Part III, Rosen's "Autographical Reminiscences"

["Judith Rosen" <***>]

Part III of
AUTOBIOGRAPHICAL REMINISCENCES
By Robert Rosen
Copyright, Judith Rosen

It might be well to spend a moment on the general scientific ambience of
those years, since they were exciting in a way which can barely be dreamed
of today. On the "theoretical" side there was Schrodinger's little book,
"What is Life?", in which, however Schrodinger did little but repeat the
words and outlook of his student Max Delbruck. From my viewpoint,
Schrodinger did not begin to answer his question; he rather equated "life"
with a kind of stability, and asserted that "life" must be molecular because
molecules are stable too. In the late 1940's appeared Norbert Weiner's book
"Cybernetics", invoking a new technological language the Cartesian equation
between animal and machine. There was the confluence then crystallizing
between foundational work in mathematics itself (exemplified primarily in
the Turing machine and the execution of algorithms) and digital computation,
and the brain, embodied in the neural networks proposed decades earlier by
Rashevsky himself; all this roughly constituted the province of "Automata
Theory". There was the Theory of Information of Shannon. There was Game
Theory. And in Biology itself, there was the increasing inroad of digital
thought, of hardware and software, which were the concomitants of "molecular
biology". And of course, part and parcel of all this, was the newly emerging
strain of General Systems Theory, associated especially with names like
Bertalanffy and Ashby. A yeasty mix indeed.

To me, though, and in the light of my own Imperative, all thes things were
potential colors for my pallette, but not the palette itself. I regarded
them as monochromes, individually perhaps lovely in themselves, but not to
be applied when a different hue was required. I could not share the
prevailing sentiment that these developments, either individually or
collectively, would paint themselves into the picture I was striving after.
Rather, I felt it was the picture which would illuminate them.

Indeed, my own scientific work of those years was pushing me against these
currents. Consider, for example, the discovery which most shocked me in
those days, when I still had unlimited faith in the physicists' Quantum
Mechanics as the ultimate bridge between the rocks and the life. I had long
been puzzled by the fact that the state spaces they posited for every
material system were mathematically indistinguishable; abstractly identical;
isomorphic (they are all separable Hilbert spaces, and there is objectively
only one such). The perceptible differences between material systems must
thus lie only in a "choice of co-ordinates", and in how the observables, the
Hermitian operators on states, were labelled; hence in what, mathematically,
constituted the subjective. This in turn implied that we could get from one
system to any other by relabelling these observables; by calling one of
them, say, a Hamiltonian instead of another. Hence that any system would
appear to be any other system, if only we looked at them with the "right
eyes". The only escape from this disturbing conclusion seemed to be to limit
the universality of Quantum Mechanics itself... or what is the same thing,
enlarge what can constitute an observable or an observation, or a state.

I was unprepared to do this for a long time. But I was forced to it by the
following considerations, which I discovered in 1959. As I have already
noted, whatever else Quantum Mechanics say, it asserts that "information"
about any material phenomenon consists of observables evaluated on states.
Hence, a fortiori, "genetic information" must be of that character too, and
this must provide the material, physical basis of the formal "coding
schemes" which then so preoccupied everyone. So I tried to find what the
observables had to be in order to manifest this "information". The shock was
in discovering that the families of observables I characterized in that way
could not contain anything which behaved like a Hamiltonian. And, of course,
without a Hamiltonian, you cannot even get started in doing traditional
Quantum Mechanics. In a sense, what I then showed was that Quantum Theory
and Quantum Mechannics do not coincide, and that the former was much bigger
than the latter.

At the root of these considerations is the indissoluble dependence of
Quantum Mechanics upon energy conservation; that is what a Hamiltonian
expresses. What happens in rocks seems to fall within such structures; what
happens in life, as I showed then, and more sharply later, need not. There
was an immediate parallel with the "open systems" of Bertalanffy and their
devastating challenge to the Second Law of Thermodynamics; it was not that
the Law was wrong; it simply did not apply. I would say that, today, there
is still no satisfactory "physics" of open systems, primarily because people
persist in thinking of closed systems as fundamental, and of open ones as
simply closed ones canonically perturbed.

At any rate, such considerations provided the soil for a constant
preoccupation with when, and under what circumstances, two systems could be
considered in any sense identical; such studies ran a gamut from the physics
of the Gibbs Paradox, and the objectivity of entropy, to considerations of
similitude and conjugacy.

Such considerations, and many others like them, from many different
perspectives, led me away from the facile Reductionisms which almost all of
my colleagues were rushing to embrace, and which they identified with
science itself. From my perspectives, physics could not swallow Biology;
rather, any attempt to do so would have to radically transform physics.

Fortunately, I had a positive alternative to such negative, pessimistic
conclusions, in the spirit of Rashevsky's Relational Biology, and manifested
in my own (M,R)- systems. As I have characterized this spirit, it involves
"throwing away the physics and keeping the organization," instead of the
reverse. What remains then is an abstract pattern of functional
organization, which has properties of its own, independent of any particular
way it might be materially realized. Indeed, it is what remains invariant in
the class of all such material realizations, and hence characterizes that
class. It is my ultimate object of study' it, and not thos material objects
which happend to be available to realize it.

To me, such patterns, and the elements and relations which comprise them,
are as real and objective and perceptible as the products of any
Reductionistic fragmentation; indeed, in some ways more so. In my view, a
science too narrowly construed to encompass them from the outset is too
narrow to do Biology in, just as narrow identification of mathematics with
computability excludes thereby almost all of mathematics. More of this
later.

