|
Author
|
Topic: Designing Complex Causation
|
Rex Kerr
Member
Member # 632
|
posted 13. January 2004 21:26
Well, the point is that variation and selection aren't elementary, isn't it?
If one were to take them as a given (i.e. elementary given the scope of problem under consideration), then an evolutionary process would, perhaps, be based directly on these "elementary" concepts. If your point is that one should be careful about making too much of the elementarity--this is not elementary in the way that the law of identity is elementary, for instance!--then I wholeheartedly agree. It is always good to keep the scope and assumptions of one's analysis in mind. If your point was something else, I fear I've lost it.
IP: Logged
|
|
Pim van Meurs
Member
Member # 541
|
posted 14. January 2004 12:55
Rex: Variation and selection are indeed emergent properties, but why suppose that they are emergent from an evolutionary process? It seems simpler to say that evolutionary processes are emergent from certain sets of more fundamental properties/qualities/rules/etc..
This is a very good point, from the view of evolutionary processes, variation and selection are a given although the concept of evolvability shows how evolutionary processes can affect the distribution of the variations and thus evolvability is the emergent property.
IP: Logged
|
|
warren_bergerson
Member
Member # 262
|
posted 14. January 2004 16:18
Rex,
To clarify, a GA is a complex mathematical function which is reducible to sets of interacting elementary mathematical functions. None of the elementary units making up a GA algorithm or program is a variation process, a mutation process, a selection process or a natural selection process. There are in fact no logical/mathematical operations corresponding to random mutation or natural selection. If you defined a variation process and a selection process, you could not construct a GA simply from the two component processes. It is therefore not technically correct to suggest that a GA is manifestation of RM&NS.
If the GA is not derived from or constructed from the interaction of selection and variation processes, then, it is reasonable to ask, is it possible to construct or formally define an evolutionary process in terms of the interaction between a variation process and a selection process? It would seem that ‘evolutionary processes’ from the interaction of ‘selection and variation’ does not and can not satisfy the level of logical/mathematical precision typically required in science.
If we accept that proposed principle that complex causation is constructed from or derived from or reducible to sets of simple causal relationships following the derivation of complex functions from simple functions (and subject to real world constraints), then a GA becomes an expression of a certain type or class of complex causal relationship. Complex causal relationships belonging to this class are, the evidence suggests, capable of modeling or simulating some aspects of the behavior of evolutionary processes.
Again, analyzed in terms of the derivation of complex functions from simple functions, it would appear that neither evolutionary processes nor GA’s can be formulated or constructed from RM&NS. However, GA’s seem to provide useful insights into evolutionary processes when defined and interpreted in terms of complex causation.
IP: Logged
|
|
RBH
Member
Member # 380
|
posted 14. January 2004 20:48
warren_bergerson wrote quote:
Again, analyzed in terms of the derivation of complex functions from simple functions, it would appear that neither evolutionary processes nor GA?s can be formulated or constructed from RM&NS.
What then are the core functions we call "mutate" and "rank_fitness" doing in our GAs? The one randomly selects a gene string and a gene within it for point mutation; the other assesses the fitness of each gene string (actually, each phenotype induced by a gene string) in order to assign probabilities for mating, and hence differential probability of reproduction via recombination (called, appropriately enough, "have_sex"). Anyway, if GA's cannot be constructed from RM&NS, what are those core functions doing according to warren_bergerson's analysis?
RBH
IP: Logged
|
|
Rex Kerr
Member
Member # 632
|
posted 14. January 2004 22:17
Suppose that we have a function called RM which takes as input a population and returns that population plus one new member. This is our variation process (called such because typically, the new member is a slight variation of one of the existing members).
Suppose further that we have a function called NS which takes as input a population and returns that population minus one member. This is our selection process (called such because typically the removed member is chosen based on a probability distribution that is a function of the genome of each member of the population).
Then we have an algorithm:
code:
while (1)
{
population = RM( population );
population = NS( population );
}
Warren: is this a genetic algorithm, yes or no?
