Confusing Probability: The “Every-Sequence-Is-Equally-Improbable” Argument

_{June 4, 2017

Design inference, Information, Intelligent Design, Mathematics, specified complexity}

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Note to Readers:

The past few days on this thread there has been tremendous activity and much discussion about the concept of probability. I had intended to post this OP months ago, but found it still in my drafts folder yesterday mostly, but not quite fully, complete. In the interest of highlighting a couple of the issues hinted at in the recent thread, I decided to quickly dust off this post and publish it right away. This is not intended to be a response to everything in the other thread. In addition, I have dusted this off rather hastily (hopefully not too hastily), so please let me know if you find any errors in the math or otherwise, and I will be happy to correct them.

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Confusing Probability: The “Every-Sequence-Is-Equally-Improbable” Argument

In order to help explain the concept of probability, mathematicians often talk about the flip of a “fair coin.” Intelligent design proponents, including William Dembski, have also used the coin flip example as a simplified way to help explain the concept of specified complexity.

For example, a flip of a fair coin 500 times can be calculated as a simple 2 to the 500th power, with the odds of such a sequence being approximately 1 in 3.3*10^150. Based on this simple example, I have heard some intelligent design proponents, perhaps a little too simplistically, ask: “What would we infer if we saw 500 heads flipped in a row?”

At this point in the conversation the opponent of intelligent design often counters with various distractions, but perhaps the favorite argument – certainly the one that at least at first blush appears to address the question with some level of rationality – is that every sequence is just as improbable as another. And therefore, comes the always implied (and occasionally stated) conclusion, there is nothing special about 500 heads in a row. Nothing to see here; move along, folks. This same argument at times rears its head when discussing other sequences, such as nucleotides in DNA or amino acid sequences in proteins.

For simplicity’s sake, I will discuss two examples to highlight the issue: the coin toss example and the example of generating a string of English characters.

Initial Impressions

At first blush, the “every-sequence-is-just-as-improbable-as-the-next” (“ESII” hereafter) argument appears to make some sense. After all, if we have a random character generator that generates a random lowercase letter from the 26 characters in the English alphabet, where each character is generated without reference to any prior characters, then in that sense, yes, any particular equal-length sequence is just as improbable as any other.

As a result, one might be tempted to conclude that there is nothing special about any particular string – all are equally likely. Thus, if we see a string of 500 heads in a row, or HTHTHT . . . repeating, or the first dozen prime numbers in binary, or the beginning of Hamlet, then, according to the ESII argument, there is nothing unusual about it. After all, any particular sequence is just as improbable as the next.

This is nonsense.

Everyone, including the person making the ESII argument, knows it is nonsense.

A ~~Bridge~~ Random Generator for Sale

Imagine you are in the market for a new random character generator. I invite you to my computer lab and announce that I have developed a wonderful new random character generator that with perfect randomness selects one of 26 lowercase letters in the English alphabet and displays it, then moves on to the next position, with each character selection independent of the prior. If I then ran my generator and it spit out 500 a’s in a row, everyone in the world would immediately and clearly and unequivocally recognize that something funny was going on.

But if the ESII argument is valid, no such recognition is possible. After all, every sequence is just as improbable as the next, the argument goes.

Yet, contrary to that claim, we would know, with great certainty, that something was amiss. Any rational person would immediately realize that either (i) there was a mistake in the random character generator, perhaps a bad line of code, or (ii) I had produced the 500 a’s in a row purposely. In either case, you would certainly refuse to turn over your hard-earned cash and purchase my random character generator.

Why does the ESII argument so fully and abruptly contradict our intuition? Could our intuition about the random character generator be wrong? Is it likely that the 500 a’s in a row was indeed produced through a legitimate random draw? Where is the disconnect?

Sometimes intelligent design proponents, when faced with the ESII argument, are at a loss as to how to respond. They know – everyone knows – that there is something not quite right about the ESII argument, but they can’t quite put a finger on it. The ESII argument seems correct on its face, so why does it so strongly contradict our real-world experience about what we know to be the case?

My purpose today is to put a solid finger on the problems with the ESII argument.

In the paragraphs that follow, I will demonstrate that it is indeed our experience that is on solid ground, and that the ESII argument suffers from two significant, and fatal, logical flaws: (1) assuming the conclusion and (2) a category mistake.

Assuming the Conclusion

On this thread R0bb stated:

Randomly generate a string of 50 English characters. The following string is an improbable outcome (as is every other string of 50 English characters): aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

R0bb goes on to note that the probability of a particular string occurring is dependent on the process that produced it. I agree on that point.

Yet there is a serious problem with the “everything-is-just-as-improbable” line of argumentation when we are talking about ascertaining the origin of something.

When R0bb claims his string of a’s is just as improbable as any other string of equal length, that is only true by assuming the string was generated by a random generator, which, if we examine his example, is exactly what he did.

However, the way in which an artifact was generated when we are examining it to determine its origin is precisely the question at issue. Saying that every string of equal length is just as improbable as any other, in the context of design detection, is to assume as a premise the very conclusion we are trying to reach.

We cannot say, when we see a string of characters (or any other artifact) that exhibits a specification or particular pattern, that “Well, every other outcome is just as improbable, so nothing special to see here.” The improbability, as Robb pointed out, is based on the process that produced it. And the process that produced it is precisely the question at issue.

When we come across a string like: aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa or some physical equivalent, like a crystal structure or a repeating pulse from a pulsar, we most definitely do not conclude it was produced by some random process that just happened to produce all a’s this time around, because, hey, every sequence is just as improbable as the next.

Flow of Analysis for Design Detection

Let’s dig in just a bit deeper and examine the proper flow of analysis in the context of design detection – in other words in the context of determining the origin of, or the process that produced, a particular sequence.

