Re: Last from me on Rosen for a while
DON MIKULECKY (MIKULECKY@VCUVAX.BITNET)
Fri, 3 Mar 1995 10:57:11 -0400
Don Mikulecky, MCV/VCU, Mikulecky@gems.vcu.edu
Reply to Cliff:
Cliff wrote:
> Thanks for everybody's comments. Even though Don and I don't appear to get
> along, I appreciate his effort and willingness to deal with me. I'm off to
> Europe Monday, and won't be able to look at any replies till I get to
> Francis' in a couple of weeks.
>
I still have trouble with this "getting along" commentary. I wish we could
simply dive in to these issues and realize that our person is not at risk
just because an idea we happen to be carrying at the moment is under heavy
scrutiny. I may turn out to be dead wrong about Rosen, but I need to
find that out by pusuing the argument as best I can to see if it really hangs
together. Let's try to forget the personality part of all this. I usually
do not commit this kind of energy, time and effort to arguing with people
I don't value and/or respect.
> Jeff:
> ====
>
>>I may be wrong about this, but I think he is saying that in the world
>>of biology, infinite regresses are here to stay. We shouldn't be
>>trying to figure out how to get rid of them (by developing reductionist
>>theory that doesn't look at the whole picture), we should be dealing
>>with them...incorporating the infinite regresses into our theory.
>
> Well, on the one hand, he notes the regress of state systems, and how
> Newton's introduction of acceleration as a state variable truncates the
> regress. He then goes on to note the potential regress in relational
> systems, and how his introduction of the crucial level of closure of
> efficient causation truncates the regress. In so doing, he claims to turn a
> regress into a CYCLE of causal explanation (yes, Don, I understand
> perfectly). Regresses and cycles are not the same, but they are related:
> cycles can generate regresses when they are approached linearly and teased
> apart; but regresses can result from other processes as well. That is what
> I showed in the former post: unpacking Rosen's relational scheme for the
> organism, which is itself cyclic, results in a regress. Newton's Taylor's
> series expansion is also a regress, but does not result from a cycle.
>
Yes, and I believe both Jeff and I have also pointed out that this is
precisely why Rosen said that you should expect to get just that if you treat
it in that way. This is also why Jeff says they are here to stay.
This is also why Jeff pleaded that we not get sidetracked about this and
focus on the issue of whether rosen's unique handling of the problem
can lead us somewhere.
> Onar:
> ====
>
>>If Rosen is right, why hasn't he come into the light of the scientific
>>community?
>
> As Don has said, Rosen is a highly respected and sought-after member of the
> systems theoretical community, at least. I can't speak to "science" in
> general. But, as I'm sure you appreciate, popularity during one's lifetime
> is hardly the standard one would want to apply to assess scientific
> validity or value.
>
> Don:
> ====
>
> I think that you think that I want to understand relational biology (RB)
> from the reductionist mathematical view AS OPPOSED TO the holistic,
> relational, gestalt view. In fact, Don, I WANT TO DO BOTH. The relational
> whole is something I think I understand already. It's the math that I don't
> get.
>
That, I think, is because you want the math to do something Rosen says
it can not do. His whole case seems built around that. If you use the
math alone, without the causal arguments, you fall back to the machine
metaphor.
> I understand and interpret Rosen at different levels and in different
> ways. One can take Rosen from the point of view of philosophy, of
> science, of systems theory, of category theory, of a god-damned
> first-order cybernetician left-brained modern mathematical
> reductionist (ahem :> ), indeed, of poetry.
>
> Thinking it over, I believe that this is part of the reason why you liked
> my review, but finds my later comments insufficient. In the review, I was
> attempting to put the book forward in its own terms, and at many different
> of these levels of language. Later on, I began to both develop a more
> critical perspective, and also to work more at the level of the FORMAL
> LANGUAGE.
That seems accurate. However, as we once were stuck at roughly this
same point, it seems necessary to realize that if you deal with Rosen's
argument AS A FORMALISM, you are then in a paradoxical situation. He spends
many, many, many pages on this point. No formalism canbe both complete and
consistant (Goedel).
>
> My later questions were very specific, and directly related to the formal
> level. Indeed, one of Rosen's strong claims (I can't find the page right
> now) is that not only can we tease apart these elusive, complex relations
> present in organisms, but we can do so in RB through FORMAL MODELING in a
> way not done in other systems theories. In paritcular, he suggests that
> category theory is the proper language, which has advantages over others
> (e.g. recursive functions).
>
> Let me cut to the mathematical chase and then get back to more general
> issues:
>
>>Notice also that your rendition of what is in the book reduces his
>>content and meaning BY IGNORING THE FACT THAT HE NEEDS TWO KINDS OF
>>ARROWS TO REPRESENT THE MAPPINGS. This should have been a clue.
