Wednesday, February 24, 2010


In this post atheist Larry Moran criticizes attempts to “prove God” (sic; how can we expect to “prove God” if Larry can’t even expect to “prove evolution”?) from the appearance of design. In his opinion life shows signs of not being designed: He is probably thinking of some of those biological structures that look as though they have been cobbled together as a result of the accumulation of historical accidents. The end product is the kind of legacy architecture one sees in old towns where the next development is constrained by and has to work from the fiat of what has gone before. (If you ask Larry he could probably reel off a whole list of biological examples) In Larry Moran’s mind this concept of haphazard accumulative development is set against the notion of the intelligent planner who starts from a blank sheet and can therefore design a much more direct solution to a problem, a solution unencumbered by past random legacies.

There is, needless to say, a hidden counterfactual theology in the atheism here; namely the assumption that God is a kind of technical whiz who sits down like a human engineer with a virgin drawing board in front of Him and designs his best solutions. (Ironically many anti-evolutionists conceive a similar concept of designer). But perhaps God is a story teller first and an engineer second? Clearly ours is a story, a cosmic story of change, evolution and contingency snatched from the platonic limbo land of possibility, that can and has been told. Perhaps like a human author Deity has sat down not in front of the engineer’s drawing board, but rather in an armchair beside a fire and told our story. If God is God, infinite and inscrutable, how can we be so sure (and naïve) about His motives?

But whatever; at the end of the day we are always left with the Logical Hiatus of having something for nothing; why is there something rather than nothing? Where, if it exists, is the logical necessity to support the apparent contingency of our cosmos? So, in a more abstract sense than we find in the engineering metaphor we seem to have a design question, a question of, as Paul Davies puts it in the “Cosmic Jackpot”: Why this universe and not another? Is it all just random? But what is randomness other than a mathematical description of a particular class of pattern, a pattern that creaks under a huge burden of complex brute contingency. The big question then is who or what sources such complex patterns? Or is the source a hidden ontology that somehow reifies our notion of “chance” in the sense of being a source that can make choices mindlessly?* But to envisage such a source of mindless purposelessness working behind a facade of pattern is itself a perverse kind of theology; an “atheology” that makes the ontology of chance into a god and stultifies further questions because it believes there is neither point nor meaning in asking them. This is the theology of the absurdity of it all.

* What does it mean to make choices without mind? It can’t be randomness because randomness is to do with pattern description and as such makes no necessary allusion to the mechanism of “choice” that sources the pattern. As human minds we can only empathize with mind as the source of choice, so it seems that an ontology of mindless “chance choices” is forever utterly beyond our understanding; we can no more understand what it is like to be a mindless “chance source” than we can understand what it is like to be an ant.

Friday, February 12, 2010

Thermodynamics and Evolution – Again.

Is the relative statistical weight of life containing states great enough at some point in the history of the universe to give those states a realistic probability?

(See also

Whether or not abiogenesis and evolution are facts, there is one argument that the anti-evolution ID theorists are ill-advised to use: The argument that abiogenesis and evolution violate the second law of thermodynamics. In two posts on Uncommon Descent (here and here) we find Granville Sewell still publicizing this erroneous view. The line of argument used by Sewell is based on the observation that a local increase in order can only occur if negative entropy is transmitted across the boundary of a locality into a system (that’s the equivalent of saying positive entropy is exported out of the system). Sewell identifies this negative entropy (or “negentropy”) with the input of information across the boundary of the system. Therefore in his opinion it follows that some kind of information must be injected into the subsystem from without if the ordered structures of life have any chance of coming into existence. Ergo, since abiogenesis and evolution make no recourse to the input of information (or negentropy) beyond the confines of the Earth it follows that thermodynamics prohibits the formation of organic structures.

The observation that local increases in order must be accompanied by the transmission of negentropy into the locality is, of course, correct, but Sewell seems to hold the erroneous view that this negentropy must be reified as explicit information crossing the boundary into that locality. In Sewell's view this explicit information is the only way of offsetting the extremely small probabilities associated with organic structures. He rightly observers that at the bottom of the second law are probabilities, but he neglects to say that these probabilities are conditional probabilities. True, living structures are such a tiny class of what is possible that it is clear they have a negligible absolute probability of formation. But in reality the development of living things is a conditional probability, a probability conditioned on the given physical regime of the cosmos. Given this regime here is the big question: Is the conditional probability of evolution and abiogenist raised to realistic levels by physical conditions alone? If so then the “information cost” of this high conditional probability must reside in the improbability of the physical regime that supports abiogenesis and evolution.