The proper flow of analysis is not:

Assume that two sequences, specified sequence A and unspecified sequence B, arose from a random generator.
Calculate the odds of sequence A arising.
Calculate the odds of sequence B arising.
Compare the odds and observe that the odds are equal.
Conclude that every sequence is “just as likely” and, therefore, there is nothing special about a sequence that constitutes a specification.

Rather, the proper flow of analysis is:

Observe the existence of specified sequence A.
Calculate the odds of sequence A arising, assuming a random generator.
Observe that a different cause, namely an intelligent agent, has the ability to produce sequence A with a probability of 1.
Compare the odds and observe that there is a massive difference between the odds of the two causal explanations.
Conclude, based on our uniform and repeated experience and by way of inference to the best explanation, that the more likely source of the sequence was an intelligent agent.

The problem with the first approach – the approach leading to the conclusion that every sequence is just as improbable as the next – is that it assumes the sequence under scrutiny was produced by a random generator. Yet the origin of the sequence is precisely the issue in question.

This is the first problem with the ESII claim. It commits a logical error in thinking that the flow of analysis is to assume a random generator and then compare sequences, when the question of whether a random generator produced the specified sequence in the first place is precisely the issue in question. As a result, the ESII argument against design detection fails on logical grounds because it assumes as a premise the very conclusion it is attempting to reach.

The Category Mistake

Now let us examine a more nuanced, but equally important and substantive, problem with the ESII argument. Consider the following two strings:

ababababababababababababababab

qngweyalbpelrngihseobkzpplmwny

When we consider these two strings in the context of design detection, we immediately notice a pattern in the first string, in this case a short-period repeating pattern ‘ab’. That pattern is a specification. In contrast, the second string exhibits no clear pattern and would not be flagged as a specification.

At this point the ESII argument rears its head and asserts that both sequences are just as improbable. We have already dispensed with that argument by showing that it assumes as its premise the very conclusion it is trying to reach. Yet there is a second fundamental problem with the ESII argument.

Specifically, when we are looking at a new artifact to see whether it was designed, we need not be checking to see if it conforms to an exact, previously-designated, down-to-the-letter specification. Although it is possible that in some particular instance we might want to home in on a very specific pre-defined sequence for some purpose (such as when checking a password), in most cases we are interested in a general assessment as to whether the artifact exhibits a specification.

If I design a new product, if I write a new book, if I paint a new painting – in any of these cases, someone could come along afterwards and recognize clear indicia of design. And that is true even if they did not have in mind a precise, fully-detailed description of the specification up front. It is true even if they are making what we might call a “post specification.”

Indeed, if the outside observer did have such a fully-detailed specification up front, then it would have been them, not I, that had designed the product, or wrote the book, or painted the painting.

Yet, the absence of a pre specification does not deter their ability to — correctly and accurately — infer design in the slightest. As with the product or the book or the painting, every time we recognize design after the fact, which we do regularly every day, we are drawing an inference based on a post specification.

The reason for this is that when we are looking at an artifact to determine whether it is designed, we are usually analyzing its general properties of specification and complexity rather than the very specific sequence in question. Stated another way, it is the fact of a particular type of pattern that gives away the design, not necessarily the specific pattern itself.

Back to our example. If instead of aaaaaaaaaaaaaaaaaaaaaaaaaaaaaa, our random character generator produced ababababababababababababababab, we would still be confident that something was fishy with the random character generator. The same would be true with acacacacacacacacacacacacacacac and so on. We could also alter the pattern to make it somewhat longer, perhaps abcdabcdabcdabcdabcdabcdabcdabcd or even abcdefghabcdefghabcdefghabcdefgh and so on.

Indeed, there are many periodic repetitive patterns that would raise our suspicions just as much and would cause us to conclude that the sequence was not in fact produced by a legitimate random draw.

How many repetitive sequences would raise our suspicions – how many would we flag as a “specification”? Certainly dozens or even hundreds. Likely many thousands. A million? Yes, perhaps.

“But, Anderson,” you complain, “doesn’t your admission that there are many such repetitive sequences mean that we have to increase the likelihood of a random process stumbling upon a sequence that might be considered a “specification”? Absolutely. But let’s keep the numbers in context.

From Repetition to Communication

I’ll return to this in a moment, but first another example to drive the point home. In addition to many repetitive sequences, don’t we also have to consider non-repetitive, but meaningful sequences? Absolutely.

David Berlinski, in his classic essay, The Deniable Darwin, notes the situation thusly:

Linguists in the 1950’s, most notably Noam Chomsky and George Miller, asked dramatically how many grammatical English sentences could be constructed with 100 letters. Approximately 10 to the 25th power, they answered. This is a very large number. But a sentence is one thing; a sequence, another. A sentence obeys the laws of English grammar; a sequence is lawless and comprises any concatenation of those 100 letters. If there are roughly 10^25 sentences at hand, the number of sequences 100 letters in length is, by way of contrast, 26 to the 100th power. This is an inconceivably greater number. The space of possibilities has blown up, the explosive process being one of combinatorial inflation.

Berlinski’s point is well taken, but let’s push him even further. What about other languages? Might we see a coherent sentence show up in Spanish or French? If we optimistically include 1,000 languages in the mix, not just English, we start to move the needle slightly. But, remarkably, still not very much. Even generously ignoring the very real problem of additional characters in other languages, we end up with an estimate of something on the order of 10^28 language sequences – 10^28 patterns that we might reasonably consider as specifications.

In addition to Chomsky’s and Miller’s impressive estimate of coherent language sentences, let’s now go back to where we started and add in the repetitive patterns we mentioned above. A million? A billion? Let’s be generous and add 100 billion repetitive patterns that we think might be flagged as a specification. It hardly budges the calculation. It is a rounding error. We still have approximately 10^28 potential specifications.

