In the recently released A New Kind of Science, Stephen Wolfram posits a few radical ideas about the evolution of individual traits in species, and further about differentiation of the species themselves. From his introduction to the section, on page 383:
Biological systems are often cited as supreme examples of complexity in nature, and it is not uncommon for it to be assumed that their complexity must be somehow of a fundamentally higher order than other systems. And typically it is thought that this must be a consequence of the rather unique processes of adaption and natural selection that operate in biological systems. ... what I have come to believe is that many of the most obvious examples of complexity in biological systems actually have very little to do with adaption or natural selection.
Like I said, pretty radical ideas, and counter (or at least perpendicular) to what science has been working with for, oh, the past 150 years or so. Indeed, the great Charles Darwin said himself in On the Origin of Species by Means of Natural Selection, on page 83:
It may be said that natural selection is daily and hourly scrutinising throughout the world, every variation, even the slightest; rejecting that which is bad, preserving and adding up all that is good; silently and insensibly working, whenever and wherever opportunity offers, at the improvement of each organic being in relation to its organic and inorganic conditions of life.
Or in other words, Darwin sees the complexity of biological systems building upon itself every day, as subtly better variations survive while subtly lesser variations perish. In this way, living organisms adapt to their conditions, ever so slowly reaching toward perfection in their niche, while the organisms around them are doing the same things and thus ever so slowly changing exactly what that niche consists of. It is a slow dance of blooming complexity, entropic explosion at a snail's pace.

This contrasts with one of the primary findings presented in Wolfram's book, that complexity or random behavior is probably as likely to have arisen naturally in any system as it is to have been explicitly introduced. Wolfram shows how even painfully simple sets of rules, like those found in a one-dimensional cellular automaton, can quite often produce extreme degrees of complexity, even with equally simple starting conditions. On page 388, Wolfram writes:

On the basis of traditional biological thinking one would tend to assume that whatever complexity one saw must in the end be carefully crafted to satisfy some elaborate set of constraints. But what I believe instead is that the vast majority of the complexity we see in biological systems actually has its origin in the purely abstract fact that among randomly chosen programs many give rise to complex behavior.
The practical upshots of this are that A) changes in an organism's structure, even fairly radical ones, can often be explained by a single, simple mutation somewhere along the line; and B) changes aren't always, or even often, going to lead towards some recognizable goal state, but instead may be considered well and truly random. Both of these taken together devalue the notion of natural selection by assigning it not the role of arbiter of biological change, but instead the role of janitor of unworkable variations. If we take Wolfram's viewpoint as fact, than we must in so doing deny Darwin's (p. 103) assertion that:
Slow though the process of selection may be, ... I can see no limit to the amount of change, to the beauty and infinite complexity of the co-adaptation between all organic beings, one with another and with their physical conditions of life, which may be effected in the long course of time by nature's power of selection.
Wolfram isn't finished, though. He has further argument against natural selection being the cause of the complexity we see in nature every day. His argument is that changes made to a complex system will affect more than one trait, and so it is difficult for natural selection to act consistently with them -- or in other words, random searches (e.g. random mutations) usually just get stuck, or at best give very slow progress to any optimal configuration. His conclusion from that fact -- and problem with using random searches is factual rather than conjecture on Wolfram's part, see also NP-Complete -- is that when natural selection does actually take place, it can only select for relatively simple traits, like appendage length or exact shade of coloration. He justifies all of this with the argument that trying to get random behavior to fit a given model is hopeless, as well stated (though cushioned in weird "program" terminology) on page 393:
In a sense it is not surprising that natural selection can achieve little when confronted with complex behavior. For in effect it is being asked to predict what changes would need to be made in an underlying program in order to produce or enhance a certain form of overall behavior. Yet one of the main conclusions of this book is that even given a particular program, it can be very difficult to see what the behavior of the program will be. And to go backwards from behavior to programs is a still much more difficult task.
To summarize, the lines have been drawn thus: Darwin says that natural selection causes complexity by continuously moving organisms into tighter synergy with their environment, necessitating said complexity. Wolfram says complexity arises naturally with even the smallest change in the organism's genetic makeup, and that natural selection serves mainly to rein it in by culling the unworkable variations.

So, who is right and who is wrong? Of course, the easy answer is "both of them."

Wolfram, for all of his years of research and almost breathtaking hubris, may be overestimating the relevance of his discoveries in the mathematical realm to the realities of the biological. Even given that huge complexity can blossom from a relatively simple change in the rules, there's little evidence that changing a protein to nonworking configuration (a rare but obvious mutation), or even changing it to a subtly different-working one (even rarer) is enough of a change to cause this chance in complexity. In fact, as seen in many, many experiments, knocking out a gene or two can quite often leave the system in more-or-less perfect working order, not always leaving the organism with a "disease" or other (obvious) systemic problem that would be selected against in nature.

Darwin, for having written perhaps the most important work in all of Western science, had no way of anticipating some of Wolfram's more radical findings about the nature and causation of complexity. Without regard to that, he also may have given too much credit to subtle changes over time versus more striking changes happening in a few generations -- the now-accepted idea of punctuated equilibrium being closer to Wolfram's model than Darwin's, and so forth. Regardless of these shortcomings, he was infinitely closer to the truth than his Creationist contemporaries, and his work is still deservedly uniformly salient among those who study science.

I'll close with Darwin's final recapitulation of his theory, the theory upon which (like it or not) the whole of Wolfram's speculation rests. It is taken from the last paragraph of his masterwork, on page 403:

Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals, directly follows. There is a grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved.

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