Addressing Loet, then Pedro
S: My reply is that the difficulty (?impossibility) of
quantitatively estimating the maximum entropy of a natural system
does not derive from our inability to foresee its future states, but
from an inability to categorize its many present possible states.
Consider the human body. How may conformations shall we say that it
could assume in the next moment? Of course, if we are attempting
this from some narrowly pragmatic project, we could impose, say,
three categories of conformations relative to the problem at hand
and sample only for these, thus eliminating an unknown number of
conformations of no interest. Perhaps I am too 'philosophical, but
it seems to me that the 'entropy' concept is no longer of much
interest here.
1. I agree that the concept of probabilistic entropy (information)
is yet content-free and cannot provide you with the specification of
biological categories. It is more like a calculus.
2. The claim that the maximum entropy of natural systems cannot be
specified in principle because the number of categories remains
unknown for philosophical reasons can easily be read as vitalism.
S: Well, but the problem is even worse for abiotic dissipative
structures like tornadoes.
Methodologically, however, the possibility to specify the number of
categories and hence the maximum entropy depends on the research
question. In population dynamics, for example, this may be more easy
than in the case of the human body. Stuart Kauffman once proposed to
consider the number of functionally differentiated cell types as a
variable across species.
S: Yes. As I said above, if we define the states of interest,
and subsume many similar states under some of these, we may be able
to contrive a maximum entropy. Thus, for people: standing, sitting,
lying down.
Wouldn't the inability to specify the number of categories mean that
the system is not properly specified? A human body, for example, is
specified only phenotypically? Would one not have to specify the
number of categories once one specifies in terms of what one wishes
to describe/explain the phenomena? (The human body is then an
explandum, but the crucial specification is the one of the
explanantes.)
S: Yes. But you see, this loses its philosophical interest in
favor of some pragmatic task.
My main argument, however, was that we do not have a parsimonous
alternative at the methodological level. In the social sciences, for
example, one is able to decompose the static complexity using
multi-variate analysis or to a very limited extent to do time-series
analysis with two co-variates. When there are three sources of
variance, it often becomes too complex for the methodological
apparatus (e.g., SPSS). This brought me to entropy statistics long
ago. One can extend the dimensionality by writing the number of
subscripts. The time dimension can additionally be brought in as
another set of subscripts (t, t-1, t+1, etc.). In addition to the
Shannon formulas, one can elaborate into Kullback-Leibler, etc.
It is a pity if this would not work also for biological systems.
S: I suspect that a clever experimental design could handle it.
I sometimes get the impression that with these Piercean notions
which you propose as an alternative, vitalism comes back on stage as
another (non-mechanistic) explanatory scheme. Perhaps, this would
explain the differences of opinion that pop up on this list from
time to time. For example, I would consider your systems of
interpretance -- yes, I read your book! -- as theoretical, while you
may wish to consider them as a (Piercean) methodology.
S: On this vitalism issue:
(a) my main point on this has been to push the importance of
vagueness, which though very difficult to handle technologically, is
a rich property of natural things, including 'parole' as opposed to
'langue'. You can see, I think, how this applies above.
(b) On vitalism, I have deconstructed this recently for an
encyclopedia. I will send you a copy separately. Basically my point
is that vitalism was an early glimpse of the problem (for science) of
historicity.
---------------------------
Pedro said:
I keep thinking that the pragmatic way that disciplines interact is
important regarding any order/disorder characterization. For
instance, let me return to the "water droplet" I mentioned weeks ago.
When the water droplet "decides" on its motion, it may be receiving
several strong dynamic influences (from the very local, to the most
general: a punctual splash, a wave, winds, a tide, a tsunami...).
The case is that the concept of "force" running throughout all
scales allows the integration or better the "averaging" of any
dynamic influence impinging on the system.
S: I would opt for 'integrate; inasmuch as these forces are
found at different scales in different strengths. Thus, I think that
the average of 1000 and 0.01 will not contribute to anything.
If the local and general influences cancel among themselves, the
droplet will just stay.
S: I think this is not quite just right. The Second Law will
invite something to happen to dissipate some of its embodied
energies. I think evaporation is the most likely.
A remark to make is that the different categories of forces which
are efficiently present will be brought to the analysis by
particular disciplines (if some relevant factor or discipline was
missing in our analysis, the prediction will fail).
The difference with the human case is interesting. Let us imagine
an individual in a big building, staying at the 25 th flour. Some
parties are soliciting him/her say for a dinner at the penthouse
(50 flour), while other parties are inviting to a concert at the
Atrium (ground flour). Will the individual happily rest on the
average 25 th flour, motionless like the droplet? Nope. It is an
"informational entity", and in order to make sense of his/her
moving-reactions to "meaningful" informations received, we need the
overall reference of his life cycle (or an abbreviated set of
states, preferences, experiences, etc.). Again, in the scientific
analysis a plurality of disciplines are called, even for very
trivial cases.
Alas, providing the integrative guidelines for the merely mechanical
response is pretty well established in our system of knowledge, but
a similar construct for informational entities is missing yet. Maybe
that quotation from Whitehead I stated days ago deserves more
attention ("operations of thought are like cavalry charges...") in
order to continue the discussion. Seriously, how science, the
sciences, are affected by the limitations of the individual?
S: Completely. Science cannot fathom individual cases. It can
only deal with ensembles using various statistical methods.
STAN
Best wishes,
Loet
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