Is this algorithm composed of the elementary units of RM and NS, yes or no?
Note: if the answers depend on the identity of the RM and NS functions, please give some indication of which RM,NS pairs give "yes", which give "no", and how you can tell.
P.S. "I can describe the contents of this message as the sequence of numbers that are the values of the unicode characters that comprise it; therefore, it is not technically correct to suggest that this message is constructed from English words." What logical error am I making here, and how is this analagous to the claims of Warren's previous message?
IP: Logged
|
|
warren_bergerson
Member
Member # 262
|
posted 15. January 2004 07:47
Rex and RBH,
My comments only state the obvious. If you look at a typical GA program, you will see a certain number of lines of code. Usually none of the code in the program will be operators RM or NS and certainly the program is very unlikely to consist entirely of RM and NS operators. Thus the conclusion GA programs do not appear to be reducible to RM and NS processes. If GA’s are not logically and mathematically constructed entirely from RM and NS processes, then it seems reasonable to conclude that real world evolutionary processes can not be defined and models entirely in terms of RM and NS.
If you disagree with these conclusions, computer mathematics provides you with the perfect opportunity to provide mathematically precise definitions of RM and NS operators and to demonstrate that useful effective GA computer programs can be constructed entirely from the RM and NS operators you define. You might even wish to propose some less rigid construction or derivations of GA’s from classes of operators which satisfy some specified RM and NS criteria. The point here is that until and unless someone specifically defines and demonstrates that GA’s are derived from or constructed from or reducible to RM and NS operators, there is no mathematical/logical evidence that such derivations, constructions or reductions are possible.
As should be apparent, the ability to formally define RM and NS as logical functions or operators and then construct GA’s and evolutionary processes from such logical operators, is not a requirement of evolutionary science or Darwinian theory.
To return to the main subject of this thread, complex mathematical functions, such as computer programs, can be constructed from, derived from or reduced to simple mathematical functions. Recognizing real world constraints, it is reasonable to conclude that complex causal relationships or processes can in the same manner be constructed from, derived from or reduced to simple causal relationships. Computer programs such as GA programs can thus be viewed or described as expressions of complex causal relationships.
There are a number of important implications of this interpretation. First, it is neither practical nor useful to apply the scientific method to the analysis of the elementary causal relationships making up these complex causal relationships. Second, there are well established engineering or applied science techniques for analyzing and applying complex models. Third, and not universally recognized, certain types of complex causal processes or complex functions generate testable predictions. The scientific method or paradigm can be used to test hypotheses formulated using these predictive models of complex causation. Again, the purpose of this thread is not to evaluate GA’s or Darwinian theory. The purpose this thread is to point out that there exist techniques for expressing complex causal relationships.
IP: Logged
|
|
Rex Kerr
Member
Member # 632
|
posted 15. January 2004 21:50
I propose that I write just such a program. It will have a bunch of code relating to the "NS" and "RM" functions--because they are not elementary aspects of computer languages!--and then the main GA routine will call only those functions.
If I am able to do this, or point to code that does this already, will you concede the point? Or are you looking for something else?
[ 15. January 2004, 21:56: Message edited by: Rex Kerr ]
IP: Logged
|
|
warren_bergerson
Member
Member # 262
|
posted 16. January 2004 07:22
Rex,
If you wish to show that GA’s and models of evolutionary processes can, in fact, be constructed from RM and NS processes, then the criteria you need to satisfy will depend on what type of claim you intend to support. If are supporting the claim that ‘under some very limited conditions it is possible to construct a very limited form of GA mostly from some specially defined forms of RM and NS processes’, then all you need to do is produce the program you suggested.
As should be apparent, if you wish to support a claim such as ‘most GA programs could be constructed mostly from the specifically defined forms of RM and NS processes’ then you would need to satisfy additional criteria such as showing your RM and NS based GA’s could match the specific performance of existing GA’s that were not constructed from your defined sub-processes. Such an effort will almost certainly fail, but you are welcome to try.
