Basins,
Evolutionary Leaps, and Morphogenesis:
Early Rough Draft
Link to August, 2003, SCTPLS Convention paper: Steps
to an Ecology of Emergence
This page builds
on the ideas developed in E42:
The logic of discrete dynamic systems. Familiarity that tutorial
or with the basin structure of dynamic systems in general and of N,
K, Boolean Systems in particular is important to understanding this
page.
E42 is designed primarily to address issues in human
epistemology. To understand how it might do so, especially in the context
of Bateson's equating the processes of evolution with those of learning,
requires that we examine how models of this type might provide insight
into evolutionary processes. Consequently this page will on the surface
address current issues the conversation about how evolution works. The
question running in the the background is how are such evolutionary
issues applicable to how knowing works?
Mitochondria
Lynn Margulis
(e.g., 1991) has proposed an evolutionary hypothesis, once controversial,
now widely accepted and where not fully accepted given careful consideration,
that the evolutionary move from prokaryote (single celled organisms without
a nucleus per se) to eukaryote (multi-celled organisms with true
nuclei) involved the joining of the simpler forms.
"Mitochondria
live inside our cells but reproduce at different times with different methods
from the rest of our bodies' cells. They are descendants of ancient bacteria.
Either engulfed as prey or invading as predators, these bacteria took up residence
inside foreign cells, forming an uneasy alliance that provided waste disposal
and oxygen-derived energy in return for food and shelter. Without mitochondria,
the nucleated plant or animal cell cannot breathe and therefore dies.
Every cell in our body contains a (former) bacterium, Mitochondria,
in co-evolutionary, symbiotic relationship without which the cell would die.
And what would we be without "our" cells?
Lichen
Lichens live in nearly
every terran environment from antarctic to the hottest desert to the Arctic.
They are a symbiont composed of an alga, a single celled plant, living inside
a fungus. Normally algae can only live in water or as a thin slime on wet
surfaces. As plant, the specific alga in lichen can create sunlight and carbon
dioxide to make food. In turn, fungi generally must live on decaying wood
and leaf mold as a food source. As a symbiont, with the alga inside the fungus,
they can live on rock surfaces to skulls bleaching in a desert. The fungus
provides an encapsulated environment that allows the alga to live out of water
while the alga converts sunlight and CO2 into food for both organisms.
Stem Cells
Stem cells are unique
in that they are unspecialized, they have no tissue-specific structures that
allow them to perform specific functions as do nerve cells, muscle cells,
or blood cells. Stem cells have two distinguishing and interesting characteristics:
First, they can divide and replicate themselves many times, a process called
proliferation; second, albeit unspecialized, they can give rise to the body's
specialized cells, including bone cells, lymph cells, blood cells, and so
on.
Which kind of specialized
cell arises from a stem cell depends on the context that the stem cells is
in, what its relationship is to surrounding cells is, and what sort of signals
it receives from the surrounding cells.
(Holland)
Add text.
Relationship
"May
I have a flower?
"How do you know the thing between an elephants eyes
is a trunk? Well what you actually want to say is that it is a nose. Why is
it a nose? Well it's a nose because it has two eyes, one on each side...
"So we've got these formal structures running through
the world. The most famous is the one that Goethe discovered which is that
stems... What he did to plant anatomy is what Chomsky has more recently done
to grammar. You were probably brought up to believe that a noun is the name
of a person, place or thing. A verb is the name of an action. And go is a
verb. Right? Now if you begin looking at that, it's very unsatisfactory. It
is much more satisfactory to say that a noun is a subject of sentences containing
verbs. Verbs are in a certain relationship to nouns, having them as their
subjects and objects. And go in the sentence Go is a verb is undoubtedly a
noun because it is the subject of a sentence. That is, Chomsky is substituting
a language of relationship for a language of relata (the things related).
He only named them by virtue of their relationship. That's the trick of it.
"And what Goethe discovered is that a stem is that part
of a plant that bears leaves. And what is a leaf? A leaf is that part of a
plant in the angle of which stems grow (called buds)...
