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Author
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Topic: Designing Complex Causation
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warren_bergerson
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Member # 262
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posted 19. January 2004 07:37
Rex,
Science in general prefers definitions based on objective observable criteria over definitions based on vague subjective concepts. It is my understanding that it is preferable to define a concept such as purposeful or goal-directed in terms of objective verifiable criteria rather than vague mental states such as intent, consciousness or volition. As you point out, defining goal-directed behavior in terms of the observed behavior or ‘predictably pursuing a goal’, mean that the behavior of rivers in ‘seeking the shortest route to the sea’ or a GA program ‘seeking a fitness optimum’ meet the criteria of being purposeful or goal directed(not dependent on the intent of the user or builder of the program).
As I have stated before, I do not claim to know what the position of evolutionary biology is with respect to defining purpose. I define purpose or goal-directed in terms of objective, observable criteria which avoids reference to vague mental concepts like intent, consciousness, external designers, or volition. I believe my approach is compatible with at least some scientific approaches to the issue.
Defining purposefulness in terms of observable behavior means that 1)while purposefulness or goal-directed behavior is clearly a property of intelligent systems, 2)the existence of purposefulness in itself is not adequate to distinguish intelligent from non-intelligent systems. Using the definition I proposed, purposeful behavior is defined as intelligent if and only if it was produced, created or ‘engineered’ by a complex causal process I label LEPS. Using the definition I propose, a river seeking the shortest route to the sea(without human intervention) is purposeful but not intelligent. Evolutionary change processes and GA programs, on the other hand are defined as both purposeful and intelligent.
It is a common practice in mathematical modeling to assign a common name to a set of phenomena or relationships based on a limited set of shared properties, but recognizing that different members of the set will not identical. I am proposing that evolutionary processes are a set of complex causal processes which share certain common properties. I am also proposing that different occurrences or manifestations of evolutionary processes can have different properties. Evolutionary change processes as diverse or modifiable processes is certainly not a new concept.
The suggestion that evolutionary processes may be complex causal processes is also not a new concept, although it is far from clear what the term or concept complex causation means in different fields of science. The suggestion that evolutionary processes may be designed or engineered or intelligently designed is a somewhat novel idea. As I stated earlier, there is general agreement that GA’s can model or simulate some aspects of evolutionary change processes. It is generally recognized that GA’s constitute a diverse set of complex algorithms. It is generally recognized that the transition from one form of GA to another involves engineering or design or intelligent design processes.
Somewhat speculative at the moment, but apparently people are currently working on complex processes or programs which are capable of modifying at least some features of computer programs such as GA’s. It is therefore at least theoretically possible that there exist sets or classes of complex ‘causal’ processes capable of redesigning or reengineering both GA’s and evolutionary processes.
It may be useful to note that ‘scientific’ AI involves among other things the search for logical processes or algorithms capable of explaining and simulating how humans perform intelligent design processes. At least to some people in AI, it would not be a complete surprise to discover that the logical process or algorithm responsible for ‘human design of GA programs’ is also responsible for the design or engineering of evolutionary processes.
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Rex Kerr
Member
Member # 632
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posted 19. January 2004 14:21
I find your definition of "purposeful" unhelpful, since a thing's purpose is its reason for existing, or the intended result it is supposed to bring about. Using "purposeful" to refer to things that may have no reason for existing and which may not be intended by or for anyone or anything is, therefore, confusing. I can't think of anything that Dembski calls a "regularity" that wouldn't be "purposeful" under this definition.
Given that I may not understand what you mean when you say "purposeful", I also may not understand what you mean by "designed" or "engineered", so at this point I'm just going to bow out of the thread.
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warren_bergerson
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Member # 262
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posted 23. January 2004 08:27
On another forum, there was a discussion of the criteria to be satisfied if a causal relationship was to be considered complex causation. This led to the idea that complex causal relationships can be characterized as having ‘strings attached. This in turn led to the following proposed definitions of complex controlled causation and simple causation. Comments would be appreciated.
SIMPLE CAUSATION- Any relationship represented or modeled by a mathematical function that can be assumed to operate in essentially the same manner at all times and places. The process or relationship can be analyzed by reduction to pure isolated instances of the relationship.
COMPLEX CAUSATION OR COMPLEX CONTROLLED-CONTROLLING CAUSATION- Any relationship represented or modeled by a mathematical function that can be modified, influenced or controlled by external processes and that can in turn modify, influence, or control external processes. The analysis of such a process needs to recognize both the type and source of external modifiers, influences and controls.
