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Author
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Topic: Mathematical Impossibility of RM&NS Evolution
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warren_bergerson
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Member # 262
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posted 07. December 2002 15:16
In the thread on Biological Information I proposed mathematical definitions of biological information and biological information processing. In that thread, I suggested that these definitions made it possible to test the mathematical feasibility of evolution by RM&NS processes. I am pursuing that subject here. I offer for discussion a preliminary analysis of the validity of the following mathematical assertion:
ASSERTION: For most evolutionary changes, it is mathematically impossible that the changes resulted from an RM&NS type process.
AN EXPLANATION OF THE ASSERTION
The above assertion is a mathematical rather than a scientific assertion. The assertion states that if 1)you precisely and mathematically define evolutionary change(a type of change), and 2)if you mathematically and precisely define RM&NS (a particular type of change process), then you can demonstrate mathematically that most types of evolutionary change can not have been produced by RM&NS type processes.
Evolutionary change is defined here as a change in the complexity or information content of a system over a period of time. An occurrence of evolutionary change over an interval of time from time t to time t+k is defined here by 1)the information content of the system at time t (denoted by It) and 2)by the information content of the system at time t+k (denoted by It+k). Evolutionary change is defined here in terms of the state or condition of a system at different points in time. The concepts of biological information defined in the earlier thread provide the basis for quantifying It and It+k.
RM&NS (random mutation and natural selection) refers to a type or class of change process. Again, using the definitions developed in the biological information thread, we can provide precise mathematical definitions of what is and what is not an RM&NS change process.
Evolutionary change as defined is change in information or complexity over a period of time. RM&NS is a type of change process which produces change in information or complexity. RM&NS, however, is also a type of change process with limitations or constraints on the rate or speed at which changes in information can occur.
As defined, the proposed assertion is valid if the ‘volume of information change’ in most changes from It to It+k is greater than the maximum volume of change that can be produced by an RM&NS process during the time period k (under the constraints applicable in the change from It to It+k).
It will be noted that testing the above assertion involves standard mathematical concepts and techniques.
PRELIMINARY FINDINGS
In order to get a ball park estimate of the likely validity of the proposed hypothesis, we consider ‘simple’ examples. Specifically we consider common evolutionary changes such as changes in the shape of some body part like a beak or wing, or changes in a chemical compound such as a protein. In design science terminology, changes in physical features are the result of changes in causal relationships called ‘assembly instructions’. For the sake of discussion here, we assume that the feature we are concerned with requires J assembly instructions, and that there are K different forms each of the J assembly instructions can take. Assuming there is only 1 set of instructions that will produce the form present at time t, then the complexity of the feature being analyzed is K ^ J (K to the Jth power).
In our starting point analysis, we assume that a generation has a duration of one year. We also assume that each generation ‘selects’ the better of two possible forms( the existing form and one alternative). Using these assumptions or constraints, a change in form using an RM&NS process is expected to take .5*(K^J) years.
Since an RM&NS process requires a ‘random’ or non-directed search of the set of possible forms, the rate of change will be the same whether the change being considered involves 1 assembly instruction or all J assembly instructions. Preliminary analysis would suggest that using RM&NS, the rate of evolutionary change is inversely proportional to the complexity of the system. It would therefore appear to follow that a system can not be both ‘highly complex’ (as biological systems clearly are), and capable of evolving based on an true ‘RM&NS’ basis.
Based on the number and complexity of assembly instructions, we can conclude that all life forms have a complexity greater than Dembski’s 10 ^ 150. The time required for any evolutionary change using a true RM&NS process would thus be substantially greater than .5 *((10 ^150)/(average population). This strongly suggests that no evolutionary change can be the result of an RM&NS type process.
The findings outlined here are ‘preliminary’ results based on the design science definitions of biological information. The preliminary results suggest the proposed assertion is trivial or obvious.
INTERPRETATION OF RESULTS
As should be apparent, the preliminary findings are the result of a strict interpretation of the term ‘random’. If the search for an adaptive solution to a problem is truly random, then each option is as likely to be considered as another. If the search for solutions is truly random, and if the adaptive or teleological solution changes, then the time required to find a solution depends directly on the size of the potential solution set, the number of options evaluated per cycle, and the cycle time. As systems become more complex, the rate of evolutionary change using RM&NS processes slows down. Given the actual complexity of biological systems, it appears that true RM&NS processes could not possibly explain evolutionary change.
The preliminary mathematical findings outlined here are only interesting because they appear to directly conflict with the widely accepted ‘scientific views’. It would appear, IMO, that the evolutionary biology views on RM&NS are not based on mathematically and logically precise definitions of the concepts involved.
