|
Author
|
Topic: Simplicity, Complexity & Order
|
Doug Wedel
Member
Member # 1901
|
posted 12. March 2006 13:50
[SUMMARY: In another post I struggled with the aid of several in here to try to understand CSI. I have reviewed a number of William Dembski's publications, as well as the papers of Wolpert and Macready. I believe I have finally figured out _exactly_ the problem I am having with CSI. I hasten to add, however, that I fundamentally agree with Dembski's core insight – that the smorgasbord of systems, machines, devices, books, organisms, et cetera, that we see around us are far too ordered to have arisen via primarily stochastic processes. Despite this deep point of agreement, however, I feel it's constructive to point out what I believe to be the exact point of "fatal imprecision" in Dembski's conceptual apparatus. What I have concluded is that Dembski fails to distinguish adequately between two concepts -- the concepts of simplicity and order. In this post I explain _exactly_ how this confusion arose, pointing out that Dembski himself cannot be faulted for this conceptual ambiguity. The failure lies not in Dembski but within complexity theory itself, the theory upon which Dembski has tried to construct his formal description of CSI. It is in complexity theory, and in algorithmic information theory, where the "fatal imprecision" is to be found. This is my effort to clear up this confusion ;-)]
In 1937 one of the greatest 20th century scientific geniuses, Claude Shannon, wrote a paper providing a mathematical way of resolving certain problems pertaining to the transmission of information through a communication channel. Shannon's paper launched what today is called "information theory." What was so revolutionary about Shannon's ideas and formulas? It was this: Shannon showed that all messages that contain meaning have patterns that can be detected even if one doesn't understand the language that they are written in, or the code by which they are to be deciphered. Regardless of the semantic content of the message, if the message did contain meaning (was not random), then it could be predicted to use some letters or digits or patterns of letters and/or digits more frequently than others The idea that all meaningful information had patterns in it that could be detected precisely by elegant algorithms such as Lev Zempel Welch (LZW), and that by using this knowledge one could compress the data at one end of a transmission and decompress it at the other, thus saving time and energy, was a matter of great interest specifically to Shannon's employer, Bell Telephone (proving that necessity and deep pockets are the mother and father of invention ;-) ).
Subsequently, the formal conceptual apparatus for studying information systematically was widened and deepened by Kolmagorov, et al, who extended Shannon's core idea of compression and made it the foundation for what has come to be known as algorithmic information theory, which itself has become part of complexity theory (specifically, algorithmic information theory provides a formal method for measuring the complexity not just of messages in a channel but of the complexity of any formal system). Dembski discusses the emergence of algorithmic information theory in his 2005 work "Specification: The Pattern that Signifies Intelligence":
quote:
"In the 1960s, Chaitin, Kolmogorov, and Solomonoff investigated what makes a sequence of coin flips random. Also known as algorithmic information theory, the Chaitin-Kolmogorov-Solomonoff theory began by noting that conventional probability theory is incapable of distinguishing between bit strings of identical length…
Dembski illustrates with two 100- digit binary numbers, one produced by coin flips (labeled R for random), the other consisting of all ones (labeled N for nonrandom). Probability theory by itself had now way to distinguish between these two numbers, R and N. Both had the same probability of occurring by pure chance, namely, one in 2^100. This obviously is not in accord with our intuition. Dembski continues…
quote:
"To get around this difficulty Chaitin, Kolmogorov, and Solomonoff supplemented conventional probability theory with some ideas from recursion theory… What they said was that a string of 0s and 1s becomes increasingly random as the shortest computer program that generates the string increases in length."
Another way to say precisely the same thing is to say that the randomness of a number is directly proportional to the incompressibility of the number. To take Debmski's example above of R, the 100-digit number created by tossing a coin. Like most data generated by stochastic processes, this number is _incompressible_. There is no formula or short sentence to adequately describe such a number. The only algorithm for expressing the number is : PRINT R, and then you of course have to list R digit by digit.
With N, Dembski's example of a nonrandom number containing all 1s, the situation is very different. This string can be maximally compressed by the sentence: Print 100 ones (and now of course we do NOT have to list the actual string of 100 digits).
So algorithmic information theory extended Shannon's original compression principle to apply much more broadly. The conceptual principles are these:
COMPLEX = RANDOM
SIMPLE = ORDERED
So what so "fatally imprecise" about this?
Let me try an "intuition test" on the reader: when you say something is highly ordered, is it your intuition that it is also simple?
