Complexity and Randomness revisited

I have posted before (post 1 and post 2) about order, complexity, and randomness. The image above shows the spectrum from organised order to random disorder, with structured complexity somewhere in between. The three textual examples below illustrate the same idea.

Regular Complex Random
AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA AAAAAAAAAA … It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, … ShrfT e6IJ5 eRU5s nNcat qnI8N m-cm5 seZ6v 5GeYc w2jpg Vp5Lx V4fR7 hhoc- 81ZHi 5qntn ErQ2- uv3UE MnFpy rLD0Y DI3GW p23UF FQwl1 BgP36 RK6Gb 6lpzR nV03H W5X3z 2f1u8 OgpXy tY-6H HkwEU s0xLN 9W8H …

These three examples, and many intermediate cases, can be distinguished by the amount of information they contain. The leading way of measuring that information is with Kolmogorov complexity. The Kolmogorov complexity of a block of text is the length of the shortest program producing that text. Kolmogorov complexity is difficult to calculate in practice, but an approximation is the size of the compressed file produced by good compression software, such as 7-Zip. The chart below shows the number of bytes (a byte is 8 bits) for a compressed version of A Tale of Two Cities, a block of the letter ‘A’ repeated to the same length, and a block of random characters of the same length:

The random characters are chosen to have 64 possible options, which need 6 bits to describe, so a compression to about 75% of the original size is as expected. The novel by Dickens compresses to 31% of its original size.

But does this chart show information? Grassberger notes that Kolmogorov complexity is essentially just a measure of randomness. On this definition, random-number generators would be the best source of new information – but that’s not what most people mean by “information.”

An improvement is to introduce an equivalence relation “means the same.” We write X ≈ Y if X and Y have the same meaning. In particular, versions of A Tale of Two Cities with different capitalisation have the same meaning. Likewise, all meaningless random sequences have the same meaning. The complexity of a block of text is then the length of the shortest program producing something with the same meaning as that text (i.e. the complexity of X is the length of the shortest program producing some Y with X ≈ Y).

In particular, the complexity of a specific block of random text is the length of the shortest program producing random text (my R program for random text is 263 bytes), and we can approximate the complexity of A Tale of Two Cities by compressing an uppercase version of the novel. This definition of complexity starts to look a lot more like what we normally mean by “information.” The novel contains a large amount of information, while random sequences or “AAAAA…” contain almost none:

Those who hold that information satisfies the rule ex nihilo nihil fit can thus be reassured that random-number generators cannot create new information out of nothing. However, if we combine random-number generators with a selection procedure which filters out anything that “means the same” as meaningless sequences, we can indeed create new information, as genetic algorithms and genetic programming have demonstrated – although Stuart Kauffman and others believe that the evolution of biological complexity also requires additional principles, like self-organisation.


Endless Forms Most Beautiful: a book review


Endless Forms Most Beautiful by Sean B. Carroll (2005)

I recently read, somewhat belatedly, Endless Forms Most Beautiful by evolutionary developmental biology pioneer Sean B. Carroll (the title derives from a line in On the Origin of Species: “from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved”).

This well-written book provides an excellent explanation for how a toolkit of genes like the Hox genes (see image below) control embryonic development in animals. The discovery of these genes shows that fruit flies, starfish, and people are more closely related than was once believed.

These genes work by producing proteins which in turn control the expression of other genes, in what is effectively a kind of computer program that can be visualised (and Endless Forms Most Beautiful contains several lovely colour plates which confirm this).


Photo: Caitlin Sedwick (from this paper)

The book includes chapters on the Cambrian explosion, melanic forms (such as black panthers), and the formation of spots on butterfly wings:

Carroll concludes with a plea for teaching more evolutionary biology in schools. Personally, I think a greater priority would be an increased emphasis on teaching ecology, given the serious consequences which human activities (even well-meaning ones) can have for the planet. However, that quibble does not stop me from recommending this book to anyone who has not read it yet.


