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Author
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Topic: Is 2nd Law a special case of 4th Law?
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Christopher D. Beling
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Member # 723
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posted 09. September 2006 12:17
2ndclass and William, forgive me for talking about pi again It seems it is not as “easy as pie”! ![[Smile]](smile.gif) I gave the last post to try and clear things up. You both said that the pi string was not CSI. Interestingly neither of you suggested it lacked the “specification” component (after all it is K-simple and non-ordered)– but you both disagreed on the “complexity” component – saying it was a high probability. I hope I have convinced you this is not so- i.e. that by definition the string is complex [complexity =-log2(P)]– providing one has an equal bias for 0 and 1 – in which case we have an omega space then of 2 E50 possible strings and P=2E-50. This seems physically reasonable to me; If for example the pi string was found embedded in a string of DNA: here quite clearly there can be no prior reason to suppose any bias for a C, G, A or T.
I know the pi string's specification is not questioned, but I would like to quote from the 5th miracle by Paul Davies (p117) which first got me thinking on this. Talking about the requirement of coding for life Paul says . . .
quote:
Randomness is the way to go. The following:
11001001000011111101101010100010001000010110100011
shows a string of ones and zeros that looks pretty random. But can we be sure? How do we know that there isn’t a subtle pattern lurking in the sequence? Actually there is. The sequence shown is the first 50 digits of number pi. It can be generated by a few lines of computer programming. However, if you didn’t know this you wouldn’t spot any pattern -
i.e. the string looks random but is in fact non-random. Another interesting example Paul gives relates to physical reality – and this may interest Sal because of the resonance between the laws of physics and maths: quoting:
quote:
A law of nature is, in essence, just a simple way to describe (or predict) complicated behavior. To take a well-known example, consider eclipses of the Sun. If you wrote down the date of each successive eclipse and expressed it in binary, you would get a string of ones and zeros that looked random. But that appearance would be deceptive. We can use Newton’s laws to predict the dates of eclipses and all other features of planetary orbits. Newton’s laws are simple mathematical formulae that can be written on a small postcard, so the information about all those eclipses .. is already implicit in a rather short algorithm.
I'm quite mad, I took time to do this – The eclipses occured on 6 /21/01 ;12/4/02 ;11/23/03 ;4/8/05 ;6/29/06 - ; expressed in binary with a 4 bit month, a 5 bit day and a 3bit year one has the string:
011010101001110000100010101110111011010001000101011011101110
29, zeros and 31 ones and looking very random!. This number is non the less non-random – machinated out by computer code following the simple laws of physics in the Sun-Earth-Moon system. It is human CSI – based on our knowledge of regularity (necessity - a 1st stage EF phenomenon). Hope you find this interesting. Chris
PS. William I do hope to comment on your nice diagram - I mainly agree with it but have a few questions.
[ 09. September 2006, 12:35: Message edited by: Christopher D. Beling ]
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Melvin H. Fox
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posted 10. September 2006 21:28
Please excuse if this perspective is too basic.
Is not pi specified because it is the exact ratio [perimeter/diameter] for any circle? Is not pi complex because it can’t be represented exactly by any rational number or in decimal form?
-Mel
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William Brookfield
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Member # 565
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posted 10. September 2006 22:02
quote:
Christopher:
quote:The complexity part of Pi string is certainly not in doubt
2nd Class.
Actually, I find it very doubtful, although my reason is not the same as William's.
Hi 2nd Class.
Thankyou for your input,
Actually 2ndclass, I agree with Chris here. I was not talking about "the PI string" but "Pi the thing." I see the Pi amplitude as simple, but its decimal expansion (the Pi string) as {m}K-complex. The Pi amplitude and its decimal representation are two different things. The Pi string is what I would call a "Platonic Train Wreck" -- a "hideous" collision of platonic curvature and platonic straightness. The interesting thing about platonic train wrecks is that (unlike normal train wrecks) they always crash exactly the same way every single time.
Hi Chris,
Thankyou very much for your effort and thank you for bringing up Pi.
Pi is a very interesting case. As I see it the elements here include #1 a perfect platonic circle (specified simplicity) #2. A perfect platonic diameter line (specified simplicty). #3. A linear (line-like) method of representation -- representing the ratio of #1 and #2. This representation method #3. permits the expression of remainders (left overs) in a series of adjacent but "decimated" (amplitude reduced) omega spaces. Where amplitudes (numbers) do not fit neatly into the intial decimals (1234..) remainder omega-spaces are generated for any residuals. With every further decimal place the pertinent omega space (and subsequent information regarding the Pi amplitude) is reduced by an order of magnitude. With every new decimal place, the specificity (new information regarding the Pi amplitude) is less. At infinity, the remainder's omega space becomes zero and residual information gain and omega space reduction (information loss) are zero. At infinity Pi has been fully expressed.
