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Topic: new paper on information
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Rex Kerr
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Member # 632
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posted 09. July 2004 00:29
There is a font change to a sans-serif typeface in two letters "fi" in section heading 3. This is probably not intentional. Also "revolving power" should probably be "resolving power" in the footnote on page 14. There are probably other minor errors.
Beyond that, there's a little too much heavy-duty measure and probability theory and the like for me to follow the derivations in enough detail to give useful feedback (e.g. check whether they're true or not). Example applications highlighting the difference between variational information and entropic information would be helpful.
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Rex Kerr
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Member # 632
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posted 09. July 2004 02:04
Also (please forgive the double post), I would encourage Dembski to submit the mathematical results in this paper to an appropriate journal, if he hasn't already. Very few non-mathematicians have the background to check the results, and very few mathematicians read ISCID. Plus, despite the annoyingly long time it takes to get mathematical papers published, it is one of the better ways to make one's work widely available to a relevant audience.
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William A. Dembski
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Member # 7
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posted 24. July 2004 09:16
Thanks, Rex. I've revised the paper and it is now available on the ISCID Archives. I also have submitted it for publication.
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Evan
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Member # 164
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posted 25. July 2004 09:47
Dr. Dembski, could you tell us where you have submitted the article?
Thanks
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Salvador T. Cordova
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Member # 959
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posted 26. July 2004 01:00
Bill,
I read through your paper today. This is daring, good luck, I like it.
One application of this could be in the analysis of biological Turing Machines. I have tried to show that the information content in a biological Turing Machine is independent of the chemistry. Biological Turing Machines are a necessary (but not sufficient) condition for life and therefore would be a good candidate for your CSI concepts and analysis using your variational approach.
A variational approach would help demonstrate that complaints of post-diction would drop out of both sides of the equations so to speak in the analysis of biological Turing Machines. Post-diction has been a major complaint against ID paradigms, and a variational approach might help provide a means demonstrating that there is more information than just our subjective projections. If so, this would lead directly to a design inference.
Some of the stuff you wrote to arrive at your proof I admit is not in my domain. I only briefly touched on sigma alegbras and Lebesgue measures in my studies. I do believe, however I understand your bottom line conclusions. I'll pass it on to any professors or colleagues who might be interested.
One problem with modeling information transfer is how to measure the information content in the totality of a system over time.
This formalism would be useful for example in arriving at an estimate for information content in a factory process. We know that the product of the process has less information than the process itself, but in practice this has been difficult to apply metrics. For example, how much information content is in one section of an automobile factory? These considerations have obvious implications for inferring origin of biological information.
The problem in doing the accounting was it was difficult to apply a uniform information measure to each step of the factory process. For example in Avida we could measure the bits and bytes of the genome, but the authors provided no means for assigning the level of information content to those wonderful "selection pressures" which created upward evolution in Avida. The variational approach could help normalize out problems with postdiction and any smuggled in circular reasonings.
Also, I very much like that you tied this to quantum mechanics. ID I believe is a fundamentally an interpretation of Quantum Mechanics.
If your reviewers sign off on your proof, my intuition tells me it will be a good mathematical foundation for ID, because for the first time we have universally applicable metric for information.
Further, because information has some observer dependence, definitions of information were vulnerable to accusations of subjectivity. Now we have a means of perhaps making the subjectivity drop out of both sides of the equation, so to speak.
If I have time, I'll try to give some examples to try to gather information measures using your variational approach.
regards,
Salvador
PS
On the epistemological side, in response to your critics I wrote: ARN Post 8 to your invitation. I wrote that to help give you a strategy to deal with some of the way I anticipate critics will attempt to misrepresent your work.
[ 26. July 2004, 11:54: Message edited by: Salvador T. Cordova ]
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Salvador T. Cordova
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Member # 959
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posted 26. July 2004 16:11
Bill,
page 7.
you wrote
quote:
(d_mu1 / d_mu2) d_mu2 = d_mu1
I want to double check. Did you mean:
quote:
(d_mu1 / d_mu2) mu2 = mu1
also in that same paragraph
quote:
d_mu1/d_mu2 = [ P(B) / P(AB) ] 1AB
the term 1B seemed to drop out. If I'm off base, I'll bail, but I'm asking just for my re-assurance.
Salvador
[ 26. July 2004, 16:20: Message edited by: Salvador T. Cordova ]
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William A. Dembski
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Member # 7
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posted 28. July 2004 23:50
Evan: If you look at my CV at http://www.designinference.com, you'll see I've submitted the paper to Complexity. This is not a straight mathematics journal, but given the historical and motivational padding in the first two sections of my paper, it seemed advisable to submit the paper to a journal like Complexity.
Salvador: referring to a measure with a "d" in front or without it is largely equivalent. The "d" simply indicates that the measure will be used in integration. As for indicator functions, I omitted some steps. Indicator functions correspond to sets (they're equal to 1 on the set, 0 off), so multiplying indicator functions corresponds to the intersection of sets (the intersection of A and B being represented by AB). Let me know if you need more clarification.
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Salvador T. Cordova
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Member # 959
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posted 29. July 2004 00:43
quote:
Salvador: referring to a measure with a "d" in front or without it is largely equivalent. The "d" simply indicates that the measure will be used in integration. As for indicator functions, I omitted some steps. Indicator functions correspond to sets (they're equal to 1 on the set, 0 off), so multiplying indicator functions corresponds to the intersection of sets (the intersection of A and B being represented by AB). Let me know if you need more clarification.
Thank you Bill for re-assuring me, it was my lack of familiarity that raised my concern. I have little doubt your ultimate conclusion is materially correct, and I was more concerned about typos, etc.