Endless Forms Most Beautiful by Sean B. Carroll: 3½ stars

Complexity vs Randomness

I’ve posted before about randomness and complexity. The montage above illustrates the distinction sometimes made between regular, complex, and random patterns. The text examples below provide another illustration:

Regular Complex Random
aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa aaaaa … It was the best of times, it was the worst of times, it was the age of wisdom, it was the age of foolishness, it was the epoch of belief, it was the epoch of incredulity, it was the season of Light, it was the season of Darkness, it was the spring of hope, it was the winter of despair, … BdhBt BMgkn YCbfR enFwJ DlMyq KFNoi rRdlu JwdTc IPoim oeFnQ gnhqq pqXon cIVVn rAOrx XtbcQ rZTBF sxeTi hLmBt gREOe Udrwt QHEMW OCBeV gQrHb gKbWa lklBL ivZMg JJrGa xVOZj QQBpb rfZWQ qRKTa ZEktK ofhTD UOXrm ZJAJs LPloV NhFjy …

But how does one measure complexity? Grassberger notes that the widely-used Kolmogorov complexity is simply a measure of randomness. In other words, the use of Kolmogorov complexity implicitly assumes that complexity is just “randomness lite.”

There are three significant groups of people who doubt this. First, those complexity scientists who speak about the “edge of chaos” see the borderlands between regularity and randomness as being critically important, and in need of formal characterisation. However, rather than attempting to measure “complexity” in a way which would give both regular and random patterns low scores, this behavioural zone is now typically studied in terms of correlation length and other critical phenomena.

The second group are those critics of evolution who, believing ex nihilo nihil fit, assert that complexity has to come “from somewhere.” If complexity is just “randomness lite,” then random variation plus natural selection are sufficient to produce complex structures (indeed, in silico, the successes of genetic algorithms and genetic programming support that idea). Doubting this, these critics of evolution (such as Michael Behe) have suggested alternate definitions of complexity (irreducible complexity and specified complexity). However, since these alternate concepts have not been rigorously defined, they are not generally accepted outside the “intelligent design” community.

The third group, which includes figures such as Stuart Kauffman, also claim that random variation plus natural selection is inadequate to explain the evolution of biological complexity. However, they believe that the processes of self-organisation studied by the first group provide the missing explanation. This group does not use an agreed-upon formal definition of complexity, focussing primarily on simulation models in which non-trivial structures emerge. Their approach is interesting, but (as far as I can see) still vigorously debated.

Evolution as a Religion: a book review


Evolution as a Religion: Strange Hopes and Stranger Fears by Mary Midgley (1985, revised edition 2002)

I recently read the classic Evolution as a Religion: Strange Hopes and Stranger Fears by English philosopher Mary Midgley. In the introduction to the revised (2002) edition, Midgley explains the motivation for the book as follows: “I had been struck for some time by certain remarkable prophetic and metaphysical passages that appeared suddenly in scientific books about evolution, often in their last chapters. Though these passages were detached from the official reasoning of the books, they seemed still to be presented as science. But they made startling suggestions about vast themes such as immortality, human destiny and the meaning of life.” (p. viii). As an example, she quotes the molecular biologist William Day: “He [man] will splinter into types of humans with differing mental faculties that will lead to diversification and separate species. From among these types, a new species, Omega man, will emerge … as much beyond our imagination as our world was to the emerging eucaryotes.” (p. 36).


Mary Midgley

Such “prophetic and metaphysical passages” are also familiar from the fictional works of Olaf Stapledon and H. G. Wells. Midgley argues that they represent bad science, twisted to have characteristics of a religion, such as assigning meaning to life (pp. 15, 71). The myth of the “Evolutionary Escalator,” extrapolated to some glorious imaginary future, is one example. Nothing in evolutionary science justifies this view, comforting though it may seem (p. 38). Furthermore, past attempts to accelerate the process by breeding an “Übermensch” have not ended at all well (p. 9), and more recent proposals are also disturbing (pp. 48–49).


The “Evolutionary Escalator” or “March of Progress”

Midgley claims that prophecies based on the “Evolutionary Escalator” myth “are quite simply exaltations of particular ideals within human life at their own epoch, projected on to the screen of a vague and vast ‘future’ – a term which, since Nietzsche and Wells, is not a name for what is particularly likely to happen, but for a fantasy realm devoted to the staging of visionary dramas. In their content, these dramas plainly depend on the moral convictions of their author and of his age, not on scientific theories of any kind.” (pp. 81–82).