The fact that information (regarding the amplitude of Pi) is more difficult to display in decimal does not mean that there is more information to be had here (no more than say, the decimal friendly number "4"). It means only that the single unit of information (Pi) has to be re-assembled (fraction by fraction) due to the shattering circle vrs. linear conflict. Pi and other such numbers are misfits in the land of decimals. Painstakingly putting Humpty(Pi) back together again does not produce any more eggs. The information we get from the fragments merely adds up to a seamless single whole. Because the complexity of the Pi string results from expression failure (due to a basic topology conflict) the complexity type here is non-informational (mock)K-complexity and not informational (i) K-complexity. Just as with randomness the complexity of Pi is in the display (the string) not in Pi itself.
[ 10. September 2006, 22:10: Message edited by: William Brookfield ]
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2ndclass
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posted 11. September 2006 15:34
Christopher:
quote:
The basic problem here is that to get that string you need BOTH the regular natural phenomenon (i.e planets and the simple form of Newton's laws) which are in the classification of necessity (regularity,order) AND sophisticated telescopes and above all a computer operating on an algorithm (that has certainly not come about by chance - i.e. is a case of human CSI).
All information that we observe is gathered and processed by complicated systems, whether it be eyes and brains or telescopes and computers. It seems, according to your logic, that everything we observe is necessarily CSI.
Your eclipse example illustrates this:
quote:
It is human CSI – based on our knowledge of regularity (necessity - a 1st stage EF phenomenon).
Are we to conclude, then, that the eclipse schedule is designed?
Dembski's tractability condition addresses the fact that nature doesn't hand us patterns; rather, it gives us physical phenomena, and it's up to us to process, interpret, and hopefully find patterns in them. Consider his Contact example. If interpreting an electromagnetic fluctuation as a binary amplitude-modulated signal with a certain threshold results in a sequence of unary primes, then we consider it specified.
If our background knowledge, which includes the ability to build telescopes and execute simple algorithms, is sufficient to recognize a pattern in a physical phenomenon, then Dembski's tractability condition is met. As Salvador reminds us, CSI is defined in terms of the conceptual pattern T and the physical event E, not in terms of the equipment or methods used to recognize the pattern.
[ 11. September 2006, 16:32: Message edited by: 2ndclass ]
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2ndclass
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posted 11. September 2006 16:31
William:
quote:
With every further decimal place the pertinent omega space (and subsequent information regarding the Pi amplitude) is reduced by an order of magnitude.
Technically, there is always a countably infinite number of digits left to decide, which means that omega doesn't shrink.
Furthermore, since Dembski uses the term information synonymously with surprisal, we need to ask what distribution the probability is conditioned on. Given a uniform distribution, every digit is decided with a probability of 1/10. But given an algorithm that generates the digits of pi, every digit is fully determined and therefore contains zero additional bits of information. Perhaps that's why the string of pi digits is mock K-complex -- it appears information-rich only under an assumption of uniformity.
quote:
Just as with randomness the complexity of Pi is in the display (the string) not in Pi itself.
I can't tell if the word complexity in this sentence refers to Dembskian complexity, K-complexity, mock K-complexity, or some other concept.
At any rate, I'm going to bow out of the discussion now, as I seem to be working from a different set of premises than the rest of you. Thank you all for your congeniality. You're a top-notch group of forum participants.
[ 11. September 2006, 17:33: Message edited by: 2ndclass ]
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William Brookfield
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posted 12. September 2006 00:04
2nd Class
quote:
I'm going to bow out of the discussion now,
I'm sorry to hear this 2nd Class. I have appreciated your expertise and contributions here and on various other threads and blogs. Hopefully you will feel free to re-join the the discussions here in the future. You are certainly welcome as far as I am concerned.
William Brookfield
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William Brookfield
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posted 12. September 2006 14:39
Hi Mel.
Welcome and thank you for your post.
quote:
posted 10. September 2006 21:28 Melvin H. Fox
Is not pi specified because it is the exact ratio [perimeter/diameter] for any circle? Is not pi complex because it can’t be represented exactly by any rational number or in decimal form?
-Mel
Yes, I agree with you but I would adjust the second sentence just a bit.
