Defining "complexity"

It is neither misleading nor inadequate.

@Giltil thinks that a boulder is more complex than the human brain, so anything he has to say on the subject is unhelpful at best.


I don’t.

I really don’t understand what you mean here

Sure, but it still remains improbable. For example, my sentence contained 45 letters. Now, imagine you are in jail. Imagine a bag containing the 26 letters of the alphabet. Imagine that you were asked to draw a letter at random, with replacement, 45 times. Imagine being able to repeat this game as many times as you like. And imagine being told that you could get out of jail if you produce any meaningful 45-letter sentence. How long do you think you will stay in prison?

Both sequences have the same complexity

Both sequences have the same complexity in the sense that they have the same probability of occurrence under the assumption that the coin is fair. But the difference between the two is that 2 is specified whereas 1, as far as we can tell, is not.

Exactly ! And rightly so. And what about you?

Great, so you’re less complex than a big rock, and complexity is a useless concept.


As I noted above, many posts ago, (a) we don’t need to find a pre-specified sentence and (b) the process is not random.

This hypothetical does not model evolution. Its probability is entirely irrelevant to evolution.


If highly functional proteins are rare in sequence space, you are wrong on this matter. And I think a case can be made that highly functional proteins are indeed rare in sequence space.

That case would need to be made. And that includes the cases where (a) there are other proteins that could serve the same function and (b) the systems with which the proteins interact could have evolved differently so that that a different protein would perform a ‘similar enough’ function.

Happy to see the case argued in a scientifically informed and sophisticated way.

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Random sequences are an abundant source of bioactive RNAs or peptides

Essentially all sites of a protein are mutable given other compensatory mutations

There are 1. 6 x 10^13 sequences of 35 amino acids that would fold like villin, and 7.9 x 10^96 171 amino acid sequences that fold like OmpA.

If you want the original article, it is here

This high number actually poses a problem for creationists - if there are so many alternative sequences with the same function, with all amino acid sites mutable while retaining function, why do organisms’ DNA homology sort into clades, giving us evidence for common descent?

What is even more interesting that “complexity” is inversely proportional to age of the protein.

This is evidence that proteins of certain function start off smaller and less complex, then with time they evolve and become more complicated.

But hey, you should already know all this, given this was all presented to you previously here at peacefulscience.


You did and you know it. That’s why I quoted your misrepresentation and you omitted it.

The claim of yours that I quoted sneaks in an untested hypothesis using false definitions.

Your omission of it speaks volumes.

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Okay, so what exactly is it about corn that you consider more complex than a microbe? Would you consider a multicellular organism more complex than a single-celled organism? It seems to me this is some of what occurred to change microbes into corn.

Corn are eukaryotes, which have photosynthetic chloroplast endosymbionts living inside them. So how about endosymbiosis, where one organism evolves to live inside another and they both become dependent on each other to survive? Has that system become more complex than either of these organisms living alone?

Then I really don’t see why you are using the term “complexity” for this at all. You could just as easily say you are measuring the “sharpness” or “loudness” or “greeness” or “dignity” of those sequences. Why not just stick with “probability”, if that is what you are measuring?

I would only suspect that because it is a pattern that is easily memorized and, therefore, recognized. If you have memorized sequence 1, you should be just as suspicious if that sequence actually occurs.


William Dembski? Rigorous? :rofl:

This is the guy whose work was described by David Wolpert as:

Like monographs on any philosophical topic in the first category, Dembski's is written in jello. There simply is not enough that is firm in his text, not sufficient precision of formulation, to allow one to declare unambiguously 'right' or 'wrong' when reading through the argument. All one can do is squint, furrow one's brows, and then shrug.

Dembski has all the rigor of a wet noodle.

The definition in question is not so much rigorous, as redundant and highly idiosyncratic. I could define ‘elephant’ as ‘all types of cheese’ with equal “rigor” – but I should not expect anybody to take me seriously.

And last I checked, Dembski has no chops (either qualifications or peer-reviewed research experience) in Complexity Theory. So his “deriv[ation] from the complexity theory”, unless explicitly endorsed by experts in that theory, would appear to give it no extra credibility.

Where in that book? You cannot expect me to read all 336 pages of Behe’s error-ridden blunderfest, just to look for a single definition. (Oh, the version I’ve got is electronic, and lacks page numbers, so I’ll need chapter number and subchapter title, please.)

I also find it highly anomalous, and somewhat suspicious, that Behe defines ‘complexity’ eleven years after he introduced Irreducible Complexity in DBB. Somewhat putting the cart before the horse.


I agree with you that it is highly improbable to get a particular sequence of words or letters by randomly drawing from the bag of letters.

However, if there are many meaningful 45-letter sentences in the overall sample space, that increases the probability, to some extent, of finding one. That means you have to quantify all possible meaningful 45-letter sentences for me to estimate this probability. Do you have the maths?

Finally, if the prison guard was drunk and asked me to draw any sequence of 45-letter sentences, its pretty obvious the odds will be in my favor.

@Giltil would you classify buckminsterfullerene (C60) and C70-fullerene as a complex/improbable molecules?


A definition of complexity that I’ve often seen used here at Peaceful Science but that doesn’t seem to have popped up so far in this thread is the notion of ‘irreducible complexity’ as:

‘If it works and you take away a piece and it stops working, it was complex’

In his book The Design Inference, Dembski says that complexity assesses the difficultly of solving a problem using the resources given. By this definition, and given what I’ve understood from the Wikipedia link, I would say that buckminsterfullerene is neither very complex nor highly improbable.

Buckminsterfullerene is but one possible arrangement of carbon atoms in an infinite number of possible arrangements of carbon atoms (infinite number of possible graphene sheets, diamond lattices, carbon nanotubes. There are other classes such as polycyclic aromatic hydrocarbons into an infinite number of series in each of which successive isomer groups differ by C4H2.)

Just like one sentence is but one possible arrangement of letters.

So by what criterion does one assess “how difficult a problem” is?

How commonly occuring something is in nature? How spontaneously it forms in nature?

If so, then would not the sentence “akwjrjdnei ajeifn wirhb” be more complex than “this is a sentence”?

Would complexity also be context-dependent?

What if a certain sequence is non-functional for life today, but for an alien species, is also functional? Say an alien species has different mRNA correlations with amino acids? Different number of codons per amino acid?

What if “akwjrjdnei ajeifn wirhb” is a meaningful sentence for an alien species?

Hypothetically, if we discovered life on a multitude of planets in the universe, would this alter how improbable / complex life is?

What if we found hydrothermal vent conditions spontaneously forming peptides/RNA sequences, would that alter how complex or improbable life is?

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