Dembski: Building a Better Definition of Intelligent Design

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Thanks for the helpful comments on my example. I am satisfied this is good enough for the purpose of discussion. Back to it …

Let’s look again at Demski’s equation:
SC(E ) = I(E) - K(E) ≥ I(E) - |D|

And plugging in the values from the example
SC(E) ≥ 499 - 352 = 147 bits

FIRST, we know that Shannon Information describes a “bandwidth” needed for communications. "352 bits of Kolmogorov Information is the compressed length of D. This gives us “147 bits” of some quantity that is undefined in mathematical theory. Dembski calling it “Specified Complexity” does not make it meaningful. There is no meaning or interpretation for the difference of Shannon and Kolmogorov information. None. This is hot nonsense.

I got the same response when I posted this to FB:

In other words, Dembski is comparing unitless apples to unitless oranges. Matthew has more good comments in that discussion.

Second, we can’t actually get Shannon Information in this example because (A) we don’t have a probability distribution for E, or (B) we have a sample size of N=1. In the case of the discrete uniform distribution Dembski knows what the SI will be because he assumes the length of the sequences. He never estimates the probability of E from any data, he just assumes a longer (shorter) sequence when he needs a smaller (larger) probability. (Footnote #1)

Not only is Dembski comparing apples to oranges, but he doesn’t actually have any apples.

That should probably be the end of the story. I have a few additional notes and comments, but I will post them separately.

Footnotes
#1: I did the same thing in my example by taking an arbitrary precision of 150 digits. My first attempt had 50 digits of precision, giving
SC(E) ≥ 166.1 - 352 = -185.9 bits
Technically information cannot be negative and we should say “0 bits” if we get a negative number. But since we don’t actually have Information, I guess anything goes? That didn’t fit the original example which had non-zero SC, so I arbitrarily added another 100 digits to E to get a positive value. Problem solved.

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It would be more interesting to consider the OP question: Does there exists a better way to consider such questions. The answer is “YES”, of course there is …

  1. Get some data, not just a single event but lots of them.
  2. Look for unexpected patterns in the data.
  3. Formulate an idea to explain those patterns. [@Paul_King gives more details]
  4. Determine the idea helps to explain the patterns in a parsimonious way.
  5. Repeat steps 1-4 until all competing explanations are exhausted.

Which most will recognise as the scientific method. This does not require (or allow) comparing apples to oranges, unless you happen to be comparing apples to oranges.

There are good statistical methods that can be applied to steps 1-4.

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Claim rejected due to the lack of calculations.

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147

In science there is an important step that I think you’ve missed.

Use the patterns to predict currently unknown data (accessible data where it is practical)

Gather that data and confirm that it fits the patterns

Just looking at the data in hindsight is a major weakness of Dembski’s methods.

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148

As C/d = pi, and pi is irrational, then either C or d (or both) must likewise be irrational. An irrational number has an infinite number of non-repeating digits, so would appear to have infinite Shannon Information.

Therefore it would seem erroneous to claim that “the first one exhibits much more Shannon information that the second.”

Alternatively, we may have simply (again) gone beyond the limits for which Shannon Information (and thus Specified Complexity) is well-defined – and we can’t say anything about which exhibits more Shannon Information.

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I edited. :slight_smile:

@Giltil @RonSewell @Tim
No single event has Shannon Information.

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That depends what you mean by contextual. It is true that Ron’s question lack sufficient context to calculate the SC associated with the two events. In order to do that, one should know the probability distribution associated with the two events.

Now, let’s suppose that Ron had formulated things as follow:

My friend Peter told me that he has built a machine with a screen and a lever, and each time the lever is operated, one of the ten digits or a comma is outputted on the screen, with each of the ten digits and the comma having the same probability of 1/11 of being outputted. Peter then brought me to the machine and asked me to operate the lever 55 times, each time recording which symbol is displayed. I did so and got the following event denoted Ep:

3,14159265358979323846264338327950288419716939937510582

John, another friend of mine, told me that he blindly and randomly pressed 3 keys on his computer’ keyboard and so doing, he got the following event denoted Ej: c/d.

Questions:

  1. Can we trust Peter when he says that his machine always outputs randomly generated digits?

  2. Is there any good reason to doubt John’s story?

Intuitively, the answer to 1) and 2) is no and this intuition is confirmed when one compute the SC associated with both events. Let’s see.

First, let’s estimate the SC associated with the event Ep in Peter’s story.

According to Dembski:
SC(Ep) = I (Ep)– K(Ep) ≥ I(Ep)– |Dp|

With
SC: specified complexity
I: Shannon information
K: Kolmogorov Information
Dp: description of Ep
|Dp|: the number of bits making up Dp

The probability of Ep is 1 in 11^55. This corresponds to ~182 bits of Shannon information. IOW, I(Ep)=182 bits

Now, Ep can be described using a single word, namely pi. Given that there are approximately 200,000 words in common usage in English, it takes approximately 18 bits to select one of these 200,000 words. IOW, |D|~ 18 bits.