Anyone disagreeing with the above preliminary findings has the opportunity to offer mathematically precise definitions which might produce different results.
SUMMARY
The above preliminary mathematical analysis based on design science mathematics would appear to directly contradict a widely held opinions in evolutionary biology. I look forward to seeing mathematical analysis and/or new mathematically precise definitions which contradict my preliminary findings.
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Frances
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Member # 169
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posted 07. December 2002 17:41
Isn't is fascinating how theoretical models may be so different from the actual situation. In fact perhaps Warren may be unfamiliar with estimated mutations rates and time lines for many organisms. It seems that these results contradict with Warren's simplified model. I believe this is why Evan and others are asking Warren for applications of his theoretical models since the proof is in the pudding. In this case it seems overly clear that the model does not capture the reality.
I will be adding some references that may be helpful for Warren to fine tune his model to reality later.
For a more succesful application of information/complexity see for instance
ev: Evolution of Biological Information or
What is Complexity
Evolution of complexity
[ 07. December 2002, 18:13: Message edited by: Frances ]
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Moderator
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Member # 1
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posted 07. December 2002 21:25
Warren,
Seems like we're covering old ground in this thread. I'd like it if you could avoid the impulse to start new threads unless the topic absolutely does not fit in another that has already been started.
Is this agreeable. Plus, the topic of this thread is a negative claim. Starting in January we are going to be cracking down hard with Moderation in an effort to steer Brainstorms in a better direction. Three things you need to work on are:
1. Avoid making the same positive claims over and over in new threads if you don't have any new material to discuss
2. Avoid the tendency to make negative arguments against other theories, especially when they are claims of logical defeat or impossibility
3. Spend some time putting some meat onto your ideas. Wrap them up in concrete details. Bring in some empirical data.
Warren, we appreciate your presence at Brainstorms...we really do. However, it would be good for you to tighten up and lessen your posting a bit in the future. Sometimes less can be more.
[ 08. December 2002, 10:22: Message edited by: Moderator ]
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warren_bergerson
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Member # 262
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posted 08. December 2002 11:52
Moderator,
I am in the rather interesting position of agreeing with you on the issues of moderating the site while disagreeing with you on issues of mathematics. While I fully intend to respect you requests, I would like the take this opportunity to explain my position.
POSTINGS
I will respect your request to reduce the number of postings. Believe it or not, but this was something I was already considering. I still consider this one of the best moderated and fairest sights I have encountered and I do intend to continue posting from time to time.
AN OFT REPEATED ISSUE
I agree that I have raised the issues of the validity of RM&NS and the validity of Darwinian evolutionary theory on a number of occasions. I believe, however, that each time I raised the issue it was from a new angle. I have, in effect, been searching for a general approach which 1)will falsify RM&NS and Darwin, 2)can be verified and confirmed by a broader audience and 3)will allow me to introduce or present the alternative theory of biological change processes which I developed before I first came to ISCID.
I am pursuing a ‘falsify and replace Darwin’ approach to presenting my model or theory because 1)my theory has a complex and unconventional form which is difficult to interest people in and 2)there are large number of individuals actively interested in the validity of Darwinian theory.
I have presented a number of arguments which, in my opinion, showed that Darwinian theory could be falsified using readily available evidence. However, since evolutionary biology does not follow a rigorous ‘one failure falsifies’ standard, it is uncertain whether any experimental evidence can ever falsify Darwinian theory (unless the peer review supporters decide they want Darwinian theory falsified).
Since, IMO is wasn’t possible to falsify Darwin based on experimental evidence, I began looking at the possibility of falsifying Darwin with mathematical arguments. As you will recall, I made an effort this fall to present one such mathematical falsification argument. Unfortunately, the argument depended on some relatively complex actuarial mathematics. The validity of the argument I presented was discredited by denying the validity of actuarial mathematics. [If you prefer, the argument was not accepted by the intended audience.]
The argument for mathematical falsification of RM&NS presented here is much simpler than my previous effort and depends on mathematical arguments that should be understandable by a large number of individuals. To summarize, the argument presented takes the following form:
1. Some types of evolutionary/adaptive change can be modeled as searching a set of possible solutions to find an adaptive solution.
2. In the ‘search type’ evolutionary change, a specific type of change process cannot explain the change if the search process can not search a substantial portion of the search space during the interval of time during which the evolutionary change occurs.
3. Using the assembly process definition, the search space for assembly instructions for life forms is always very large (far greater than 10^150 or 10^200).