In contrast, Midgley quotes a more pessimistic perspective from the physicist Steven Weinberg: “The more the universe seems comprehensible, the more it also seems pointless. But if there is no solace in the fruits of our research, there is at least some consolation in the research itself. Men and women are not content to comfort themselves with tales of gods and giants, or to confine their thoughts to the daily affairs of life; they also build telescopes and satellites and accelerators, and sit at their desk for endless hours working out the meaning of the data they gather. The effort to understand the universe is one of the very few things that lifts human life a little above the level of farce, and gives it some of the grace of tragedy.” (pp. 86–87). This perspective is very different from that of the evolutionary optimists, but it does share a certain scientist-centric bias.

Tho’ Nature, red in tooth and claw
With ravin, shriek’d against his creed, –

Are God and Nature then at strife,
That Nature lends such evil dreams?
So careful of the type she seems,
So careless of the single life;

‘So careful of the type?’ but no.
From scarped cliff and quarried stone
She cries, ‘A thousand types are gone:
I care for nothing, all shall go.’

(from Alfred, Lord Tennyson, In Memoriam A.H.H., LIV and LV)

Midgley is particularly negative about the “red in tooth and claw” view of evolution, which emphasises competition as against cooperation. She sees the “selfish gene” concept popularised by Richard Dawkins as an example of this. In a 2007 interview with The Independent, she claimed “The ideology Dawkins is selling is the worship of competition. It is projecting a Thatcherite take on economics on to evolution. It’s not an impartial scientific view; it’s a political drama.


Honeybees are great cooperators (photo: Todd Huffman), and symbiosis is common in nature

Indeed, when an organism succeeds by occupying a new ecological niche (as, for example, urban coyotes do), there need not be any competition at all (at least, not initially).


A coyote in an urban niche (photo: Dru Bloomfield)

Extreme forms of sociobiology comes in for particular criticism from Midgley. They produce, she claims, bad science: “Environmental causes are neglected without any justification being given, and so are causes which flow from an individual itself during its lifetime … In human affairs, both these areas are of course of the first importance, since they cover the whole range of culture and individual action.” (p. 151). She is far from being the only scholar to make such criticisms.

Less common is the way in which she blames the growth of creationism on the rhetoric of sociobiologists themselves: “The project of treating the time scale of the Genesis story literally, as a piece of history, is an amazing one, which serious biblical scholars at least as far back as Origen (AD 200) have seen to be unworkable and unnecessary. The reason why people turn to it now seems to be that the only obvious alternative story – evolution – has become linked with a view of human psychology which they rightly think both false and immoral.” (p. 172).

See also this talk by Midgley, related to a more recent book on a similar topic:

In essence, Mary Midgley strongly supports scientists when they do science, but does not always accept the results of scientists doing philosophy (and especially moral philosophy). This little book sounds a helpful note of caution for those scientists who have become interested in philosophical speculation.

* * * *
Evolution as a Religion, by Mary Midgley: 4 stars

Science and Religion: a book review


Science and Religion: Are They Compatible? by Daniel C. Dennett and Alvin C. Plantinga

I recently read Science and Religion: Are They Compatible?, a brief (77 page) record and extension of a 2009 debate between atheist philosopher Daniel Dennett and Christian philosopher Alvin Plantinga. Many books of this kind exist, but this one is better than most, since both participants think and write quite clearly on the topic.


Daniel Dennett (left, photo: David Orban) & Alvin Plantinga (right, photo: “Jonathunder”)

In a sense, the compatibility between Science and Religion is an obvious empirical truth. Science began in the Age of Cathedrals. The philosopher Alfred North Whitehead suggested that “the greatest contribution of medievalism to the formation of the scientific movement … must come from the medieval insistence on the rationality of God” (Science and the Modern World, p. 15). Even today, a significant number of scientists in the West are Christian (about 30%, according to this study). Globally, there are also very substantial numbers of Muslims and Hindus.