I would say that the pi string is complex because Pi the ratio can’t be represented exactly in decimal form.
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Christopher D. Beling
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posted 12. September 2006 20:47
I liked your statement Mel - thought it kind of neat
quote:
Is not pi specified because it is the exact ratio [perimeter/diameter] for any circle? Is not pi complex because it can’t be represented exactly by any rational number or in decimal form?
but it does bring up some questions:
(i) and this is to William too, based upon his comments in previous post (10th Sept): Are all platonic entities (shapes and solids - and numbers derived from these) - specified? I think they are but on what basis - gut feeling? Is it simply a definite concept (conceptual reduction [p141 NFL]) all would agree on from some logical reason (i.e. they are of axiomatic nature)- or is it the fact that platonic things are just so special (i.e. they are very uncommon -in their pure form - in real experience). If there can be common agreement tha platonic entities are by their form specified, then we know at least one entity for which there is no subjectivity issue in the CSI specification component.
(ii) Not so important: I think there is a problem mathematically with pi being a rational number. I read from Wikipedia that:
quote:
The decimal expansion of a rational number is eventually periodic (in the case of a finite expansion the zeroes which implicitly follow it form the periodic part).
So perhaps it is the "decimal form" part that is the essential incrediant - agree? Chris
[ 12. September 2006, 21:18: Message edited by: Christopher D. Beling ]
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Melvin H. Fox
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posted 14. September 2006 08:16
I am honored to be welcomed to this thread. I agree with 2ndclass when he says, “this is a top notch group.” I was led to brainstorms by this thread and have followed it from the beginning [reviewed last couple pages last night]. I confess that some missives contained here are a good distance above my head [not evoking Ad misericordiam] but all have caused me to dig deeper and reinvestigate concepts I had foolishly thought were settled in my own mind.
Take pi for example. I would never have thought to question its complexity verse say the decimal friendly number 4. Both 4 and pi can be written as an infinite series. Actually in neither case would the series be unique. For example,
4 = 1/(1/2) + 1/1 + 1/2 + 1/4 + 1/8 + … (1)
and
4 = 4 + 0/10 + 0/100 + 0/1000 + 0/10000 +… (2)
As it is for the decimal representation, coming up with a series for pi is a more complicated matter. Leave it to Euler to derive a plethora of formulas for pi. William suggests that if we leave off the infinite tail of series (1) no real information is lost. This makes good sense. At some point during the sum virtually everyone will agree that what is left to sum is insignificant or infinitesimal. By this agreement we would advocate a discrete space. What of the one who says: “No, it is not 4 without the entire sum?” The good news for 4 is we have the second sum (2). All agree the infinite tail of this sum amounts to no new information about 4. The bad news for pi is that we have no sum like (2) for this or any other irrational number.
Are we missing information about pi in the translation to decimal form or are we not? The answer depends on your goal. If you would like to predict the location of any of the planets [8 now, I guess] in our solar system then the infinite tail is of no consequence. However, if you are the pure mathematician on a treasure hunt for the exact value of pi, then you need every digit or the entire hunt is in vain. With the planet, the next digit is of less importance [contains less information] than the last. With the hunt, the next digit is of more importance [contains more information] than the last.
Is pi complex? My conjecture is that it is more complex than 4. Pi is irrational [can’t be represented by the ratio of integers] not to mention transcendental [can’t be the root of an algebraic equation]. For this reason, pi lives in a continuous space and can’t exist in a discrete space. A continuous space contains infinitely more information than does a discrete space. After all, a horse can be taught to count to 4 but my computer can’t hold all of the information contained in pi. The number 4 does exist in the continuous space but only in the intersection with the discrete. This is analogous to the planarity of graphs in graph theory. If a graph can be drawn without crossing any two edges, then it is planar. The complete graph with 4 vertices [K4] is planar because it can be drawn in the plane without crossing edges. The complete graph with 5 vertices [K5] can’t be drawn in a plane without crossing edges. The complete bipartite graph – K3,3 is also not planar. Both of these graphs contain information that can’t be expressed in the plane. By Kuratowski’s theorem we know that all non-planar graphs are homeomorphic to K5 or K3,3. That is, all non-planar graphs are such because of the same basic information contained in K5 or K3,3.
Irrational numbers as more complex does fly in the face of a statistical 2nd law in that there are far more irrationals than there are rational numbers. I do not know how the cardinality of planar verse non-planar graphs compares
William, do you agree that your post of 10 Sep. 22:02 advocates a discrete space?