Complex controllable causation is, I suggest, a widely recognized phenomena at least in the applied sciences. The computer program is a clear illustration of such a complex, controllable causal relationship. Designed or engineered machines which interact with the environment in a controlled or designed manner are others.
To my knowledge, complex controlled causation is a concept which is neither formally addressed by or formally recognized by any existing theoretical science. I would be very much interested in hearing of specific evidence to the contrary. Certainly the concept of complex causation is discussed in the literature in a speculative manner, and individuals like Rob have proposed sets of criteria to be identify complex causation. Such speculation is not the same as official recognition.
As far as I am aware, my proposed AI Engineering, Life Engineering, and Decision Engineering are the only ‘theoretical’ sciences to formally define and recognize the concept of complex controllable causation.
To look down the road a bit, the recognition of complex controllable causation is, I suggest, critical to the successful scientific analysis of life forms because of the following proposed principle:
PRINCIPLE OF BIOLOGICAL REDUCTIONISM- Biological and intelligent processes and behaviors are reducible to complex controllable causation, but are not in any practical or useful manner reducible to simple causation.
On another thread, someone brought up the lack of scientific theories supporting AI research. The above principle suggests that there is no theory relating to the modeling and simulation of intelligence, and there can be no such theory, without first defining and recognizing complex controllable causation.
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Rex Kerr
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Member # 632
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posted 23. January 2004 08:46
Is the "three body problem" an instance of complex causation?
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warren_bergerson
Member
Member # 262
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posted 23. January 2004 09:30
Rex,
Based on the definitions proposed, simple versus complex causation is distinguished not by the problem addressed but by type of solution or model used. Technically the proposed definitions differentiate simple and complex controlled causation based on the form of the ‘under ideal conditions assumption’ used in generating a solution. Simple causation is based on the assumption that the relationship being analyzed can be described, modeled and analyzed assuming outside influences or variables can be ignored. As defined, complex causation is described, modeled and analyzed with assumptions recognizing certain external influences or strings.
If I recall correctly, the three body problem can be addressed using either the ‘ignoring external influences’ assumption or by treating the influence of the third body as external influence or string. As a general principle, I believe, simple causation is a special case of complex causation and any process or relationship which can be effectively analyzed as simple can also be analyzed as complex. The reverse is not true. Processes or causal relationships such as evolutionary change processes, I suggest, can only be described, modeled and analyzed as complex causal processes.
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Rex Kerr
Member
Member # 632
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posted 23. January 2004 20:51
There is no closed-form solution in terms of elementary functions to the three-body problem (i.e. the orbital pattern of three masses about each other), as each pair affects the position of the third, which in turn affects the other two, etc..
It seems as though any successful solution would therefore be based on complex causation. Although each particle obeys the Newtonian law of universal gravitation, you can't treat each particle independently in any meaningful sense.
Is this enough for solutions to the problem to be classified as causally complex?
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warren_bergerson
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Member # 262
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posted 24. January 2004 06:25
Rex,
The physical sciences clearly define, model, analyze and develop predictive hypotheses of simple permanent and universal and simple stochastic causal relationship. The physical sciences also clearly define, and create computer models and simulations of what I call complex causal processes. The physical sciences create and accept models and simulations of dynamic, controllable, and goal-directed processes. The issue here is neither the existence of complex controllable causation nor the recognition of the phenomena. The issue here is the recognition or lack of recognition of the relationship between simple and complex controllable causation.
I have offered a definition that makes it possible 1) to construct or derive complex controllable causation, and 2)to recognize a distinction between simple and complex causation based on the form of the ‘ideal conditions’ assumption being used. The definition offered would appear to be compatible with the rules and concepts implicit in the treatment of complex causation in the physical sciences. In addition the definition offered, I suggest, 1)provides a logical mathematical framework for developing predictive theories based on complex causation, and 2)provides a logical mathematical framework for the analysis of phenomena in the life sciences which do not appear to be usefully reduced from complex causation to simple causation.
The lack of an explicit explanation or rationale for the transition from simple to complex causation does not, at least to an outsider, appear to be problematic in the physical sciences. In the physical sciences, the engineering and applied science standards used to model and simulate complex controllable causation appear to as well developed and rigorous as the standards used to model and formulate hypotheses of simple causation.