>
> OK, maybe. Perhaps I have a problem with extended block diagrams in
> general. Let's consider the simple example on p. 250, with no closure or
> recursion. My understanding is that the single arrow
>
> f
> A ---> B
>
> means
>
> f:A->B ($)
>
> in function notation, where A and B are sets, and that that is equivalent
> to the compound arrow:
>
> f
> /
> /
> @
> A ---> B ($$)
Ah! Maybe we have it here. That is not my understanding at all.
Some of the mappings are between sets of "objects" and some are between
sets of mappings. Final cause deals with a mapping on mappings and
this is the key point in the closure argument. Beause the cause
is coming from a future, anticipated event, a mapping which seemed to
be unentailed is entailed, hence the closure. The KEY infinite regress
being ended (anologous to what Newton did) is in the fact that for
machines the use of final cause is of no help. There is still always
something unentailed. Extending the diagram to include this leaves
something unintailed again, and so on.
>
> where f--@A is the other color arrow. Then on p. 250 Rosen gives the
> diagram
>
> f
> / ^
> / \
> @ \
> A ---> B @--- Phi ($$$)
>
> f Phi
> which he claims is equivalent to A ---> B ---> H(A,B) where
>
> H(A,B) = { A->B }
>
> in function notation. But interpreting ($$$) in the function notation of
> ($) and ($$), I get f:A->B and Phi:B->f. But Phi:B->f cannot be correct,
> since f is an ELEMENT of H(A,B), not a whole set as it must be to be in
> the range of a mapping.
>
Here's where the mappings are of totally different character. Phi maps
onto a set of mappings, not a set like A or B. Only in causal terms
does this have the correct meaning. Ignore that and the whole thing
takes on a very sterile interpretation.
> Now back to the general argument:
>
>>Rosen accomplishes this
>>by finding a particular f which has a purpose, which has an answer to
>>the question why f? The trick is in that final cause means that SOME
>>B gives the reason for some f! This allows amapping from a B to f
>>and it closes the diagram.
>>The entire
>>argument above manifests itself in the turning around of one arrow in a
>>diagram, resulting in its achieving closure and terminating the regression.
>
> Yes, I think I understand all that at the level of English. What I find is
> that real understanding doesn't come until you work through all the horrid
> details of the math, though.
Well, here's where you either demand that the notions are totally formalizable
or accept that in the class of phenomena (complex systems and organisms)
of interest the impact of Goedel is dominant. At that juncture, it is not
merely holism ve reductionism in the usual parlance for that, too, has been
framed in a reductionist way. Rosen asks for more. He demands that
we recognize (as Hilbert was so reluctant to) thateven number theory
is a complex system and the attempts to formalize it are doomed to failure.
This is a true version of holism, but not the popular one.
>
>>Why this seems ironic with respect to our discussion is that our
>>reductionist training blinds us to the significance of such a ploy.
>
> Not mine. I, at least, feel capabale of talking and thinking about
> something in more than one way. In this case, I've been stubborn to keep to
> that way, and thought I made that clear (perhaps not). So when I ask "How
> does category theory help RB?", don't think that I can't or don't or don't
> want to understand RB in any other terms. On the contrary, I dwell on the
> mathematical questions precicely BECAUSE I believe I understand RB in the
> OTHER languages.
>
> Nor is a syntactical, reductionistic approach a priori invalid. Don't
> replace a dogma of modern reductionism with one of post-modern
> contextualism. One powerful view, filtered through Rosen and Pattee, that I
> have brought deeply into myself is that of COMPLEMENTARITY: there are many,
> alternate, non-comparably valid ways of looking at anything complex. Your
> "reductionist" insults are mere ad hominem.
I wonder? To the extent that I feel like I understand Rosen, Bohm, Casti
and a few others, I believe stongly that we may have a foot in booth worlds,
but we can't really have it both ways. We can ignore the Goedel result or
we can try to incorporate it. If we choose the latter, we can no
longer insist on formalizing everything. Even the Santa Fe institute
group who seem to have not quite come as far as the above mentioned group
in their philosophical handling of complexity, are willing to predict
that the days in which science is to "predict and control" are essentially
over. We will be forced to either stick to simple systems or be
satisfied with "mere" understanding.
>
>>Rosen accomplishes this
>>by finding a particular f which has a purpose, which has an answer to
>>the question why f? The trick is in that final cause means that SOME
>>B gives the reason for some f! This allows amapping from a B to f
>>and it closes the diagram.
>
> I presume that you understand that I understand all this already. But
> again, this is in ENGLISH. Rosen claims a valid MATHEMATICAL model. This is
> what I'm trying to understand.
>
>>As I understand, you are looking for the above explanation to come from
>>category theory or some other part of the logic in the argument.
>
> Yes.
>
>>This would
>>be exactly what we'd expect in a syntactical, reductionist scheme.
>
> Well, that may be. But you say:
>
>>Once again, the answer is not in the formalism.