4. The search speeds of RM&NS type processes are very slow relative to the size of the search space. (for most organisms, an RM&NS process can only search spaces much smaller than 10 ^ 100 in one billion years).
5. CONCLUSION: Most evolutionary changes involving adaptive change can not have been produced by RM&NS processes.
The above is a rigorous mathematical argument and each of the four premises supporting the conclusion is readily verifiable. I do not claim to have proved the above argument, but the demonstration would appear to be rigorous and well supported by the evidence.
POSITIVE RATHER THAN NEGATIVE CONCLUSIONS
Your second complaint concerning this thread was that it addressed a negative (falsification) rather than positive hypothesis. The subject being discussed in this thread was only intended as a segment of a larger falsify and replace subject. Hopefully I can address your concerns about the negative aspect of the subject by providing an overview of the larger subject. The broader subject matter can be described in term of explanatory filters.
Consider a multiple layer filter with the following three types of filters:
1. RM&NS processes
2. Darwinian Natural selection processes
3. Information generating machine processes
Applying these three filters to evolutionary change would produce the following four ‘layers’ of explanation.
1. Can be explained by RM&NS.
2. Can not be explained by RM&NS but can be explained by Darwinian NS processes
3. Can not be explained by RM&NS or NS only but can be explained by Information processing machines
4. Can not be explained by any know materialistic/deterministic process and may imply actions by an external designer.
The argument presented here suggests that there are essentially no features of biological systems or features which satisfy the layer one level of explanation. I had intended in subsequent discussions to show that there are essentially no biological phenomena that fit the second or fourth level. Finally, I intended to show that there is a fourth set of filters representing models or theories of biological information processing which provide limit the third explanatory level.
CONCLUSION
I respect your right as a moderator limit the topics discussed here. If you feel this is not a productive topic I accept that decision. The above comments are simply intended to state my position and indicate that while I respect your decision, I do not agree with your interpretation of a valid mathematical argument.
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Frances
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Member # 169
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posted 08. December 2002 13:22
Warren
quote:
Consider a multiple layer filter with the following three types of filters:
1. RM&NS processes
2. Darwinian Natural selection processes
3. Information generating machine processes
Applying these three filters to evolutionary change would produce the following four ‘layers’ of explanation.
May I point out to you that RM&NS processes include Darwinian natural selection. Why would you want to apply a filter twice? I would also like to add that Darwinian processes (RM&NS) seem to be able to generate information as well and thus the third layer is not independent of the first layer(s) either.
May I finally point out that your original posting did not address RM&NS as much as just RM (random mutation). I think you would find that no scientist would be surprised to find out that RM is not sufficient.
May I finally ask if the fourth layer expects the external designer to not use materialistic/deterministic processes to generate information/systems?
[ 08. December 2002, 13:25: Message edited by: Frances ]
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warren_bergerson
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Member # 262
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posted 08. December 2002 17:34
Frances,
Quote: Isn't is fascinating how theoretical models may be so different from the actual situation. In fact perhaps Warren may be unfamiliar with estimated mutations rates and time lines for many organisms.
If it wasn’t apparent, my comments are directed at the validity of RM&NS ‘Theory’. The point I am making is that evolutionary reality is not logically or mathematically consistent with evolutionary theory.
Quote: May I finally point out that your original posting did not address RM&NS as much as just RM (random mutation). I think you would find that no scientist would be surprised to find out that RM is not sufficient.
Random mutation AND natural selection is a more limiting filter, a more restrictive theory than natural selection and any type of variation. The point of my mathematical analysis is that the combination of the requirements for 1)random mutation or random search and 2)natural selection, selection applied to the organisms rather than to individual trait, is so restrictive as to make it mathematically impossible for evolutionary change to be produced by an RM&NS process.
If one concedes that variation is directed rather then one concedes that RM&NS processes can not explain evolutionary change. One concedes that RM&NS is not a valid theory of evolutionary change. One concedes in effect that it is inappropriate for scientists to make claims of the type ‘RM&NS explains…’.
I would agree that most scientists would not be surprised if the random variation component of neo-Darwin theory had to be abandoned. The mathematical demonstration that RM&NS processes can not produce evolutionary change would seem to support what I many scientists already expect.
However, despite evidence to the contrary, claims continue to be made for the scientific validity of RM&NS. Maybe you can explain the difference between what scientists understand and what they say?
If this discussion is allowed to continue, the next question is what types of evolutionary change would pass the Darwinian ‘Natural Selection and any type of variation’ filter. It would be more difficult to claim that scientists ‘expect’ observed evolutionary change to fail the natural selection filter.
Level 4 is what I think of as the ‘I don’t know level’. I leave speculation on the nature of this level to others.