Let's take DNA. Does DNA contain order? Obviously? Is DNA simple? Hmmm…. I for one have heard the DNA molecule described as the most complex object in the physical universe.
Thus, what is fatally imprecise in algorithmic information theory is the equation of simplicity with order. This equation will not fly, either for formal systems, or for living systems, or for human intuition. Life is not simple…but life IS ordered.
Let's go back to the 100-digit numbers for a moment and return to a purely formal exposition of this point. In a prior post I offered up my own 100-digit number which I copy here:
7245870066063155881748815209209628292540917153643
6789259036001133053054882046652138414695194151160
This number (let's just call it "Wedel's Number" for modesty's sake ;-) has some very interesting mathematical properties when you consider it from the perspective of algorithmic information theory. For example, when I first presented this number it appeared purely random and maximally complex, though some of you were at least suspicious that it might contain some kind of highly specified order like say a VISA card number. But now look carefully at what happens, at the amazing transformation that takes place, in terms of algorithmic information theory, when the actual "secret" of this number is revealed. Before, it was maximally complex and was considered random and incompressible. Now, after its secret is known, it becomes highly compressible, and so it loses its complexity in a flash and at that moment it becomes – what? – simple? Does that satisfy our intuition about what kind of number Pi is? That Pi is really one of the simplest numbers known, like a string of 100 zeroes? I don't think so. I don't think it makes intuitive sense to say that because you find a way to compress an information-rich number like pi that therefore you have changed it into a simple number. Pi is a highly ORDERED number, and THAT'S why it's highly compressible – but you have to know its secret. You have to know the formula. The commonsense intuitive notion here is that order is the compressibility that comes from _understanding_ the true nature of a system, or of somehow seeing patterns that weren't detected by the measurements of superficial complexity that resulted from the initial compression attempts.
Thus, the confusion in algorithmic information theory comes from a trait it inherited from Shannon's original ideas – an indifference to semantics. Both Shannon and Kolmagorov-Chaitini ignore semantics, but it is precisely semantics – and syntax, and grammar -- that give information its "deep order". We have already discussed how Shannon's algorithms were famously blind to the semantics of the messages, i.e. what the messages might actually be about in the real world, what language they were in, et cetera. Similarly, this methodological indifference to semantics continued into algorithmic information theory as well. Neither Shannon nor Kolmagorov nor Chaitin take meaning into account, and this is what leads to the fatal imprecision of equating a number like Pi, absolutely chock full of mathematical meaning, with a ultra simple number like 100 zeroes, a "nothing" number virtually devoid of meaning.
How can we rectify this omission? How can we take semantics into account, as it were, and strengthen our conceptual apparatus so that we can finally sharply and quantitatively distinguish between the boring information sahara of a number with 100 zeros and Pi, which is more like the mother of all numbers (Pi, if normal and if it does not repeat, will upon some discrete finite expansion be shown to contain any finite random number string, i.e. Pi may actually contain all finite numbers within its very warp and woof ;-))
One way to clarify the confusion between order and simplicity would be to make algorithmic information theory axiomatic and then add the concept of order to it. How would one do this? Algorithmic information theory itself would remain exactly the same as it is now – but all the compression algorithms that you want to use to test complexity must be specified up front as axioms of the system – none can be added later.
Thus, in this new revised approach, the axioms consist of any (and all) compression algorithms which the system designer may wish to include to measure complexity, but all the algorithms have to be completely specified and defined up front.
How does that change anything? It changes the model because it means that the measure of "complexity" can never change. The system is axiomatized, complexity is measured once and for all by the compression algorithms specified in the axioms, and then in the future, if some method is discovered of further compressing the number, then that further compression will be specified not as complexity but as order, and I will show in a moment how to quantify it.
Thus, in our so far only slightly altered algorithmic information theory, we have required the axiomatization of the system by _specifying in advance_ all the compression algorithms to be used to measure what we call complexity. And the degree of compression that is actually achieved by running the test number through the axiomatic compression routines will be the PERMANENT measure of the complexity of the number. Any further compression of the number we will consider as what we define as ORDER.
ORDER is thus formally defined as compression achieved beyond (or subsequent to) axiomatic compression. It can be due to a human hypothesis – hey! Maybe that number is actually taken from Pi – or some algorithm may be found which can compress the number beyond what was achieved by the axiomatic system. Either way, order is now formally defined as compression that is achieved beyond axiomatic compression.