10^28 is a most impressive number, to be sure.

But, as Berlinski notes, the odds of a specific sequence in a 100-character string, is 1 in 26^100, or 3.14 x 10^141. Just to make the number simpler for discussion, let’s again be more generous and divide by a third: 1 x 10^141. If we subtract out the broad range of potential specifications from this number, we are still left with an astronomically large number of sequences that would not be flagged as a specification. How large? Stated comparatively, given a 100-letter randomly-generated sequence, the odds of us getting a specification — not a particular pre-determined specification, any specification — are only 1 in 10^113.

What Are the Odds?

What this means in practice is that even if we take an expansive view of what can constitute a “specification,” the odds of a random process ever stumbling upon any one of these 10^28 specifications is still only approximately 1 in 10^113. This is an outrageously large number and one that gives us excellent confidence, based on what we know and our real-world experience, that if we see any of these specifications – not just a particular one, but any one of them out of the entire group of specifications, that it likely did not come from a random draw. And it doesn’t even make much difference if our estimate of specifications is off by a couple orders of magnitude. The difference between the number of specifications and non-specifications is so great it would still be a drop in the proverbial bucket.

Now 1 in 10^113 is a long shot to be sure; it is difficult if not impossible to grasp such a number. But intelligent design proponents are willing to go further and propose that a higher level of confidence should be required. Dembski, for example, proposed 1 in 10^150 as a universal probability bound. In the above example, Berlinski and I talked of a 100-character string. But if we increase it to 130 characters then we start bumping up against the universal probability bound. More characters would of course compound the odds.

Furthermore, when we have, as we do with living systems, multiple such sequences that are required for a molecular machine or a biological process or a biological system – arranged as they are in their own additional specified configuration that would compound the odds – then such calculations quickly go off the charts.

We can quibble about the exact calculations. We can add more languages and can dream up other repetitive patterns that might, perhaps, be flagged as specifications. We can tweak the length of the sequence and argue about minutiae. Yet the fundamental lesson remains: the class of nonsense sequences vastly outnumbers the class of meaningful and/or repetitive sequences.

To sum, when we see the following sequences:

(1) ababababababababababababababab

(2) tobeornottobethatisthequestion

(3) qngweyalbpelrngihseobkzpplmwny

We need to understand that rather than comparing one improbable sequence with another equally improbably sequence, what we are really comparing is a recognizable pattern, in the form of either (1) a repetitive sequence or (2) a meaningful sequence, versus (3) what appears to be a nonsense, random draw.

Properly formulated thusly, the probability of (1) or (2) versus (3) is definitely not equal.

Not even close.

Not even in the ballpark.

Thus, the failure to carefully identify what we are dealing with for purposes of design detection gives the ESII proponent the false impression that when choosing between a recognizable pattern and a random draw we are dealing with equivalent odds. We are not.

—–

Conclusion

While examples of coin tosses and character strings may be oversimplifications in comparison to biological systems, such examples do give us an idea of the basic probabilistic hurdles faced by any random-based process.

The ESII argument, popular though it may be among some intelligent design opponents, is fatally flawed. First, because it assumes as a premise (random generation) the very conclusion it seeks to reach. Second, because it fails to properly define sequences, mistakenly assuming that a random sequence is on the same probabilistic footing as a patterned/specified sequence, rather than properly looking at the relative sizes of the two categories of sequences.

Opponents of intelligent design may be able to muster rational arguments that question the strength of the design inference, but the “every-sequence-is-equally-improbable” argument is not one of them.