Chris, a materialist will surly balk at your platonic olive branch. Their hard line is that any specification is subjective.
Chris put forward that there are three possible final causes; necessity, chance, and design. As Chris knows, I reject chance as the cause of anything. Is my premise too polar for this discussion or may I still play?
It is possible that my concept of information is too ambiguous but indulge me one more point. There exists information too high for man to attain by his own efforts.
Romans 8:26
In the same way, the Spirit helps us in our weakness. We do not know what we ought to pray for, but the Spirit himself intercedes for us with groans that words cannot express.
-Mel
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Christopher D. Beling
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posted 14. September 2006 11:05
Mel, honored to have you! and the mathematicians perspective. An apology though - I misread your sentence "it can’t be represented" as "it can be represented" - that is why I thought you were saying pi was rational!
When it comes to the issue of a "complexity" measure of a string I feel we should stick with the standard definition so as to avoid cross-talk (disagree if you must). In normal ID parlance, however, "complexity" is defined as
C=-log2(P)
where P is the probability of the string happening by chance [Well I know you don't believe chance can do anything - I don't either, see below, - but one can perhaps imagine a "random touch down" on a space (i.e. one containing all binary strings of length n) with cardinality 2^n. Where would probability theory be if one could not make such a proposition!. The probability then of randomly selecting any string is P=2^-n -the same for any string. Thus the complexity of a binary string length n - is simply n bits. Another way of saying this is that:
Shannon Entropy of string's family (2^n members) = C = -log2(2^-n)=n
Now assume that a continuous space in reality will always be a discrete space - due to a finite storage medium - then one can imagine the continuous space being overlaid by the fine mesh of the discrete space. One can keep on making the mesh finer and finer (depending on the size of ones storage medium) and all this does is to increase the number of bits "n" in the complexity. Thus in this sense the number:
4 = 10000000000000000000000000000000000000000000000000
to 50 bit accuracy has the same complexity as pi expressed to 50 bits
pi=01100100100001111110110101010001000100001011010001
Both strings are equally probable - right?
Both strings if found did not occur "by chance" though, because they have "specification" (i.e. present too small a target for the random touch down)- this specification comes from them being K-simple [imagine a 2^25x2^25 2D image; we are talking about the liklihood of coming down on a single pixel, both for pi and 4!]. i.e both strings are CSI (of the human category! - because only humans can write algorithms). quote:
Chris, a materialist will surly balk at your platonic olive branch. Their hard line is that any specification is subjective.
Well Mel, I guess you are right on this one, but Einstein believed in metaphysics, and Godel in metamaths (something of a platonist) - so I think we are on good grounds because of their great minds and where their philosophy took them. Taking things that are axiomatic in maths is indeed good grounds for suggesting they are specified. As Godel would agree - things can be true without being proved to be so. Moreover, materialists are free to believe things that are not true without effecting the truth of those things.
quote:
As Chris knows, I reject chance as the cause of anything.
Yes I believe you are dead on-line here. Chance is just a way of saying we don't have all the info. For example if we knew all the neural states of a dice player, and everyting about his muscles and hand control, and the laws of gravity then we could predict the outcome of the throw. We just don't have this information. So necessity is physical law with all known boundary conditions and info; chance is physical law with only partial info IMO (and Einstein would have agreed on the quantum level). "information too high for man to attain by his own efforts" - we see this even on an earthly level in what we call "chance" how much more w.r.t. higher realms. - Chris
[ 15. September 2006, 02:21: Message edited by: Christopher D. Beling ]
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Salvador T. Cordova
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posted 14. September 2006 12:49
Greetings Melvin. Welcome to our discussion.
Regarding your question, I can understand your perplexity.
To help set the record straight, let me extend the question and ask, are the first 500 digits of Pi CSI?
Consider the following question:
quote:
Are square circles triangular?
First square circles don't exist, and saying yes or no, one will get trapped in a logical fallacy (like the question "have you stopped beating your dog").
CSI deals with physical obects with the capacity for different outcomes (like rolls of dice). The question of PI being specified somewhat echos the question of square circles being triangular. The question is not applicable, imho. I could be wrong of course, but that is how I see it.
However to clarify, PI is a specification, but whehter it is specified, at least in terms of ID literature is probably an in-applicable question.
Though it is incorrect to answer the question of PI being CSI, it is closer to the truth the say it is not CSI, but formally speaking it is an inappropriate question, but perhaps for simplicity or approximation, it is not a bad answer.