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Frances
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Member # 169
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posted 08. December 2002 20:23
Warren" If it wasn’t apparent, my comments are directed at the validity of RM&NS ‘Theory’. The point I am making is that evolutionary reality is not logically or mathematically consistent with evolutionary theory.
At most one could argue that "Warren's interpretation of evolutionary theory is at odds with reality". In this case the obvious that the following argument has been addressed by Warren:
"Random variation is unable to explain the complexity in nature"
As I have shown however, Random variation AND natural selection seem quite able to explain complexity in the genome. If Warren wants to create and attack a strawman of evolution in the form of 'random mutations/variation' alone then fine but one should realize the limited value of such an excercise.
Random mutation and selection may be more limiting than any other form but random mutation, and it is important to understand that random refers to function, is what is observed. If Warren wants to argue that science should not model what is observed then he should say so. The further claims that "natural selection, selection applied to the organisms rather than to individual trait, is so restrictive as to make it mathematically impossible for evolutionary change to be produced by an RM&NS procesee" remains once again unsupported.
Perhaps Warren could make an effort to seperate his speculative thoughts from the actually supported ones.
I find it hopelessly frustrating to have to argue these simple facts time after time in response to postings by Warren but I find it still invaluable to point out the logical shortcomings in Warren's arguments.
So let me once again try to help Warren focus on what RM&NS is all about:
1. It claims that variation that arises is random with respect to function. It does not claim that mutations are random with respect to location in the genome, random with respect to time etc. It merely states that variation arises random with respect to the value of such variation in the environment.
2. Natural selection is a process in which traits which have a higher fitness value are more likely to be propagated through the species.
If Warren is interested in some thorough definitions of natural selection then I propose he checks out Endler's excellent book on this topic.
quote:
natural selection, selection applied to the organisms rather than to individual trait, is so restrictive as to make it mathematically impossible for evolutionary change to be produced by an RM&NS proce
So if Warren wants to show that "It would appear, IMO, that the evolutionary biology views on RM&NS are not based on mathematically and logically precise definitions of the concepts involved. " I would argue that Warren may be unfamiliar with how these concepts have been defined and used in biology.
Scientists have indeed observed that variations are random with respect to (future) use. Warren may be familiar with the experiments of Luria and Debruck
I have furthermore directed Warren to several researchers who seem to have developed quite well supported mathematical theories of complexity/information and the genome, allowing for many succesful predictions. Simulations using these mathematical models have shown how complexity and information can increase in the genome when variation and selection are applied.
Thus the conclusions proposed by Warren based on his limited evolutionary model show 1) that it is likely his model and not evolutionary theory which may have problems 2) that when theoretical models are applied, the results once again seem to contradict Warren's conclusions.
I would say that either one would by itself be a powerful falsification of Warren's theoretical efforts.
Thus "The point I am making is that evolutionary reality is not logically or mathematically consistent with evolutionary theory. " has been falsified.
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warren_bergerson
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Member # 262
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posted 09. December 2002 08:43
Frances,
Quote: As I have shown however, Random variation AND natural selection seem quite able to explain complexity in the genome. If Warren wants to create and attack a strawman of evolution in the form of 'random mutations/variation' alone then fine but one should realize the limited value of such an excercise.
Your statement is clearly at variance with the facts. My demonstration clearly shows the inadequacy of a process based on both random variation AND natural or whole organism selection.
Quote: So if Warren wants to show that "It would appear, IMO, that the evolutionary biology views on RM&NS are not based on mathematically and logically precise definitions of the concepts involved. " I would argue that Warren may be unfamiliar with how these concepts have been defined and used in biology.
Again, I have made it very clear that my concern is with mathematically precise definitions of variation and selection. Some evolutionary biologists may use definitions of variation and selection which have not or can not be expressed in a mathematically imprecise form. My concern is limited to concepts that can and have been expressed in mathematically precise form.
I have provided a set of mathematically precise definitions that make it possible to model and mathematically analyze one basic type of evolutionary change (finding an adaptive solution from a set of possible solutions). Using the definitions provided, I have provided a demonstration which strongly suggests that ‘an evolutionary change process relying only on random type variation AND only on Natural type selection’ [all find adaptive solution type search programs have some type or types of variance processes and some type or types of selection processes. The demonstration presented here relates to search processes with specific restrictions on both variation and selection processes.] can not produce or simulate, in an acceptable time frame, the types of evolutionary changes observed in nature.
I made it very clear that I presented a demonstration not a proof. I also made it very clear that my demonstration was based on the definitions I provided. I welcome any one to produce a mathematical demonstration showing that realistic evolutionary change can be produced by a process based on an RM&NS type process. The demonstration can be based either on the definitions I developed or on some alternative set of mathematically precise definitions.
