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Background Note: On Orderly, Random and Functional Sequence Complexity


In 2005, David L Abel and Jack T Trevors published a key article on order, randomness and functionality, that sets a further context for appreciating the warrant for the design inference.

The publication data and title for the peer-reviewed article are as follows:

Theor Biol Med Model. 2005; 2: 29.
Published online 2005 August 11. doi: 10.1186/1742-4682-2-29.
PMCID: PMC1208958
Copyright © 2005 Abel and Trevors; licensee BioMed Central Ltd.

Three subsets of sequence complexity and their relevance to biopolymeric information
A key figure (NB: in the public domain)  in the article was their Fig. 4:
Figure 4: Superimposition of Functional Sequence Complexity onto Figure 2. The Y1 axis plane plots the decreasing degree of algorithmic compressibility as complexity increases from order towards randomness. The Y2 (Z) axis plane shows where along the same complexity gradient (X-axis) that highly instructional sequences are generally found. The Functional Sequence Complexity (FSC) curve includes all algorithmic sequences that work at all (W). The peak of this curve (w*) represents “what works best.” The FSC curve is usually quite narrow and is located closer to the random end than to the ordered end of the complexity scale. Compression of an instructive sequence slides the FSC curve towards the right (away from order, towards maximum complexity, maximum Shannon uncertainty, and seeming randomness) with no loss of function.


We may discuss this figure in steps:

1 –> The data structure T & A have in view is the string, where symbols are chained in a line like:


2 –> Since any other data structure can be built up from a combination of strings, this is without loss of generality.

3 –> They then envision three types of sequences:

(a) orderly ones that are repetitive:


(b) random ones that are essentially incompressible:


(c) functional ones, that are almost as incompressible, but are constrained by that functionality:

this is a functional, non- orderly and non-random sequence

4 –> Fig 4 then shows how these three types of sequences can be represented in a 3-dimensional space that in principle can be a metric: for, order and randomness are on two ends of a continuum of compressibility and a similar continuum of complexity, both being low on algorithmic [or, by extension, linguistic-contextual] functionality.

5 –> The location of the FSC peak is particularly revealing: first, it is not quite as incompressible as a truly random sequence, because there is normally some redundancy in meaningful messages. So, the Shannon Information carrying capacity metric is not quite what is needed.

6 –> Compressibility metrics will show that FSC sequences will be slightly less resistant to compression than are truly random sequences — for the latter, to communicate them, you essentially have to quote them.

7  –> By contrast, an orderly sequence can be compressed by giving its unit cell then saying replicate n times. It is highly compressible.

8 –> But neither orderly nor random sequences are generally able to function, and so we see a sharp peak in the curve as we hit the FSC.

9 –> If we imagine the curve as sitting in a sea that floods the diagram, we can see how the image of islands of isolated function can emerge: FSC peaks up out of the sea of non-functional orderly or random sequences. And of course, functionality is always in a context: parts or components or elements combine to do the job in hand.

10 –> J S Wicken, in his key 1979 remarks, captures the next key point: we routinely and habitually observe that functional sequences are the product of design, and thus they are a longstanding puzzle for those who would account for living forms on natural selection:

‘Organized’ systems are to be carefully distinguished from ‘ordered’ systems. Neither kind of system is ‘random,’ but whereas ordered systems are generated according to simple algorithms [i.e. “simple” force laws acting on objects starting from arbitrary and common- place initial conditions] and therefore lack complexity, organized systems must be assembled element by element according to an external ‘wiring diagram’ with a high information content . . . Organization, then, is functional complexity and carries information. It is non-random by design or by selection, rather than by the a priori necessity of crystallographic ‘order.’[“The Generation of Complexity in Evolution: A Thermodynamic and Information-Theoretical Discussion,” Journal of Theoretical Biology, 77 (April 1979): p. 353, of pp. 349-65. (Emphases and note added. Also, the idea-roots of a term commonly encountered at UD, functionally specific, complex information [FSCI], should be obvious. The onward restriction to digitally coded FSCI [dFSCI] as is seen in DNA — and as will feature below, should also be obvious.)]

11 –>We can compose a simple metric that would capture the idea: Where function is f, and takes values 1 or 0 [as in pass/fail], complexity threshold is c [1 if over 1,000 bits, 0 otherwise] and number of bits used is b, we can measure FSCI in functionally specific bits, as the simple product:

FX = f*c*b, in functionally specific bits

12 –> Actually, we commonly see such a measure; e.g. when we see that a document is say 197 kbits long, that means it is functional as say an Open Office Writer document, is complex and uses 197 k bits storage space.

[Continued, here]

GP: Thanks for the thought. I have now gone on to put up the main post, on the design inference, here. GEM of TKI kairosfocus
kf: very good work, as usual. I hope this may open a fruitful discussion with our darwinist friends on these very important questions, which they usually prefer to ignore. I suppose the most common position among darwinists is to just pretend that functional complexity simply does not exist, or that it has no formal properties which may allow its definition and detection. And they are ready to pursue any irrational line of thought, to simply avoid truth. gpuccio

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