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Author
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Topic: The Microscopic Implications of "Specification."
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William Brookfield
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Member # 565
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posted 23. September 2008 13:55
In order to resolve the Poincare Recurrence problem in thermodynamics, the Second law can be posited, not as a law of thermodynamics but as a law of order (or information) decaying over time to randomness (zero information/order). This allows the finite-system constraint (order) and indeed mathematics itself (an orderly system of non-decaying platonic symbols) to be re-entered as a residual order-adulterating influence upon systems (or system tracking) -- that produces the Poincare recurrence artifact. In a new recurrence-free formulation, "entropy" is indeed synonymous to "randomness" and "low entropy" is indeed synonymous to "order."
The result of this however is that Shannon's "Information entropy" becomes a nonsense phrase. "In-form-ation" is a form of order (of “form”) and "entropy" refers to "randomness" -- the absence of order/form.
It seems to me that Shannon's equation (equation #1.) does not quantify randomness/entropy but instead quantifies independent correlational events of "information" while the Gibbs equation (#2.) quantifies independent fortuitous (random) events. What these two "entropy's" have in common is the notion of "independence" not "randomness/entropy." In Algorithmic Information Theory this "independence," leads to the Kolmogorov complexity of both informational ({i}K-complexity) and random events ({m}K-complexity) -- I.E., algorithmic incompressibility follows logically from "independence."
While the orthodox Second law initially arose from observations of physical systems, the Second Law of Black Hole dynamics arose, not from observations, but as a consequence/prediction of Einstein's theory. "Luckily" Einstein’s theory included an element of continuously variable cosmic decay (curvature) not present in finite* Statistical Mechanics. Both Second Laws can be seen as laws of order/information loss in their respective domains. In order to understand and unify these laws within a “info-dynamic” framework, a solid understanding of “information” is required and the lacuna in Shannon’s information theory needs to be filled.
I see William Dembski’s “specified complexity” as an important step towards the filling of the Shannon-ian lacuna. Dembski’s “specification” however, seems to address only the macroscopic properties of specificity while ignoring the microscopic implications. Thermodynamics originally addressed only the macroscopic properties of “temperature” “pressure” and “volume” until a microscopic formulation (statistical mechanics) was developed. I am suggesting brainstorming the microscopic implication of “specifications” and I am here proposing my notion of “correlational improbability” as the microscopic quantifier of informational “specificity.”
Another way of looking at it is that equations 1 & 2 both quantify “uncertainty” but in the case of the specified “information” (I {A}) all events as “information” are bound to be A>B correlated/ordered due to information’s specified nature. Thus, the pertinent phase space must be doubled to accommodate these orderly correlations. The result of this is that the improbability must be squared for any given informational event (I {A}). The (Event probability) times the (Correlational Probability) provides a new combined Information Event Probability (IEP). (EP)(CP) = P^2
An Example
(1a)rmkjcieroalsjhlj (random letters {naked K-complexity})
(A)rmkjcieroalsjhlj>
(B)rmkjcieroalsjhlj (Compressed “information” is K-complex but is none-the-less A>B correlated {ordered}) = p^2
“Information” (A>) is always “information about something” (B). It is therefore always in a correlated relationship with at least one (B). Random gibberish (1a) is un-correlated.
Random letters or numbers (1a) can indeed be turned into information by choosing to use them in a correlated manner. For example, an initially random number (1a) could be used as an access code to identify a single user within a large system, but once it is thus chosen (specified) correlations are now established and its function is no longer random. Its pattern of use/re-use corresponds to A>B (information) and not randomness (1a).
*By making the phase space infinite, continuous variability can be achieved for Stat.Mech.
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Melvin H. Fox
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posted 28. September 2008 08:33
William,
Are the correlations necessarily intelligent or could they be purely mechanical? I ask this because Dembski’s work here was done to devise a filter by which design could be detected. If the correlations can be a product of “just so” mechanical properties, then their presence is neutral with respect to intelligent design. True?
-Mel
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William Brookfield
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Member # 565
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posted 29. September 2008 12:25
Hi Mel,
Thanks for dropping back in!