I believe that in mathematics the claims of the form, ‘It can be demonstrated that ….’,
are only considered valid when there is enough information publicly available to review and confirm the claim. As it stands today, there are no mathematical demonstration that an RM&NS type process can solve an evolutionary ‘find the adaptive solution’ problem in an acceptable amount of time where the complexity of the problem is greater than some number like 10 ^ 150. The assembly instruction definition of evolutionary change suggests that essentially all evolutionary changes must involve complexity greater than 10 ^ 150.
Quote: I find it hopelessly frustrating to have to argue these simple facts time after time in response to postings by Warren but I find it still invaluable to point out the logical shortcomings in Warren's arguments.
The issue, as I have pointed out on a number of occasions, is not the facts, but the set of rules by which the facts are interpreted and evaluated. Evolutionary biology does appear to operate on a set of rules that insures that Darwinian and neo-Darwinian theory always win. The discussion here involves mathematics and the rules and standards used to interpret and evaluate facts should be mathematical rules and standards. As I understand your comments, you to continue to suggest that my demonstrations and arguments are unsound because they do not conform to the rules and standards of evolutionary biology. We might debate the applicability of evolutionary biology rules to the analysis of evolution, but I don’t see that there is any basis for insisting those rules be applied in mathematical analysis.
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Frances
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posted 09. December 2002 12:59
Warren,
You argue that my statement is at variance with the facts. But let's first point out that you are not arguing facts, you are arguing your mathematical model. That my statement is at variance with the 'facts' or better stated 'Warren's mathematical model' has some implications.
One may for instance argue that
1. My statement is wrong
2. Warren's mathematical model is wrong
Since I have supported my statement with various references to actual research, it seems hard to argue that my statement is wrong without delving somewhat further into the research.
If Warren wants to argue that my examples do not disprove his purely mathematical model of chance, then I invite him to explain why the examples I have shown are either irrelevant or have been falsified?
The researchers in this case used mathematical models of variation and information/complexity to show how the latter one increase under the
'forces' of variation and selection.
While your definitions may be precise they also seem to be irrelevant to the discussion since they have been falsified. Needless to say a mathematical theory can be precise and still wrong. This seems to be the case here. The 'demonstration' was based on a precise mathematical model that however did not accurately represent the processes involved in real life. While often simplification of models is needed to be able to simulate real life processes, the simplification in this case has gone too far and has omitted the important part of natural selection.
For Warren's benefit let me once again repeat the references with which I provided him before.
For a more succesful application of information/complexity see for instance
ev: Evolution of Biological Information or
What is Complexity
Evolution of complexity
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Evan
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posted 09. December 2002 14:29
I believe the points Frances is making are critical, not only to his critique of Warren's ideas but also to other arguments, such as those of Dembski's and Langan's.
It is possible to have a model that is well defined, precise, logically consistent, etc. that is yet wrong because it doesn't actually model the real world. This is why empirical data and empirically replicable tests are critical, and more personally, why I have been interested in both the problems of quantifying biological information and in assessing the probabilities of systems of events.
If a model doesn't also propose a way to test itself against the world, it can't add to scientific knowledge. If it does test itself against the world and the anticipated results are not borne out, then the model (or its tests) need to be looked at. (Of course, we also look for errors and improvements in the experiment also.)
But you can't just assume some things which may or may not be true, and then logically reach true conclusions.
[ 09. December 2002, 18:26: Message edited by: Evan ]
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gedanken
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Member # 594
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posted 10. December 2002 02:08
I normally would not get involved in a discussion like this, but I am confused by both the originating postings and some of the responses in both this and the “biological information” threads to which this thread refers. What I am interested in is clearer posts in providing responses to the ideas posed here.
Warren states:
quote:
ASSERTION: For most evolutionary changes, it is mathematically impossible that the changes resulted from an RM&NS type process.
Then he states:
quote:
The above assertion is a mathematical rather than a scientific assertion. The assertion states that if 1)you precisely and mathematically define evolutionary change(a type of change), and 2)if you mathematically and precisely define RM&NS (a particular type of change process), then you can demonstrate mathematically that most types of evolutionary change can not have been produced by RM&NS type processes.
Furthermore the opening statement implies (if I am not misunderstanding) that further clarification could be found in the “biological information” thread.
My first confusion is that in neither thread do I actually see any mathematical proofs, based on any such proposed mathematical definitions that any such conclusions can be reached. Furthermore I don’t see any references to any such mathematical demonstrations external to this thread, or in or external to the “biological information” thread. (I recognize that Warren has said that he has not provided any such proofs.)