Now let us focus directly on order, the thing that we are all really interested in, the thing that makes cathedrals and watches and human eyes so interesting, the careful and precise arrangement of parts, the interoperability of the parts, the spirit of order that the system imbues. Specifically we can now discuss how to quantify exactly the amount of order in a system which at last permits us to distinguish effectively between simplicity and order and to exactly quantify the difference between a simple number and a highly ordered number.
If you don't mind, let's go back to Wedel's Number (I hope this isn't irritating; I was thinking the other day about this particular number and about Champernowne's Number, and I was thinking it would be nice to have one's "own" number so I just kind of adopted this number that has popped up in these dialogues).
7245870066063155881748815209209628292540917153643
6789259036001133053054882046652138414695194151160
Wedel's Number appears totally random. There is no formal compression technique that can discover its "secret" – unless, of course, one of the compression routines you designate in your formal system is to search through pi to see if you can find the number there, a special case which we can deal with later.
When the secret of Wedel's Number is revealed, we can then see that it is in fact highly compressible. It does not compress all the way down, of course, like say, a 100 zeroes. But as we study this problem with strings of larger and larger size, the degree of compression found in Pi would approach that level asymptotically.
So how do we quantify this FURTHER COMPRESSION beyond axiomatic expression, and what do we call it? We call it ORDER and we measure it this way, as a ratio:
ORDER = AXIOMATIC COMPRESSION/MAXIMAL COMPRESSION
What does this mean? Suppose after discovering the secret of a highly complex seemingly random number, it now becomes compressed by, say, 90%. We could express the "quantity" of order contained in this "piece of pi" as 1/.1, or 10. If we used larger and larger strings of pi in our example, the compression could be considerably more than this, and would in fact approach zero asymptotically (a trillion trillion digits of pi can be compressed almost as much as 100 digits), so the order would increase without an upper bound.
What does this do for us? It allows us to avoid the "fatal imprecision" that we are talking about, that of equating simplicity with order, or perhaps we should say, failing to precisely distinguish between simplicity and order. In this way of looking at the quantification of complexity, the compression achieved with a simple number and a highly ordered number may be almost identical, but the very simple number, agreeing with our intuition, will have a formal order measure of zero or near zero, while the order contained in the highly ordered number would be a comparatively large number.
One interesting result of re-thinking complexity theory this way is that it allows us to more precisely restate Dembski's core point. After all, Dembski is talking about ORDER, he's not talking about SIMPLICITY. Life is not simple, but life IS highly ordered. It is the conflation of these ideas that constitutes the fatal imprecision. The way out of the trap is as described, for what Dembski is trying to bring to our attention, and what has occurred to anyone who would take the time to read posts in here, is that life has an order that far exceeds even Pi. The tremendous recursive order seen in life –organisms within organisms, ecosystems with ecosystems – suggests deep profound ever increasing but as yet-hidden "secret" order in the superficially complex exfoliation of events and forms in the biosphere.
To talk formally about the order in life, we have to develop the mathematical and intellectual apparatus to distinguish order from simplicity. With the formal apparatus I have described here, it is at least possible to show that living things contain far more order than nonliving things, although of course it does not finally tell us where that order comes from.
IP: Logged
|
|
Bruce Fast
Member
Member # 924
|
posted 12. March 2006 17:29
Hi Doug,
I read your post (and your other post) with intrigue. I then clicked on your profile. Ah, software designer, no wonder. I think that us software developers have an instinctive understanding of DNA like information that others just don't have, after all we conjur up the stuff all of the time.
The fact that information as generated in a computer program, or a book for that matter, is so poorly understood seems a key to this whole question. The better we understand humanly created information, the better we will understand DNA's information independantly of the source of DNA's information. Whether it is created by a creative mind, or by RM+NS, it is clearly the same stuff.
I find your suggestion that information = order / simplicity to have validity. (That's about what you said, isn't it?) I am still trying to work out: ORDER = AXIOMATIC COMPRESSION/MAXIMAL COMPRESSION. I very well understand that maximal compression can often only be achieved when the nature of that which is being compressed is known.
I consider the leap that was made between tiff group 3 and group 4 image compression. (In both cases technology devised to compress bitonal images of documents. Group 3 is at the core of fax technology.) In both cases the compressed image consists of scan lines. Group 3 compression uses huffman compression based upon the expectation that black and white run-lengths will follow a certain pattern in printed matter. Already this is counting on a certain understanding of the data. Group 4 says, "hey, the second line is awfully like the first, let's just record the changes." It's so simple. If you know that you are dealing with scan line data, this knowledge gives you all sorts of compressability. This, I believe is at the heart of your definition of maximal compression. Maximal compression is the kind of compression which can be achieved if the nature of the data is known.