Comments

--If they do not violate the laws of physics, by which process do they create knowledge, which other processes cannot?-- If something doesn't violate the laws of physics, the laws of physics don't happen.tribune7_{June 25, 2017
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The only known source of meaningful information is an intelligent agent. Information is created by and grows by intelligence, not by some hypothetical constructor. UB has talked you patiently through this patently obvious issue. Constructor theory (which you managed to bring in, even when talking about probability) seems completely impotent in this regard.
First, if by "known" you mean "have experienced", you are appealing to inductivism, which is impossible. Second, if you do not know how intelligent agents create knowledge, or you're confused about the means by which they do, why would you expect to know if only intelligent agents can create it? The fact that you keep appealing to induction indicates you're confused about how knowledge grows. But, by all means, feel free to formulate a principle of induction that works in practice.
(And, by the way, the word you keep using “knowledge” requires an intelligent agent, not only for the source of the information but to be able to “know” the information.)
As I've pointed out elsewhere, the term "knowledge", as I'm using it here, represents a unification. Specifically, it refers to information that plays a causal role in being retained when embedded in a storage medium. That doesn't require a knowing subject.
Why would design require violating the laws of physics? It obviously doesn’t require or even imply any such thing.
So, then what's so special about designers? If they do not violate the laws of physics, by which process do they create knowledge, which other processes cannot?critical rationalist_{June 25, 2017
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--there is nothing special about 500 heads in a row-- Anyone who concludes that 500 heads in a row is chance is, literally, a fool. Really, as in literally. https://www.merriam-webster.com/dictionary/fool But take it a step further. Suppose you flip 500 heads in a row and the overhead light comes on i.e. a specific event. Suppose you flip another 500 heads in a row and the light goes off. Suppose this pattern is consistent. Suppose you still insist that it is the result of chance. Yes, there is a literal word for one who insist this.tribune7_{June 25, 2017
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The necessary knowledge must be present there. What is the probab[ilit]ly of that? IOW, what we need is not probab[ilit]ly, but an explanation for how knowledge grows, as it’s possible. That’s why constructor theory is about what tasks are possible, which are impossible and why.
The only known source of meaningful information is an intelligent agent. Information is created by and grows by intelligence, not by some hypothetical constructor. UB has talked you patiently through this patently obvious issue. Constructor theory (which you managed to bring in, even when talking about probability) seems completely impotent in this regard. You have consistently and repeatedly failed to understand the difference between a source of information and how it can be instantiated in a physical medium. (And, by the way, the word you keep using "knowledge" requires an intelligent agent, not only for the source of the information but to be able to "know" the information.)
If the probably of a designer designing a sequence is always 1, does that require them to somehow violate the laws of physics? I don’t see how this a nonsense or irrelevant question.
Why would design require violating the laws of physics? It obviously doesn't require or even imply any such thing.Eric Anderson_{June 15, 2017
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@Eric
In the meantime, please stop posting this nonsense and derailing other threads, as you have now done multiple times.
The criticism in comment #93 was regarding the validity of probability, or the lack there off, which was the topic of OP. Nor did it use constructor theory to argue against probability. Rather it went in the opposite direction. It’s not constructor theory specific, so it’s unclear what your objection to it is. This lecture expands on this in detail. It’s unclear what a theory about how people should behave if they want to win at games of chance has to do with physical reality. Do you have any criticism of it? Furthermore, I pointed out the problems with your claim that the probably of a designer creating specific sequences was 1. To reemphasize one in particular, one of those sequences could be used to cure cancer. However, if the probably of an mere “intelligent agent” creating it was 1, we should have a cure cancer by now, right? Yet, we do not. So, merely being an “intelligent agent” simply isn’t sufficient. Nothing about this criticism is constructor theory specific. IOW, saying it’s “constructor theory nonsense” seems to be an attempt to avoid it. In addition, take the representation of binary data in a computer. Anything below 0.6v is considered a 0, while equal to or above 0.6v is a 1. This allows for error correction. A series of voltages that is randomly distributed from 0.0 to 0.5 would all appear as 00000000000000000 in that system. That’s how a imperfect voltage regulation is corrected in transistor based digital systems. (In mechanical computers, cogs snapped into place, rather than being continually variable) If a sequence only triggers something in biology when such a threshold was met, it too could appear as a sequence of the same value over and over again, despite not being uniform either. Yet, you would assume that sequence was somehow designed.
Most recently on the Antikythera thread, UB walked very patiently through the basic issues for you. Please take some time to think through the issues and make sure you can both understand and articulate them before dumping more comments about this constructor theory on threads.
So, where is UB’s head post that I can reference? Where are the references to papers that expand on his theory I’ve requested. For example, I’ve asked multiple time for him to indicate what theory of information he was referring to, but he has still yet to provide one. Then, when someone else posted a link to the Biosemiotics site, what did I find? A link to Shannon’s theory. Then, later, UB said that people fifty years ago weren’t concerned whether information was Shannon information.(People 300 years ago were not concerned if motion was based on Einstein's, theory either as he had not conceived it yet. That doesn't mean GR is not relevant.) So, apparently, the site some one else referred me to has links to papers that are irrelevant to UB’s theory. I really don’t see how a single paragraph he has repeated without virtually any attempt of his own at clarification represents “walk[ing] very patiently through the basic issues for you” As for comment #94, it’s really a simple question, which is again relevant to the OP. If the probably of a designer designing a sequence is always 1, does that require them to somehow violate the laws of physics? I don’t see how this a nonsense or irrelevant question.critical rationalist_{June 12, 2017
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critical rationalist, I apologize in advance for my frank tone, but I need to be up front with you: I have offered you multiple opportunities to write up this so-called "constructor theory" for a head post so people can critique it. If you want to offer it for discussion, please do so. In the meantime, please stop posting this nonsense and derailing other threads, as you have now done multiple times. Most recently on the Antikythera thread, UB walked very patiently through the basic issues for you. Please take some time to think through the issues and make sure you can both understand and articulate them before dumping more comments about this constructor theory on threads. I have never, to my recollection, censored, removed, banned, or otherwise prevented anyone from commenting on my threads. But understand you are duly warned. You owe it to yourself and to everyone else to learn the issues, instead of repeating, ad nauseam, this constructor theory business. You can have your own thread if you want, but you need to stop polluting numerous other threads with this stuff.Eric Anderson_{June 12, 2017
