In this installment we will build on the previous one Reading Ramblings: The danger of simplifying the notion of cause and move further to understanding what relational models are all about.  Again we draw on Rosen's books Anticipatory Systems, Life Itself, Essays on Life Itself The use of functional components to make relational models allows us to focus on organization and relationships between the many activities going on in a complex system.  If you are still in the Newtonian mindset maybe Rosen's suggestion that you think of these functional components as "particles of function" will help.  He points out that the Newtonian paradigm dealing with actual material prticles is a synthetic theory that builds from the the behaviors of individual particles to families of particles.  It is this synthetic theory combined with the atomic hypothesis that leads to the reductionist belief that every material system can be analyzed back to these families of particles.  Thus partical mechanics became the largest model as we have discussed in earlier diaries.  It is possible to do something more than this bottoms up modeling and that's where systems theory comes in.  Later on we will look at rosen's concept of systems with more care. Read on below and we will now show how relational models use causality to look at the organization and function of a system without needing the particle physics at all.

Here's Rosen's idea:

It is clear that a corresponding synthetic relational theory of systems is incipient in the encoding of components into abstract mappings.  For instance, we have at our disposal the formal concept of composition of mappings.  In simplest terms, whenever the domain of one mapping intersects the range of another, the mappings may be composed to yield a composite mapping.
He goes on to show how this is represented by diagrams that  look like A ----->B  and C---->D.  If the sets B and C have members in common it is possible to compose these mappings into a simpler one A--->D.  That is an important parallel to the particle analysis of a system.
Thus we can see that the analysis of relational systems is associated with the factorization of mappings, the synthesis of relational systems is associated with the composition of mappings...In these terms, then,  we can now be a little clearer about the term "organization."   Namely: organization is that attribute of a natural system which codes into the form of an abstract block diagram.   To enlarge on our earlier image: if the component is an atom of organization, then a general abstract block diagram is a molecule of organisation.

Then for us, organization is itself a rather complicated concept; itinvolves a family of sets, a corresponding family of mappings defined on these sets, and above all, the abstract block diagram that interrelates them, that give us functions.

What is next is the way entailment enters the picture.  here is where the causalities we have considered earier come into play.  Further, it should be noted the distinction between the Newtonian (direct cause) form of entailment and this; namely in that the Newtonian version takes place in a state space  while Rosen calls this entailment without states.  The importance of this distinction can not be over emphasized.

Let's do a part of the Metabolism repair model. This reference is to its beginnings is from the Rosen Bibliography on my web page: AN UPDATED ROSEN BIBLIOGRAPHY:  Rosen, R. (1958)  A relational theory of biological systems, Bull. Math. Biophys. 20:245-260.     I still think his best explanation is in this magnificent work: Rosen, R. (1972)    Some Relational Cell Models: The Metabolism-Repair System." Chapter 4 of Foundations of Mathematical Biology Vol. 2, 217-253. N.Y. & London, Academic Press.

We atrat with representing functional components as abstract block diagrams in terms of their causal roots.   We start with the basis of all biological activity metabolism.  Ithas this representation as anabstract block diagram reprsenting its  material cause

A--->B
We are no where near finished with this one functional component and its material cause relationship.  Yet is important to stop here and help you understand.   If you were ever in a lab where they had one of those metabolic charts posted on the wall this should seem laughable!     Well if it is then I will come back with the idea that you can create a model that takes in all of what is in one of those charts is far more laughable.  What is included in this simple diagram?  The whole of the material aspects of metabolism including the working of the genetic mechanism, etc.    Many of the things at the level of biochemistry are things that do not have a unique mapping to this abstract block diagram.  They, in fact, are often able to function in multiple ways depending on where they are in the organism and what is happening at the time.  We lnow this to be tru of the DNA that is the "genetic code".  The code is one of the most context dependent things we know.

Back to the relational model and causality.  The next thing we need toask is "Why metabolism?"  What entails metabolism.  It has to have an efficient cause, call it f.  Then the diagram can be extended showing the relationship of metabolism to its cause:

f  >>>>>> A---->B
The next step comes from the fact that we have introduced f seemingly from nowhere (yet we know that metabolism has an efficient cause) so we can ask causal questions about f.  This could lead to an infinite regression of causal questiions as it does in machines until an external efficient cause is supplied.  In the organism, due to certain well known aspects of the3 genetic mechanism, the diagram closes on itself rather early in the game.  This was Rosen's big discovery.  Before you come up with the anticipated "so what" let us review what has been accomplished.

First of all we have a way of seeing complex systems that is independent from the traditional Newtonian decomposition and then replacement with a particle model that attempts to restore it as a whole system.  Clearly this is a formidable (if even possible) task  It is important to recognize the folly of statements about "wait until we know more" for we can not handle the details we have now.  There has to be a way of avoiding that trap and going on and this is it!