Doug, I like your line of thinking here. Based upon the dialog in your last thread, it is clear to me that the nature of information, order, and complexity are not nearly well enough understood yet. I think that Shannon has rendered a valuable tool for quantifying information -- compressability. I think that you bring something very valuable to the table when you add to the picture "maximal compressability"
IP: Logged
|
|
Doug Wedel
Member
Member # 1901
|
posted 12. March 2006 21:10
Bruce,
Thanks for your post.
quote:
I think that us software developers have an instinctive understanding of DNA like information that others just don't have, after all we conjur[e] up the stuff all of the time.
You got it. We work with data like the butcher works with hog jowls. We design information representation systems. It absolutely gives us an advantage in reverse engineering biological info;-)
quote:
I find your suggestion that information = order / simplicity to have validity. (That's about what you said, isn't it?) I am still trying to work out: ORDER = AXIOMATIC COMPRESSION/MAXIMAL COMPRESSION. I very well understand that maximal compression can often only be achieved when the nature of that which is being compressed is known.
In this thread I was distinguishing order from simplicity. I probably should have said:
ORDER = COMPLEXITY/MAXIMAL COMPRESSION
Here complexity is established once and for all by running a number through the axiomatic compression algorithms of your system. That will establish a measure of compression that will be permanent. However, as we have known since Shannon's time, just because you can compress data with certain "axiomatic" compression algorithms (LZV, Hufman coding like you mentioned, et cetera) doesn't mean you have exhausted all compression possibilities. To the contrary, as we know now, Shannon compression just scratches the surface of possible compression of data.
Kolmogorov complexity sort of straddles both worlds, the indifference to semantics exhibited by Shannon coupled with an openness to using methods of compression that reflect an understanding of the deeper order in a number or system. However, Kolmogorov-inspired methods algorithmic information theory introduce a "fatal imprecision" by failing to distinguish between order and simplicity, which is what I was specifically trying to avoid by axiomatizing the system and adding order as a distinct element/quantity.
So you start with a highly complex number that your axiomatic compression routines can't compress at all. It's Complexity = 1. Then you find it's a part of Pi and you can compress it say 90%. The important thing here that I failed to point out in the first post was that while we can now quantify the order of this number by the ratio of .1 to 1, the complexity of the number stays the same.
What this means is that if you can greatly compress a highly complex number, it will have a much higher order quotient than if you can compress to exactly the same level of "absolute compression" a number that started off not as complex.
Thus the measure of order I propose reflects not only the original (and permanent) complexity of the number, but also the final degree of absolute compression achieved when we derive its mathematical formula.
You mentioned information -- as I use it information is _not_ part of this formal system that I'm discussing in this thread, but rather, part of the larger model of biological information discussed in the other thread.
Your discussion of image compression is an excellent example. As you point out, a _full_ "understanding" of an image is _not_ required for further compression. Compression can be built up from incredibly simple rules applied iteratively and recursively, as you well know. This is what I am interested in is the construction of "order" by simple iterative and recursive processes.
IP: Logged
|
|
Bruce Fast
Member
Member # 924
|
posted 12. March 2006 22:28
I know you didn't directly say that information = order / simplicity, but I gleaned that from what you said. Further, think about it. If order is 0, ie random, then despite a lack of simplicity, information = 0. If simplicity is really high, well, no matter how much order there is no information. So, as order increases information increases. As simplicity increases, information decreases.
Hey, the opposite of simplicity is complexity. Now we have I=OC. (Hey maybe the ratios aren't right, could it be that the square of the complexity is more accurate. Maybe it's I=OC^2. Ooooh, Einstinian.)
I'm fine to suggest that you didn't say it. I said it. Information = order / simplicity.
[ 12. March 2006, 22:34: Message edited by: Bruce Fast ]
IP: Logged
|
|
Doug Wedel
Member
Member # 1901
|
posted 13. March 2006 10:27
Bruce,
I am _highly_ amused by your post, and am willing to play along if I can just figure out your scheme;-)
The question is, how do you define information? I think my basic intuition about information is that it bears roughly the same kind of relationship to order that, say, a lever bears to energy. In other words, a lever is a basic _mechanism_ or _instrument_ by which energy can be expressed as work. So I view information as a compound object, built up from things like signals and patterns and correlations, and that information can be used by an organism to improve its survival probabilities.