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IOW, what we need is not probably, but an explanation for how knowledge grows, as it’s possible.
To clarify, in constructor theory either things are possible, in that they do not violate the laws of physics, or they are impossible in that they violate the laws of physics. And we already know the growth of knowledge is possible, as opposed to impossible. So, the question is, why is knowledge possible? That's an explanation for the growth of knowledge. Then again, perhaps that's not quite the position of ID proponents here. Does the growth of knowledge violate the laws of physics, despite being possible?critical rationalist_{June 12, 2017
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@Eric First, the mistake isn’t ESII. The mistake is assuming probably is relevant at all as it refers to what will probably happen, not what will happen, what actually happened, etc. So, you’re correct in that a category error is in play, just not the one you’re referring to. Probability was invented in the 16th century by people who only wanted to win at games of chance. That was the brith of game theory. This was a mathematical model to say that something was equally likely was in regards to a fair draw of cards or a fair die. So, this was geared towards games of chance, as to what we should or should not do if we wanted to win. As such, should be surprising that probability is found in some kind of fundamental role in physics or detecting design. Yes, it seems to work, but when you try to take is seriously, it fails. See this lecture for details. Saying something was probably designed doesn’t really help. Saying in a cell should have a function isn’t testable (what function?) Furthermore, that’s not even accurate as you would say probably has a function. Even then, designers sometimes create things that are purely ornamental, while others are unintended and even undesired consequences. Second, you seem to have grasped why constructor theory is relevant when you put the probably of a designer creating sequence A as 1. For example, I’d ask what is the probably of a designer existing to design the biosphere at the necessary time and place? How do you calculate that? What is the probably of a designer, as all the designers we've observed only occur in conjunction with those types of sequences, which apparently, need a designer. etc.? In addition, one possible sequence A would cure cancer. I’m an intelligent agent. What is the possibility that I can create that sequence? Merely being intelligent and making choices is not enough, as I’ve illustrated elsewhere. The necessary knowledge must be present there. What is the probably of that? IOW, what we need is not probably, but an explanation for how knowledge grows, as it’s possible. That’s why constructor theory is about what tasks are possible, which are impossible and why.critical rationalist_{June 12, 2017
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wd400 @46:
There are protein famalies in which no amino acid at all is conserved across all species.
How many a.a.s long are the proteins, and what function do they perform?PaV_{June 11, 2017
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WD400, FYI, the CSI concept traces to Orgel, 1973 and was further used by Wicken, 1979. These were seen as significant by Thaxton et al c 1984 in the first ID technical work, long before Dembski et al. The attempt to suggest a dubious concept introduced by those IDiots (that is how too many objectors will read "IDists") fails. Instead of the genetic fallacy, why not examine the concept, especially given Orgel's FUNCTION-OF-THE-CELL context? KF PS: Orgel:
living organisms are distinguished by theirspecified complexity. Crystals are usually taken as the prototypes of simple well-specified structures, because they consist of a very large number of identical molecules packed together in a uniform way. Lumps of granite or random mixtures of polymers are examples of structures that are complex but not specified. The crystals fail to qualify as living because they lack complexity; the mixtures of polymers fail to qualify because they lack specificity . . . . [HT, Mung, fr. p. 190 & 196:] These vague idea can be made more precise by introducing the idea of information. Roughly speaking, the information content of a structure is the minimum number of instructions needed to specify the structure.
[--> this is of course equivalent to the string of yes/no questions required to specify the relevant J S Wicken "wiring diagram" for the set of functional states, T, in the much larger space of possible clumped or scattered configurations, W, as Dembski would go on to define in NFL in 2002, also cf here, -- here and -- here -- (with here on self-moved agents as designing causes).]
One can see intuitively that many instructions are needed to specify a complex structure. [--> so if the q's to be answered are Y/N, the chain length is an information measure that indicates complexity in bits . . . ] On the other hand a simple repeating structure can be specified in rather few instructions. [--> do once and repeat over and over in a loop . . . ] Complex but random structures, by definition, need hardly be specified at all . . . . Paley was right to emphasize the need for special explanations of the existence of objects with high information content, for they cannot be formed in nonevolutionary, inorganic processes [--> Orgel had high hopes for what Chem evo and body-plan evo could do by way of info generation beyond the FSCO/I threshold, 500 - 1,000 bits.] [The Origins of Life (John Wiley, 1973), p. 189, p. 190, p. 196.]
kairosfocus_{June 10, 2017
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EA, I suggest LK Nash's 1,000 coin example is far more instructive, given Mandl's direct translation into a physical system and the utility of binary text strings. KFkairosfocus_{June 10, 2017
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JDK, Have you done any statistical thermodynamics? If not, I suspect that gap is the root problem. If so, do you appreciate that the issue is not so much the particular detailed microstate but the CLUSTERS of sufficiently similar microstates, and the linked pattern that there tend to be overwhelmingly dominant clustersof microstates, due to their relative statistical weight? (Indeed, that is essentially how Dembski wrote in NFL, and his use of Omega as the set of possible states is a dead giveaway to one familiar with the usual symbols used in statistical thermodynamics, as in s = k log OMEGA, from Boltzmann.) So, for example with a tray of 1,000 fair coins, there is a well known binomial distribution that peaks near 500:500 H/T with a span of fluctuations that may be readily seen to span about +/- 200 or so, where the coins are overwhelmingly not in any particular order like HT-HT-HT . . . etc. This is of course readily translated into a paramagnetic substance in a weak B-field [Cf. here, Mandl], i.e. L K Nash's introductory coins example is physically relevant. In this context, meaningfully functional strings -- this includes EVERY possible meaningful 500-bit pattern in say ASCII English text -- are vanishingly rare relative to the dominant pattern, i.e. isolated islands of simply describable function are "lost" in an overwhelming sea of meaningless patterns that are beyond the blind search capacity of the observed cosmos. We are looking at 1.07*10^301 possibilities, in a context where our observed cosmos' 10^80 atoms, at say 10^14 observations of 1,000-coin strings per sec, for 10^17 s would max out at 10^111 observations, 1 in 10^190. A vanishingly small relative scope of blind search. Thus, we do not need to work out precise probability estimates, degree of blind search challenge is more than enough. Especially, when we can readily see -- think AutoCAD file -- that discussion on bit-strings is WLOG. (Any 3-d pattern can be informationally reduced to a string of structured answers to Y/N q's in a description language, that lays out the relevant node-arc mesh.) Beyond a reasonable threshold of 500-1,000 bits, the likelihood of getting to an island of function in the config space by blind search is clearly indistinguishable from zero. So, if we come across a bit pattern of 1,000 bits [143 ASCII characters] in recognisable English text or the like, we are well justified in inferring that this came about by intelligently directed configuration, not blind search. Especially when, if the direct search space is of order 10^301, as a search is a sample, search for a golden search comes from the power set, 2^[10^301]. That is why after the fact recognisable patterns such as the specification on functioning as English text in ASCII code or the like, are strong signs of origin of the said pattern by design. There is nothing intrinsically difficult in this basic reasoning, the problem is its import: in the heart of the living cell is DNA, with coded algorithmically functional text far, far beyond the 1,000 bit threshold. KFkairosfocus_{June 10, 2017