Although, the simple causation-complex causation relationship does not appear problematic in the physical sciences, it would be both interesting and useful to see formal mathematical-logical explanations of the relationship. It would be even more interesting and useful to see the formal mathematical logical explanations of this relationship which might exist in the life sciences.
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Rex Kerr
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Member # 632
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posted 24. January 2004 10:18
I am trying to apply your classification scheme to a specific, well-known case. Unfortunately, your last comments were too general to help.
It appears to me as though the three-body problem meets your definition for complexity. Am I right? Or is there a reason why the time evolution of the system of equations
d^2 r1/dt^2 = G*m2*(r2-r1)/||r2-r1||^3 + G*m3*(r3-r1)/||r3-r1||^3 + g(r1)
d^2 r2/dt^2 = G*m1*(r1-r2)/||r1-r2||^3 + G*m3*(r3-r2)/||r3-r2||^3 + g(r2)
d^2 r3/dt^2 = G*m2*(r2-r3)/||r2-r3||^3 + G*m1*(r1-r3)/||r1-r3||^3 + g(r3)
(where g is the external gravitational field (which may be altered by the gravitational field of the three-body system, if the external system contains movable masses))
cannot be called complex? We do know that the three body problem follows exactly this set of second order ordinary differential equations. Unfortunately, the solution isn't separable (except in certain limiting cases), and the general solution cannot be expressed in terms of standard elementary functions.
The reason I'm having difficulty classifying this as complex or not is because your definition seems to admit it, while your claims about sciences ignoring complexity seem to rule it out. Obviously, this class of problems are well-recognized in mechanics. (Indeed, by your definition, any problem using fields seems to be an instance of complex causation.) They aren't grouped in with evolution and control theory and so on probably because the label "complex" does essentially nothing to help you solve the problem, or even to recognize what you're dealing with.
[ 24. January 2004, 10:19: Message edited by: Rex Kerr ]
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warren_bergerson
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Member # 262
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posted 24. January 2004 12:39
Rex,
Maybe it would be useful to review.
1. The physical sciences clearly recognize and formulate predictive theories from causal relationships that fit my definition of ‘simple’.
2. The physical sciences, particularly engineering and the applied sciences, clearly appear to recognize phenomena that would fit my definition of complex controllable causation.
3. Using my concepts and techniques, you can reduce complex causal processes (represented by complex mathematical functions such as computer programs) to simple causal processes. However, when you perform such reductions, you end up with many more components or sub-functions than can be explained by the set of scientific theories.
4. It is not clear, at least to me, how any of the existing science address this issue of the relationship between simple causation and complex controllable causation.
5. The approach I advocate addresses this issue by avoiding it. Scientific analysis in the form of ‘falsify and replace’ hypotheses testing is performed on complex controllable causal relationships not simple causal relationships. The approach I advocate recognizes reductionism, not not reduction to simple permanent and universal or stochastic causal relationships.
Again, I am not saying that science does not recognize both simple causation and complex controllable causation. I am saying that conventional science does not appear to provide explicit explanations and reconciliations between the two types of causation.
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RBH
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Member # 380
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posted 24. January 2004 17:36
Rex Kerr wrote quote:
We do know that the three body problem follows exactly this set of second order ordinary differential equations. Unfortunately, the solution isn't separable (except in certain limiting cases), and the general solution cannot be expressed in terms of standard elementary functions. (Emphasis added)
Then warren_bergerson wrote quote:
3. Using my concepts and techniques, you can reduce complex causal processes (represented by complex mathematical functions such as computer programs) to simple causal processes. However, when you perform such reductions, you end up with many more components or sub-functions than can be explained by the set of scientific theories. (Emphasis added)
Rex has provided an example, a set of second order differential equations that is not reducible to "standard elementary functions." How does that example fit into warren_bergson's analytic system?
Second, warren_bergerson wrote quote:
Again, I am not saying that science does not recognize both simple causation and complex controllable causation. I am saying that conventional science does not appear to provide explicit explanations and reconciliations between the two types of causation.
Can warren_bergerson provide a concrete example of what a "reconciliation" between the two types of causation might look like? What specific phenomenon displays both sorts of causation, and how are those two sorts of causation "reconciled" for that phenomenon?
RBH
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warren_bergerson
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Member # 262
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posted 25. January 2004 11:01
RBH,
You ask two interesting questions relating to reconciliation of simple and complex causation and instances where complex and simple causation occur together. You are, however, asking the wrong person. Life Engineering and AI Engineering are concerned with reducing complex models of complex controlled causation (represented by complex mathematical functions such as computer programs) to ‘simpler’ causal processes(represented by ‘simple’ mathematical functions or operations). Life Engineering is concerned with the capability of reducing complex causal processes to simpler causal processes and with the capability of constructing complex causal processes from simpler causal processes.