Salvador
[ 14. September 2006, 13:51: Message edited by: Salvador T. Cordova ]
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Christopher D. Beling
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posted 15. September 2006 00:45
Sal, glad to hear you again. You say: quote:
CSI deals with physical obects with the capacity for different outcomes (like rolls of dice). The question of PI being specified somewhat echos the question of square circles being triangular.
Let me ask you this: If you decoded a strand of DNA and found the number pi to 500bits (i.e. building it in double digits with A=00, T=11, G=01, C=10) then would this not be a physical object?
Quoting Mel:
quote:
a materialist will surly balk at your platonic olive branch. Their hard line is that any specification is subjective.
I just wonder how a materialist would respond if he/she found the first 500 bits of pi encoded on a strand of DNA - I wonder if he/she would react by saying "we must not be subjective - this occurance is not specified"! - Chris
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Salvador T. Cordova
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posted 15. September 2006 01:31
quote:
Chris asked:
Let me ask you this: If you decoded a strand of DNA and found the number pi to 500bits (i.e. building it in double digits with A=00, T=11, G=01, C=10) then would this not be a physical object?
It is indeed a physical object, and if Pi's description were discovered in such a strand, the strand would be a very strong candidate for evidencing CSI.
The reason Pi would not be considered CSI in the ratios of a physical circle is that there is no opportunity for physical contingency if one's starting point is a physical circle. A physical circle will always be related to Pi in a certain way.
In contrast, there is no pre-disposition for DNA to encode the digits of Pi. Thus, there is surprisal value in discovering Pi in DNA. The amount of surprisal is what is known in Shannon theory as information. There is no surprisal value in the Pi relationship with a circles circumference and diameter.
This is an important point, what can be used as a specification in one context to identify CSI (like Pi in a context like DNA) can be of no use whatsoever in another context (like Pi found in the relationships of diameter and circumference in a circle).
Salvador
[ 15. September 2006, 01:42: Message edited by: Salvador T. Cordova ]
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Salvador T. Cordova
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posted 15. September 2006 01:40
quote:
A question was raised:
a materialist will surly balk at your platonic olive branch. Their hard line is that any specification is subjective.
It may be subjective, but it still raises the issue of correlation which Wigner and other find peculiar. Why do so many physical structure correlate to our subjective conceptions of what looks designed?
If I wanted someone to recognize something as designed, like say the Voyager Plaque:
I would architect the artifact such that it would match what I believed the observers subjective patterns would recognize. At the heart of design theory is what Bill Dembski said:
quote:
Masters of stealth intent on concealing their actions may successfully evade the explanatory filter. But masters of self-promotion intent on making sure their intellectual property gets properly attributed find in the explanatory filter a ready friend.
Mere Creation
Even if the specifications are subjective, if they can be shown to be non-postdictive (meaning non-after-the-fact fitting), then this raises the issue that amzed Wigner and Einstein? WHY is there this wonderful correlation of some many of nature's toward human convenience and understanding and recognition? Why do cells correlate so well with our conception of computers? In fact they correlate in an astonishing manner!
[ 15. September 2006, 01:41: Message edited by: Salvador T. Cordova ]
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Melvin H. Fox
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posted 15. September 2006 15:43
Chris
I will make every conscious effort to adhere to definitions established in “normal ID parlance” and readily will I accept correction for misuse of terms.
I hope this interlude taken to dissect pi is not too tedious. It has helped me to understand information entropy to a greater degree. I agree, both n-strings, pi and 4, are equally probable for any natural number n and therefore have the same Shannon entropy or complexity at that degree of specification. We need not go to infinity on my account, if this is the original point being made by the pi string example. As far as both strings being CSI, I make no comment. It seems only slightly more probable to get two ID’ers to agree on the CSI of a string than it is to get two Darwinists to agree whether or not two organisms are in the same species or not.
I have nothing against probability theory. It is a very useful branch of mathematics and in no way am I saying it is evil or anything like that. I have nothing against a fallen tree either. I myself have a wood burning stove and heat my home [in Erie PA – latitude 42 north] entirely by this method. But when a piece of it is carved up, set on a high platform and mystical powers are attributed to it I will remind people of Isaiah 44: 15-19. I fully agree with your statement “chance is physical law with only partial info.” Incidentally, I have instructed a group of my students to design a contraption that will release a die from a height of 5 cm in exactly the same manner each time – trying to take control of as many variables as possible. We will collect data and determine the effects of this control on the probabilities of individual outcomes.
-Mel
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