Since this is Rosen's work I should not have to say this but experience tells me that I must!  We have in no way negated the potential validity of models spawned from the Newtonian paradigm.  They will stand or fall on their own merits.  What has been clearly demonstrated here is that the Newtonian model has other models that can coexist with it and shed light on the nature of complex reality by asking and answering very different questions.

Whether or not you choose to preserve the exclusiveness of that paradigm you should be now ready to accept this one as being useful and able to stand side by side with the other.

There  are many more questions to be answered regarding this new paradigm.  I will be returning to that venture soon.  Tomorrow (Thursday) I will take a break while preparing my annual rant for my birthday Friday.  I am a very political person and my sense of urgency about the current political situation requires me to plunge in and rant!

#### Tags

EMAIL TO A FRIEND X
You must add at least one tag to this diary before publishing it.

Add keywords that describe this diary. Separate multiple keywords with commas.
Tagging tips - Search For Tags - Browse For Tags

?

More Tagging tips:

A tag is a way to search for this diary. If someone is searching for "Barack Obama," is this a diary they'd be trying to find?

Use a person's full name, without any title. Senator Obama may become President Obama, and Michelle Obama might run for office.

If your diary covers an election or elected official, use election tags, which are generally the state abbreviation followed by the office. CA-01 is the first district House seat. CA-Sen covers both senate races. NY-GOV covers the New York governor's race.

Tags do not compound: that is, "education reform" is a completely different tag from "education". A tag like "reform" alone is probably not meaningful.

Consider if one or more of these tags fits your diary: Civil Rights, Community, Congress, Culture, Economy, Education, Elections, Energy, Environment, Health Care, International, Labor, Law, Media, Meta, National Security, Science, Transportation, or White House. If your diary is specific to a state, consider adding the state (California, Texas, etc). Keep in mind, though, that there are many wonderful and important diaries that don't fit in any of these tags. Don't worry if yours doesn't.

You can add a private note to this diary when hotlisting it:
Are you sure you want to remove this diary from your hotlist?
Are you sure you want to remove your recommendation? You can only recommend a diary once, so you will not be able to re-recommend it afterwards.
Rescue this diary, and add a note:
Are you sure you want to remove this diary from Rescue?
Choose where to republish this diary. The diary will be added to the queue for that group. Publish it from the queue to make it appear.

You must be a member of a group to use this feature.

Add a quick update to your diary without changing the diary itself:
Are you sure you want to remove this diary?
 Unpublish Diary (The diary will be removed from the site and returned to your drafts for further editing.) Delete Diary (The diary will be removed.)
Are you sure you want to save these changes to the published diary?

#### Comment Preferences

• ##### Tip Jar(10+ / 0-)

An idea is not responsible for who happens to be carrying it at the moment. It stands or falls on its own merits.

• ##### I'll have to go to the source materials(2+ / 0-)
Recommended by:
Gooserock, don mikulecky

because this is not getting me anywhere.  I think I understand mappings and factorization and subtleties of causation but I'm not grokking this.

Where are we, now that we need us most?

• ##### Sorry about that.....n/t(0+ / 0-)

An idea is not responsible for who happens to be carrying it at the moment. It stands or falls on its own merits.

[ Parent ]

• ##### Missing Poll Option(0+ / 0-)

° Could be time delayed so EDT time zone wasn't going to bed every time these diaries appear.

We are called to speak for the weak, for the voiceless, for victims of our nation and for those it calls enemy.... --ML King "Beyond Vietnam"

• ##### Have a great ...(2+ / 0-)
Recommended by:
don mikulecky, basquebob

birthday Don.  I'm looking forward to your next diary. I'm spending a little time each day studying all this.

JON

"Upward, not Northward" - Flatland, by EA Abbott

• ##### ty...it comes on at 12:01 EDT Friday.(2+ / 0-)
Recommended by:
basquebob, Bob Guyer

I suspect it will makes big waves if anyone reads it.

An idea is not responsible for who happens to be carrying it at the moment. It stands or falls on its own merits.

[ Parent ]

• ##### Almost Infinite Numbers Of States......(4+ / 0-)

....plus  layer upon layer of recursion, as well as temporal and developmental regulation acting through unknown mechanisms, pretty much guarantee no great truths will emerge from this approach.

The smallest bit of empirical data crushes the best models. Like this
http://www.nature.com/...

The mystery of how mutations in a gene called isocitrate dehydrogenase 1 (IDH1) cause brain cancer and leukaemia is beginning to be unravelled. Researchers have discovered that the mutations cause the production of an enzyme that can reconfigure on–off switches across the genome and stop cells from differentiating.
That being said it makes far more sense to represent these processes relationally than the weirdly obsessive procedural approach, which inevitably dead ends in primitive APIs and a half million lines of code.  Did anyone ever build a SQL engine that will truly traverse a hierarchical system?

There’s always free cheddar in a mousetrap, baby