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The statement, "the probability of that having happened was 1/8", presupposes the favorable outcome of the event. Because otherwise, how would you calculate the probability? The probability of an event A is defined as P(A) = number of favorable outcomes/ total number of possible outcomes. By saying: "the probability WAS..."... you are actually saying: "the number of favorable outcomes WAS..." But if all that you did was coin tossing, then you obviously didn't specify what outcomes are favorable so the probability formula is not applicable.forexhr_{June 9, 2017
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OK, so I didn't understand you correctly. I disagree with your conclusion that if I throw three coins and get HTH I can't say that the probability of that having happened was 1/8 because I didn't specify HTH before the throw (which is what I think you are saying, although I'm probably wrong), but I've discussed this at length with others in this thread and others, and I think I'm done. Thanks.jdk_{June 9, 2017
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jdk @70 Both of your interpretations are incorrect. To explain why, we first need to define three preconditions for calculating probability: 1) Event 2) Outcome of the event 3) Favorable outcome Given these preconditions we also must know whether an event is real or imagined. If you throw a coin three times(real event) and get HTH(outcome of the event) than you cannot talk about probability because this REAL event cannot be related back to some REAL environment that would have determined the favorable outcome of the event. But, let's imagine you have a bet with a friend on flipping a coin three times. Your friend would give you $100 if the outcome is HTH. Now you throw a coin three times and you get HTH. In this scenario you can relate this REAL outcome(HTH) back to the REAL environment - one where you made the bet, and then conclude that the probability of the outcome was 1/8. In your example, you started with the REAL event(coin throwing) and then you interpreted its outcome(HTH) as if it was predicted in some REAL environment. But no such prediction existed. On the other hand, in the case of imagined events, where we would say: "Let’s figure out the probability of getting HTH", the prediction of the outcome is already presupposed, so there is no need to establish connection between outcome and some prior environment. Regarding the claim that probability does not apply after the fact it is also incorrect because, in the context of probability, "fact" is just another word for "outcome of the event". If we know what the favorable outcome is than there is no problem to figure out the probability("after the fact").forexhr_{June 9, 2017
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john_a_designer: Thanks for stopping in and for the good thoughts. I'm not sure what you're saying in the first sentence, so maybe you can clarify. It doesn't matter for the design inference whether we are dealing with a pre-specification or a post-specification. In terms of origins in biology (or the cosmos), we are always dealing with a post-specification. Your other points are well taken. I like your point about the casino operators -- yet another example of design inference that no-one objects to. Presumably because it isn't philosophically troubling.
Are there sequences, unlike cards, which are actually intrinsically specified? I think there are.
In terms of having meaning, yes. This is the difference I've tried to highlight between repetitive/ordered sequences that are often (although not strictly always) meaningless, and non-repetitive meaningful sequences. ----- Finally, we have to be a little bit careful to make sure we distinguish the sequence from the medium. I think you are, but just for readers out there I want to make that clear. The medium has no inherent specification or meaning in and of itself. But the medium can be organized to represent or "contain" information through the sequencing.Eric Anderson_{June 8, 2017
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I’m late to this discussion but let me summarize, very succinctly, what I think is the main issue here. From an ID perspective probability is irrelevant unless there is specification, or more precisely pre-specification, involved. I won’t rehash the discussion about playing cards, coins or dice except to say that casino operators invest a lot money in eye-in-the-sky cameras to catch cheaters. Do they have a right to a accuse some of their patrons of cheating at cards when they appear to get too lucky? After all, any hand is just as probable as any other, right? Obviously one wins or loses at cards, for example, based on a pre-specified criteria of what constitute a winning hand. For example, the cards 10, J, Q, K, A, all of the same suit, will make you a winner in poker, unless we agreed to change the rules-- which we could do. Technically there no intrinsic reason to consider one set of five cards to be any more significant than any other. Yet for the game to be meaningful or fun you have to specify what set of cards signifies winning. However, we (humans) don’t necessarily need to be the one’s specifying. In his novel Contact, for example, Carl Sagan explains how ET’s living hundreds of light years away might try to communicate with us by transmitting a signal that stands out from the background noise, which we would recognize as intelligent. On the other hand, is all specification the same? Are there sequences, unlike cards, which are actually intrinsically specified? I think there are. I think they occur with human designs and the “apparent design” we observe in the natural biological world. It is with this kind of intrinsic specification that arguments using probabilities have some real merit, especially when you are considering whether the cause of the “design” is some kind of intelligence or some kind of mindless natural process.john_a_designer_{June 8, 2017
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wd400 @69:
Why would you think that? The “islands” are formed by billions of years of divergent evolution. When lineages evolve apart from each other for billions of years they become quite distinct, I’m not sure why you think selection can’t drive that process.
No. We aren't looking for just those functional islands that are currently being occupied, by whatever hypothetical means you think they have been filled. We are talking about functions that can realistically exist in the given system, as an objective functional matter. As a result, I'm happy to assume that there are more possible islands of function than those currently occupied. But even with some very generous assumptions, the number is still miniscule compared to the search space. And, no, you don't get to claim that natural selection has the ability to do all this creative work and reach these islands of function, by assuming that these islands of function were "formed by billions of years of divergent evolution." It would be hard to think of a more blatant example of circular reasoning. The very question on the table is whether the Darwinian mechanism in fact has the ability to do what is claimed. Unfortunately, the math doesn't add up, and when we look at the actual observations and experiments that have been done, all we see the Darwinian mechanism doing is minor tweaks around the edges, largely insignificant and nowhere near the kind of creative power that is claimed.