The evidence for ID, as I see it, arises from the observation of certain patterns/structures in nature that have no legitimate causal antecedent in the material (non-telic) world. I am proposing that the "specified correlation" is the smallest logical sub-unit of these larger "patterns."
I am also thinking that both Shannon Information and Kolmogorov Information, are assuming (without explicity stating) the specificity and subsequently correlated (orderly) nature of "information." Digital information is not just "bits" but is instead "specified correlated bits." As I see it, "bits" can be random, meaningless and deviod of information -- or they can be "information" carriers.
quote:
Are the correlations necessarily intelligent or could they be purely mechanical?
In terms of information theory the correlations are necessarily telic. "Randomness/chance" is devoid of correlations. Random events are independent,uncoordinated and uncorrelated events, by definition. "Information" is calibrated in terms of a background uniform probability distribution (randomness).
An inference to intelligent design however requires a statistical argument based upon numerous correlations that together form a complex independent "pattern."
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William Brookfield
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posted 14. January 2009 13:08
Complexity:
Jeff Shallit recently posted an Information quiz. To all of these questions Jeff gets the answer "yes" (information can be produced) To all of these same questions I get the the answer "no." (information cannot be produced)
As I see it, what can be produced by these random and mindless transformations is not meaningful "information" as I/we understand the word, but raw {m}K-complexity.
(And even this raw complexity is wholly parasitic upon the complexity of the underlying system. That is to say, the complexity of a random string may well give you information about the bandwidth of the underlying system but this is system information and not information in transit through the system.)
I have long since made a distinction between non-informational "system" {m}K-complexity and informational {i}K-complexity. Just as with Shannon's theory - that I believe to be incomplete -- Kolmogorov's theory as I see it needs another element for its completion --irreducible/incompessible information couplings.
In Kolmogorov's standard one dimensional theory such couplings (001100111100110000..) would be compressible. But when it comes to "information" the correlations (couples) cannot be removed without destroying the information.
Information:
In writing this post I am projecting “informational” patterns that initially existed in my mind (A) outward in correlated and coordinated form into my computer (B) and over the Internet (C) for others to read (D) at distant places with distant minds. I am suggesting that a valid theoretical model of “information” must include information’s correlated and projected nature -- and that any valid mathematical model of information must provide a numeric quantification of this ongoing “coordinated projectionality.” As far as I can tell neither Komogorov nor Shannon’s theories of information include any such quantification. The introduction of incompressible couplings to Kolmogorov's theory would remove a lot of confusion regarding "in-FORM-ation" in that it would make the distiction between "randomness" and "form" (as in "in-FORM-ation") clear. With the addition of these couplings The irreducible nugget of digital "information" would be twice the size.
Design:
Only minds can give birth to information. This is because only the “minds eye” (with its insight, hindsight and foresight) possesses an in inner mental space, large enough to initially nurture and hold information for subsequent projection outward.
Thanks to the massive effort of computer inventors and designers we now have stable correlated computer environments safe/stable enough for the processing, storage and transmission of digitized information. It is the shape that information takes when digitized that is of interest to information theorists (such as myself). I am thinking that this hard-won correlational stability, upon which information critically depends, should not be taken for granted by information theorist.
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Christopher D. Beling
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Member # 723
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posted 26. January 2009 06:55
Hi William,
quote:
In order to resolve the Poincare Recurrence problem in thermodynamics, the Second law can be posited, not as a law of thermodynamics but as a law of order (or information) decaying over time to randomness (zero information/order).
I kind of see what you are saying. The Poincare recurrence problem, as I understand it is that a system of interacting particles will return to the same phase point state after a certain recurrence time. The entropy of the system thus does not change theoretically - but of course we know that the entropy does increase. For myself I believe this is due to stochastic collisions of the gas with the walls (which must also be considered as part of the system trajectory - and which is not). But certainly stochastic collisions destroy any information that was encoded in the gas (e.g. half the gas atoms on one side of the container). As the entropy increases so the information decreases with the sum of the two being a constnt. Are you thinking in terms of a gas like I am?
Best,
Chris
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William Brookfield
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Member # 565
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posted 02. February 2009 22:41
HI Chris,
Thank you very much for your response. Hope you are doing well.
quote:
"Are you thinking in terms of a gas like I am?"
