Intelligent Reasoning

Promoting, advancing and defending Intelligent Design via data, logic and Intelligent Reasoning and exposing the alleged theory of evolution as the nonsense it is. I also educate evotards about ID and the alleged theory of evolution one tard at a time and sometimes in groups

Thursday, December 28, 2006

A Summary of the Principles of Hierarchy Theory

I should have posted this months ago, not that it would have done any good.

A Summary of the Principles of Hierarchy Theory

The Hierarchy theory is a dialect of general systems theory. It has emerged as part of a movement toward a general science of complexity. Rooted in the work of economist, Herbert Simon, chemist, Ilya Prigogine, and psychologist, Jean Piaget, hierarchy theory focuses upon levels of organization and issues of scale. There is significant emphasis upon the observer in the system.

Hierarchies occur in social systems, biological structures, and in the biological taxonomies. Since scholars and laypersons use hierarchy and hierarchical concepts commonly, it would seem reasonable to have a theory of hierarchies. Hierarchy theory uses a relatively small set of principles to keep track of the complex structure and a behavior of systems with multiple levels. A set of definitions and principles follows immediately:

Hierarchy: in mathematical terms, it is a partially ordered set. In less austere terms, a hierarchy is a collection of parts with ordered asymmetric relationships inside a whole. That is to say, upper levels are above lower levels, and the relationship upwards is asymmetric with the relationships downwards.

Hierarchical levels: levels are populated by entities whose properties characterize the level in question. A given entity may belong to any number of levels, depending on the criteria used to link levels above and below. For example, an individual human being may be a member of the level i) human, ii) primate, iii) organism or iv) host of a parasite, depending on the relationship of the level in question to those above and below.

Level of organization: this type of level fits into its hierarchy by virtue of set of definitions that lock the level in question to those above and below. For example, a biological population level is an aggregate of entities from the organism level of organization, but it is only so by definition. There is no particular scale involved in the population level of organization, in that some organisms are larger than some populations, as in the case of skin parasites.

Level of observation: this type of level fits into its hierarchy by virtue of relative scaling considerations. For example, the host of a skin parasite represents the context for the population of parasites; it is a landscape, even though the host may be seen as belonging to a level of organization, organism, that is lower than the collection of parasites, a population.

The criterion for observation: when a system is observed, there are two separate considerations. One is the spatiotemporal scale at which the observations are made. The other is the criterion for observation, which defines the system in the foreground away from all the rest in the background. The criterion for observation uses the types of parts and their relationships to each other to characterize the system in the foreground. If criteria for observation are linked together in an asymmetric fashion, then the criteria lead to levels of organization. Otherwise, criteria for observation merely generate isolated classes.

The ordering of levels: there are several criteria whereby other levels reside above lower levels. These criteria often run in parallel, but sometimes only one or a few of them apply. Upper levels are above lower levels by virtue of: 1) being the context of, 2) offering constraint to, 3) behaving more slowly at a lower frequency than, 4) being populated by entities with greater integrity and higher bond strength than, and 5), containing and being made of - lower levels.

Nested and non-nested hierarchies: nested hierarchies involve levels which consist of, and contain, lower levels. Non-nested hierarchies are more general in that the requirement of containment of lower levels is relaxed. For example, an army consists of a collection of soldiers and is made up of them. Thus an army is a nested hierarchy. On the other hand, the general at the top of a military command does not consist of his soldiers and so the military command is a non-nested hierarchy with regard to the soldiers in the army. Pecking orders and a food chains are also non-nested hierarchies.

Duality in hierarchies: the dualism in hierarchies appears to come from a set of complementarities that line up with: observer-observed, process-structure, rate-dependent versus rate-independent, and part-whole. Arthur Koestler in his "Ghost in The Machine" referred to the notion of holon, which means an entity in a hierarchy that is at once a whole and at the same time a part. Thus a holon at once operates as a quasi-autonomous whole that integrates its parts, while working to integrate itself into an upper level purpose or role. The lower level answers the question "How?" and the upper level answers the question, "So what?"

Constraint versus possibilities: when one looks at a system there are two separate reasons behind what one sees. First, it is not possible to see something if the parts of the system cannot do what is required of them to achieve the arrangement in the whole. These are the limits of physical possibility. The limits of possibility come from lower levels in the hierarchy. The second entirely separate reason for what one sees is to do with what is allowed by the upper level constraints. An example here would be that mammals have five digits. There is no physical reason for mammals having five digits on their hands and feet, because it comes not from physical limits, but from the constraints of having a mammal heritage. Any number of the digits is possible within the physical limits, but in mammals only five digits are allowed by the biological constraints. Constraints come from above, while the limits as to what is possible come from below. The concept of hierarchy becomes confused unless one makes the distinction between limits from below and limits from above. The distinction between mechanisms below and purposes above turn on the issue of constraint versus possibility. Forget the distinction, and biology becomes pointlessly confused, impossibly complicated chemistry, while chemistry becomes unwieldy physics.