"The biological world is organized in terms of formal
relationships.." (Bateson, Butterflies and Metaphors, Audio
Tape)
Natural Selection AND Emergent Self-organizing relations
"One of the purposes of an examination of self-organization
in complex systems is the that spontaneous order will help account for origin
problems in evolution. Everywhere in thinking about evolution, one confronts
the question of how hard it may have been to "find" a particular
structure or property. Such problems appear most trying when the structure
or property in question requires the concerted action of a large number
of constituents." Kauffman (1993, p. 21)
"Evolution is shaped not by one but by two sources
of order, natural selection and self-organization." Kauffman, (????)
Were we to propose,
as conventional evolutionary theory does, that natural selection is the
sole mechanism affecting evolutionary leaps, we
would be faced with awkward arguments about the details of how those leaps
take place. The fundamental awkwardness is that an enormous number of irregular
(some would say random) genetic variations would have to occur thereby producing
an enormous number of candidate beings against whom natural selection would
act, carving away all but the one (or those few) that functionally solved
whatever evolutionary puzzle was presented. Lots of monkeys, lots of years
typing irregularly on typewriters, and we will get the manuscript of Hamlet.
(Which Hamlet? Which folio? Which published copy in modern type instead
of the handwriting of the folio? Which edition with which footnotes? And,
after you choose one specific Hamlet, what about all the others?) The permutational
logic of generating the vast numbers required for natural selection to design
new forms dictates against there being enough time to come up with the sudden
shift to complex new solutions that is witnessed in the fossil record. A
second awkward issue is the pervasiveness of certain solutions, e.g., bilateral
symmetry, and within bilateral symmetry all the ways of getting two eyes,
and within two eyes, all the different ways of getting depth perception.
The third awkwardness is the suddenness of shifts, at least in come cases.
These awkwarnesses are not impossibilities they are simply raw implausibilities.
We've only become used to them because the slow random walk of natural selection
has come to be an almost unconscious scientific tenet.
A current and interesting
solution to the awkwardness of these arguments is that dynamic relations
among components of a system mathematically and logically produce emergent
order, what Kauffman calls "order for free," and that this new
emergent order can shift (basins) suddenly and swiftly to a whole new order
due to very few and small changes in the components. {The components themselves
can be conceptualized as emergent orders emerging from relations of sub
components.] Perhaps Hamlet is not a person, place or thing but rather a
name referring to a set of complex relationships among components (sentences?
themes in human stories?) that are themselves, in Chomsky's terms, a set
of relationships.
The
manner in which dynamic systems shift suddenly from one basin to another
is evocative (at least for some theorists) of fundamental issues both
in evolution and in the ontogeny of form (aka morphogenesis, aka development).
A basin
model provides, beyond natural selection, a second mechanism that, working
together with natural selection, eliminates the awkwardness in descriptions
of evolutionary change. Massive changes in form do not have to wait for
the keystrokes of monkeys, they are the expected attractor basins that
emerge from the interaction of components of a system.
Turing's
Morphogensis.
This current perspective
took impetus from a paper by Alan Turing in 1952. It has become the
most cited scientific paper of the twentieth century. Turing sought
to outline a model for how, once the zygote fertilized the egg, the
actual living form developed (morphogenesis) since morphogenesis is
not accounted for by either genetics or DNA.
Evelyn Fox Keller is a mathematical biologist
and historian of science. In her book, Making Sense of Life, she
describes Turing's paper.
"Alan Turing's name is not normally associated with
developmental biology, but his 1952 paper, "The Chemical Basis of
Morphogenesis," has had a deep and lasting influence on virtually
all subsequent attempts to model these processes mathematically. Turing's
foray into this quintessentially biological problem might come as a surprise,
but from his own point of view the connection was clear: his interest
in the problem of morphogenesis arose directly out of his preoccupation
with the design of the thinking machines, and out his curiosity both about
how human brains were designed and about how the structures of that design
came into being... Brains were too complicated to consider at first. But
how did anything know how to grow?