In both threads, responding posts have correctly pointed out that a scientific theory can fail because any included mathematics is done incorrectly (e.g. any proofs are incorrect). Also a theory can fail because the implications have been tested against observations of physical nature and that these observations are contradictory to the implications of the theory.
But a concept can also fail to be a theory, because it neither has any mathematics to be verified, or predicts any implications which have been shown to be well supported by observation of physical nature. In science, we don’t use the term “theory” when we are only suggesting ideas or propositions to be tested later. In mathematics we don’t use the term “theory” unless it is referring to a body of actual mathematics.
One cannot correctly claim that when precisely defined certain results will ensue is a “mathematical” assertion (in the sense of mathematically dictated) -- because I can show that incorrect by simply writing my own “precise” definitions that I carefully choose so that they do not entail the specified results. If the realm is mathematics, and the postulates have not been suitably defined, I am totally free to make my own postulates. Mathematics, and the lack of prior definition, allows me that freedom.
However if one is claiming that all definitions that are part of an accurate model of the physical world by some objective criterion will then have certain consequences, then one is making a statement about the physical world and not a “mathematical” statement. In this case a scientific experiment could possibly be constructed to attempt to falsify the consequences as coming from the original models. What is important is the following. It is the requirement that the definitions create accurate models of the physical world that is tying the proposition to the physical world’s structure, constraining them to be representative of the physical world. Then we are not making a “mathematical” assertion, rather we are making an assertion that might be verifiable by scientific means.
I think that what Warren is trying to claim is that any mathematical model that can be verified to accurately represent the physical properties of RM&NS will have certain mathematical consequences. This is not a “mathematical” assertion, because it is constrained by properties of the physical world, and is not a-priori provable by any mathematics without starting with already mathematically precise definitions (which were not given). It may or may not be a correct statement about the physical world, but it is the fact that these definitions are being constrained by observation (in the original claim) rather than having already been constrained by their mathematically precise language that makes this an assertion about the physical world and not a “mathematical” assertion.
We can see examples of this type of assertion being made by Dr. Dembski (which I will discus later) in the case of the NFL theorems. But Dr. Dembski’s claims are in two parts: 1) certain precise definitions have consequences, as demonstrated by the NFL theorems, and 2) these definitions model what is claimed by scientists as the propositions of certain evolutionary theories of the physical world. We can in fact get some of the same sort of confusion as occurs here by reading some of Dr. Dembski’s work, if we don’t clearly understand the nature of scientific enquiry.
The assertions in part “1” are indeed “mathematical” assertions. Then Dr. Dembski points to some actual mathematics to back those assertions. They are not physical assertions, because they depend logically only on the postulates stated, and the postulates are precisely stated. The mathematics could be challenged by finding fault in the logic, but none of this has anything to do with questions of the physical world.
Then Dr. Dembski makes claims of type “2” that these definitions and postulates are entailed by the models that scientists are using. This is neither a “mathematical” nor a “scientific” claim -- rather it is a claim that can be analyzed by examination of what scientists have written. Because a claim that certain scientists’ definitions and models fit certain criterions is not itself a “scientific” claim. (It could only be viewed as a “scientific” claim by making a science of analyzing the writings. It is not tested by direct observation of the physical nature being discussed by those scientists, it is a question of whether the models used by those scientists have those particular properties and match the properties of the definitions in question.)
Whether Dr. Dembski’s findings have applicability to scientific theory will first depend on identifying if this connection is correctly made -- an issue that I and others dispute in the Evolution’s Logic of Credulity thread. (And that is the relation of this thread to my interests.) Various postings have shown problems in both area “1” and “2” of Dr. Dembski’s presentation. The consequences have not been properly shown to follow (mathematically) from the problem description as given. And the claims may not have accurately represented what the original scientists were stating. This makes claims that I have seen that Dr. Dembski has mathematically shown that evolution is incorrect seem doubly fanciful.
I would like to caution against escalating levels of claims, raising the level of such a claim from “scientific” to “mathematical”, as a rhetorical device. For indeed, “mathematical” proofs bear a much greater degree of certainty than do any “scientific” claims, because they flow from pure logic and not the logical conjunction of logic and observation of the physical universe. The problem is that to make a “mathematical claim,” one must make mathematically precise definitions and then back them up with demonstrated mathematical proof.
