At 12:34 AM 2006/01/30, Stanley N. Salthe wrote:
Loet said:
>Dear John and colleagues:
>
>The issue is, in my opinion: under which conditions is the emerging
system
>able to develop an additional degree of freedom? If this is the case, the
>situation cannot be contained in the phase space ex ante.
We may ask, what is entailed by the addition of a degree of freedom? In my
just previous posting (pasted in below) I noted that the addition of
biological constraints to a chemical system, or the addition of social
contraints to a biological system, each time limits further the freedom
with which involved molecules can take up positions in spacetime with
respect to each other, by initiating strong correlations between them. As
well, increasing amounts of entropy production would be taken over by
activities involving supramolecular configurations. From the point of view
of the involved molecules, the impostion of biology and sociality amount to
increasing degrees of UNfreedom. In fact, the degrees of freedom that are
instituted by biological and social informational constraints would not
have existed, as such, in a purely physical-chemical system, and so the
molecules would have been freer to move around as individuals. I think it
is not always clearly seen that the emergence of new realms in nature
(e.g., biology, sociality) involves the imposition of MORE constraints upon
a phsical-chemical system).
Yes. This was basically my point when I said originally in reply to Loet
that additional levels don't open more possibilities, but constrain the
possibilities. Loet tries to distinguish in recent posts between the
model and the object. This principal applies to either, and the
distinction is irrelevant.
An interesting question is how we can add dimensions to a model of a
system that is justified by our knowledge of the system. We do know that
in standard physics, all possibilities are given by the phase space of
the system. That is a matter of definition, so Loet is simply violating
technical terminology in the passage quoted above. If we add dimensions
to a model without justification, it is very easy to get the appearance
of emergence without any reality to back it up.
A standard procedure in classical physics is to include constraints on
the system in the dimensionality of the system by using generalized
coordinates. A simple but typical case is a bead on a ring, which has
the constraint of being on the ring. So we can reduce the dimensionality
by taking a one dimensional bounded space with the spatial dimensions of
angle (and dynamic dimension of angular momentum), yielding a
two-dimensional problem. A good internalist model of a system
(endophysics) should always use the minimal generalized dimensions that
are empirically required to describe the system. That gives the best
empirically supported dimensionality of the system.
Failure to see this, I think, happens because
these emergences are often viewed as ways that the world comes to transcend
its previous limitations. I think this perspective is misleading. What
substance this viewpoint has can be appreciated when -- after instituting
new degrees of freedom -- it happens that they do NOT get fixed, but remain
as part of informational entropy instead. Now the emergent system seems
to have acquired, indeed, more degrees of freedom to play with, even though
degrees of freedom have been lost at the lower levels.
I am unclear that degrees of freedom are lost in this case. I think that
typically the size of the space, not the number of degrees of freedom is
reduced. On the other hand, despite the loss in size, in an emergent
(non-Laplacean -- see below) system may have more dimensions, since the
new higher level order is not fully deducible from the lower, nor, as
Loet sort of noted in a previous post, can the higher level fully
control the lower level. In emergent systems there is in increase in
logical independence of the constraints on the system, and hence an
increase in dimensionality (understood as per the endophysics approach).s
This is to say that
degrees of freedom appear as openings and opportunities only when they are
NOT fixed. To the extent that a system acquires more and more degrees of
freedom AND they also get fixed, that system gets inceasingly nailed down
by information (this information 'overload' is the basis of a strong theory
of senescence). Thus, a biological system, say, or social system, is
interesting only to the extent that its various possibilities remain
uncertain. From the point of view of molecules at lower than biological /
social levels, degrees of freedom opened by the emergence of these higher
integrative levels impose barriers to their freedom to move whether they
are fixed or not. These new degrees of freedom can create openings and
possibilities ONLY at the higher levels, after closing down possibilities
at the lower levels. With emergence, some of the possibilities of
activity by a system will have moved upscale from the molecular level.
Assuming this can be restated without blurring dimension in the sense of
size with dimension in terms of degree of freedom, this would be right.
That is presupposing a lot of technical work, however. I think it is
very important that we keep as clear as possible what problems have been
solved and which are still open.