If you follow my proposed complex causation approach, you will most likely conclude that GA’s are a type or class of complex function which share certain emergent properties including 1)the use of some sort of variation process, 2)the use of some sort of selection process, 3)the dispersed processing property, 4)the dynamic or programmable property , 4) the property of being goal directed or purposeful, and 5)the property of being designed or engineered. You will also conclude that 1)GA’s are capable of modeling and simulating at least some aspects of evolutionary processes and therefore 2)evolutionary processes are likely to share the emergent properties identified for GA’s.
The concepts and techniques associated with reducing complex computer functions to elementary mathematical functions are reasonably well established. The concepts and techniques for demonstrating logical equivalence between different expressions of complex programs are reasonably well established. The concepts and techniques for classifying and grouping complex programs based on shared emergent properties is reasonably well established.
The concepts and techniques for formulating testable predictive scientific hypotheses in terms of complex functions or complex causation, and then using the ‘falsify and replace’ scientific paradigm to progressively improve such a testable predictive hypotheses is reasonably well established in engineering and some applied sciences. While, IMO, it would or at least might be possible to construct such progressive complex causation hypotheses of evolutionary processes, the construction of such complex causation hypotheses would not appear possible in evolutionary biology because the needed concepts and techniques do not appear to be a recognized part of evolutionary biology.
Evolutionary biology, or so I have been led to believe, accepts on authority and without the need for testing, the assertion GA’s are in some manner a manifestation of RM and NS. As I have been led to believe, neither contrary evidence nor the lack of supporting evidence are relevant to the conclusion that GA’s in evolutionary biology are derived from and NS.
IP: Logged
|
|
RBH
Member
Member # 380
|
posted 16. January 2004 08:22
warren_bergerson wrote quote:
Evolutionary biology, or so I have been led to believe, accepts on authority and without the need for testing, the assertion GA's are in some manner a manifestation of RM and NS. As I have been led to believe, neither contrary evidence nor the lack of supporting evidence are relevant to the conclusion that GA's in evolutionary biology are derived from and NS.
I ask warren_bergerson to read the paper noted below and describe how it exemplifies "accepts on authority amd without the need for testing, the assertion that GA's are in some manner a manifestation of RM and NS."
This is a test. warren_bergerson regularly makes claims about one or another field of study, never supplying a single reference. I genuinely want to know the basis for those claims, and the only way I know to find that basis is to ask questions about warren_bergerson's acquaintance with the professional literature of the disciplines in which he makes those claims.
Here is the page giving access to the paper, to the source code for the evolutionary algorithm used in the research, and to the necessary supplemental material.
This is the abstract: quote:
Genome complexity, robustness, and genetic interactions in digital organisms
Nature 400 (1999) 661-664
R.E. Lenski, C. Ofria, T.C. Collier, and C. Adami
Digital organisms are computer programs that self-replicate, mutate, and adapt by natural selection. They offer an opportunity to test generalizations about living systems that may extend beyond the organic life that biologists usually study. We generated two classes of organisms: simple programs selected solely for rapid replication, and complex programs selected to perform mathematical operations that accelerate replication through a set of defined "metabolic" rewards. To examine the differences in their genetic architecture, we introduced millions of single and multiple mutations into each organism and measured the effects on the organism's fitness. The complex organisms are more robust than the simple ones with respect to average effects of single mutations. Interactions among mutations are common and usually yield higher fitness than predicted from the component mutations assuming multiplicative effects; such interactions are especially important in the complex organisms. Frequent interactions among mutations were also seen in recent experiments with bacteria, fungi and fruitflies. Our findings support the view that interactions are a general feature of genetic systems.
Notice that the abstract mentions that the findings from the digital simulation are related back to findings in real biology on bacteria, fungi, and fruitflies.
