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| Knotty Pine and Corroding Coins
In his Metanexus critique of William Dembski, Matt Young presented an example that purportedly demonstrates how complex, specified information may arise through the combined actions of chance and natural law. He describes a thought experiment involving imaginary coin-tossing machines. Here is the relevant passage:
"Natural selection. Suppose now that we have a very large number, or ensemble, of coin-tossing machines. These machines toss their coins at irregular intervals. The base of each machine is made of knotty pine, and knots in the pine sometimes leak sap and create a sticky surface. As a result, the coins sometimes stick to the surface and are not tossed when the machine is activated.
"For unknown reasons, machines that have a larger number of, say, heads have a lower probability of malfunctioning. Perhaps the reverse side of the coins is light-sensitive, corrodes, and damages the working of the machine. For whatever reason, heads confers an advantage to the machines
"As time progresses, many of the machines malfunction. But sometimes a coin sticks to the knotty pine heads up. A machine with just a few heads permanently showing is fitter than those with a few tails permanently showing or those with randomly changing permutations (because those last show tails half the time, on average). Given enough machines and enough time (and enough knots!), at least some of the machines will necessarily end up with five heads showing. These are the fittest and will survive the longest.
"You do not need reproduction for natural selection. Nevertheless, it must be obvious by now that the coins represent the genome. If the machines were capable of reproducing, then machines with more heads would pass their "headedness" to their descendants, and those descendants would outcompete machines that displayed 'tailedness.'
"Thus do we see a combination of regularity (the coin-tossing machines) and chance (the sticky knots) increasing the information in a genome."
Let us neglect the question of where these machines and coins came from in the first place, though it is obvious that they cannot be accounted for purely in terms of natural processes like chance and law. A careful exploration of these machines illustrates how Young is cheating in his example by smuggling in the very information his machines ultimately produce.
Begin by imagining a slightly altered scenario. Young postulates that if a coin gets stuck with tails facing up it will corrode and damage the machine. But imagine instead that it is not tails, but heads that tend to corrode when exposed. In this case, the system will select for a string of all tails.
But now, imagine that we arbitrarily determine which side of the coin corrodes for each coin. Thus, we might arrange the coins such that the first one will corrode if heads are exposed, while the second coin corrodes if it is tail-up, and so on. In this case, the system will simply tend toward whatever sequence we pre-determine will be selected for by our choice of the corrosive side of each coin. In other words, by adjusting the parameters of the coin tossing system we can cause any possible sequence of heads and tails to occur, and whichever sequence we select is the one that will inevitably be produced. By making our choice of parameters (especially in selecting which side of each coin will be corrosion-sensitive) we are giving the system all the information it eventually outputs.
To see this clearly we need the concept of a fitness landscape. Imagine that all possible sequences of heads and tails (for a given sequence-length) are represented in a flat plane; in the terminology of William Dembski this is a reference class of all possible outcomes.[1] Now, we can further imagine a three-dimensional mountainous landscape hovering over this plane of all possible outcomes. This landscape is known as a fitness function and it assigns a (fitness) value to each possible set of heads and tails. Now the interesting thing is that the fitness function can reach a maximum over any sequence. It is fully arbitrary; there is nothing in the sequences of heads and tails themselves that determines how "fit" they are. By choosing which sides of coins will corrode, we have seen that we can pre-determine which sequence the system will select for. In other words, we were setting up the fitness function such that a large mountain peak centers over the desired sequence.
Now let's consider the concept of information. Information, in Shannon-Weaver theory, is simply the ruling out of possibilities. This is often described as a reduction of "uncertainty" which correlates well with our intuitive sense that information is meaningful precisely because it rules out certain things. To know a piece of information is to know what things are precluded by its truth. Furthermore, information is quantified by how many possibilities are ruled out, so to gain more information requires that one rule out more options. In mathematical terms, this ruling out of possibilities is captured in a probability measurement (information is defined as -log(P), where the logarithm is to the base 2). This makes sense because with more possibilities, the chance of selecting any given option becomes more improbable and hence that selection generates more information. In other words a more improbable event rules out a larger set of options than a more probable one, and consequently creates more information.