"An obvious place to begin was at the beginning,
at the start of an organism's life--that is, with the fertilized egg...
--Evelyn Fox Keller (2002, p. 89).
"[genetics] offered little if anything toward a
solution of the problems of differentiation and morphogenesis. If all
the cells of an organism have the same genes, and hence the same enzymes,
how is one to account for the development of and organization of the many
different kinds of cells required for the characteristic structure and
form of a complex organism? How could one bridge the gap between genetics
and ontogenetics?
"Turing, it seems, was determined to find an answer to this question;
once and for all, as he told his friend and former student Robin Gandy,
he meant "to defeat the Argument from Design." ... The specific
purpose of his paper as he wrote in he abstract was "to discuss a
possible mechanism by which the genes of a zygote may determine the anatomical
structure of the resulting organism." --Evelyn Fox Keller (2002,
p. 90)
"The usual assumption in the literature on explanation
is that the primary task of a scientific explanation is to provide a causal
account of a phenomenon. But what, we need to ask, is to be understood
as a causal account? For many people, the notion of cause implies a motive
force emanating either from some pre-existing material entity or entities
(such as germs that cause disease, or genes that cause the appearance
of traits) or from some precipitating event (in the sense that flipping
a switch causes a light to go on). Accordingly, the expectation of a causal
account is that it will identify the agent or event responsible for the
effect. Does Turing's model provide such an account, even in principle?
If so, to what does his analysis point as the locus of the cause?
"Here [i.e., Turing's model], the form of an organism is self-generating
and self-organizing, arising de novo in each generation out of the dynamical
interactions among the chemical products which the genes had (somehow)
catalyzed into being. Genes are assigned causal responsibility for producing
the relevant players but not for the subsequent generation of spatial
structure. In fact, no locus of cause--no prior agency or pre-existing
determinism--is invoked in the account of morphogenesis: causal responsibility
is assigned not to particular material or events but rather to a set of
interaction dynamics that might or might not be sensitive to the particular
players involved. For those who expect an explanation to identify particular
causal loci, such an account is a priori unsatisfying. Yet for
others, it is the attribution of causal responsibility to particular entities
or events that often appears unsatisfying, even to beg the question--especially
when the role (or even presence) of such entities or events seems itself
to require explanation. .... From such a perspective, Turing's analysis
is appealing precisely because it "offered a way out of the infinite
regress into which thinking about the development of biological structure
so often falls. That is, it did not pre-suppose the existence of a prior
pattern, or difference, out of which the observed structure could form.
Instead, it offered a mechanism for self-organization in which structure
could emerge spontaneously from homogeneity."" --Evelyn Fox
Keller (2002, p. 101, 102)
Turing modeled, using chemical equations, the nonlinear
dynamic relations among basic chemicals in morphogenesis. A key point of
his article, arrived at through intense derivation, was that form arose
from the interactions of linked equations without in any sense that form
(e.g., whorl pattern in leaves grouping up a stem) being located in or a
characteristic of the interactions between the equations themselves. He
found systems of stationary and moving waves that could describe the whorl
of leaves on a plant, tentacle pattern of a hydra, or the dappled patterns
of spots in animal fur. This is the core of morphogenesis, the emergence
of form anew each time that a set of coupled processes run together. No
"designer" need be postulated; the form comes into being through
the relations of the components. Turing, ironically lacking the computers
we have today, was forced to perform tedious calculations by hand and noted
that, as computers developed more fully, the kinds of forms his approach
would be able describe would also develop.