I ask again, what warrant is there for warren_bergerson's claim that quote:
... neither contrary evidence nor the lack of supporting evidence are relevant to the conclusion that GA's in evolutionary biology are derived from and NS.
What is it that has "led" warren_bergerson to that belief? In his response I will be looking for evidence that warren_bergerson has actually read the paper itself, and not merely the abstract I supplied.
RBH
IP: Logged
|
|
warren_bergerson
Member
Member # 262
|
posted 16. January 2004 09:08
RBH,
I have tried to make it clear that my comments on GA’s as complex causal processes and on the issue of deriving or constructing GA’s from RM and NS processes are NOT based on the concepts and principles of evolutionary biology. I have also tried to make it clear that I do not claim to know or understand what concepts and principles of evolutionary biology apply to these issues. I noted my impression, based primarily are posting here and on other sites, that biologists appear to accept what I would characterize as a ‘hand waving derivation of GA’s from RM and NS’ as opposed to a more formal mathematical derivation. I made it clear that this was my personal impression.
I will admit to some curiosity as to exactly what concepts and techniques are used in evolutionary to justify the claimed relationship between RM&NS and GA’s and evolutionary processes but that is not the subject of this thread. Furthermore, the moderator here has generally discouraged discussions of such subjects.
Again, I was trying to make it clear to Rex that my comments on constructing GA’s from RM and NS were not based on evolutionary biology standards and the conclusions drawn were not necessarily applicable to evolutionary biology or Darwinian theory.
It might, IMO, be interesting to discuss reconciling evolutionary biology concepts and principles to the concepts and principles associated with what I am calling complex causation, but this is not the thread for such a discussion.
IP: Logged
|
|
Rex Kerr
Member
Member # 632
|
posted 17. January 2004 01:42
Warren mentioned six features that a genetic algorithm was likely to have.
The first was the use of some sort of variation process. This is typically "random mutation"--indeed, if it is too deterministic, we have other names for the algorithm (e.g. "gradient descent").
The second was the use of some sort of selection process. If we're designing the algorithm, we can put in all kinds of things here--but with respect to evolution, we suppose that these are natural (e.g. survival/reproduction). When we design limits like these into our GAs, they still find locally optimal solutions (to the selection-maximization problem). So limiting GAs to natural selection only doesn't necessarily break them.
The third was "the dispersed processing property". I'm not sure what that means. Organisms running around in the environment are dispersed, so evolution has dispersed processing. But most genetic algorithms run on serial machines (i.e. not dispersed), and many parts of the algorithm are global, not local (e.g. it is very common to pick out the fittest organisms globally from the entire population, rather than have them survive or die locally), and thus this really isn't dispersed processing. So I'm not sure what to make of this criterion.
The fourth was "the dynamic or programmable property", but I'm not sure what this means either. Of course, the organisms themselves are dynamic or programmable--this is implied in the notion of variation. So saying that adds nothing new. On the other hand, the implementation code of the GA typically doesn't vary dynamically; it is a (fixed) simulation environment during any one run. Of course, if we are the ones who programmed it in the first place, we can go change it later, but this doesn't have anything to do with whether something is a genetic algorithm or not. It has to do with computer programs written by humans necessarily being programmable.
The fifth property (mislabeled with a second 4) was "being goal directed or purposeful". But this is confusing the use of a tool for engineering purposes--that is, when you have a goal in mind, and use a GA as a tool to meet that goal--from what makes a GA worthy of the name. If one has a particular design problem, one might be able to formulate the problem so that its solution occurs when some evaluation(selection) function is maximized. If one can do this, then a GA can perhaps help find this solution. But if you set up a GA without any goal in mind, the GA will still (under appropriate conditions) find maxima. Goal-free, purposeless maxima, but it will find them nonetheless. (One doesn't say that the equation df(x)/dx = 0 is "goal-directed or purposeful", even though you can use it to find maxima and minima of f(x)!)