But hey! I've been looking for the kind of formulation you suggest so please pursue it;-).
IP: Logged
|
|
William Brookfield
Member
Member # 565
|
posted 13. March 2006 12:42
Hi Doug,
I am delighted to see that someone else got caught up at that same point in Dembski's specification article. Perhaps I am not crazy after all. ![[Smile]](smile.gif) The initial problem I had however was not with the definition of "order" at this point but the definition of "randomness." I had written a little blurb on this but did not know where to post it.. till now...
Re- Chaitin, Kolmogrov, Solomonoff
Algorithmic information theory
Infodomain, Boundary Confusion (IdBC)
(a) HHHHHH (111111)
This fair coin-toss pattern (a) is random within the context of the pertinent coin-toss infodomain because it is necessary to complete the distribution . Without pattern (a) the statistical distribution would be biased --non-uniform (non-random). It appears non-random because the human "victim" (of confusion) is out-godeling the system, jumping out of the pertinent internal infodomain to an external infodomain and then confusing the order of the system (external order) with the system's random internal infodomain. The system, being finite, is littered with residual order. It is both pixilated (system order) and finite( system order). Within such a limited system, the internal "face" of randomness is necessarily distorted. Such distortion means that we have to be careful with such systems (with their system-level) order and their subsequent deceptive configurations.
The other boundary config (b) TTTTTT is just as likely to produce internal/external
confusion and projection in humans.
On the "Is the 2nd Law a special case of 4th Law?" thread, our good friend Salvador
provided a simple coin toss "infodomain" beginning with the "all tails" boundary
configuration;
"T T T T T" , "T T T T H..." listing all available combinations through to
"...H H H H T" and finally ending with the "all heads" boundary configuration "H H H H H."
Boundary configurations, while externally non-random (representing the system's non-random limit or "system-state order"), may be considered internal non-randomness, if and only if, the occurence of these diverges from the uniform probability distribution (internal randomness). If a boundary config appears too frequently then there exists internal non-randomness. If a boundary config appears too infrequently then there is also internal non-randomness. If any configuration (boundary or otherwise) diverges from the uniform probability distribution in statistical frequency then there is *internal* non-randomness and possible information (coordinated order or "hyper-specificity"). If however, the boundary configurations (a and b) appear at a frequency consistent with the uniform probability distribution then, regardless of appearance, there is no internal order and no information in the internal infodomain that results from these configs.
The fact that randomness (in such systems) is algorithmically incompressible is "trivially true." As an instruction set of laws/order, algorithms are the opposite of randomness lawlessness/disorder). Order is the opposite of randomness.
Kolmogrovian incompressibility analysis however, always depends upon the existence of an underlying infodomain. Without an underlying "pixelation" one would have an eternal complex superposition of heads and tails. At no point would a discrete heads (pixel/information) or a tails(pixel/information) ever appear. The "algorithm" for pure randomness therefore might be the famous QM anti-algorithm "don't make an observation." I,E, "don't collapse the wave function."
If pure randomness could appear in the coin toss infodomain it would appear as a static, uniformly distributed, complex superposition of..
HHHHHH...
and
TTTTTT...
Dembski,
quote:
(R) 11000011010110001101111111010001100011011001110111
00011001000010111101110110011111010010100101011110.
"This string in fact resulted from tossing a fair coin and treating heads as “1” and tails as “0” (we saw this string earlier in section 4). Now, imagine the following scenario. Suppose you just tossed a coin 100 times and observed this sequence. In addition, suppose a friend was watching, asked for the coin, and you gave it to him. Finally, suppose the next day you meet your friend and he remarks, “It’s the craziest thing, but last night I was tossing that coin you gave me and I observed the exact same sequence of coin tosses you observed yesterday [i.e., the sequence (R)].” After some questioning on your part, he assures you that he was in fact tossing that very coin you gave him, giving it good jolts, trying to keep things random, and in no way cheating."
Question: Do you believe your friend? The natural reaction is to be suspicious and think that somewhere, somehow, your friend (or perhaps some other trickster) was playing shenanigans. Why? Because prespecified events of small probability are very difficult to recreate by chance. It’s one thing for highly improbable chance events to happen once. But for them to happen twice is just too unlikely."