There may, of course, be conflicts between specific scientific theories and specific interpretations of religious writings. In Galileo’s time, the Ptolemaic astronomical system and the Tychonian astronomical system were seen by many Catholic theologians as compatible with their interpretation of Joshua 10:13, while the Copernican astronomical system was seen as incompatible. The Tychonian and Copernican systems were both roughly consistent with empirical data (the Tychonian system was less elegant, but the Copernican system predicted stellar parallax, which was not observed until the 19thcentury). The Copernican system won out, though the Jesuits taught the Tychonian system for some time. Today, both the anti-Copernican interpretation of Joshua 10:13 and the concept of an absolutely stationary “centre” of the universe have been abandoned, and so conflict no longer exists in that field.


The Tychonian astronomical system

In this book, Plantinga (p. 2) re-focuses the question on the compatibility between, on the one hand, generic Christianity (as defined in, for example, C.S. Lewis’ Mere Christianity) and, on the other hand, evolutionary theory (the “hot topic” of recent centuries). Even here, the existence of believers in theistic evolution seems to make the compatibility an empirical truth. C.S. Lewis once wroteI believe that Christianity can still be believed, even if Evolution is true.” A recent poll in the US found the following beliefs among college graduates and postgrads (N = 269):

Plantinga argues (p. 4) that the only evolutionary concept incompatible with Christianity is the idea that mutations are “unplanned and unintended” (theistic evolution, of course, takes mutations to be divinely guided), but that truly random mutations are not actually essential to the theory. In support of this, Plantinga (p. 6) quotes Ernst Mayr: “When it is said that mutation or variation is random, the statement simply means that there is no correlation between the production of new genotypes and the adaptational needs of an organism in the given environment” (Toward a New Philosophy of Biology, p. 99). Dennett agrees (p. 26) with the compatibility between evolution and theistic belief (though himself denying theism for other reasons), and also agrees (p. 29) that evolution does not require mutations to be truly random. As evidence of this (p. 30), Dennett points at computer simulations of evolution, where things evolve in spite of the use of pseudorandom number generators which are, in fact, completely deterministic.

Having so quickly come to agreement on the main topic, much of the book is concerned with naturalism in Science and with the rationality of religious belief in general. Plantinga attempts (p. 19) an interesting argument suggesting that atheistic evolution gives no foundation for Science, in that we have no reason to believe that the beliefs in our brains are true (merely that they are adaptive). Dennett disagrees strongly here (p. 35) arguing that evolution has made our brains “highly reliable truth trackers.” It’s not at all obvious to me that this is true (we may well have evolved, for example, to have false but beneficial beliefs about other people), and Dennett provides little real argument for his position here (referring primarily to his other books on the topic).

Dennett goes on to argue (p. 31) that “naturalism is tacitly assumed … throughout scientific investigation.” He uses what is in my view a somewhat shaky courtroom analogy (courts will acquit a murder suspect if accidental death is a viable alternative, but do not “tacitly assume” that accidental death is the only option). If Dennett means metaphysical naturalism (as Plantinga does), his point is clearly empirically false, given the large number of religious scientists, and Plantinga points that out (p. 42, p. 63). If Dennett means methodological naturalism, it’s probably true, but not particularly relevant to the point being argued. Dennett’s response to Plantinga (p. 48) doesn’t really clarify the issue.

Towards the end of the book are arguments for and against the ideas of Michael Behe which I found less interesting (it might perhaps have been more interesting had Behe himself been involved, but there is probably little new to say about his ideas). The surprising thing about this book was discovering the extent of agreement on the main topic. On theism generally, Plantinga and Dennett were always going to have radically different perspectives, for reasons outside the scope of this book, and rehashing those perspectives provides few new insights. To quote Teilhard de Chardin, “after close on two centuries of passionate struggle, neither science nor faith has succeeded in discrediting its adversary.”

Plantinga’s final conclusion is that “there isn’t any conflict between Christian belief and science in the area we’ve been investigating. Christian belief and evolutionary science are entirely compatible. Perpetuating the myth that there is conflict, furthermore, is harmful both to religion and to science.” Dennett accepts this compatibility but denies that Plantinga has proved the stronger claim that “Science depends on theism to underwrite its epistemic self-confidence.” Neither author follows up on the question of how the myth of conflict might be harmful.

See also plurilogue.com, skepticfreethought.com, thinkingfaith.org, and The American Scientific Affiliation for other reviews of this book.


Science and Religion by Daniel C. Dennett and Alvin C. Plantinga: 3½ stars