And finally, the sixth property (mislabeled 5) is the property of being designed or engineered. Well, gee, anything we create is designed or engineered, so this is no surprise. However, a GA doesn't work by virtue of its designedness--it works by virtue of its logical structure. Of course, most things are not GAs, so if we want to use them, we'd better build them. Most things are not on fire, but we arrange for them to be if we want to cook our food. This doesn't mean that combustion has the property of being designed or engineered--it's just something that is pretty rare on its own, but which we can make happen to gain an advantage. I see no a priori reason why GAs are any different.
So, at the end of all this, we have selection and variation--of which RM&NS will do fine--and a bunch of other apparently superfluous points.
P.S. added in edit: if one reads the literature, one's personal impression might change. Becoming familiar with a field helps one develop accurate impressions.
P.P.S. added in edit: many biologists do not treat anything particularly mathematically. One cannot infer from this that mathematical approaches are never taken, or that they will fail; it is just a reflection of your typical biologist not receiving much mathematical training (more for historical than practical reasons these days, but there still is much interesting work that can be done with limited mathematical skills).
[ 17. January 2004, 02:16: Message edited by: Rex Kerr ]
IP: Logged
|
|
warren_bergerson
Member
Member # 262
|
posted 17. January 2004 10:20
Rex,
As I stated yesterday, and as your comments illustrate, there appears to be major differences between GA’s interpreted as by evolutionary biology and biologists and GA’s interpreted in terms of complex causation. Take as a simple example the emergent property labeled ‘goal-directed’ or ‘purposeful’ or ‘teleological’. In the terminology of complex causation, a system is purposeful or goal directed or purposeful or teleological if under appropriate conditions it consistently and predictably moves towards a goal. From the perspective of complex causation, ‘conscious awareness of a goal’ is irrelevant. A system is defined as goal directed if it exhibits goal directed behavior. As you suggest, this apparently is not the standard used in evolutionary biology.
It should be noted that from the perspective of complex causation, the goal directed property is important because a type of complex causation or complex algorithms with this property generate testable predictions. This in turn means that testable, predictive scientific hypotheses can be formulated from this type or class of complex causation. As far as I am aware, evolutionary biology does not recognize scientific hypotheses constructed from complex causal relationships with the teleological property.
Your comments also suggest that evolutionary biology does not recognize the significance of the ‘dynamic or programmable property’. Complex causation recognizes sets or classes of complex algorithms and complex causal processes. Specifically, complex causation recognizes that two programs GA1 and GA2 can be different programs made up of different logical operations, but still members of the same general set. In complex causation, if the claim is made that both GA1 and GA2 can model the same phenomena ‘evolutionary change’, then it is necessary to provide an explanation for the differences between GA1 and GA2. In the definition of intelligence proposed in a separate thread, I proposed that there exists a complex causal process called LEPS which is responsible for redesigning or reprogramming evolutionary change processes. This is one possible explanation for apparent fact that different occurrences of evolutionary change are modeled by different members of the general class of genetic algorithms.
There clearly appear to be differences between evolution and GA’s viewed from the perspectives of evolutionary biology and complex causation. I suspect the apparent differences could eventually can be explained or reconciled.
IP: Logged
|
|
Rex Kerr
Member
Member # 632
|
posted 17. January 2004 12:08
There also appear to be major differences between GA's interpreted in terms of "complex causation" and GA's interpreted from a computer science, statistical learning, physical, or mathematical approach.
Liquid water consistently and predictably moves towards lower elevations. The series x(n+1) = (x(n)+5)/2 consistently and predictably moves towards the number 5. (And so on.) Calling these "goal-directed" is not particularly illuminating in any field.
I still don't understand what you're getting at with the "dynamic or programmable property". You seem not to have addressed my comments above at all. 2 and 7 are different but are members of the same general set (i.e. "numbers")...what does this have to do with being "dynamic" or "programmable"?
Edited a - sign to a +, as it was supposed to be, to have the series converge to +5 rather than -5. Whoops.