Now apply this to Young's original coin-flipping machines (selecting for a sequence of heads). The machines begin by randomly flipping coins and over time, by the action of selection, they produce a single sequence of all heads. They begin with a great number of options and end up with all but one ruled out. In excluding possibilities these machines are producing information. But where did that information come from?
It is clear that the machines simply followed the fitness function to the optimum sequence consisting entirely of heads. But the fitness function had to come from somewhere, and it is not too much of a stretch to see that there is also a reference class of all possible fitness functions from which this particular fitness function was drawn (remember, the fitness function can center upon any sequence of heads and tails and is fully arbitrary). Thus, the selection of this fitness function must have generated information by ruling out all other possible fitness functions. So the information output by the system was first generated by Young's choice of fitness functions, which set up the machines to transmit that information to the outcome sequence.
How much information was generated by the choice of fitness function? Was it greater or less than the amount of information generated by the coin-flipping machines themselves? It turns out that the class of possible fitness functions is much greater than the class of possible coin sequences. There are multiple mountain peaks for each coin sequence: some sharp and steep, some gentle and low. Some fitness functions may have multiple peaks and low-lying foothills (we can generate multiple peaks by having some coins be completely non-corrosive, or only corrosive in combination with some particular combination of heads and tails on other coins; the steepness can be adjusted by altering the degree of corrosiveness of the coins). And, of course, there are vast numbers of fitness functions that will have absolutely nothing to do with our coin-tossing machines because they measure parameters that are irrelevant (the biological fitness of finches in the Galapagos or the LSAT scores of students applying to law school are two examples).
In choosing a fitness function for our coin-tossing machines, we first had to narrow down the class of all possible fitness functions to those fitness functions that are relevant to coin-tossing machines. Even within that subset of fitness functions the choices are vast, far more than possible coin sequences. Averaged over all these potential fitness functions, no coin sequence will be favored over any other, so any biasing of the outcome will require selecting just one fitness function from this entire collection. Furthermore, not just any fitness function that centers on the desired sequence will do. Many will be too sharp and steep for the mutation and selection algorithm to work effectively. In order to be effective, the fitness function must be smooth and should give useful information over the entire range of possible sequences. In practical terms, this means that the mountain peak should be spread over the entire set of possible sequences, gradually rising from the edge of the reference class of possibilities to a single, universal maximum over the target sequence. If there are large areas of flat space around the base of the mountain, a selection algorithm will not be able to distinguish between those sequences in the flat area and the search will be no better than blind search until the edge of the mountain is found by chance and selection can begin to work its magic. In the extreme case, in which the mountain is a single point rising from an otherwise flat plane, the evolutionary algorithm is no better than blind search-the target sequence (and the associated mountain) can only be found by randomly moving around in the flat plain.
In other words, the fitness function needs to be properly targeted and properly shaped to allow the evolutionary process to operate. This targeting and shaping of the fitness function is itself an instance of ruling out possibilities and generating information. Notice that Young's coin-tossing machines utilize precisely the finely-tuned fitness function described above: it is fully informative for every sequence, having a gradual rise from zero heads (lowest fitness) to all heads (highest fitness), with intermediate values for intermediate numbers of heads. This produces a smooth, gradually rising function that targets the desired sequence and allows the mutation and selection process to work with maximal efficiency.
Furthermore, selecting a single fitness function from this class of all possible fitness functions generates more information than the machines generate in following that fitness function to the target sequence of all heads. Remember, the reference class of possible fitness functions is much greater than the reference class of possible coin sequences, so ruling out all but one of them is a much more informative event than ruling out all but one coin sequence. In other words, the information has been displaced. Yes, the machines generate information. But Matt Young has generated even more information in setting up those machines than they ever output. The information has not been generated de novo; rather, it has been conserved from its initial input to its output.