John said:
>In my original complaint I was objecting
>to the idea that sociality alone is sufficient to produce new
>information (or new information capacity). The issue is similar to
>that of whether or not neural nets can produce anything new
>(substitute social nets to get the argument for the social case
>mutatis mutandis). Jerry Fodor argues that they cannot, since space
>of possibilities is not increased by anything that happens in the
>net.
I think that this might not be quite correct. If there
come to be
habitual connections between certain nodes, like feedbacks in emergent
'autocatalytic' loops, the rates of reaction of such regions will become
slower than the average for the network, and if that rate is significantly
different, even a new level of scale might emerge. In the 'unevolved'
network it might be that the rates of communication between nodes would be
power law distributed, but if different rates are not allocated to certain
regions (as would be the case that I just described) but could emerge
anywhere in the network, then there would have been no emergence of a new
level.
I once thought that this would do, Stan, but I no longer think so. Habit
is not enough. However habits typically do form from autocatalytic
loops, and something like these are required. More so, just mechanical
loops are not enough, since these can be reduced to the component
contributions (by numerical approximation, if nothing else, so they are
amenable to a Lapalcian analysis). The cases I mentioned are not
amenable to Laplacian analysis. I think this is the correct test for
emergence, and it requires a dissipative system (or at least an
available potential energy source or sink -- we know only of the
latter). Fodor is right about connectionism. It is not sufficient. I do
not mean by sufficient necessary. Of course there are networks in which
emergence is possible. Specifically, ones that are not amenable to
Laplacian analysis.
STAN's posting:
>Suppose we have two heterogeneous systems with the same numbers of the
>same kinds of molecular constituents.
>System A is purely physical/chemical. The states of the system pass on
>endlessly to new configurations, each one >is historically unique but
in
>the long run the system is ergodic. It is not very far from the most
>likely >configuration of thermodynamic equilibrium.
>System B has further levels of organization (say, both 'biological' and
>'social'). But we are reductionists, and we >seek to observe only the
>chemical level constituents at any time. We will find that these low
>level configurations >in System B are selected from possibilities that
>might arise in System A. There is no new information here -- >except
>INFORMATION itself. That is, System A (except for the heterogeneity
>itself) is one of pure informational >entropy, while system B has had
>constraints put on possible configurations -- the emergent biological and
>>social level constraints.
>History has worked in System B too, but so has selection and preservation
>of (using a Peircean term) 'habits' (= >information). So there is no
>statistical difference in these systems at the phys-chem level, except
>that state >transitions have been drastically slowed down (generating
>friction) in System B. The generation of new historical >states (and
of
>entropy! -- which is produced as well during the higher level arrangings)
>has been partially moved >upscale, to the higher levels in System B.
But
>at the molecular level, we find no states not observable in System >A,
>merely strange associations of such states and lags in their
replacements.
>How might the transition from System A to System B be generated? By
>accelerated expansion of the overall >system (as in the Big Bang). In
the
>Universe this has increased the force pulling matter together, so that
>bigger >and bigger configurations (or configurational constraints)
become
>possible.
>Is it possible that some phsical-chemical configurations might be reached
>during imposition of the higher level >constraints that could not be
>possible in System A? I don't think it is possible to know the answer to
>this. If not, >then the only new thing to have emerged has been
stability
>of states, which, again, = information.
Comment [JDC]: I think the last question should be posed in terms of
likelihood rather than in terms of possibility. The intelligent
designers (intelligent designians? intelligent designators? -- the
IDniks) argue that what we see is impossible without guidance, but they
mean highly unlikely. The possibility of self-organization increases the
likelihood of macroscopic organization and its retention, since it
presupposes cohesion (see my stuff on this very useful concept), making
the unlikely much more likely. In fact from the lower level a
non-Laplacean system will seem possible, but highly unlikely, which
IDniks exploit. And the bulk of biologists (pace Dawkins) have left
themselves open to this by not being sufficiently self-critical. The
IDniks feed off scientific arrogance. (As does Fodor, actually -- he is
a predeterminist, but hardly an IDnik, though I have never understood
where he thought meaning does originate.)
Enough for now. That ties up a bunch of things into a nice knot -- Fodor
and the IDniks indeed.
John
--------------------------------------------------------------------------------
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Konrad Lorenz
Professor John Collier
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Philosophy and Ethics, University of KwaZulu-Natal, Durban 4041 South Africa
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Received on Wed Feb 1 08:19:35 2006