[ 18. January 2004, 08:27: Message edited by: Rex Kerr ]
IP: Logged
|
|
warren_bergerson
Member
Member # 262
|
posted 18. January 2004 10:52
Rex,
I have some difficulty in understanding how GA program A is ‘purposeful or goal directed if the user wants it to solve a problem’ and the very same program would not be purposeful or goal-directed in the absence of the users desire’. IMO, it is more objective and more scientifically sound to define a computer program or algorithm as purposeful or goal directed based either on the properties of the program or the observable results produced by the program.
Viewed in terms of complex causation, a complex algorithm or program is an expression of a complex causal process. From this perspective, if a particular algorithm or class of algorithms exhibits the observable behavior of ‘consistently achieving a goal’ the function is said to model an example of goal-directed, purposeful, or teleological causation. The transition from ‘complex algorithm’ to ‘model of complex causation’ might be unconventional, but the practice of classify algorithms based on exhibited properties rather than the intent of the user seems to me to be fairly standard practice.
Again with respect to the ‘designed or engineered property’ the concepts involved seem fairly standard. It is generally recognized that 1)GA programs are engineered or designed, 2)GA programs constitute as diverse set of programs where there are substantial differences between the members of the set and 3)different members of the set of GA can model or simulate different aspects of different occurrences of evolutionary processes.
Interpreted from the perspective of complex causation, it seems reasonable to conclude that evolutionary change is a complex causal process. It is further reasonable to conclude that evolutionary change processes will be modeled by a set or class of functions, in the same way the a GA algorithms are a set or collection of different algorithms. Finally, at least some aspects of evolutionary processes are modeled by algorithms with the ‘engineered or designed property’ it is not unreasonable to conclude or assume that evolutionary processes, viewed in terms of complex causation, are modeled by algorithms the engineered or designed property. Again, if you accept that complex algorithms model complex causation, then concluding that evolutionary processes are modeled by designed or engineered algorithms is equivalent to asserting that evolutionary processes are designed or engineered. This conclusion is further supported by the existence of a set or class of complex process or algorithm which appears capable of creating and modifying algorithms such as GA programs.
IP: Logged
|
|
Rex Kerr
Member
Member # 632
|
posted 18. January 2004 17:36
Normally, one says that something is "goal-directed" when it is designed to produce a goal. A goal is an outcome that someone has thought of ahead of time. Normally, one uses "purposeful" in a similar way. These words, conventionally, assume an agent's involvement.
Using them in the way you are is misleading. It will lead to reasoning of the following form:
"When humans make ditches for water to flow between two points, these ditches are goal-directed or purposeful. Therefore, it is natural to assume that all depressions in the ground that carry water between two places are goal-directed or purposeful. People studying river formation do not recognize the significance of goals and purpose in their work."
Some of the arguments you are making sound exactly like this--just as much of a non sequitur--except you use "GA" instead of "ditch" and wrap goal and purpose inside the "complex causation" label.
Yes, all human endeavors are laced with goals and purpose. Is this any more illuminating when trying to understand the functioning and general properties of GAs than when understanding ditches, first-order derivatives of functions of a single variable, and the photoelectric effect (for instance)? I don't think so. I don't think so precisely because our power in understanding each of these things comes in abstracting the problem away from the details of human goals (or any goals); we understand how the system functions in a goal-free manner, and then can use the properties of the systems to meet our goals, perhaps.
You claim that
quote:
Again, if you accept that complex algorithms model complex causation, then concluding that evolutionary processes are modeled by designed or engineered algorithms is equivalent to asserting that evolutionary processes are designed or engineered.
This is complete nonsense, an elementary confusion of the difference between implication and equivalence, or a radical redefinition of what it means for something to be "designed or engineered".
All models of Mt. Everest are designed and engineered. Does it follow logically that Mt. Everest itself is designed and engineered?
IP: Logged
|
|
|
Printer-friendly view of this topic