Now consider two scenarios:

ONE) Firstly crystallization. Speaking in absolute terms probabilities favour crystallization even less than they do biological structures; with respect to the huge mathematical space of platonic configurational possibility the high organization of crystals is very a unrepresentative arrangement of particles; the low statistical weight of crystal configurations, a lot lower, in fact, than even the statistical weight of living structures (which can be realized in enumerable ways) ensures that crystals have a very low absolute probability. However, in real physical terms the relatively tiny statistical weight of the class of crystals is more than compensated for by the constraint imposed by the laws of physics, a constraint which eliminates huge numbers of cases, thus considerably raising the conditional probability of crystallization. For under the right physical conditions crystals easily form: A solution with the right concentration, temperature and pressure results in a bit by bit construction of the crystal as atoms randomly find their place in the crystal lattice and are fixed into position. This considerable increase in local order is offset by the appropriate entropy transactions with the surroundings, thus preserving the overall upward trend in entropy.

There is one important remark about crystallisation that I would want to make here. As I have just said entropy is exported out of the crystal locality thus preserving the second law. Another way of looking at this is to think of negentropy crossing over into the locality, increasing the order of this locality. But in fact if we look at the boundary of the locality closely we find nothing resembling the import across this boundary of instructions telling the atoms how to assemble; the assembly is inherent in the information contained in the laws of physics which constrain the locality sufficiently to render an absolutely improbable configuration very probable.

TWO) Now consider the case of a seed landing in a locality and a plant consequently growing. The growth of the plant constitutes a local increase in order. As in the case of crystallization this local increase in order is offset by the appropriate entropy transactions with the surroundings thus preserving an overall upward trend in entropy. However, this system is very different from crystallization on two counts. Firstly, the plant is not a manifestation of simple order like a crystal; it is of course very ordered but it is a very complex form of order at the same time. Secondly, the elementary entropy transactions with the surroundings are not the only thing that crosses the boundary of the locality: From the outset there is the input of a seed which is a very complex piece of genetic machinery and information. Thus, this system is very much in line with Sewell’s expectation that the locality needs some fundamental informational input before a highly ordered yet very complex structure can be constructed.


We have above then two scenarios where there is a local increase in order and yet no violation of the second law of thermodynamics. Both systems represent a generalized form of “crystallisation” in the sense that an ordered structure is built up atom by atom, molecule by molecule, as randomly jiggling particles find a place in the structure and then are locked into place. But, of course, there are obvious differences between these two forms of “crystallization”. For mineral crystallization the “information” present in the local laws of physics is sufficient to “instruct” the process, whereas for the “crystallization” of a living structure the complex machinery in the seed packet is needed. For mineral crystallization the very regular and simple order of the crystal is in absolute terms highly improbable, but that improbability need only be bought at the price of a relatively elementary set of physical equations; a scenario that presents no obvious intuitive problem to us. On the other hand the growth of complex flora requires the laws of physics to be supplemented by the input of the complex structure found in a seed; once again a scenario that presents no serious intuitive problems for us.

In terms of absolute probabilities both mineral crystallization and the growth of an organism (in this case a plant) represent the appearance of highly improbable structures. But in terms of conditional probabilities both processes have high probabilities; for mineral crystallization a high conditional probability is bought at the price of the laws of physics and the given boundary conditions of the physical system. In the case of plant life the boundary conditions are supplemented by the complex seed packet that boot straps the growth of an organism. Taken together the laws of physics and the boundary conditions of these two systems have the effect of putting a very tight constraint on their respective systems, so tight in fact that in spite of the general trend of an overall increase in disorder there is a high (conditional) probability of a very unrepresentative, albeit localized, configuration making an appearance. The constraints on the systems have the effect of removing myriad mathematically possible scenarios so that amongst the remaining class of possibility, the statistical weight associated with the development of localised order is relatively high, thus considerably enhancing the probability of the formation of that local order.

So given these two scenarios, is it at least conceivable that some combination of abiogenesis and evolution can result in the “crystallization” (metaphorically speaking) of living things and yet not violate the second law of thermodynamics? The trouble is that neither of the above two scenarios do exactly what is required of abiogenesis and evolution: Although mineral crystallization only buys order from the laws of physics and simple boundary conditions, the result is a very bland and dead form of order. In contrast the “crystallization” of actual living things, in all cases we observe, supplements the laws of physics with a complex boundary condition in the form of the input of an intricate genetic machine needed to seed the formation of life. If the concept of evolution and abiogenesis are to work as conventionally envisaged then they must work less like the concept of seed growth, and more like crystal growth, where the only information resources are some simple boundary conditions and the laws of physics. The question then is this: Can life originate without the boundary condition of an initial input of complex informational machinery? Can we get ordered complexity from simple laws and algorithms?