Yes, to a large extent I am – at least as a starting point.
quote:
"For myself I believe this is due to stochastic collisions of the gas with the walls."
“Stochastic” as I understand the word refers to interactions that are not “clean” in that while being quite deterministic, also contain an element of pure randomness. Assuming that collisions/interactions of gas particles with themselves and with the walls are not perfectly ”clean” (perhaps due to relativity) then there would be an emerging randomness and subsequent irreversible equilibrium. This would solve the Poincare Recurrence problem by assuming that otherwise determinist (information preserving) Newtonian kinetics were actually information losing interactions. Of course one might point out that the math of relativity and QM is information preserving, but given what we know about black holes I am doubtful that informational correlations (order) can be preserved through singularity.
If on the other hand, the interactions are indeed “clean” and subsequently information preserving, then merely enlarging the phase space by including the walls would not solve the recurrence problem – for this new larger phase space would have its own recurrence problem. In such a platonic world, as long as the phase space is finite, a recurrence problem (however minor) would still exist. In the infinite case however there is no constraint (order) being imposed upon the “contents” and recurrence (residual order) is no longer a possibility.
In both of these scenarios however, the solution to the recurrence problem seems to involve a model of order loss (or information loss) and an ensuing randomness. My suspicion is that the perfectly ordered (non-decaying) platonic world of mathematics can only approximately track the actual Second Law of cosmic decay.
BTW. I am looking forward to reading your article on the fourth law that you recently presented at Oxford. Please let us know if it becomes available. Thanks --WB
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Bruce Fast
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Member # 924
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posted 03. February 2009 18:10
Hi William,
Nice to see some activity on this board.
I am intrigued by the "information quiz" that you linked to.
I propose my response to the quiz, as my response is different than yours (all no) and the author's (all yes).
Q1: Can information be created by gene duplication or polyploidy?
I would suggest that Gene duplication, in itself, will not create new information. However, I think that gene duplication sets up a situation where the creation of new information, without a balanced loss of information, is feasible.
Q2: Can information be created by point mutations?
It is possible, I think, to create meaningful information via point mutations. If a gene, for instance, becomes better at what it is trying to do because of a point mutation, the mutation has increased its meaningful information.
If, for instance, a gene duplication has happened. If copy a continues to be used for a well established purpose, but copy b is now co-opted for some other purpose, then copy b becomes suseptible to reasonable information increase. A point mutation may make it better at its coopted task.
I find it rather amazing -- unlikely -- however, that a gene duplication would occur on a gene that is being used for two purposes, then that the organism would separate the two tasks, letting one follow each of the two gene copies. This does seem to happen in nature, but I find it challenging to believe that nature has pulled such an event off without foresight.
quote:
More specifically, if xay is a string of symbols, is it possible that xby contains significantly more information?
To get "significantly more information" from a point mutation is painfully unlikely except in a set-up. If I were to see a specific point mutation producing "significantly" more information, I would strongly assume that the scenerio was rigged. Possible? Yes. Frequently, well, no! Once in 800 gazillion, maybe.
Q3: Can information be created by deletion?
Oh great scott! Maybe, if a deletion is just so, the deletion will result in increased information, but its highly, very highly, unlikely.
Q4: Can information be created by random rearrangement?
Oh great scott! Maybe, if a random shuffling is just so, the random shuffling might result in increased information. However, such an event is so highly unlikely as to be ignorable.
Q5. Can information be created by recombination?
Oh great scott! Maybe, if a recombination is just so, the recombination might result in increased information. However, such an event is so highly unlikely as to be ignorable.
My conclusion:
Q1 - Sets up for possible increase of information, but unlikely that a meaningful setup would occur without foresighted guidance.
Q2 - Increase, once in a blue moon. "Significantly"? Not witout a setup.
Q3 - Can? Yes. Common? Hardly.
Q4 - Can? Yes. Common? Hardly.
Q5 - Can? Yes. Common? Hardly.
In every scenerio, it is possible to rig a scenerio where the results are positive. It is conceivable that once in a blue moon chance does exactly that. However, within the limits of biological reproduction, these phenomena have only happened a handful of times by chance. If these phenomena are commonplace in the genome (I believe they are) it is because an intelligence is at work arranging for the little miracles to happen.