Zebra stripes
E42 is based on simpler, Boolean operators than the functions
used by Turing. Even in E42's simple realm (see
E42 tutorial) deriving the transition tables and hand coloring visual
representations of the flow of logic would be onerous. It would be onerous
for the simple zebra stripe examples presented immediately below. Fortunately
for this train of thought, we have more useable computers today than Turing
had in 1952. Therefore we will be able to demonstrate a core sense of the
idea that Turing was communicating without the extensive handwork and difficult
derivations he performed. Not only that, but we will be able to move beyond
static snapshots (as in his figure depicting dappling) of the form-generating
process and demonstrate the forms as that dynamic processes Turing was addressing
in his derivations. This is a key insight to the approach to form started
by Turning. Forms are not things, although as with leaf patterns or animal
spots, they may appear to be things. In fact they are emergent processes,
always being generated dynamically in the moment by the relations between
other processes. They are more like standing waves or moving waves. A stationary
wave in a mountain stream may appear to be static and stable; yet it is
in each moment holding its form by the interactions of fluid processes.
Table 1 shows static snapshots of basin patterns from two
small discrete dynamic systems generated by E42. Panels (a) through (d)
are all from the same dynamic system. (While only four are shown, that system
has eight basins, two with length L=1, and six with basins of length L=5.)
Panel (e) shows one basin from a different system; it is included merely
to show that there are many systems that can produce an at least vaguely
similar form. There are many ways to get striped camouflage.
The four patterns of zebra stripes shown in (a) through
(d) can shift, one to another, based on changing the state (0 to 1 or 1
to 0) of a single node on a particular iteration in the dynamics of the
system. (The analysis which let's us know the details of the previous statement
is beyond the scope of this web page.) The point is that very small changes
in the state of the underlying system can provoke a large change of form.
This is very different than saying that a process like natural selection
must do a massive random walk by permutationally changing the values of
all the nodes in combination to get from one form to another.
Table
1. Camouflage-like striped patterns |
| The
first four columns (a to d) are four basins from the same dynamic system.
The fifth column (e) is a basin from a different dynamic system. |
a |
b |
c |
d |
|
e |
|
|
|
|
|
|
The web
applications below will give you some experience with the dynamic systems
contribution to the discussion about these evolutionary and morphogenetic
issues.
Zebra
Stripes with Motion and Perturbation
Tabby
Stripes
Discussion
(Is still being developed)
I want to be clear that I am using the E42 dynamic
systems model to conceptualize two related but distinguishable process: evolution
and morphogenesis. That the model's application is apt (at least as I've framed
the issues) in both cases may or may not be a conceptual problem. On the surface
it would seem that the simplicity of having the same type of model describe
issues in the development of form and in the way evolution might work seems
desireable. If indeed "Ontology recapitulates phylogeny" is a useful
descriptive principle, then evolution and morphogenesis would be expected
to have a tight relationship. Desireable or not, our discussions have mixed
these two cases.
Evolutionary
Insights. I'll begin the discussion be repeating the major
points (in exactly the same words) that was made in the Zebra Stripes page,
in case you skipped that web page.
The Interplay of the processes of
Natural Selection and Self-Organizing Form. A single, focused perturbation
can provoke a system to produce very different kinds of forms (patterns).
Kauffman's (1993) theory proposes that evolution is shaped by two processes,
self-organized emergence of form (morphogenesis) and natural selection. Experiments
1 and 2, which demonstrated a sudden shift of form from one striped pattern
to another, simulates the contribution of self-organization to evolution.
Concurrently, in a ecological context, natural selection would be working
in conjunction with self-organization: Which of the various camouflage patterns
(found in Experiments 1 and 2) would survive in a given context? That would
be shaped by natural selection. For example if night
migration became desirable, the rare black camouflage would be more functional
than other patterns. Those other patterns would be selected against in the
context of night migration because predators would kill more of the young
and vulnerable beings with those striped fur patterns before they could reproduce.
In contrast, if a snow adaptation became desirable, then the rare white pattern
would be more functional in that context than other patterns, particularly
than the all black pattern. The black and the striped patterns would be selected
against. In the context of a particular kind of change of context in vegetation
color, one of the striped patterns might be more functional and other patterns
selected against.
Natural Selection is a theory about how
various pressures act on a whole population to shift the statistical occurrence
of particular gene patterns within that population.