My confusion on responses in the two threads in question is as follows: I have seen posts that request to see the mathematics (showing that it is a mathematical assertion), and then requesting that Warren “show the numbers”. The problem is that these are mixing up the areas of mathematical assertion and question of the physical world. One can use physical examples in developing the underlying mathematics, and I suppose this may have been the basis of such requests. But the use of physical examples of the real world is an act of tying or constraining to the physical and precisely not a case of producing a mathematical assertion.
Then I would like to see better differentiation of what are mathematical questions, and what are scientific questions in the responses.
Mathematical questions can only be answered when we have precisely mathematically defined postulates. These depend on precisely defined definitions, defined in mathematical terms. To answer mathematical questions, we must examine the logic of a mathematical exposition based on these initial, carefully defined definitions and propositions.
Scientific questions can only be answered then by observing the physical world for conformance to the proposition in question. A question is not “mathematical” except to the extent that it relies on the precise logic of mathematical reasoning on precisely defined terms. A question is then “scientific” to the extent that it can be answered by careful observation of the physical world. A scientific explanation can contain an embedded mathematical exposition, and the science can depend on that exposition. But the mathematical logic can stand alone from the science and is not itself (standing alone) “science”.
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warren_bergerson
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posted 10. December 2002 08:52
gedanken,
Thank you for your thoughtful response.
To begin, I tried to make it clear that I am presenting a mathematical demonstration, not a mathematical proof. What I am proposing is similar to an argument ‘given a mathematical model of a bridge with certain mathematical characteristics then mathematical calculations analysis show or suggest the bridge will collapse". In the demonstration proposed here, I suggested that ‘given a certain type of model of a certain common type of evolutionary situation, and given known empirical features of biological systems, then if evolutionary change were exclusively of the RM&NS type then evolutionary change would not occur"( a conclusion, calculation or prediction in direct conflict with accepted facts).
This is a standard mathematical analysis/test. This is a standard engineering/hypothesis testing mathematical analysis. Based on the results of this analysis we would conclude,
1. The empirical data used to estimate the complexity of a biological system is wrong.
2. The empirical data used to estimate the maximum speed of an RM&NS process is wrong.
3. The mathematical model is unsound.
4. There is an alternative definition of RM&NS which would produce evolutionary change
5. Evolutionary change does not occur. or
6. RM&NS type processes alone can not produce evolutionary change.
Clearly items 1, 2, and 5 are based on real world properties. However, the real world properties assumed are so obvious or trivial as not to have a material impact on the discussion. The proposed analysis is thus, as I suggested, primarily mathematical in nature. More specifically, I suggest the validity of the argument should be evaluated based on mathematical standards and rules, not on the highly subjective standards and rules used in evolutionary biology.
Anyone is welcome to offer evidence contradicting the empirical evidence on which this argument is based.
The validity/soundness of the assembly instructions model of evolutionary/adaptive changes in physical traits would seem to logically and mathematically sound. Again, I welcome anyone to propose an alternative model that actually works. [I believe a genetic DNA code model of evolutionary change produces exactly the same results as the assembly instructions model, but it would be more difficult to provide empirical evidence.]
The most likely ‘flaw’ in the mathematical demonstration I presented is the definition of RM&NS type processes. It can be argued that there may possibly be alternative, mathematically precise definitions of RM&NS processes. I do not make the claim that no such alternative definitions exist. I only make the claim that there are no known, mathematically precise definitions which can produce the type of evolutionary change observed in nature under the common conditions defined in the demonstration.
While I concede there may be alternative definitions of RM&NS type processes, I suggest that the development of such an alternative which can actually pass the test I defined, would constitute a new theory of evolutionary change. As I stated in response to the moderator comments, my ultimate goal is to present an alternate to both RM&NS type and Natural Selection/Darwinian type models of evolutionary change. The first steps in introducing alternative models is to demonstrate that the existing models and theories don’t work.
Quote: Also a theory can fail because the implications have been tested against observations of physical nature and that these observations are contradictory to the implications of the theory.
It is important to note that this is only valid if theory and terms of the theory are precisely defined. If you use non-precise, metaphysical, ‘now you see it now you don’t’ definitions then a ‘theory’ is not testable.
I offer what I believe is a mathematical demonstration that using the precise definitions provided, evolutionary change can not be produced by an RM&NS type process under commonly occurring conditions. I do not claim the demonstration proved RM&NS processes cannot produce evolutionary change under the defined commonly (essentially universal) occurring conditions. I only claim that it is inappropriate and misleading(or worse) for evolutionary biologists to make the claim that RM&NS processes can explain or simulate evolutionary changes when in fact no such mathematical demonstration exist for common or realistic sets of conditions.