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Christopher D. Beling
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posted 05. February 2009 08:06
William,
Thanks for that last post. It is nice to see that we are on the same page. There are some difficulties with this idea of information embedded in gases which I can see emerging but I think this is a fascinating area of discourse. One reason is that the behvior of particles that are "free" in space is closely related to the information content of the universe as it expands and whether one can meaningfully talk about the information content of the universe.
I understand what you mean by stochastic refering to interactions that are "not clean". As you say another way of seeing this is that such interactions are not deterministic. To me this means that the interactions of a "clean" system are purely classical. That is they are governed by Newtonian (or Einstinian) mechanics. I would refer to "stochastic" as having a QM element of "randomness" involved in the interaction on top of the classical (deterministic) component.
I take back what I said about the walls as a reason for the 2nd law and the lack of Poincare recurrence. I think this is a factor but a more important effect is the Stochastic QM randomness of trajectories after atom-atom collisions. Poincare recurrence is surely only for classical systems? The gas system is continually scattering from one unknown state to another.
Experiment. 1: Consider a reasonable container with colorless atoms in the right half and "red" atoms in the left half - separated by a partition. Remove the partition - the gases mix. The phase state of this system is not going to recur - not even given the lifetime of the universe. I think it is because (i) the stochastic (QM) nature of the collisions but believe (ii) that because even if the collisions were classical (clean) the recurrence time would be zillions of universe lifetimes.
Experiment 2. Consider a Platonic case. Compress a gas into a special container - a container that can have its wall taken away at close to the speed of light (well anyway - much faster than gas molecular velocities). Even a classical "clean" atomic gas will have a phase space trajectory that will never come back on itself (recurrence) because the spatial coordinates of the atoms will continue to increase as the gas expands outwards. This is an interesting case, because the information content of the gas would be small to begin with because of the spatial confinement of the atoms. And yet information is conserved - so that information present at the compressed state must still be there in the expanding state?
Thanks for the encouragement to post the Oxford paper. You can find it at
http://hkusua.hku.hk/~cdbeling/4thLawOxford.pdf
Chris
[ 06. February 2009, 23:18: Message edited by: Christopher D. Beling ]
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nosivad
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posted 08. February 2009 17:03
Gentlemen,
it is good to see some more action here at brainstorms.
I discussed the question of thermodynamic laws as they apply to evolution in my essay on St. George Mivart.
http://jadavison.wordpress.com/2007/12/16/th-prescribed-evolutionary-hypothesis/#comment-1594
message #244
At present I do not see how known physical laws can account for any aspect of organic evolution except, of course, extinction which has been the ultimate fate of the vast majority of all the organisms that ever existed. Until such laws can be discovered I must remain a non-sectarian Creationist. Furthermore, I do not believe such laws will ever be found.
"A past evolution is undeniable, a present evolution undemonstrable."
John A. Davison
[ 08. February 2009, 17:13: Message edited by: nosivad ]
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William Brookfield
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posted 09. February 2009 13:28
Hi Bruce,
Thank you for your comment.
You know, there was once a great hope in science that monkeys (if given enough time) would eventually produce some Shakespeare. However after many long decades of waiting, some exasperated scientists finally decided to cheat by giving the monkeys typewriters (actually computer keyboards). Thanks to these intelligently designed (gasp) human inventions any downward motion on the keys would produce letters (the very building blocks of shakespeare!). Downward motions however, can be caused by many things -- monkey fingers, monkey poop, monkey feet, monkey-launched rocks and other monkey projectiles that fail to attain orbit and subsequently come down. The hope was that the “typing monkeys” could represent a kind of proto-Shakespearean randomness-in-type, but alas the monkeys were far worse than randomness, attacking the orderly typing machine itself.
The very essence of fine English literature and scholarship is somehow lacking in monkeys. To this day however, the myth of the typing monkey persists in popular culture as a representation of “creative randomness.” Even more persistent than the Monkeys-did-it myth is the Randomness-did-it myth.