The first time (R) happens, the event is consistent with the uniform probability distribution (which would always produce rare, but unspecified improbable events). "Something had to happen and I guess (R) was it" would be a likely comment. An immediate second occurence of (R), say (R') however represents a severe divergence/transcendance away from randomness -- away from the assumption of probablistic uniformity. Even though a second ocurrence is not utterly impossible, (R) together with (R') constitute an astronomically improbable orderly correlation and this pushes the chance hypothesis out the door and the shenanegans (design) hypothesis forward.
--
Hopefully this is helpful in moving your thread forward. WB
[ 13. March 2006, 12:50: Message edited by: William Brookfield ]
IP: Logged
|
|
Bruce Fast
Member
Member # 924
|
posted 13. March 2006 13:07
quote:
I am _highly_ amused by your post, and am willing to play along if I can just figure out your scheme;-)
Sorry, Doug. Hate to confuse you. The I=OC^2 crack was just the lateness of the hour talking. I do think there's validity in the I=OC equation, however, I also think that it is post-robbing, so I started my own thread to pursue the matter. Let's let your thread be yours.
IP: Logged
|
|
Doug Wedel
Member
Member # 1901
|
posted 13. March 2006 15:54
William,
Thanks for your very interest post!
quote:
(a) HHHHHH (111111)
This fair coin-toss pattern (a) is random within the context of the pertinent coin-toss infodomain because it is necessary to complete the distribution . Without pattern (a) the statistical distribution would be biased --non-uniform (non-random). It appears non-random because the human "victim" (of confusion) is out-godeling the system, jumping out of the pertinent internal infodomain to an external infodomain and then confusing the order of the system (external order) with the system's random internal infodomain.
I like your concept of "out-godeling" the system;-)
quote:
If any configuration (boundary or otherwise) diverges from the uniform probability distribution in statistical frequency then there is *internal* non-randomness and possible information (coordinated order or "hyper-specificity"). If however, the boundary configurations (a and b) appear at a frequency consistent with the uniform probability distribution then, regardless of appearance, there is no internal order and no information in the internal infodomain that results from these configs.
This is very interesting vis-a-vis an exchange I had in another thread. A poster asserted that if a pulsar emitted digits corresponding to Pi that would be CSI. I asked if the pulsar emitted an apparently random stream of digits that, however, never contained an "8", would that be "information". He said no. You, however, confirm my own intuition, that this "lack of normality" in the number does suggest that it may contain information.
quote:
Order is the opposite of randomness.
Yes, but at the same time, a highly ordered number may also be highly complex. This truth cannot be seen using the rubric and tools of algorithmic information theory, because in AIT, as soon as you find the "order" in a number, poof, it loses its complexity and becomes "simple."
quote:
Even though a second ocurrence is not utterly impossible, (R) together with (R') constitute an astronomically improbable orderly correlation and this pushes the chance hypothesis out the door and the shenanegans (design) hypothesis forward.
I know next to nothing about probability; however I do have one question for you about your statement. I had the understanding that one of the core foundational ideas in probability theory was that one roll of the dice _has no influence_ on another roll of the dice -- which of course is the opposite of the typical gambler's belief. How does your assessment of the inferences that can be properly drawn from finding R and R' together jibe with this?
IP: Logged
|
|
William Brookfield
Member
Member # 565
|
posted 09. April 2006 21:05
Hi Doug, sorry to take so long to respond.
quote:
Doug,
A poster asserted that if a pulsar emitted digits corresponding to Pi that would be CSI. I asked if the pulsar emitted an apparently random stream of digits that, however, never contained an "8", would that be "information". He said no. You, however, confirm my own intuition, that this "lack of normality" in the number does suggest that it may contain information.
As a "cosmic infodynamicist" I consider anything beyond primal equilibrium (the initial cosmic singularity) as a primitive form of information. CSI however is an extremely refined type of order/info and is not primitive at all.
quote:
quote:
William --Order is the opposite of randomness.
Doug,-- Yes, but at the same time, a highly ordered number may also be highly complex.
Yes indeed. I see CSI as a highly complex form of order.
Here is "Order" and "Randomness" as I see it..
#1. "Randomness" --- Brutally simple (think "black hole"). Too simple in fact for the busy western mind to easily comprehend. Consult a Tibetan monk - ignore what he says if he says something (something = order).