Life Engineering has no practical interest in the question of how far the reduction can go. Nor does Life Engineering have any particular interest in the specific nature of the elementary units which may or may not result from ultimate reduction to elementary forms of causation. From the Life Engineering and AI Engineering, the universe can be viewed and analyzed entirely in terms of complex controlled causation.
The issue of reconciling simple ‘permanent and universal’ causation and complex causation would only arise in a sciences that recognize both scientific hypotheses based on simple permanent and universal causal relationships and engineering models based on the phenomena I have labeled complex controllable causation. In the physical sciences, it appears, while there may not be formal techniques for reconciling what I have defined as simple and complex causation, the transition between the two does not appear problematic. The question of how the two phenomena are reconciled should, however, be addressed scientists in engineering and the physical sciences.
In AI and evolutionary biology the situation is somewhat more complicated. Life Engineering and AI Engineering note that it appears that some aspects of both intelligent behavior and evolutionary processes can be modeled and simulated by what is labeled ‘complex controllable causation’. As has been discussed, it is further noted that aspects of both intelligent behaviors and evolutionary processes can be modeled and simulated by types of complex controllable causation which are defined in AI Engineering as intelligent and engineered or designed. Although the topic has not been discussed, AI Engineering proposes that testable, predictive scientific hypotheses relating to both evolutionary processes and intelligent behavior can be formulated in terms these ‘intelligent, engineered complex controllable causation’.
At least on the surface, the conclusions or interpretations generated by AI Engineering would appear to conflict with evolutionary biology claims that evolutionary processes are not intelligent engineering processes. In order to determine if the inconsistency between AI Engineering and evolutionary biology is real or a matter of appearance, we need a clearer understanding of the evolutionary biology position on the phenomena labeled complex controllable causation and on the relationship between simple and complex causation.
Again, you raise a couple of good questions. But the questions should be addressed to those who develop scientific explanations in terms of simple permanent and universal causation.
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Rex Kerr
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Member # 632
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posted 25. January 2004 15:38
Warren continues to say nothing useful about the specific complex (?) controllable (?) causal system that I've described. What could be the reasons for this?
- Warren doesn't understand the system I've described.
- Warren is unfamiliar with gravitation or solving ODEs and therefore doesn't have the technical backgroud to say anything useful about a three-body gravitational system.
- Warren doesn't have the motivation to apply his theory to even one well-understood test case.
- Warren suspects that his "appearances" will be shown to be misleading, and his "proposals" shown to be wrong if he actually works out a test case.
- Warren prefers talking in generalities than
bothering with specifics.
I don't much care which of these it is, or whether it's something else. As a brainstorm, his ideas have enough merit to be worth a little bit of further consideration, despite some serious problems that I and others have pointed out (mostly in overzealous interpretation and faulty logic).
[list][/list]
But it is standard in engineering, physics, chemistry, the life sciences, AI research, and pretty much any other scholarly scientific or practical endeavor to try out new ideas on a test case. Since Warren is apparently unwilling or unable to perform this step, the appropriate scientific or engineering approach would be to either work on developing a test case (if mine is unsuitable for some mysterous reason), or drop the whole idea and brainstorm something else that could or would be given a trial run.
[ 25. January 2004, 15:40: Message edited by: Rex Kerr ]
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warren_bergerson
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Member # 262
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posted 26. January 2004 10:20
Rex,
The 3 body problem is not, IMO, a good starting point for discussing the reduction of complex casual relationships to simple causal relationships. The 3 body problem primarily raises what I would ‘technical side issues’. Such issues are probably important from a technical perspective but are not particularly useful or interesting in the type of discussion here. But since you insist, I will point out a couple of technical complications involved with this issue.
One of the general problems involved in either constructing complex causation from simple causation or in reducing complex causation to simple causation is the lack of an unambiguous step be step mathematical trail. A person might have an intuitive sense that a solution to the 3 body problem can be constructed from simple causal relationships defined by scientific theories. But does this intuitive impression mean that solutions to the 3 body problem are reducible entirely from scientific theories or does it mean they are constructed from scientific theories plus a variety of other causal relationships not formally defined as scientific theories. Finally, to make the issue even more complicated, there is no single unique mathematical expression for a particular causal relationship. A particular causal relationship, this is true for both simple and complex relationships, can be expressed in an infinite number of different ways. The results reducing complex causal models would seem to depend to some extent on how the relationship is expressed.