“Randomness” however can be mathematically quantified as a uniform probability distribution -- the opposite of information (orderly non-uniformities). The upshot of this is that, even if the monkeys did indeed type some “shakespearean” letters, the letters in question would not be Shakespeare (a unified, holisitic work bound by laws of spelling, grammar, syntax and plot development) but merely a string of independent, fortuitous events (bound only by the fact that the output must consist of letters {and not monkey poop}).
So while monkey letters might seem like information/Shakepeare (to the unwary), they are not. There is no information (no Shakespeare -- no orderly non-uniformity) to be had as the result of such “once in a blue moon” chance events. “Once in a blue moon” events are merely statistical fluctuations devoid of information.
Bruce quote:
"It is possible, I think, to create meaningful information via point mutations. If a gene, for instance, becomes better at what it is trying to do because of a point mutation, the mutation has increased its meaningful information."
I don't see a direct correlation between survival advantage and information as you seem to. Depending on the conditions, a survival advantage may be had by either information gain or information loss (as in the case of say sickle cell anemia and subsequent resistance to malaria).
I am proposing an independent and different definition of information than Jeff Shallit’s weak (in my opinion) definition of information.
Hi Chris,
Thanks for posting your very interesting article. I was struck by your statement..
quote:
“One of the mysterious outcomes of this law seems to be that it predicts that science itself is unable to answer that all important question as to the origin of genetic information.”
Jeff Shallit claims to have solved this very problem.
quote:
"Bethell shows a profound misunderstanding of information theory when he claims, 'Francis Crick, the co-discoverer of the structure of DNA was asked how the all-important coding information found its way into the DNA in the first place. It's so complex that a reliance on random events will never get us there.' Bethell apparently doesn't understand that in the Kolmogorov theory of information, complexity is the same as randomness. It's easy to get complexity; .all you need is a source of random events." -- "Bethell the Buffoon"
Apparently all you need is “a source of random events” IE “Randomness-did-it” or maybe it was those damn monkeys. ![[Roll Eyes]](rolleyes.gif)
Chris,
quote:
(Experiment #2)This is an interesting case, because the information content of the gas would be small to begin with because of the spatial confinement of the atoms. And yet information is conserved - so that information present at the compressed state must still be there in the expanding state?
I think you may be focusing on the wrong level of information here (the wrong information domain). I am modeling “information” on a randomness->order continuum in which “targeting” or “constraint” is the essence of both order and information. “Information” as I see it, is composed of many successfully targeted correlations. When the “targeting” or “constraint” of the gas is removed (in experiment #2) the “proto-information” or “ordering” is removed. What ensues is a zero information cosmic equilibrium (at the level in question). The macroscopic motion of the system therefore is from order (constraint) to randomness (equilibrium /no constraint).
Hi John,
Thank you very much for calling us “gentlemen.” I have been called many things. Some folks are not even sure if I am human!
quote:
John,
“At present I do not see how known physical laws can account for any aspect of organic evolution”
I don’t think I am as pessimistic as you and Chris here regarding the future reach of science. Can’t we start looking at psycho-physical laws and psycho-physical dynamics, or is science bound forever to the physical? Can’t scientists observe and test the physical effects of mental activities, or is that just forbidden?
[ 09. February 2009, 17:28: Message edited by: William Brookfield ]
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nosivad
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posted 09. February 2009 16:02
There is no objection to pursuing any line of inquiry. I am simply unable to imagine the origin and subseqent evolution of life by any presently known physical processes.
With Pierre Grasse, I reject any system which relies on probability or chance.
"Any system that purports to account for evolution must invoke a mechanism not mutational and aleatory."
"Evolution of Living Organisms," page 245.
That is why I proposed the Prescribed Evolutionary Hypothesis. I also suffer from another intellectual defect. I am, like Einstein, a convinced determinist.
"EVERYTHING is determined...by forces over which we have no control."
Albert Einstein, my emphasis
There is nothing that can be done for me, just as there is nothing that can be done for Paul Zachary Myers and Richard Dawkins. We are all victims. Some of us have been luckier than others and of course each of us is convinced he is one of the lucky ones!
It is hard to believe isn't it?