So, finally, SC(Ep) ≥ 182 - 18 = 164 bits

Now, let’s estimate the SC associated with the event Ej in John’s story. If we assume his keyboard is composed of 65 keys with one of them corresponding to «c », another one to « / » and another one to « d », the probability of Ej is 1/(65^3), that is 1/274625.
This corresponds to 18 bits of Shannon information, meaning that I(Ej)=18 bits.
Now, Ej can be described by the same single word than Ep, namely pi. Accordingly, |Dj|=|Dp|=18 bits.
So, finally, SC(Ej) ≥ 18 - 18 = 0 bits

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The Wikipedia article below seems to contradict your claim (see the example of the fair coin toss)

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See the calculations at 147

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Thank you Gil for making that admission.

As we do not know the probability distribution of such events as the existence of cells, bacterial flagella, etc, etc, it would appear that Specified Complexity has nothing to say about Evolution, or Biology more generally.

SC, even if somebody could demonstrate that subtracting Kolmogorov Information from Shannon information had any real-world meaning (see Matthew Pocock’s comment in this post), we are left with something that doesn’t appear to have any utility beyond entertaining your friend Peter, and similar meaningless examples.

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Spontaneous emergence of a kind of digital life in a simulation
Origin of Life and Information Theory
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@Dan_Eastwood is a professional statistician. No offense, but I would trust his understanding of Shannon information over your reading of a Wikipedia article.

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There are other problems, but this is the most obvious:

If the same description is used for two different results, it can’t be a sufficient specification of either of them.

(Also, what if Ej was “3.1”?)

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Is that actually true ? It can only be the case if |Dp| ≥ K(Ep) but is that always going to be true? For shorter descriptions - which supposedly increase ASC - isn’t that likely to be false?

That also seems really questionable - indeed arbitrary. Indeed it suggests that using a portmanteau word rather than two separate words reduces the information in the description (and why English?) Or why can’t we take the number of words with two or fewer letters?

If it’s allowable to choose arbitrary measures for |Dp| then it must be shown that for that measure |Dp| ≥ K(Ep) - can you show that anything describeable in a single English word has no more than 18 bits of Kolmogorov information?

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A question:

How is @Giltil’s ‘Pi and Peter’ example informative?

Irrational numbers are not designed.

And, AFAIK, no natural process builds structures, bit-by-bit, in a uniformly-random, independent-of-previous-additions, manner. Even ‘random’ processes like errosion or depositation follow patterns – which is why we observe similar structures formed by similar natural processes.

‘Pi and Peter’, and I would argue Dembski’s formula and Specified Complexity, tells us nothing about the real world.

The question should not be whether Dembski’s formula can be made to work for a carefully curated example, but whether it can tell us something meaningful about the real world?

And I’ve seen nothing to date that even attempts to answer that question.

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… to be a Wikipedia article, not a textbook. I can’t fault you for not really understanding - it requires several years of graduate level math in statistical theory to be able to understand it.

I CAN fault Dembski,who has an MS in statistics and a Post-hole-Digger in something else. He should be capable of getting these concepts right, but he fails again and again.

BUT, let’s suppose for a moment that Dembski can get SI - it doesn’t help - because it’s meaningless to take the difference between SI and KI. Dembski has no mathematical theory to support this. It’s not math any more again; he’s just making stuff up.

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159

A question to you. In the case of Peter’s story, should we trust him when he says that his machine always randomly generates either one of the 10 digits or the comma?

So what?

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Don’t think this is true. Imagine asking 5 painters to paint a picture of the Eiffel Tower. Wouldn’t we end up with 5 different works that could all be associated with the same specification, ie., « Eiffel Tower »?

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I think you’re missing the point here. If the two results have the same specification then it can’t completely specify one either one - it must specify a collection of results including both of them.

But the description must completely specify the event - thus, since your description doesn’t fully specify either result your calculations of the (supposed) Shannon information are incorrect. You must either use a more detailed description or calculate the “Shannon information” on the basis that anything specified by the description “pi” will do.

If it’s this hard to handle a simple artificial example, imagine how difficult it would be to use ASC to handle real cases.

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And a question for you: why did you ask an irrelevant question about your example, rather than answering my question about the relevance of your example. You appear to be following a well-trod ID-Creationist tactic on this forum – when you find yourself in a difficult spot, try to draw the other person into a rabbit-hole to distract them.

My response to your question is I don’t care whether Peter is trustworthy or not – as his hypothetical machine is completely disanalogous to any known real-world process:

So it further emphasises the (complete) disanalogy:

  1. Peter’s machine ≠ evolution (or any other natural process)

  2. Pi (or any other irrational number) ≠ design.

Therefore your ‘Pi and Peter’ example tells us nothing about the applicability of Dembski’s formula to evaluating biological events for design.

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That’s multiple descriptions of the same thing, not the same description of multiple things. You’d need one work by one artist that depicted the Eiffel tower "and* the Colosseum, in such a way that both buildings were the only thing depicted.

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