I had forgotten about this, but I have to say I am amazed that you would link a thread that puts you in such a terrible light. If you read back over the threads you will see that you made the claim that the probability of a given sequence arising by naturalistic process, termed P(T|H) in CSI and essential for calculating this statistic, could be calculated by 20^(n.amino acids). This is so wrong that it’s kind of breathtaking (in fact I used it as an example of an obviously silly calculation above, forgetting that you had done this).
I'm happy to be corrected on any math mistakes I've made, but that doesn't seem to be the case. I'm not sure if you've understood the points made in the other threads. I discussed a chance-based formation in a side conversation with keiths and showed how a chance-based calculation was easy for a simple situation like that. What you seem to be arguing is that because a protein comes about through the Darwinian mechanism, then the odds of it arising through the Darwinian mechanism are much greater than under a chance-based scenario alone. Let's set aside the fact that your argument assumes the Darwinian mechanism produced the proteins in question, which is part of the very issue on the table. Let's even, just for a moment, set aside the question of whether the Darwinian mechanism provides anything other than a chance-based scenario anyway (given that selection is not directional). Given your apparently vastly greater understanding than mine of the naturalistic explanations out there, tell us: What do you think the odds are of the Darwinian mechanism stumbling across a functional biological system? Can you calculate it? Are the odds such that we should consider the Darwinian mechanism a realistic explanatory cause? And if you can't provide me a calculation of the odds, then I'm sorry to tell you, but you are right back squarely in the middle of the illogical and self-serving position I pointed out: namely, demanding that a calculation of the Darwinian mechanism be done by ID proponents when Darwinian proponents have never even offered one themselves.
IDists invented CSI, if they want to show that biology displays it then it is really up to them to do the calculations.
Do you think ID proponents came up with the concept of complex specified information? In any event, various calculations have been done, including an exceedingly simple example in this very OP. Others, have of course done much more rigorous calculations than my simple example. If you disagree, let's hear it. What do you think the odds of Darwinian evolution stumbling upon something like the bacterial flagellum are? Never mind that, what about a single medium-length protein like the 100 amino acid length protein that you reminded us of?
Of course, Dembski and others do not claim that CSI is evidence that modern evolutionary biology is an improbable explanation for biological diversity (they simply assume it, and demonstrate how making this assumption can lead to probability argument for design).
I'm surprised that after this many years in the debate you are still incorrectly describing the design inference. Furthermore, why should intelligent design proponents have to take the evolutionary "explanation for biological diversity" seriously when no realistic materialistic explanation has ever been offered? Unfortunately, what we are dealing with when the rubber meets the road is that there is this persistent and pervasive and perverse attempt on the part of the proponents of Darwinian theory (started blatantly by Darwin in The Origin) to insulate their theory against criticism by asserting that the opponents have the burden of demonstrating (with mathematical precision, it is occasionally demanded) that the Darwinian story is false, when the Darwinists themselves have never provided any empirical demonstration (certainly not one with any math; that is scrupulously avoided) that the Darwinian theory should be taken seriously in the first place.Eric Anderson_{June 8, 2017
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Eric, yes, that's the video. And you have a point; Le Conte's comments were made in 1888 though, when the belief that science had or would soon have all the answers was even more pervasive than today. BTW, when I click on the link to the UD post I left at #34, I do see the video embedded there, not sure why you don't see it.Granville Sewell_{June 8, 2017
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Granville, your link to the prior post works, but there is no link in the prior post to your video? In any event, I found your other video here: https://www.youtube.com/watch?v=VpEXXNxjWYE I don't know if this is the new one or not. ---- One quick thing that jumped out at me from the beginning of the video is the materialistic claim that we should hold out for naturalistic explanations because they have been supremely successful in all other fields. This is not actually true. Note my comment to Seversky on this very point here (middle portion of comment 67): https://uncommondescent.com/fine-tuning/fine-tuning-and-the-claim-that-unlikely-things-happen-all-the-time/#comment-633321 Yes, purely naturalistic explanations have been very successful in some fields. But they have been spectacularly unsuccessful in the very fields we are dealing with in the present debate. So at the very least the materialist makes a category mistake by insisting a naturalistic explanation should be the default with respect to information-rich, functionally-integrated biological systems. I realize you are addressing other problems with the materialistic claim in your video, but I wanted to point this out as well.Eric Anderson_{June 8, 2017
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I'm on my smartphone, so I won't have much to say right now until I get in front of a regular computer. First, GBDixon makes a good observation in terms of information needing, if you will, a receiver. My idea of "matching" is the idea of there being both a sender and a receiver, otherwise, you might say, the information that were dealing with, and it's correlated probability, are suspended in what I termed in the last thread "dual space." Second, and this has reference to a post by wd400, the fact that a protein is functional, whether it comes from yeast or a human, is incidental. What is critical, is that the cell machinery recognizes the protein and is able to perform its normal function. This creates a linkage between the translation properties of the cell machinery and the functional properties of the protein which is a product of this translation. Based on what I said in my last post in the last thread, the "real" probabilities of the cell machinery then match the "real" probabilities of the functional protein, and here as I mentioned in the last post on the last thread I have in mind protein complexes which need properly fitted binding sites in order to function. "Real" probabilities of the cell machinery, and its mutational characteristics, must match the protein structure in such a way that the protein acts in a functional way. This "matching " of probabilities, or more properly in probabilities, turns into what I've turned "real" probabilities. And these "real" probabilities are not favorable to a Darwinian understanding of protein-protein complexes. More when I get in front of a computer.PaV_{June 8, 2017
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Hi forexhr. First, as I've said many times (although you may not have read any of my posts), I'm discussing pure probability and simple models such as coins and dice: I'm not interested in any arguments about how this apples to evolution or fine-tuning or anything like that. You write,