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William Brookfield
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posted 09. February 2009 17:01
Hi John,
Just to be clear, I agree with you that physical laws alone cannot explain the emergence and development of life. I do however disagree with you and Einstein regarding determinism -- though the freewill vs determinism debate should probably have its own thread...
[ 09. February 2009, 17:03: Message edited by: William Brookfield ]
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nosivad
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posted 10. February 2009 15:00
I understand about your reaction to Free Will and Einstein. I have yet to find anyone else who DOES agree with Einstein and myself about Free Will. As near as I can tell he and I are the only ones that take it seriously. My status is based on the conviction that both ontogeny and phylogeny have been determined phenomena in which chance and probability have played no role whatsoever.
I am not alone in that perspective either. Referring to ontogeny and phylogeny -
"Neither in the one nor in the other is their room for chance."
Leo Berg, Nomogenesis, page 134
I don't believe Einstein ever addressed the issue of organic evolution, but if he had I am convinced he would have laughed at the Darwinan interpretation. Indeterminacy was foreign to his psyche as it is to mine. It is probably a congenital condition. What isn't?
It is a bitter pill to swallow when one must recognize that he is not intellectually free. It was for me but when I accepted it I found it to be very rewarding. Even Einstein was never able to accept black holes. They are well beyond my comprehension as well but I am no physicist.
Does anyone participating in this forum believe that Richard Dawkins and P.Z. Myers have reached their rabid atheism through rational processes? I sure don't. I believe they were, as William Wright's book declares and substantiates, "Born That Way."
Another Darwinian, Ernst Mayr, feely admitted his condition when he referred to himself as a "dyed-in-the-wool Darwinian"
The Growth of Biological Thought, page 132.
It is hard to believe isn't it?
"Everything is determined...by forces over which we have no control."
Albert Einstein
Please excuse my obstinate determinacy.
"A past evolution is undeniable, a present evolution undemonstrable."
[ 10. February 2009, 15:04: Message edited by: nosivad ]
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William Brookfield
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posted 14. February 2009 00:16
Bruce,
I am thinking I could make things clearer. (BTW I am very familiar with the Yukon having spent much time in Watson Lake and I also lived just north of Whitehorse over one summer. I hope all is well up north).
When it snows here this snow is added to the roofs of our houses and often icicles are formed and adding “even more to the houses.” These random “additions” to northern houses however, are not “built up” structural additions. They are instead threats to the structure of the houses. The weight of too much snow could collapse the roofs and icicles can damage the gutters.
The same is true with random (uncorrelated/ucoordinated) events and information. “Information” as I am defining it here is a type of FORM or structure – just as a house is a type of form or structure. A one-dimensional representation of a house is necessarily incomplete. Houses are three-dimensional structures. A one-dimensional representation of “inFORMation” is likewise incomplete, in my opinion. I could be right or wrong about this, but what I am putting up here for debate is my (correlated/coordinated) two-dimensional model of information.
The debate regarding three-dimensional vs. one-dimensional houses is over. Everyone agrees that houses are indeed three-dimensional structures. (Nobody wants the weight of snow to reduce their houses to two dimensional structures). The debate regarding one vs two dimensional “information” is ongoing. Jeff Shallit (appears to be) supporting one-dimensional “information” whereas I am claiming that two-dimensions, at least, are required.
[ 14. February 2009, 00:36: Message edited by: William Brookfield ]
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William Brookfield
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posted 24. June 2009 20:55
Well Jeff Shallit's information quiz thread seems to have petered out. The last comment on that thread at this time is one by a "Dr. No" who says..
quote:
Although I am sure that they are measuring something that is a real attribute of a system I cannot pragmatically see how they can call it information. When the information content of a random string of characters is calculated by accepted techniques as being maximal this to me is nothing but a reductio adsurbum indicating a systematic problem with basic assumptions.
I don't know who "Dr No" is but this statement reflects what I have been trying to say all along. While a random set of coin flips is indeed maximally K-complex, this does not mean that those coin flips are maximally loaded with information. And if they were indeed loaded with information, then what on earth would these random coin flips be providing information about?! The weather in Kansas!?!
Clearly there is a "systematic problem with basic assumptions" in Jeff Shallit's definition of "information." Something like "correlational information" or "functional information" is required to avoid the coin flip absurdum.
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