For my own reassurance, I looked in Real Analysis by Gerald B. Folland page 85 regarding the Radon-Nikodym theorem. It is in agreement with what you have just said:
quote:
d_nu = f d_mu for some f. This result is usually known as the Radon-Nikodym theorem, and f is called the Radon-Nikodym derivative of nu with repect to mu. We denote it by d_nu / d_mu. (Stictly speaking, d_nu / d_mu should be construed as the class of functions equal to f mu-almost everywhere).
good luck, and I hope you find capable reviewers.
Salvador
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Salvador T. Cordova
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Member # 959
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posted 13. August 2004 17:28
Bill,
If I could offer just pure brainstorm of an idea (it may be worthless), but we have used traditional information metrics to solve Hilbert Space problems in Quantum Cryptography. We can detect the presense of Intelligent Agencies acting upon systems in Hilbert Space.
Now, as in the case of ID detection, when events look correlated which should not other wise be from physical stochastic properties, we suspect design.
I have a hunch at least one worthwhile example of using your "Dembski Information" would be to take an existing ID detection done in traditional information technology, that has been researched, and couch it in "Dembski Information". Such is the case with Quantum Cryptography.
It's just a thought, it may or may not be worth pursuing. I have no doubt you'll get equivalent results and ID inferences in these cases using "Dembski Information" vs. Shannon information. But if "Dembski Information" is operationally useful to the analysis of Hilbert Spaces, here might be an operationa usage for the th metric. It would be great if it were used from a purely technological standpoint!
Quantum Cryptography July 2004
[ 13. August 2004, 17:43: Message edited by: Salvador T. Cordova ]
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Salvador T. Cordova
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Member # 959
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posted 02. February 2005 16:46
Dr. Dembski,
If I could beg your slight indulgence so that I could help see through equations a little more clearly....
I'm able for example to recognize the melody of Bethoven's "Ode to Joy" in a 44khz-16-bit resolution-CD-quality recording. I can also recognize it in a 3khz 8-bit resolution recording.
I've been thus able to glean a level of complexity that is not higher than that generated by the 3khz 8-bit recording in beethoven's "Ode to Joy". Thus 10 secons of "Ode to Joy" at most has complexity :
3,000 samples/sec x 10 seconds x 8 bits/sample = 240,000 bits
it has far less complexity that what the CD recorder/player captures with at 44khz and 16bit resolution
44,000 bytes/sec x 10 seconds x 16 bits/sample
= 7,040,000 bits
This is of interest as I'm trying to see how we can calibrate ID detection methods without explicit calculation of Probabilities. That is, we can actually measure complexity without explicit calculation. Can we empirically measure "variation" and thus infer information, since "information is a measure of variation".
As in the case of Beethoven's "Ode to Joy" the calculation of complexity is not straight forward, however the ability to detect it is beyond question empirically....
My intuition is that "Information as Measure of Variation" will help us assign a generalized complexity to something like Beethoven's "Ode to Joy".
As I've shown above, the 44khz CD quality versus the 3khz "AM radio" quality are able to convey the same information with respect to the target "Ode to Joy" and that through the process of detection we improve our estimate of the complexity in "Ode to Joy" and can assign a certain number of bits of complexity to "Ode to Joy".
Am I off the mark, or does this fall into what you may have in mind for "Information as a measure of Variation"?
Salvador
[ 02. February 2005, 16:59: Message edited by: Salvador T. Cordova ]
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Jim Skipper
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Member # 1510
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posted 18. February 2005 15:59
I would like to address the straw man you set up in the first couple of pages, the idea that information is the elimination of alternatives. You set up two statements RF and !RF and say:
quote:
Nevertheless, if our measure of information is simply an enumeration of eliminated possibilities, the same numerical value must be assigned in both instances since, in each instance, a single possibility is eliminated.
That quote makes me think you do not know much about poker or the size of the information set with which you are dealing. Neither of those statements elimate single possibilty.
The statement RF (the player has a royal flush) specifies exactly four possibilites. The statement !RF specifies 2,598,956 possiblities. Your use later on of omega is approriate since it is often used for heirarchies of infinities and demonstrates the impracticality of using the negative space as the value of information in a statement since it will frequently equate to infinity.
On page three, you say:
quote:
Smaller probabilities signify more information, not less.
then complain that probabilities are multiplicative rather than additive. Multiplying the probabilites give you an even smaller number and therefore more information, whereas if they were additive, it would break the rule.
I will address more of the paper as time permits.
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Jerry D. Bauer
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Member # 756
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posted 30. March 2005 03:04
*******And yet the probability of being dealt a royal flush (i.e., .000002) is minuscule compared to the probability of being dealt something other than a royal flush (i.e., .999998). Smaller probabilities signify more information, not less.*******
LOL...I hesitated posting this as Bill's going to fall out of his chair laughing at my over-simplistic interpretation of his paper (I understood about 3/4 of it as usual). But why not just base the bit measurement on the specificity of the information? Smaller probabilities signify a higher specificity in information content. If we view specificity as inversely proportional to the probability of an event occurring then the RF weighs in at 1/.000002 = 500,000, H = log2(500,000) = 18.93 bits. But ¬RF is only 1/.999998 = 1.000002000004. H = log2(1.000002000004) = 2.9e-6 bits. Or, H can be calculated with Shannon's H = sum(p1)log2(p2) if preferred (as it probably is at his level). To me simple is better, of course, you won't be reading any papers by me in peer-reviewed journals, either. ![[Wink]](wink.gif)
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