>
> But that's exactly what Rosen PROMISES in his own theory.
Here's where we diverge fundamentally. We now are going through
his work since 1958 and have spent time with his books other than life
itself. His main take home message is the opposite of what you claim.
>
>>HOWEVER,
>>Rosen brought this notion of anticipation and final cause in INDEPENDENT
>>of the rest of the argument and merely uses category theory as a
>>rigorous way of representing the interplay of the ideas.
>
> It may be that category theory is not necessary for RB. Indeed, I think I
> understand it without category theory. It is not clear to me that Rosen is
> making this claim. But Rosen is surely claiming that you CAN express RB in
> category theory, as distinct from recursive equations. And this is the
> thrust of my questions.
Yes you can express it in a form of category theory. His own form
which builds in causal arguements foreign to any other application I've
ever seen, including the version you had in your message and letter to Turchin.
>
>> Now, forgive me, but I will avoid trying to unscramble the notation
>>in the rest of the message until you tell me whether or not this
>>answers your question.
>
> No. I already understood everything above this. It's the math I don't get.
O.K. I read your message to Turchin and found that it bore little
resemblance to Rosen's argument other than the sysmols. We've now been
over this point.
>
>>Just to be
>>argumentative, did you ever ponder the possibility that emotions
>>compliment reason at times?
>
> Of course. Depends on what you're doing. And how far out of balance you
> get.
>
>>(Don't you pity my students?)
>
> Nah, you'd be a great teacher. Undergrad, at least. I don't think I'd want
> you as a thesis advisor.
Poor Jeff!
>
>>I never learned a better way to operate, so maybe I can be
>>eligible for some handicapped status?
>
> OK, I'll check the ADA on your behalf.
>
Please, before Newt's crew repeals that too!
>>As I said above final cause does not always end a regression, only in
>>complex systems.
>
> Yes, the claim is for systems closed to efficient causation.
>
>>We did find that one diagram was
>>misprinted and the arrow of crucial interest was still poining in the
>>old direction allthough the argument in the text said it was turned
>>around and this of course had to be the one that ended the regression.
>
> Yes, the crucial diagram is hopelessly full of typos. But I got by that.
>
>>I say this because, as I recall, this was not in your list of errors.
>
> I believe it was.
>
>>> (**) A = { a }
>>> B = { b } b:F -> \Phi b(f) = \phi
>>> F = { f } f:A -> B f(a) = b
>>> \Phi = { \phi } \phi:B -> F \phi(b) = f
>>
>>O. K. I think I see what is troubling you. You are calling the very closure
>>in the relational diagram which Rosen claims breaks the sequence of
>>regression a regression!!!! In your description of the math, you correctly
>>show that the diagram contains a cycle and therefore the same sequence of
>>mappings occurs again and again. YES!!!! THAT'S THE POINT!!!
>>In section you quote (and elsewhere, he shows that the diagrams MUST BE
>>EXTENDED WITHOUT CLOSURE UNLESS THE CLOSING CYCLE CAN BE FORMED.
>>The very piece of math you are calling recursive is evidence that the closing
>>cycle has been formed and that the mapping goes around and around as it should
.
>>Is that now clear?
>
> Yes, I think we understand each other at one level. But I think we disagree
> about the significance. As I said above, it's obvious when you try to
> linearlize a cycle you get a regress. That might be OK sometimes, but
> instead it's better to look at the cyclic whole. But, you see, that
> approach leads DIRECTLY to the recursive function theory you so disparage.
> THIS is Turchin's view of the crucial (**), as a whole, cyclic set of
> recursive functions, and thus, to him, uninteresting.
>
Never have I even mentioned recursive function thoery in that context.
I have been refering to the recursive extension of diagrams to entail
unentailed mappings in machines. Sorry if that confused you.
> My real question is whether anything else is gained by using category
> theory on (**).
>
Clearly, for most of the world which has never heard of it, I suspect not.
However, after much struggle, I think Rosen's version is uniqely suited
to be augmented by the causality reasoning necessary to come up with a
definition of "life" and "complexity" which seems to work. I recall
a lecture on chaos in which it was defined by what it was not(equilibrium,
steady state, periodicity, quasi-periodicity). The lecturer called it
the "boomerang" definition. One Australian when asked to define a
boomerang said" pick up any object and throw it. If it doesn't come back,
it's not a boomerang."
>>What you need to do
>>is stop
>>focusing on the mathematical expression for a cycle in a map and step
>>back and see that the Newtonian ploy has been accomplished in relational
>>(augmented block diagrams) notation.
>
> Done that already. Is it OK if I try to do both, Don?
>
Sorry,Cliff, but If it means repealing Goedel, I think not. There's
the rub!
Best wishes, Don
P.S. I too will be on the road. Dad just had his prostate removed and
then my step-son gets married.