Now take these ideas into the realm of biology. Consider the intensively studied bacterial flagellum.[2] This complex biological structure is a micro-scale molecular motor that the bacterium uses to propel itself through its environment. It consists of an acid-powered engine, a drive shaft, U-joint, stator, rotor rings, and propeller. It is a highly integrated system that requires each of fifty or so different proteins in order to assemble properly and function. Furthermore, there are many bacteria that entirely lack a flagellum and are nonmotile, and they survive and reproduce perfectly well. Thus, while there may be a fitness benefit to having a flagellum, there seems to be no universal drive to acquire a flagellum since not all bacteria have one. This is a key distinction between biological organisms and Young's machines that inevitably produce the sequence favored by the pre-selected fitness function. Natural selection operates in a very different way than the fitness functions of the coin-flipping machines because it does not have a predetermined outcome. The complexities of the real-world fitness function are dependent on the environment and are difficult to conceptualize in a concrete way. However, it is abundantly clear that there is no pre-determination as in Young's coin-flipping machines. Furthermore, experiments and theory suggest that the flagellum is targeted by a sheer, sudden mountain or plateau rising from a flat plain-the sort of fitness function that is not explored well by evolutionary processes.
In order for the fitness function to have smoothly sloped sides rather than sharp cliffs, there must be a way to gradually build a flagellum with fitness increases at each step as parts of the system are added. It is common for biologists to do mutation experiments in which they destroy some component of a molecular system and see whether it still works; with the flagellum they have found that all the components are required for function. In other words, the intermediates are non-functional and thus convey no selective advantage. In contrast to the coin-flipping machines in which a sequence has progressively greater selective value the more heads it contains, there is no advantage in having a nearly complete flagellum. The system doesn't function until all the parts are assembled, so selection cannot preserve the intermediates and work gradually toward the flagellum. The lack of function for intermediates means that the functioning flagellum is the only high point on the fitness landscape; the surrounding terrain is flat and uninformative to the selection process. Only chance, stumbling upon the flagellum unaided, is capable of generating the flagellum. In such a situation we can assess the probability of chance putting all the pieces together, and the probability is far below what is reasonable to occur even once in the entire history of the universe. Thus, design theorists claim that the bacterial flagellum is beyond the reach of chance and law.
Many will accuse me of misrepresenting the Darwinian process. The flagellum wasn't produced purely by chance. Rather, the components were pre-existing in the cell and were co-opted to form the flagellum at some point in the past. To get around the improbabilities of a pure chance assembly of the flagellum system-a scenario all Darwinists reject as simply too improbable-the co-optation model hypothesizes that all the proteins were already present and performing different (non-flagellum) functions in the cell and evolution utilized these pre-existing components to cobble together the flagellum. However, this model actually makes it more difficult to generate the flagellum because it postulates that all the requisite proteins were adapted to other functions prior to being incorporated into the flagellum. This implies that the proteins would require extensive revision before they would be properly suited to work together in the novel flagellum. Furthermore, the fact that all fifty proteins are crucial for the function of the flagellum implies that the proteins must all have shifted their structure and function at the same time to come together into the new flagellum system-and this shift somehow did not disrupt any essential cellular process previously performed by these proteins. By hypothesizing that precursors to flagellum proteins had their own specialized functions the co-optation model creates a very large gap between the old system(s) and the new system-a gap that must be crossed in one step to maintain selectable function. It is this sudden, coordinated shift in protein function that is the major problem with the co-optation hypothesis. The beauty of Darwin's theory was that it replaced miracle with mechanism and gave a law-like account of how the species developed. But here we see that the Darwinian explanation of the bacterial flagellum replaces mechanism with miracle, a collective shrug and vague gesture toward a chance macromutation that modified and brought the components together in one fell swoop. The co-optation model doesn't alleviate the improbability of the flagellum's origin; it actually embraces an enormous leap of chance as a key element of the scenario.