The approach I advocate, which might be labeled the Life Engineering approach, asserts that causal relationships both simple and complex are modeled by mathematical functions. If we start with a complex causal relationship modeled by a complex function such as a computer program, then, I propose, we can reduce or deconstruct these complex causal relationship in the same way we would reduce or deconstruct the complex mathematical functions or computer programs into simpler processes or functions. [This approach also makes it possible to look upward at the complex causal processes capable of modifying or reprogramming complex causal processes.] The Life Engineering approach simply uses existing techniques for reducing and deconstructing complex functions or programs into simpler mathematical functions.
If a solution to 3 body problems was expressed as a computer program, then the Life Engineering approach could be used to reduce this complex causal process into a simpler functional units. Never having attempted such a deconstruction, I am not sure exactly what the result would be. My guess is that you would find some components that are logically similar to the laws of physics and some that have no direct counterpart in any scientific theory.
While this type analysis might be interesting and a good learning experience, I can’t see that it would lead anywhere. I would not expect such analysis to produce results that could not be reconciled with formal physical science positions on complex causation.
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Rex Kerr
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posted 26. January 2004 18:26
So, supposing that I write a program that implements a solution to the three-body problem, what would we do next?
In particular, I wonder whether it would be any different from what people already are doing with, for example, the Avida algorithm (discussed at length elsewhere on this board), and if so, how.
I'm happy to switch to something other than the three body problem for a test case, if you can propose another, but I would still like something to test. I've already written a very simple solution to the three-body problem, so we could start with that, if another test case is not forthcoming.
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warren_bergerson
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Member # 262
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posted 27. January 2004 11:13
Rex,
If you want to look at a test case, then I suggest the following simple dynamic or programmable decision making model or program. This simple computer program models and simulates a relatively simple form of what I label complex controllable causation. This example illustrates a number of interesting features not readily apparent in the programs which model or simulate 3 body behavior. If you wish, you are welcome to present the 3 body program so we can have a parallel discussion of the features of that program. If you, or the moderator prefers, this somewhat technical discussion can be moved to another site.
The following decision making model is an example of a complex controllable causal relationship of the type ‘input causes output’ or ‘stimulus causes response’. In the program to be presented, this complex process is initially reduced to three steps:
1. External or environmental stimuli or the values of environmental stimuli are recorded and stored as data elements.
2. The values of environmental stimuli and a processing algorithm are used to generate the value of an output variable(decision value). and
3. The values of the output value is translated into an external or environmental response or decision.
The only refinement to this simple input output model is that the input variable is subdivided into a number of different component variable. The set of input variables is then divided into three groups labeled 1)input variables, 2)program variables or parameters and 3)a trigger point (which is a specialized form of program variable). By introducing program variables, we can create the appearance of dynamic or programmable decision making.
The decision making model is presented in simplified pseudo code.
PART 1: READ AND STORE INPUT VALUES
1.1 for each sx from s1 to sn, read or record value sxv of sx
1.2 Assign and store recorded value of each sx in data element (sx, sxv)
1.3 go to 1.1
PART 2: READ AND STORE PROGRAM VALUES
2.1 For each px from p1 to pn, read or record value pxv of pv
2.2 Assign and store recorded value of each sx in data element (sx, sxv)
2.3 Go to 2.1
PART 3: READ AND STORE TRIGGER POINT
3.1 For tp read or record value tpv
3.2 Assign and store recorded value tpv in data element (tp, tpv)
3.3 Go to 3.1
PART 4: CALCULATE OUTPUT VALUE
4.1 Access current values for sv1,..svn, pv1,…pvn, and tpv
4.2 Calculate sum of sv1*pv1+…+svn*pvn and assign to cv
4.3 If cv greater than tpv then assign rv in (r, rv) as 1, else assign rv value of 0
4.4 go to 4.1
PART 5: GENERATE EXTERNAL DECISION
5.1 Access value rv from (r, rv)
5.2 generate the external response corresponding to value rv.
5.3 go to 5.1
Each of the five parts or subprograms is assumed to run continuously and independently. The program is continuously reading input and continuously generating output.
If the notation used is unclear, I will be glad to try to clarify. Note that each input variable and program variable represents what I referred to as a string or input or control string. The output or response variable may be an control string for some other decision making algorithm.
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