Notice here that the massive shift of design from one basin
to another is done deterministically by the interplay of the variables of
the dynamic system that determine the existence of the basins. This is kind
of process Turing's Morphogenesis paper addressed in a pioneering way. There
is no Homunculus nor is there a Great Designer. Nor does natural selection
need to be overburdened to account for the creation of the designs themselves
because the designs as Turing proposed are inherent in the recursive interplay
of the variables that define the structure of the system. Natural selection
only has to select against designs that function poorly in context.
Morphogenic Insights.
Morphogenesis (Self-organized form) is a
theory about how the actual ontological form (e.g., camouflage) comes into
being in a given existential being. Suppose that a genetic change occurs in
a particular being due to mutation or recombination (e.g., sexual mixing of
genes). What form will that being take? Self-organizing processes inherent
in the interplay of processes within that being will determine which particular
pattern of form emerges. Later, selective pressures of a given environment
will determine if the the being who has assumed that form gets to reproduce
or not.
The insights described here are no more than what Turing
described in 1952, but here perhaps they are expressed in a form that makes
them more accessible to more people. The core concept is that form emerges
from the interplay of nonlinear recursive processes. Most importantly, form
in question is not in any way to be found in any of the processes that are
interacting (they have, of course, their own form). There is nothing like
the visually evocative striped patterns we're labeling here as "Zebra
Stripes" anywhere in the truth tables or transition matrices of E42.
What we are calling the striped form is a result of the interplay of all the
logical relations as they play in unison and as they are expressed in the
visual medium of the Smilie representation. In the same way, the argument
goes, there is the form of a human being is nowhere to be found in the genetic
code. Rather, the human form is found in the interplay of the genetic variables
as they play in unisou and as they are expressed in the medium of the cells.
(Remember, fetal stem cells do not know what kind of cell to become except
in relation to the cells around them.)
Defeating "the Argument from Design."
Turing's insight, and the insights of all the researchers on emergent systems
and self-organization who have followed is profound. The emergence of complex
and elegant order from processes that don't contain those levels order does
not require an external, intelligent designer. The new order, as surprising
and as complex as it is, is found to be a mathematical and logical consequence
of the interaction of well defined processes. This does not require the universe
to BE those mathematical and logical processes (this is all just a model)
but assuming that the universe is a interplay of some sorts of processes then
those processes themselves would be susceptible to generating such self-organized,
emergent order.
Self Organization: Escaping the Infinite Regress
of Reductionism. Another part of the insight is that we do not need
to be caught in the infinite regress of reductionistic thinking, which, as
a parody, would have us all be subatomic physistis since everything we're
interested in would reduce that. The new alternative is that whole orders
of form self-organize from the interplay of variables at any level. And these
new orders are to be understood fully only at their own level. As Holland
(1998, p. 227) states it, "When macrolaws can be fromulated, the behavior
of the whole pattern can be described without recourse to the microlaws...
that determine the behavior of its components."
Of course, causal reduction to a lower levels of analysis
is explicitly included in this new alternative--the human form (or, in the
case of E42, the zebra stripes) is caused by the interplay of the genetic
(or truth table) operations. But what arises from that interplay is not to
be found in those processes per se. We can eat our reductionistic
cake and escape its stomach ache. A choreographer can express herself fully
with the human form and not be a geneticist to do it. AND she can be a geneticist
if she likes, knowing that the human form requires a genetic base. We can
live in a universe of determinisic processes and we can be poets, or, at least,
wish to be.
Back to Human Epistemology.
Sorry, I forgot the flash of insight I had about this. It'll come
back and I'll write it down.
References
Final
Quote. "Far from leaving
microorganisms behind on an evolutionary ladder, we more complex creatures
are both surrounded by them and composed of them. New knowledge of biology
alters our view of evolution as a chronic, bloody competition among individuals
and species. Life did not take over the globe by combat, but by networking.
Life forms multiplied and grew more complex by co-opting others, not just
by killing them." --Margulis & Sagan