For concreteness, consider an example. Think of a man-made outboard motor. This system contains many of the same structures found in the bacterial flagellum: a motor (including stator, rotor, and acid-powered drive), drive shaft, u-joint, and propeller. Now, imagine starting with a basic rowboat and trying to evolve an outboard motor via the co-optation model. Perhaps, somehow, the metal outer skin of the boat peels up in the back and this forms a useful rack for a fishing pole, and is available to provide the internal support and external protective casing for the motor. Perhaps a support rod works loose from the hull and is available to be made into a drive shaft. But how do we move on from here to build up the motor, in functional steps, from existing parts? The problem is this: the various parts are already adapted to their old functions. To build an outboard motor, the old functions must be replaced by new functions. New functions require modifications of the old parts, and since the motor system doesn't work until all the parts are assembled, we inevitably need a large amount of coordinated change in various components before we can build the new system. For instance, the peeled-away metal on the back (previously adapted to form a watertight hull) will have to undergo extensive modification, including careful bending or shaping, and drilling holes in appropriate places to support motor components (all without letting the hull become leaky). The support rod from the hull, destined to become the drive shaft, will also need modification for attaching gears and the universal joint (and the removal of the support rod must not weaken the structural integrity of the boat). And so on.
The bottom line is that there is no smooth gradient leading to a functioning outboard motor just as there is no smooth gradient to the production of a bacterial flagellum. This conclusion is supported by knockout experiments confirming the functional holism of the flagellum, and also by theoretical considerations of the physical, chemical, and engineering requirements for selectable motility. However, it is very interesting to consider what a smooth, gradually sloping fitness function capable of generating a bacterial flagellum would have to look like. We know it would have to select for intermediate structures and proteins to be used in the future flagellum. But the intermediate structures do not function, so the fitness function must somehow make it possible to preserve these useless, functionless proteins until the entire flagellum has been generated in small steps over many generations. Under such conditions it would be reasonable to expect the flagellum to arise with high probability, but the fitness function required is so obviously contrived as to constitute a remarkable instance of teleology: obviously, nature would have to want to produce the flagellum and to be willing to do a lot of counterproductive work to get that goal accomplished. Furthermore, the fitness function in this example contains all the details of a bacterial flagellum-nothing is output that wasn't originally present in the fitness function. This is precisely how Young's coin-tossing machines operate, and this is precisely why they fail as an example of how biological information can be generated by Darwinian processes. They incorporate a non-Darwinian teleological fitness function that sneaks in the very information they output.
In short, a smooth fitness function for a bacterial flagellum is a profoundly non-Darwinian function that specifically guides the search process, targeting a distant goal that selection can work toward. Natural selection, on the other hand, does not have a distant goal in mind, does not target any particular outcome, and relies instead upon chance for innovations that are preserved by selection. In other words, the Darwinian mechanism is extremely information-poor and relies upon chance to produce its information in small bits, by gradual steps. The problem comes when we find biological systems that cannot be assembled by gradually adding tiny bits of information and require instead multiple coordinated changes before selectable advantage arises. These sorts of biological structures require large amounts of information be generated in a single step. This is the key problem facing a Darwinian explanation, and is the reason why some doubt the efficacy of natural selection in producing these systems.
The challenge, and the essence of Darwin's theory, is to show that information can be built up gradually, step-by-step, from initial conditions lacking information. In Young's example information is conserved; we can easily trace the flow of information from the input parameters to the output sequence of heads. But this does nothing to address the central claim of the Darwinian mechanism-which is that information can gradually accrue from simple and information-poor beginnings. If Matt Young wants to demonstrate how information arises in the first place, rather than how it can be transmitted once it has arisen, he needs to do better than talk about knotty pine and corroding coins.
John Bracht Jan. 28, 2002 (revised May 12, 2002)
References:
1 See William Dembski, No Free Lunch, Chapter 2. (New York: Rowman and Littlefield, 2002.)
2 See, for instance, Michael Behe, Darwin's Black Box (New York: Simon & Schuster, 1996), 70-72 and William Dembski, Chapter 5 of No Free Lunch.
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Published 2002.05.29
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