#2. "Order" -- I see three types of order from the simplest to the most complex - 2a, 2b and 2c
#2a. "Simple Order" or "Basic Specificity:" -- Examples; A law. A frequency spectrum with one specific frequency missing. A random stream of digits that never contained an "8."
#2b. Non complex "information/order:" "Coordinated specificity" or "specified specificity." Examples; A simple software code. A short English phrase. (Any case in which a second level of specificity is apparent but is not so improbable as to transgress the Universal Probability Bound.
#2c. CSI -- "Complex Specified Information/Order." I might also use "Complex Specified Specificity." Examples; A set of physical laws (specificity #1) and physical constants (specificity #1) designed/coordinated (specified #2) to support life. Bacterial Flagella. A Space Shuttle. (Any case in which the particular specificity-complex is so improbable it transgresses the Universal Probability Bound).
quote:
Doug.
This truth cannot be seen using the rubric and tools of algorithmic information theory, because in AIT, as soon as you find the "order" in a number, poof, it loses its complexity and becomes "simple."
------------
A second independent specification ("simple" pattern) has been identified, but the complexity (volume) of the phase space remains the same. As I see, it Dembski's insight is correct because he is using "K-complexity" not as randomness or order, but as a way of measuring the relative improbability of the target. I see Kolmogrovian complexity here as a by-product of randomness in a complex system. Whether K-complexity is "randomness" or "order" seems irrelevant to the Dembski design inference's calibration. The problem is the K-confusion that occurs when people try to understand this stuff and perhaps wording could be clearer. My particular concern is that, without strict infodomain boundaries Dembski's insight cannot be expanded into other fields of science -- and into a unified cosmic theory of specified specificity (CSI).
One thing I do want to point out is that 72458700660631558817(unspecified)... as a random number is very different than 72458700660631558817(specified).. as a segment of Pi. Random "numbers" are quite wrong and deceitful. The "7"(random #) for instance, does not mean seven but instead means "I may look like a '7' but I am representing all numbers from zero to nine -- and I am blocking all the other, equally valid numbers from being seen by you ..so there!" While random K-complexity may look like complex order, it is but a careless, twisted string of lies (truth/10). Random "numbers" have no scruples -- no morals, no sense of right and wrong. The Pi numbers, on the other hand, are gracious, honest and upstanding -- representing the truth about Pi's decimal expansion. I wouldn't want any daughter of mine hanging out with any of those sleazy and deceptive random numbers. Pi numbers, on the other hand, are good solid marriage material. ![[Wink]](wink.gif)
quote:
Doug,
I had the understanding that one of the core foundational ideas in probability theory was that one roll of the dice _has no influence_ on another roll of the dice -- which of course is the opposite of the typical gambler's belief. How does your assessment of the inferences that can be properly drawn from finding R and R' together jibe with this?
The "correlations" suggest a forbidden "influence."
Note that I also said "not utterly impossible." This means that a quick second occurrence of (R) must also be "in the distribution" -- but at an extremely rarified level. For finite systems the argument thus has an "Achillies heel" -- a margin of error. Luckily, for my purposes, the phase space of the universe is infinite. See -- Tipler Frank J. 1979 "General Relativity, Thermodynamics and the Poincare Cycle." Nature: 280 203-5. and -1980. Also- "General Relativity and the Eternal Return." in Essays in General Relativity: A Festschrift for Abraham H. Taub, pp. 21-37. Ed. Frank J. Tipler. New York: Academic Press.
This result provides ample "K-complexity" (phase space volume) for the cosmic design inference. Once again, I am using "K-complexity" here as an improbability/impossibility calibration tool, not as an example of complexity, order or information.
IP: Logged
|
|
Bruce Fast
Member
Member # 924
|
posted 10. April 2006 11:10
I am not finding the very common normal distribution in this discussion. Data that maps to a bell curve is by definition somewhat compressable, therefore whould be seen by Shannon as having information, I think; yet it is usually not CSI information.
IP: Logged
|
|
Irving
Member
Member # 535
|
posted 10. April 2006 18:06
quote:
After all, Dembski is talking about ORDER, he's not talking about SIMPLICITY.
I would say he's not talking about either in their specificity, but about COMPLEXITY independent of physical manifestation.
quote:
Like most data generated by stochastic processes, this number is _incompressible_. There is no formula or short sentence to adequately describe such a number.
I wouldn't say that random data is _incompressible_. The sentence or formula need only be shorter than the original pattern.
quote:
A poster asserted that if a pulsar emitted digits corresponding to Pi that would be CSI. I asked if the pulsar emitted an apparently random stream of digits that, however, never contained an "8", would that be "information". He said no.