If evolution and abiogenesis are the source of living complexity and diversity then on current theories they are a form of generalised “crystallization” resourced only by the inherent information present in some simple starting conditions and the laws of physics. It is this contention that sticks in the gullet of the anti-evolutionists; they do not believe that such is possible. Those anti-evolutionists who have followed the work of William Dembski have conflated Dembski’s otherwise valid conservation of information argument with a conservation of complexity and concluded that the complexity of life can’t come from simplicity. In contrast I hardly need point out that the militant atheists love the idea of complexity coming from simplicity, perhaps for two reasons: 1. The origin of life is then apparently sourced in “mindless simplicity” 2. The notion of complexity coming from simplicity can be extended and with a bit of imagination it might be mooted that complexity can come from simply nothing! Although the idea of getting something for nothing is very suspect it is not true that only complexity comes from complexity; as I have remarked many times in this blog, simple algorithms and laws can generate complexity, but the big question is: Can they generate living complexity?

Crystallisation works because each stage in the crystal’s formation is a stable structure; if the current crystal contains N atoms and is stable, then so is the next crystal structure of N+1 atoms and so on in an inductive way. Each structure in this succession of structures is only separated by an atom or two and thus they effectively form a connected set of stable structures in morphospace; in other words crystals are reducibly complex. This connected object in morphospace is an implication of the laws of physics. These laws act as a constraint removing such an immense class of random possibilities that relative to this much reduced class the statistical weight of an outcome containing crystals is considerably raised. The second law of thermodynamics is an outcome of random thermal agitations ensuring that a system migrates towards macro states with the greatest number of microstates (that is, macro states with the greatest statistical weight); if because of the constraint of physics the macro states with the greatest statistical weight contain localized order then that localized order will actually be favoured. Thus crystal formation does not violate the second law of thermodynamics because the laws of physics eliminate so many mathematically possible micro states, that as the system moves toward the macro state with the greatest statistical weight, it moves toward a system that includes local ordering.

Conventional abiogenesis and evolution do not assume the input of explicit information; rather the information is conjectured to be implicit in the laws of physics. Therefore the theoretical precondition of these processes is similar to that required by crystal formation; namely, a connected set of stable bio-structures in morphospace separated by gaps small enough to be jumped by random thermal agitation and/or random mutations; that is, the theoretical precondition for the “crystallization” of life is that bio-structures are reducibly complex. As for crystal formation this kind of evolution/abiogenesis does not violate the second law of thermodynamics because the physical regime is conjectured to eliminate so many mathematically possible micro states that scenarios where there is a local increase in order occupy a considerably larger relative proportion of the now constricted space of possibilities, thereby much enhancing their probability. If at this point it seems intuitively unlikely that the second law of thermodynamics would allow the formation of such complex ordered structures, we now recall the growth of a plant from a seed: Clearly thermodynamics does not prohibit the growth of a complex organism. As for crystal growth so it is for organic growth: The twin physical constraints of boundary conditions and the laws of physics eliminate so many mathematically possible micro states that the local increase in order entailed by organic growth becomes a considerably larger relative proportion of the now constricted space of possibilities, thereby much enhancing its probability. However, it is clear that plant growth depends on the boundary condition of the initial input of organized complexity in the form of a seed: But then abiogenesis and evolution also depend on an initial input of complexity; namely, a complex arrangement in morphospace whereby stable structures form a connected set, a structure that would have to be entailed by the laws of physics. This arrangement in morphospace serves a similar purpose to the complex genetic mechanisms found in a seed. This invisible mathematical structure (if it exists) tends to confound the anti-evolutionist’s expectation that the information needed to assemble complex objects can only be found reified in complex material objects.

I must qualify the foregoing by admitting that it not at all clear that the conjectured structures in morphospace required by evolution and abiogenesis actually exist, or even can exist. Moreover, it is not at all clear that the laws of physics, as we currently understand them, imply that biological structures are reducibly complex. The anti-evolutionist’s contention that biological structures are in fact irreducibly complex may still be true. But the point I’m making here concerns the second law of thermodynamics and not (ir)reducible complexity. That point is this: If biological morphospace is populated by a set of reducibly complex stable structures (that is structures separated by small increments of change) then as in crystal formation abiogenesis and evolution would not violate the second law. Moreover, the “crystallization” of life would require no explicit information directing the process to pass through the boundary of an evolving locality in order to seed it. The information required for life would, on this conjecture, be implicit in the laws of physics in as much as that those laws entail the required arrangements in morphospace.

That simple laws of physics are information laden and can potentially define something as complex as the arrangement of structures in morphospace is another concept that anti-evolutionists may find difficult accept. As I have remarked before anti-evolutionist’s often wrongly identify simple laws and algorithms with “necessity” and thus they wrongly conclude that equations can’t carry information. Moreover they tend to conflate the concepts of complexity and information. Thus they conclude that simple algorithms and laws can’t generate complexity – this is, of course, wrong as we know that simple algorithms can generate the complexity of fractals and pseudo random sequences. Even if we concede that the anti-evolutionists are right about the irreducible complexity of bio-morphs, one thing remains clear: Whether the layout in bio-morphospace entails either reducible complexity or irreducible complexity it is clear that this space of structures is itself an extremely complex object: therefore either way the physics of our world entails a morphospace with a very complex layout. So even taking on board the anti-evolutionist’s concept of irreducible complexity we find that we have to admit that simple physical laws can generate very complex objects, whether those objects favour or block evolution!