Complexity and self-simplification: Howard Pattee has identified that as a system becomes more elaborately hierarchical its behavior becomes simple. The reason is that, with the emergence of intermediate levels, the lowest level entities become constrained to be far from equilibrium. As a result, the lowest level entities lose degrees of freedom and are held against the upper level constraint to give constant behavior. Deep hierarchical structure indicates elaborate organization, and deep hierarchies are often considered as complex systems by virtue of hierarchical depth.

Complexity versus complicatedness: a hierarchical structure with a large number of lowest level entities, but with simple organization, offers a low flat hierarchy that is complicated rather than complex. The behavior of structurally complicated systems is behaviorally elaborate and so complicated, whereas the behavior of deep hierarchically complex systems is simple.

Hierarchy theory is as much as anything a theory of observation. It has been significantly operationalized in ecology, but has been applied relatively infrequently outside that science. There is a negative reaction to hierarchy theory in the social sciences, by virtue of implications of rigid autocratic systems or authority. When applied in a more general fashion, even liberal and non-authoritarian systems can be described effectively in hierarchical terms. There is a politically correct set of labels that avoid the word hierarchy, but they unnecessarily introduce jargon into a field that has enough special vocabulary as it is.



How many of the above conditions are violated by Zachriel's continued attempts at deception?

Hierarchical levels: levels are populated by entities whose properties characterize the level in question. A given entity may belong to any number of levels, depending on the criteria used to link levels above and below. For example, an individual human being may be a member of the level i) human, ii) primate, iii) organism or iv) host of a parasite, depending on the relationship of the level in question to those above and below.

In the "paternal family tree" there is no way "A given entity may belong to any number of levels, depending on the criteria used to link levels above and below." It just cannot happen.

IOW once again I am vindicated by reality. However it is sad that neither Zachriel nor blipey will ever come to grips with that.

16 Comments:

  • At 8:10 PM, Blogger Joe G said…

    This still applies.

    No more wasting my bandwidth on irrelevant nonsense.

    Good night and, good luck...

     
  • At 1:32 AM, Blogger blipey said…

    I believe you have officially not let Zachriel comment on this thread.

    what does that say about my earlier 3 step experiment?

    I'll say confirmation. Thanks for the lab work.

    blipey

     
  • At 7:52 AM, Blogger Joe G said…

    blipey:
    I believe you have officially not let Zachriel comment on this thread.

    Who cares what you believe? Reality demonstrates otherwise:

    Conclusion: Blipey is correct in his assessment that Zachriel will not allow Zachriel, at this moment, to post at this thread.

     
  • At 8:34 AM, Blogger Joe G said…

    blipey:
    I'll say confirmation.

    Me too. You have confirmed that you either can't grasp reality or you just refuse to.

    blipey:
    Thanks for the lab work.

    It was all you, but there wasn't any lab involved, just the real world.

     
  • At 9:07 AM, Blogger blipey said…

    Joe:

    there wasn't any lab involved, just the real world.

    Gorillas in the Mist

     
  • At 9:10 AM, Blogger blipey said…

    Just to be clear on the "real world" events that went on.

    I assume it was this:

    1) Zachriel submitted a comment
    2) Zachriel hacked your site
    3) Zachriel erased his comment

    Another 3 step experiment (funny comes in threes, you know?):

    Which of these steps do you find factually incorrect?

    seemingly swimming in seamless sea of semantics,

    blipey

     
  • At 10:11 AM, Blogger Joe G said…

    blipey:
    Just to be clear on the "real world" events that went on.

    It started with Zachriel's usual lies and misrepresentations. That led me to post the following challenge:

    Calling Zachriel's Bluff- Nested Hierarchy and Common Descent

    OK Zachriel, here it is. The key to your posting privileges for Intelligent Reasoning is being placed in your hands.

    Your next post will be regardless of what you think I know or don't know, understand or don't understand about nested hierarchy and/ or set theory. It will be for our reader's benefit. It will also prevent you from continuing to waste bandwidth on my blog.


    IOW I did the responsible thing.

    And both of you are confirming my prediction. Thanks.

     
  • At 11:52 PM, Blogger blipey said…

    Are there many different ways to categorize the members of "Sons of Abdullah" using paternal descent as a critereon?

    Seems to me that there is only one possible category: Son.

    Therefore, each item is associated with only one level in a hierarchy.

    Thre is no problem with a paternal family tree being a nested hierarchy. If you think there is, please give an example of one item (person) being categorizable in two different levels of the pternal tree "Sons of Abdullah".

     
  • At 9:17 AM, Blogger Joe G said…

    blipey:
    Therefore, each item is associated with only one level in a hierarchy.