I'm not sure I said that (but maybe I did), I believe I indicated that it's CSI status would be "unknown" in that case.
The problem is in trying to define CSI wholly within the pattern space. Wedel's number is not the whole issue. The physical manifestation of Wedel's number is. To physically emit Wedel's numbers (setting paper & pencil aside), one needs a calculator with a CPU and an instruction set to emit Wedel's number through Light Emitting Diodes provided the "secret key" is properly coded to work in conjunction with the instruction set.
A pulsar contains no such circuitry. A pulsar emitting Wedel's number indicates an abstract manipulation of physical processs independent of the physical properties of a pulsar's emission.
IP: Logged
|
|
Poul Willy Eriksen
Member
Member # 1976
|
posted 18. May 2006 12:17
Hello Doug,
Interesting post; though I'm not quite sure I can follow your line of thinking ![[Big Grin]](biggrin.gif)
You write
quote:
ORDER = AXIOMATIC COMPRESSION/MAXIMAL COMPRESSION
But how do we know the maximal compression beforehand? Can't every number be compressed to 0 bits, since we can always make a decompression program that returns whatever number we choose on whatever input we choose? That is, for any number N, we can wtite a decompression program that return N given an empty string as input.
Consider also the following. For any natural number N, there are 2^N bitstrings of length N. Say we want to compress these to length ar most d for some natural number d < N. There are 1 + 2 + 4 + ... + 2^(d) = 2^(d+1) - 1 bistrings of length at most d. So we can't compress all strings of length N, since 2^(d+1) - 1 is strictly less than 2^N.
All we can do is shuffle around with which strings we want compressed and which we don't.
Let's look at those axiomatic compression programs. To make them work we would need a program that had each compression program as a subroutine and when given a number as input, sent it through all these subroutines, selecting the shortest compressed string as the result. But the result needs to be tagged with some identification of, which compression routine was used, ptherwise how is it to be decompressed? The more compression algorithms there are to choose from, the longer this tag number will be - thereby REDUCING the compression rate.
The problem is not that semantics has been ignored - even considering semantics, we cannot come around the above problem. What semantics can do is of course to let us choose some compression algorithms that in the case at hand works better than other algorithms, as long as we remember that this particular algorithm doesn't work universally.
Ib short: we cannot define order, only define something to be ordered, because we for some reason want it to be ordered
You write
quote:
What does this mean? Suppose after discovering the secret of a highly complex seemingly random number, it now becomes compressed by, say, 90%. We could express the "quantity" of order contained in this "piece of pi" as 1/.1, or 10. If we used larger and larger strings of pi in our example, the compression could be considerably more than this, and would in fact approach zero asymptotically (a trillion trillion digits of pi can be compressed almost as much as 100 digits), so the order would increase without an upper bound.
Yes, but what is the value of a compression program that can only compress pi? That are lot of other numbers out there in the wild
You write
quote:
One interesting result of re-thinking complexity theory this way is that it allows us to more precisely restate Dembski's core point. After all, Dembski is talking about ORDER, he's not talking about SIMPLICITY. Life is not simple, but life IS highly ordered. It is the conflation of these ideas that constitutes the fatal imprecision. The way out of the trap is as described, for what Dembski is trying to bring to our attention, and what has occurred to anyone who would take the time to read posts in here, is that life has an order that far exceeds even Pi. The tremendous recursive order seen in life –organisms within organisms, ecosystems with ecosystems – suggests deep profound ever increasing but as yet-hidden "secret" order in the superficially complex exfoliation of events and forms in the biosphere.
Well, all Dembski ever writes about is the bacterial flagellum, the Caputo case, coin tosses, the Caputo case, the SETI program, the bacterial flagellum, coin tosses, the Caputo case, the SETI program, coin tosses, ... . Did I remember to write "coin tosses"?
quote:
To talk formally about the order in life, we have to develop the mathematical and intellectual apparatus to distinguish order from simplicity. With the formal apparatus I have described here, it is at least possible to show that living things contain far more order than nonliving things, although of course it does not finally tell us where that order comes from.
Did I remember to tell you that the Pythagoreans dissolved themselves, when it was discovered that the world wasn't a math lesson?
cheers
- Poul Willy Eriksen
IP: Logged
|
|
|
Printer-friendly view of this topic