Although it is clear that Granville Sewell’s opinion about the second law of thermodynamics are wrong I would want to concede that abiogeneiss and evolution are subject to a reasonable doubt on basis that as far as I am concerned the questions surrounding (ir)reducible complexity are not settled in my mind. It’s a good thing that I’m not a professional scientist because even this expressed uncertainty is likely to be regarded as the slippery slope to the "scientific heresy" of ID. But as I have remarked before, whatever the arrangement of biological structures in morphospace may be, I have a funny feeling that this arrangement is computationally irreducible; that is, the only way we have of acquiring analytical evidence about that arrangement is to actually carry out a very long computation and there are no other analytical short cuts. Hence, the burden of evidence is thrown back on the actual computation itself; in this case the actual workings of natural prehistory as manifested by the existence or nonexistence of paleontological evidence. If my mathematical intuitions are right then as I am not a paleontologist it doesn’t look as though I can make much further progress on this subject.

Sunday, February 07, 2010

Fuzzy after dinner thoughts one quiet Sunday afternoon.

Brave Knight Sir Roger Penrose doesn’t know which way his Hilbert space vector is going to point next

I am hoping to kick this habit of evolution vs. anti-evilution debate posting, an activity that I have engaged in for nearly two years now: I honestly don’t think I can make much further useful progress on the question. So, I plan to make only two more posts on the debate in order to wind it up. My mind is now turning (back) to other issues.

With the authoritative and excellent help of Sir Roger Penrose’s books I have been pondering the vexed question of the evolution (“evolution” as in “change”, not as in “evilution”) of the quantum mechanical state vector. The following is a resume of my current thinking so far, thinking which I have to admit is rather at the impressionistic sketch stage. (There is no guarantee as to the correctness of the following; after all I’m not a “Sir”. Also, today was one of those days when, as H. G. Wells put it in "The Time Machine", I was experiencing "that luxurious after-dinner atmosphere, when thought runs gracefully free of the trammels of precision")

The orientation of the QM state vector in Hilbert space changes in a smooth and deterministic way until a measuring system from without hits that vector and it then appears to undergo a random discontinuous jump according to probabilities calculated with the “projection hypothesis”. Ostensibly, Hilbert space is Mathematically Isotropic. Moreover, there seems to be a complementary symmetry between position and momentum (or time and energy) and this symmetry is especially clear with relativistic renditions of quantum mechanics. So given these symmetries, on the face of it there seems be no reason why we shouldn’t observe those strange mixtures of state that involve macroscopic objects occupying two positions at once, much as do photons in Young’s slits experiment; for given the isotropy of Hilbert space obviously spatially mixed macroscopic states are no less preferred than spatially unmixed states.

It has to be admitted that decoherence theory may provide an excellent solution to this problem. Entanglement with “hot” macroscopic measuring tools will appear to collapse the wavefunction. Furthermore, thermodynamics and entanglement will ensure that for macroscopic objects some balance between a spread of momenta and distances is maintained, and this perhaps is precisely what we see in the seemingly unambiguous states of the macroscopic world. Decoherence theory still remains a very good candidate explaining the apparent random jumping of the state vector and the preference for certain kinds of macro-state. The big bonuses of this theory are that it preserves frame independence, other symmetries and above all that holy grail of reductionist science: An “in principle” determinism – the closed system. However, it has to be said that at the level of the outermost frame there are no outside “hot” measuring contexts which will help maintain the state vector in some balance between momentum and position.

For reasons I have given here, I am inclined to favour the notion of real discontinuous random jumps in the state vector. Moreover, that the Schrödinger equation is not Lorentz invariant may hint that there is an actual asymmetry between space and momentum. In fact my own attempt at explaining gravity depends on a non-linear quantum equation that makes use of postulated underlying asymmetries in frame that are only partially compensated for by Einstein relativity. Gravity is something that operates in x-space and not in momentum space; hence there is an asymmetry between space and momentum. Thus gravity is implicated as a factor explaining why we only observe spatially unambiguous macro states. Penrose’s ideas about why the state vector jumps randomly may be right: It may jump to ensure that we don’t get quantum superpositions which imply spatially ambiguous macroscopic distributions of matter entailing gravitational energy divergences violating the allowed uncertainty in energy. Such a view entails the end of the reductionist's closed system.