But given the event that already happened(for e.g. coin flips that created random sequence) you can figure out its probability only if you can relate this event back to an environment that determines the likelihood of this event before it happened. Without this pre-determination you can’t talk about probability, but only necessity.
I'm trying to figure what this means. I throw a coin three times, and get HTH. I think I can "relate this event back to an environment that determines the likelihood of this event before it happened": I threw the coins in the air and they bounced around randomly, each having a know chance of coming up heads or tails with equal probability. Thus I conclude that the probability of the result is 1/8. If it is incorrect in your eyes to say this, what do you mean by "relate this event back to an environment that determines the likelihood of this event before it happened." Also, your last line is, "Without this pre-determination you can’t talk about probability, but only necessity." This seems to say that once we have a result HTH, it is what exists and the whole notion that it might have been something else is null and void: probability does not apply after the fact, and everything that looks like it might have a probability before the fact is actually pre-determined to have a necessary result, as evidenced by the fact that once it exists, it has a 100% chance of being what it is. Do you mean anything like that?jdk_{June 8, 2017
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jdk @ 66 Sorry for the confusion. When I wrote what I did I was referring to real events, not hypothetical ones. Given a hypothetical event, of course that you can figure out the probability of it happening. That is why we have mathematics. But given the event that already happened(for e.g. coin flips that created random sequence) you can figure out its probability only if you can relate this event back to an environment that determines the likelihood of this event before it happened. Without this pre-determination you can't talk about probability, but only necessity. In the context of the ToE we have this pre-determination since the ToE view bio-structures as adaptations. Given the fact that adaptation presupposes the environment to which it has occurred it follows that environment predetermines DNA sequences that code for bio-structures. That is why when evolutionists say that 'every sequence is just as improbable/probable as another' this is not only nonsense but it negates the fundamental premise of their own theory. It it were true that every sequence is just as improbable/probable as another that would mean that an organism can adapt to a new environment with whatever sequence it has in its DNA, which is obviously absurd. That is the reason why the ToE postulates mutations as means of adaptation to an environment and then natural selection as means to increase the frequency of this adaptation in the gene pool of a population. But, of course, in reality mutations cannot produce adaptations because the number of non-adaptive mutations greatly exceeds the number of adaptive mutations. If we suppose that water is the environment to which an organism without gills is adapting, than mutations have equal potential to rearrange some duplicated DNA sequence into either, astronomical number of bio-meaningful sequences that have nothing to do with gills, or astronomical number of junk sequences which are completely useless in any environment. If we suppose that only one average eukaryotic gene codes for the structure of the gills, that means that most of its 10^810(1) potential sequences would be useless in the context of gill structure. Given the fact that there have been only 10^43 mutations in the history of life(2) it follows that mutations cannot produce the adaptation in the form of gills. The possible quantity of sequences that won't code for gill structure is simply too large for that to happen. (1)The length of an average eukaryotic gene is 1346 bp. A gene consists of four different bases. Any base can assume one of four values (ATCG). A sequence of L basis can therefore assume one out of 4^L values, which gives 4^1346 or 10^810 potential sequences. (2) http://rsif.royalsocietypublishing.org/content/5/25/953.fullforexhr_{June 7, 2017
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I, and I hope thirds time's a charm, will quit discussing this.jdk_{June 7, 2017
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Jdk: Noooooo!!! It is very exact to say “the probability of getting 5 green cards is 1/57.”
No it's not "very exact" jdk. This has been explained again and again. It allows for an specification informed by the outcome a la Kitcher. At this point I refuse to explain it again.
And I notice you didn’t respond to my comments about fantasy. Is pure math a “fantasy” because it is done abstractly and theoretically?
Don't be ridiculous. The independent specification is fantasy. I do hope you did understand that. Right? One deals cards without an independent specification and then one starts fantasizing:
Origenes: “What if I had independently specified five green cards and dealt them, what would have been the probability?”
The refers to fantasy. Got it? I am not talking about mathematics being "fantasy" or something like that. Get real.Origenes_{June 7, 2017
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You write,
That is inexact use of words. This is more exact: The probability of an independent specification matching the 5 cards being dealt is 1/57.
Noooooo!!! It is very exact to say "the probability of getting 5 green cards is 1/57." "5 green cards" is the specification: it specifies what situation we are considering. We don't need some person making an independent specification that matches an actual deal in order for the statement I made to be accurate. The five cards are considered as "dealt", in theory although nothing happens in actuality. The probability that 5 are green is calculated as 1/57. This is a theoretical statement. It can be tested empirically by "dealing" 57,000 hands (via a computer simulation) for instance as ascertaining that about 1000 are all green. And I notice you didn't respond to my comments about fantasy. Is pure math a "fantasy" because it is done abstractly and theoretically?jdk_{June 7, 2017
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jdk @73
No cards need to be dealt. The deck does not need to exist. Given the scenario (22 card deck, 11 green, 11 blue, deal 5),the probability of 5 green cards is 1/57.
That is inexact use of words. This is more exact: The probability of an independent specification matching the 5 cards being dealt is 1/57.
jdk: This is a mathematical fact.
Sure. But let us clearly state what probability is being measured.Origenes_{June 7, 2017
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But you are thus relegating the whole mathematical field of probability to "fantasy"! No cards need to be dealt. The deck does not need to exist. Given the scenario (22 card deck, 11 green, 11 blue, deal 5),the probability of 5 green cards is 1/57. This is a mathematical fact. It is not fantasy. Getting 5 green is the specification, and 1/57 is the probability. How can you call pure math "fantasy"?jdk_{June 7, 2017
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Jdk: But why do you say “only” a theoretical/hypothetical event?
As opposed to reality. "What if I had independently specified five green cards and dealt them, what would have been the probability?", is a question about a situation that did not actually happen. It is fantasy. What actually did happen was that five cards were dealt without an independent specification. And without an independent specification there is nothing to measure.Origenes_{June 7, 2017
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But why do you say "only" a theoretical/hypothetical event. That is exactly what the mathematical study of probability is about. We discuss cards, coins, etc to have concrete models to help us think and learn, but the probability theory exists on its own just as a perfect circle exists in geometry but not in the real world.jdk_{June 7, 2017
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