    Hierarchical levels: levels are populated by entities whose properties characterize the level in question. A given entity may belong to any number of levels, depending on the criteria used to link levels above and below.

    What part about that don't you understand?

    blipey:
    Thre is no problem with a paternal family tree being a nested hierarchy.

    You mean besides violating at least two of the rules of hierarchy.

    blipey:
    If you think there is, please give an example of one item (person) being categorizable in two different levels of the pternal tree "Sons of Abdullah".

    LoL! Go back to being a clown, that is if you are better at that then you are at reading.

    Here is more:

    The ordering of levels: there are several criteria whereby other levels reside above lower levels.

    SEVERAL CRITERIA, not one.

    Hierarchical levels: levels are populated by entities whose properties characterize the level in question.

    PROPERTIES not property.

     
  • At 9:35 AM, Blogger Joe G said…

    To reiterate:

    In the "paternal family tree" there is no way "A given entity may belong to any number of levels, depending on the criteria used to link levels above and below". It just cannot happen.

     
  • At 10:51 AM, Blogger Joe G said…

    To clarify-

    Look again at Zachriel's example:

    Talal can only and will always be in that one set- the set of Abdullah's sons. He cannot be the son of any other person depicted. He cannot be his own father. He cannot be his own grandfather and he cannot be his own son or grandson. He is stuck being a node in a single set. And no amount of whining can change that fact.

     
  • At 11:19 AM, Blogger Joe G said…

    LoL! Now instead of dealing with reality Zachriel wants us to believe that "Sons of" refers to ALL male descendants!

    That is nothing but semantic nonsense. A son has only one biological father. Period.

    Now someone can say "the Sons of Virginia"- ya know Confederate Army stuff- but the State of Virginia did not give birth to anyone. IOW "Sons of Virginia" is a metaphor.


    I wonder how much longer Zachriel will ignore the following:

    Here is more:

    The ordering of levels: there are several criteria whereby other levels reside above lower levels.

    SEVERAL CRITERIA, not one.

    Hierarchical levels: levels are populated by entities whose properties characterize the level in question.

    PROPERTIES not property.

    Again the challenge satnds-

    I challenge anyone to search for "paternal family tree and nested hierarchy" to see if Zachriel's bogus example comes up and is used by anyone except Zachriel- someone with expertise in the subject would be nice. Good luck.

     
  • At 1:06 PM, Blogger blipey said…

    Hierarchies don't HAVE to have a multitude of criteria, Joe. They can, but don't have to.

    A hierarchy refers to the ordering of things--the ACTUAL PROCESS OF ORDERING--not what is being ordered.

    You can order anything, including things that only have one critereon: say, like a paternal family tree.

     
  • At 9:20 AM, Blogger Joe G said…

    blipey:
    Hierarchies don't HAVE to have a multitude of criteria, Joe. They can, but don't have to.

    According to the rules, they do. You know, the rules that are posted in this thread's OP. I take it your reading comprehension problems still exist.

    blipey:
    You can order anything, including things that only have one critereon: say, like a paternal family tree.

    You can order ham & cheese on rye for all I care. However in order to fit the definition of a nested hierarchy the sets must be defined by multiple characteristics.

    If you have a problem with that just email the scientist at the bottom of the page on the original article. Be sure to tell him you are an actor. I am sure he will be impressed by that credential.

     
  • At 11:13 AM, Blogger Zachriel said…

    blipey: Hierarchies don't HAVE to have a multitude of criteria, Joe. They can, but don't have to.

    joe g: "According to the rules, they do."

    I already pointed this out to you.

    "The ordering of levels: there are several criteria whereby other levels reside above lower levels. These criteria often run in parallel, but sometimes only one or a few of them apply."

    This has to do with taxonomy, by the way. Because you have such difficulty with this, I suggested a simple and standard definition to which you agreed.

    A nested hierarchy is an ordered set such that each subset is strictly contained within its superset.

    I see you are still afraid to leave the confines of your moderation wall.

     
  • At 10:09 AM, Blogger Joe G said…

    blipey: Hierarchies don't HAVE to have a multitude of criteria, Joe. They can, but don't have to.

    joe g: "According to the rules, they do."

    Zachriel:
    I already pointed this out to you.

    And obviously you don't understand what you pointed out.

    "The ordering of levels: there are several criteria whereby other levels reside above lower levels. These criteria often run in parallel, but sometimes only one or a few of them apply."

    Several still exist and only sometimes only one or a few apply. And that is only when distinguishing between sets that share all over the other criteria.

    Zachriel:
    This has to do with taxonomy, by the way.

    Duh

    Zachriel:
    Because you have such difficulty with this,

    The difficulty is all yours.

    Zachriel:
    I see you are still afraid to leave the confines of your moderation wall.

    Umm, how can be "still afraid" of something that I was never afraid of in the first place?

    I still see you are a bloviating, backpeddling snapper.

     

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