The study of these (M,R)-systems brought my mathematical training and
instincts to uses I could not have foreseen. For one thing, the diagrams
which expressed them were in themselves an immediate invocation of the
Theory of Categories. I had started to imbibe this theory during my
otherwise wasted year at Columbia University. The graduate algebra course I
took durin gthat year was taught by Samuel Eilenberg, and was really a
course in Category Theory; sets, operations, and structure-preserving
transformations. Eilenberg, of course, was one of the creators of Category
Theory. The other creator, Saunders MacLane, was at Chicago, where I imbibed
much more. I became intrigued by the historical roots of the Rheory, which
had grown out of the attempt to make algebraic "models" of geometric objects
in order to discriminate between them. It expressed in a purely mathematical
realm the patterns of relations, between objects and models, and between one
model and another, which I was trying to find in the realm of the living.
The numbers (e.g. Betti numbers) which came out of Algebraic Topology were
like the observables of material nature, but there was much more underneath
them. It has been one of my primary ongoing concerns to make all this clear.

My adaptation of Category Theory to the )M,R)-systems, and indeed my
utilization of Category Theory itself as a kind of framework for the notion
of modelling in general, is typical of how I have used my mathematical tools
over the years. Not so much in the making of particular kinds of models of
particular biological phenomena (although I have done a substantial amount
of that), or the invocation of specific theorems from specific mathematical
domains (although I have done that too) but rather an invocation of the
entailment patterns from which the theorems arise, or sometimes do not
arise. So I seldom have occasion to invoke a particular theorem from
Algebraic Topology (say); what is more germane to me is the relation
established between a space and its models, and between one model and
another; and why such relations hold.

Indeed, I have come to regard models in general as a natural but profound
extension of the concept of observability, as the physicist understands it.
A model indeed represents to me an inherent adjective, or property, or
quality, or attribute, of the system being modelled; what the old
philosophers called an essence, no less than any measured value of some
magnitude does. But rather than trying to reduce every model to such
measured values, or alternatively, trying to syntactically build every model
out of such numerical observables, I have had to proceed in quite a
different way. Indeed, it has turned out that most qualities of interest to
me, were simply not expressible in such limited terms. One must follow one's
"observables" to assume values other than mere numbers; to assume values in
inferential patterns (in models, in short), and at the same time allow the
referents of such observables to be other than conventional reductionistic
fragments. Once again, none of this seems to me in any way "speculative"; it
is as firmly grounded in observation as any reductionistic scheme. But it
involves a notion of "observation" far more broadly conceived than has been
usual, and tailored to the demands of Biology; traditional concepts of
observability, and the kinds of models which can be based on them, appear in
this light as very, very "special" indeed.

Thus, I have come to partition Biology into that which depends on an
underlying relational pattern (e.g. an (M,R)-system independent of how it is
realized; and that which depends upon the material details of a particular
realization (and of course, that which depends on both). And of course, the
word "realization" admits a great deal of latitude. For instance, I have
come to believe that social structures, as things in themselves, realize
many of the relational patterns which individual organisms to. To that
extent, we can learn deep things about each by treating the one as a
surrogate for the other, however different they may appear in exclusively
material terms. It was in exactly that spirit that I undertook, for example,
a long-term study of "anticipatory systems", which is still going on.

My concerns with "anticipation", in which what is happening now seems
determined by someing about the future, are worth describing in more detail.
Anticipatory behavior is in fact damned as "acausal", because causality is
construed precisely as allowing only the past to affect the present. I
initially softened this by interposing a "predictive model" as a transducer
between now and later. But nevertheless, the presumed telic or finalistic
aspects of anticipation seemd to violate the one-way causal flow on which
"objective science" itself is presumed to rest. And I noticed that my own
(M,R)-systems have an inherent anticipatory aspect, built into their very
organization.

Once again, my mathematical experience served to illuminate this situation,
mathematics, the quintessence of what is objective. In mathematics, the
analog of anticipation is impredicativity' a situation in which what is
defined depends essentially on having it available from the outsel. The
associated "self-references", in which something is getting outside a
single, one-way, coherent time-frame, can lead (and have led) to devastating
paradoxes. Russel called them "vicious circles", and it was believed that
the salvation of mathematics itself depended on eliminating them; somehow
straightening out the impredicative loops, and proceeding in a purely
syntactic way only from "past" through "present" to "future". Indeed, it was
part of the allure of the algorithm, embodied in the machine, that it could
only manifest this kind of flow, from input to output, and
impredicativities, by their very nature, could not arise in them.

The trouble with this is that by thus "saving" athematics from
impredicativity by indentifying it with what machines can do (i.e. with pure
sytax, or symbol manipulation, or word processing) the cost is relinquishing
most of mathematics itself. In a certain suggestive language, there are more
things in the "mathematical universe"than can be projected down
predicatively into a single coherent time-frame. This is a very Plantonic
thing to say, but it is still true. And I believe Biology shows that it is
likewise true in the causal realms of material reality as well.

My (M,R)-systems inherently manifest such an impredicative loop; one which
cannot be straightened out without losing everything. They are thus not
approachable via "machines" in the usual sense; they are not purely
syntactic objects. They are what I call "complex"; they mnust have
non-computable models. I would argue that, precisely by excluding temporally
closed causal loops, and indeed by indentifying this exclusion with science
itself, we have lost not only life, in my sense, but most of its material
basis, its physics, as well. To invoke a parallel mentioned earlier: just as
the "closed system" is too impoverished, to special, to be a basis for (say)
the physics of morphogenesis, exactly so is the simple system, one which can
be described entirely as software to a machine, too impoverished to
accommodate the living.
In fact, these two situations are closely related, but it would take too
long to explain that relation here.

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CONTINUED*******************************************


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