At this point, LB have already
erred. LB have mistakenly interpreted the relational mappings in the
(M,R)-system diagram as equations (see bolded in quote
above). They spend p. 61 describing how the "equational formulation" is
wrong. They clearly do not understand the entire concept of relational
models. For example, here is their supposedly damning conclusion of this
discussion:
"Since metabolism and repair change
an organism, we should actually expect the function f that comes
out of p(b) to be different that the one that goes into
b(f) and transforms a to b, since the
process is actually unfolded in time (this is the "helical" argument). This
modeling approach, however, projects all of time into a single point." [p.
61]
That is, they argue that the specific
f that is acting as the function of metabolism cannot be
the same f is being output by the repair process at a given
moment in time. Hence, the logic behind the model must
be faulty. However, relational models are precisely atemporal
representations of relations. (This is why chapter 5 of Life
Itself is conspicuously entitled "Entailment Without States:
Relational Biology".) Near the beginning of chapter 5, Rosen clearly
states:
"On the formal
side, we shall see that the inferential structure characteristic of
relational biology is much richer than, and at the same time very different
from, the formalisms we have considered heretofore. Our systems are assigned
no states, no environments, and there is no
recursion." [LI p. 109, ital. orig.]
This is later reiterated. After
describing the basics of relational models, Rosen contrasts the relational
approach with the Newtonian, state-based approach:
"In the
relational approach, on the other hand, the situation is quite different. As
I have developed it so far, there is no time parameter, no states, no state
transition sequences. There are only components (mappings), and the
organizations, the abstract block diagrams, which can be built from
them." [LI p. 134]
Thus, it is entirely erroneous for LB
to interpret relational models, such as the (M,R)-system, as an "equational
formulation". They do not address their argument to a relational model,
but instead to what they think is a set of equations. Therefore, their
main argument and their main point is entirely invalid.
LB demonstrates another lack of
understanding of Rosen in sec 2.6 of their paper after summarizing their main
argument, when they say:
"More importantly, this [Rosen's
approach] is probably not the right approach. After all, claims that
complexity is non-computable contradict claims that formal systems are
computable, since computability is only defined for formal systems, and
cannot be proven or even properly defined for non-formal systems. There are
many such confusions in the literature." [p. 65]
Again, by misinterpreting
relational models as predicative equations, LB mistakenly asserts that these
models are thus computable (by virtue of being formal systems).
They further suggest that Rosen is claiming that non-computability is a
property of the organism, rather than of the formal model, and so Rosen must
be confused, since it is rightly nonsensical to speak of computability of
non-formal systems (such as organisms). On the contrary, it is LB who is
confused. Rosen is quite clear that computability criteria apply to the
models, not to the organism:
"I call a
material system with only computable models a simple system or
mechanism. A system that is not simple in this sense, I call
complex. A complex system must possess noncomputable
models." [EL p. 325]
In their next section, LB spend 3 pages
discussion analytic vs. synthetic models. They state at the beginning of
the section that "we describe some other difficulties with the
Theoretical Biology program as stated...". [p. 66] It is unclear
why LB perform this exercise, since, in fact, they end up restating the
same conclusion that Rosen makes in ch. 6 of Life
Itself. Namely, that there are generically far more
analytic models than synthetic models to a system.
As best I can discern, LB seem to
provide this argument because they mistakenly think Rosen is arguing that a
"largest model" is the universal case: that analytic models are
always only the inverse of synthetic models. Nothing could be more wrong.
Rosen remarks near the beginning of his chapter on analytic and synthetic
models:
"In a
sense, it is the thrust of this entire work that this hypothesis of
analysis = synthesis must be dropped. Above all, it must be dropped if we
are to do biology, and hence a fortiori, it must be dropped if we are to do
physics. By dropping it, we enter a new realm of system, which I call
complex, and which in certain sense needs to have no synthetic
models at all. The distinction between relational and Newtonian models of
natural systems will become crucial here, because as we shall see, the
former extend to the realm of complex systems, while the latter
cannot." [LI p. 154]
LB clearly do not realize the
consequences of dropping the "analytic = synthesis"
hypothesis (consequences which lead directly to Rosennean complexity),
even though they (apparently unwittingly) agree with Rosen that such a
hypothesis is unwarranted by purely formal considerations.
All in all, I find that this paper
by Landauer and Bellman fails to comprehend the fundamentals of Rosen's
relational modeling concepts, the import of Rosen's discussion of analytic vs.
synthetic models, Rosen's use of computability criteria of models, as well as
Rosen's concept of complexity. Their paper misinterprets these
concepts and their arguments are directed against those
misinterpretations. As such, their paper offers no legitimate argument
and thus no damage to Rosen's actual concepts; but by its gross
misstatements, this paper does a disservice to Rosen's work.
Regards,
Tim
> -----Original
Message-----
> From: ROSEN Forum [
mailto:***]On Behalf Of Tim
> Gwinn
> Sent: Wednesday,
February 18, 2004 8:03 PM
> To: ***
>
Subject: Re: Paper by Landauer and Bellman
>
>
> It is
available for purchase ($22US) from AIP at:
> http://content.aip.org/APCPCS/v627/i1/59_1.html>
> I am printing it out now...its 12 long
pages....after I digest
> it, I'll try
> to have some comments
sometime tomorrow.
>
> Regards,
> Tim
>
> >
-----Original Message-----
> > From: ROSEN Forum [mailto:***]On Behalf Of Kevin
> > de Laplante
> >
Sent: Wednesday, February 18, 2004 5:31 PM
> > To:
***
> > Subject: Re: Paper by Landauer and
Bellman
> >
> >
> > I'd be anxious to get a hold of
this myself, if it's out there.
> >
> > Kevin
>
>
> > ----- Original Message -----
> > From: "Jannie
Hofmeyr" <***>
> > To:
<***>
> > Sent: Wednesday, February 18,
2004 3:23 PM
> > Subject: Paper by Landauer and Bellman
>
>
> >
> > > Dear list-members
> >
>
> > > Does anyone perhaps have a pdf of the following paper
by Christopher
> > > Landauer and Kirstie Bellman?
> >
>
> > > Theoretical Biology: Organisms and Mechanisms
>
> > AIP Conference Proceedings Vol 627(1) pp. 59-70. September 2,
2002
> > >
> > > Abstract:
> > > The
Theoretical Biology Program initiated by Robert Rosen is
> intended
to
> > > identify the key theoretical characteristics of
organisms, especially
> > > those that distinguish organisms from
mechanisms, by looking for the
> > > proper abstractions and
defining the appropriate relationships.
> > There are
> >
> strong claims about the distinctions in Rosen's book "Life
> >
Itself", along
> > > with some purported proofs of these
assertions. Unfortunately, the
> > > Mathematics is incorrect, and
the assertions remain unproven
> > (and some of
> > >
them are simply false). In this paper, we present the ideas of Rosen's
>
> > approach, demonstrate that his Mathematical formulations and
>
proofs are
> > > wrong, and then show how they might be made more
successful.
> > >
> > > Sounds like something we could
discuss if we only knew where Rosen
> > > supposedly "went
wrong".
> > >
> > > Thanks
> > >
Jannie
> > >