different equilibria,
or fixed point attractors. Due to their restricted nature,
catastrophes can be classified based on how many
control parameters are being simultaneously varied.
For example, if there are two controls, then one finds the
most common type, called a "cusp" catastrophe. If,
however, there are more than five controls, there is no
classification.
For 4 controls there are exactly 7 elementary catastrophes
“If one must choose between rigour and meaning, I shall
unhesitatingly choose the latter”.
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The 7 elementary catastrophes
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Catastrophes in systems with only one state variable:
The fold
The cusp
The swallowtail
The butterfly
Catastrophes in systems with two state variables
The hyperbolic umbilic
The elliptic umbilic
The parabolic umbilic
http://perso.orange.fr/l.d.v.dujardin/ct/eng_index
.html (Lucien Dujardin)
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René Thom
Structural Stability and Morphogenesis English edition 1975
With a foreword by C. H. Waddington (Benjamin Publisher)
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Thom’s lexical semantics
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12 kinds of verbs in all languages
All based upon: Ending, being, beginning,
changing
Capturing, failing, emitting, rejecting, crossing,
stirring, giving, sending, taking, fastening, cutting
Concepts have a “regulation figure” a logos
analogous to that of living beings.
A grammatical category C is semantically denser
than another grammatical category C’ if a
regulation of a concept of C involves mechanisms
intervening in the regulation of C’.
Since the verb is indispensible for the stability of
the substantive, it is less dense than the noun.
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Theta roles (arguments)
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There cannot be more than 4 arguments for a
verb
In all the languages of the world
This is the result of the topology of actions
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A strange linguistic theory (see also
books by Jean Petitot)
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Morphogenetic fields determine semantics and
syntax (capture, assimilation etc.)
The stability of the subject is a central
constraint
In the “emission of the sentence” (sic) the
elements are emitted in the order of increasing
density.
The normal order is VOS
Because in a transitive interaction the object
may perish, while the subject survives
Other orders are (topological) transformations
of this basic order
Dictated by the necessity of communication
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The modern return of the laws
of form
Invariants of locomotion
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The Journal of Experimental Biology (2006) Vol. 209,
pp. 238-248 Unifying constructal theory for scale effects
in running, swimming and flying Adrian Bejan (Duke
University) and James H. Marden (Upenn)
“Animal locomotion is no different than other flows,
animate and inanimate: they all develop (morph,
evolve) architecture in space and time (selforganization, self-optimization), so that they optimize
the flow of material.” (p. 246)
Older theories: potentially common constraints
Constructal theory: universal design goals, from which
principles for optimized locomotion can be deduced.
These can explain the nature of the constraints
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The ingredients:
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Locomotion = streams of mass flow
Accomplishing the most for unit of energy
consumed
Morphing of river basins, atmospheric
circulation, design of ships, submarines etc.
Maximum range speed = U-shaped curve of
cost vs speed
One very narrow range of speeds that
maximize the ratio of distance traveled to
energy expended
Stride/stroke frequencies versus net force
output (for running, swimming and flying)
Predicts and explains the emergence of central
tendencies
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The ingredients:
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Mb = body mass
b = body density
g = gravitational acceleration
Lb = body length = (Mb/b)1/3
 = coefficient of friction
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From small insects to large mammals, the force produced when
moving at optimal speed is a multiple of body weight (applies to
running, swimming and flying)
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The return (brief list)
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Diffusion equations for gene frequencies
The Hardy-Weinberg equilibrium
Parental investment
Arborization structures (the fourth power law)
Foraging (more anon)
Biological motion (the 2/3 power law)
Connectivity in the cortex
Locomotion (crawling, walking, running,
swimming and flying)
The distribution of white matter and grey matter
in the brain
Birdsongs
Quorum-sensing (cell-to-cell and to tissue
coordination)
Kissing chromosomes and genetic waves
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Foraging
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Obviously crucial for reproductive fitness
On a par with fecundity, morbidity and mortality
rates
Essential variables:
Energy spent per unit mass of food collected
Energy for “handling”
Typical distance covered in the average
day/season
Individual strategies / collective strategies
Patterns of food sharing vs. competition
Generalists vs. specialists
Anatomical and physiological constraints
Ecological constraints (Anna Dornhaus UofA)
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Foraging
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More refined factors:
Probability of finding better food sources versus
value of a forgone available source and energy
spent in a further search
Reliability of routine strategies vs. new
strategies
Amount of information transmitted to / received
from other individuals
Hardwired habits vs. learning
Species specifications vs. individual variation
and innovation
Implicit “programs” versus cognitive capacities
(mental representations?)
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Foraging strategies as a function of the probabilities of finding a source
t = duration of food availability
Probab for a re-active searcher
Probab for a pro-active searcher
ps* = optimal proportion
of pro-active searchers
Dechaume-Moncharmont, F.-X., Dornhaus, A., Houston, A. I., McNamara, J. M., Collins, E. J.,
& Franks, N. R. (2005). The hidden cost of information in collective foraging. Proceedings of the Royal
Society (B Series), 272, 1689-1695.
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Several counter-intuitive predictions
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But well confirmed by data on honey bees
In the wild and in laboratory conditions.
Under certain environmental conditions, the optimum
strategy for a social insect colony is pure independent
foraging.
This prediction holds even when potential recruits
would benefit from information gained from successful
foragers by having a higher probability of finding food
than they would as independent foragers.
This is because of the costs of waiting for information in
the recruitment process.
Most intriguingly, such hidden costs are sufficiently
important to have noticeable effects even when the
food source is available for many days.
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Several counter-intuitive predictions
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Recruitment is not always adaptive, even when
the recruits have a higher probability of finding
food.
There is not necessarily a direct link between
an increase in individual performance after
information transfer
and collective energy gain over the whole
foraging period.
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Why do we care?
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Even “simple” species seem to have found the
optimal foraging strategy in different ecological
conditions
Something that can only be captured by quite
sophisticated mathematical computations.
How do we explain this fact?
Have they blindly explored a huge variety of
alternatives,
And natural selection has rewarded the best
ones?
Or are we witnessing the instantiation of some
general optimization principles?
Do we need genes “for” optimal foraging?
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