Quote: I would like to caution against escalating levels of claims, raising the level of such a claim from "scientific" to "mathematical", as a rhetorical device. For indeed, "mathematical" proofs bear a much greater degree of certainty than do any "scientific" claims, because they flow from pure logic and not the logical conjunction of logic and observation of the physical universe. The problem is that to make a "mathematical claim," one must make mathematically precise definitions and then back them up with demonstrated mathematical proof.
You make some valid points regarding the importance of distinguishing mathematics from science, but you take a two narrow view of the role of mathematics in scientific analysis.
The primary role of mathematics in scientific analysis is to test the logical consistency of complex sets of empirical data, assumptions, and scientific models or theories. If one prepares a model or demonstration and the model or mathematical demonstration produces an inconsistency(a result different than the result observed) then there is a flaw with some component of the model or demonstration.
Escalating claims to the level of ‘mathematical’ from ‘scientific’ is substantive not rhetorical. Escalating claims to the level of mathematics means raising the levels of rules and standards used to evaluate claims from ‘current scientific practice’ to the levels of mathematical rules and standards. The specific issue being addressed is the precise definition of terms and models. The current scientific standards on the necessity for mathematically precise definitions in ambiguous. The mathematical standard with respect to this issue is clear.
Quote: Then I would like to see better differentiation of what are mathematical questions, and what are scientific questions in the responses. Mathematical questions can only be answered when we have precisely mathematically defined postulates. These depend on precisely defined definitions, defined in mathematical terms. To answer mathematical questions, we must examine the logic of a mathematical exposition based on these initial, carefully defined definitions and propositions.
Modeling biological information processing is a complex subject. The level of detail provided here is clearly incomplete and there are both mathematical and scientific issues which will require clarification. When the question is clearly relevant to the substance of the subject being discussed I have attempted to address it.
As I mentioned above, the mathematics being discussed here is applied mathematics involving calculations, models, modeling rules, demonstrations and simulations. To require that such mathematical issues be expressed in terms of language of mathematical proofs is both inappropriate and unproductive. While I certainly welcome the efforts of theoretical mathematicians to evaluate the issues raised here, the discussion here relates primarily to applied mathematics and applied mathematical modeling.
While I don’t necessarily agree with all of your conclusions and suggestions, I appreciate the substantive and well argued nature of your comments. Thank you.
Warren
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Frances
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posted 11. December 2002 01:38
quote:
I only claim that it is inappropriate and misleading(or worse) for evolutionary biologists to make the claim that RM&NS processes can explain or simulate evolutionary changes when in fact no such mathematical demonstration exist for common or realistic sets of conditions.
Another negative claim which seems to be rebutted by the links provided by me above. Perhaps Warren may help us understand what he considers to be common or realistic sets of conditions. Perhaps that's where the problem may be located.
quote:
The first steps in introducing alternative models is to demonstrate that the existing models and theories don’t work.
I agree but so far I would argue that such demonstrations have yet to be given. Perhaps rather than focus on a strawman Warren may want to address the existing models and theories?
[ 11. December 2002, 01:39: Message edited by: Frances ]
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warren_bergerson
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posted 11. December 2002 15:11
The discussion here is based on two claims:
1. Given certain conditions and definitions, RM&NS type processes are mathematically incapable of producing evolutionary change.
2. There exist no known mathematical demonstrations that RM&NS type processes can produce evolutionary change under the defined conditions.
Discussion relevant to the topic introduced, IMO, would include:
1. Requests for clarifications of specific aspects of calculation/demonstration presented.
2. Arguments either in support of or disagreeing with some aspect of the demonstration provided. and or
3. Presentation of a counter demonstration showing that under the defined conditions RM&NS type processes could produce evolutionary change.
Except for some essentially trivial empirical data defining the conditions applicable to evolutionary change in biological systems, the argument/demonstration presented is mathematical. Well established techniques exist in mathematics for reaching consensus on claims of the type presented here. It seems appropriate, IMO, that the discussion in this thread should remain relevant to the subject/claims made and to the mathematical basis of those claims.
Requests for information not relevant to the subject being discussed or references to sources without demonstrating the relevance of the references, do not, IMO, make a positive contribution to the discussion.
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Frances
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posted 13. December 2002 01:00
Dear Warren
Could you explain to me why we should consider your 'mathematical model' as relevant? It fails to predict the observed patterns, is based on a strawman argument of evolution and is contradicted by both data and mathematical models of evolution of complexity.
No clarifications of your calculations are needed imho, they show that while the model is mathematically sound, it does not map well to the reality (not uncommon in mathematics :-))
I fail to see how your strawman makes in any way a positive contribution to either intelligent design and/or evolution.
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