In part 11 of this series I provided a digest of William Dembksi’s paper on active information, a paper that introduced us to the Avida program. Avida is an experiment in evolutionary computation and was used to evolve the complex XNOR function from basic “atomic” components consisting of NAND gates. In this post I make the assumption that Avida has abstract isomorphisms with evolution proper and consider the experiment from an evolutionist’s perspective.

The authors of the Avida program analysed the XNOR function and broke it down into a hierarchical structure of components, sub-components and sub-sub-components. The XNOR function was then subsequently evolved by building into the software a “ratchet” using a scoring system that assigned a fitness value to the components and sub-components of XNOR. Hence, the software can, in stages, arrive at the top of XNOR’s structural hierarchy because the “ratchet” suppresses the tendency to slip back down the component hierarchy if during the random shuffling of components a “higher” component happens to come together. The Avida program works, in effect, by incorporating a stratified stability into its “search”

If the dynamic in morphospace is simply that of an isotropic and homogenous diffusion, then ultimately no particular configuration is statistically weighted; for any given boundary condition the end result is that in time probability spreads itself evenly over all configurations in a light uniform grey. Thus, isotropic homogeneous diffusion is extremely unlikely to evolve any complex organized structures because these structures constitute such a small class of possibility. In any case if in the remote chance they did make an appearance they would not persist and would soon melt back into the background sea of randomness.

To get the Avida category of evolution to work the required members of the class of complex organized structures must have probabilities weighted in their favour. There is more than one way of doing this but the Avida program builds in this weighting using a “configurational ratchet”; that is, the algorithmic regime of Avida is such that should perchance a required complex ordered configuration come into existence it has a high chance of persisting and will not quickly dissolve back into its surroundings. Moreover, although the system is suppressed from going “backwards”, it is, nevertheless allowed to go “forwards” in the sense that “higher” components are allowed to be formed from assemblages of sub-components. The higher components which once formed are themselves “fixed” by the ratchet.

In terms of random walk the introduction of a configurational ratchet into the system is the equivalent of giving the random walk a directional bias; there is then a greater chance of stepping in one direction than the other because a particular configuration is more likely to be assembled than disassembled. This has the effect of introducing a directional drift in the diffusion created by the random walk.

Did I just say “directional drift”? Isn’t it the height of scientific incorrectness to say that evolutionary change has direction? Have the Avida builders committed a “scientific heresy”? It is, in fact, possible to drop an anisotropic random walk and instead introduce heterogeneity in the walk by allowing the step size of the walk to vary from place to place in morphospace. The random walk is then isotropic, but the step size is contrived to be very small around the area of certain complex organized configurations (like XNOR and its components), thus endowing them with a degree of persistence. However, my own mathematical work shows that the effect on the morphological diffusion equation of a varying step size of this sort is that it still introduces a directional drift toward the persisting configurations. Another way of favouring the required complex organized configurations is to introduce a term into the morphological diffusion equation that is analogous to the potential term in the Schrödinger equation of quantum mechanics. Yet another method is by weighting the probabilities in morphospace in favour of organized complexity by applying some kind of constraint that eliminates the enormous numbers pathways in morphospace leading to disordered configurations. However this effectively reintroduces anisotropy into morphospace.

However one cuts it, somehow those required complex organized configurations must be awarded a probability weighting that compensates for the highly atypical nature of their class. If the above considerations port to the evolution of biological configurations then it really does give the lie to the idea that complex organized configurations do not have a favoured status; clearly they must have a favoured status otherwise evolution simply cannot happen. Thus, within the visible cosmos, generalized Copernicanism, in the sense that no point is has a preferred status, does not apply to morphology; this is apparent because in morphospace, where the overwhelming numbers of configurations are disordered, complex organized configurations must be favoured with extraordinarily high probability weightings in order to compensate for their very sparse representation in the class of all possible configurations.

But Avida leaves us with another point to ponder. In Avida it is clear that the XNOR function cannot be assembled without passing through the “lower levels” of the component hierarchy; that is certain sub-components must precede “higher” components. If the initial boundary condition is that we start with a soup of basic atomic NAND gates, then Avida evolution has to proceed by first traversing the “lower” levels of the structural hierarchy and then work its way “up” the hierarchy. Once again Avida challenges “generalized Copernicanism” in the sense that the structures of morphospace don’t stand in symmetrical relationship to one another; in order to arrive at the “higher structures” certain antecedents must necessarily be realized first, but the converse is untrue: the “lower” structures need not be necessarily be preceded by the “higher” structures. In a word, the formation of the “lower” structures are necessary to the formation of the “higher” structures, but not vice versa.

The hierarchical structure of Avida’s logical components crudely echoes the hierarchal structure of biological components: Viz: atoms, organic molecules, cells, and multicell organisms. Hence biological evolution also has imposed on it a necessary sequence of events, although the real picture is complicated by the likely hood that in actual evolution the different levels of the hierarchy probably evolve in parallel.

All this, however, doesn’t tell us anything we don’t already know in a more general form: namely that some problems are intrinsically more difficult to “solve” than others because they require more steps, more time, and more resources in general. It is therefore no surprise if some structures are more complex than others in the sense that they demand more computational resources, or stand in a hierarchal relation to other less complicated structures that serve as necessary precursors. Therefore when discussing evolved structures it is difficult not to use such terms like “higher”, “lower”, “complex”, “simple”, “progress”, “developed”. These terms arise out of a natural way of describing the mathematical necessities of computation, necessities telling us that certain outcomes put a greater demand on computational resources than others. Even the word “solve” is a problem, in that it carries a goal seeking intentionality, but the fact is that evolution is a consequence of a world in morphological disequilibrium, just as it is in thermodynamic disequilibrium, and thus there is an asymmetry between beginnings and endings.

But terms like “higher”, “lower”, “progress” and “more complex” sit uneasily with an instinctive hyper Copernicanism which is inclined feel that preferred frames smack of theism and creationism; generalized cosmic mediocrity, the feeling goes, is ever the evidence of the absence of deity. But the fact is that if evolution is to work certain structures have a “preferred” status in that their probability must be elevated by the algorithmic regime to be considerably above that implied by a bland random walk. Nevertheless it has to be admitted that such terms as “preferred”, “higher”, “lower”, and “progress” have associations linked to our system of values, and religiously sensitive people, whether believers or atheists, pick up the signals immediately along with any implicit attack or corroboration of their views. This makes a detached discussion of the subject all but impossible. See for example this post on Sandwalk where I was involved in a discussion on the subject of the dynamics of evolution with an atheist who was reluctant to admit the presence of asymmetries in morphospace, perhaps because he felt this somehow threatened his world view.

If the Avida experiment has anything to tell us about real evolution, it does, as Dembksi suggests, show that a workable evolution must make use of active information. In this case intrinsic active information built into the mechanics of the system. This means that the actual outcomes of evolution have an elevated probability which in turn depresses their information value on occurrence because the information is intrinsic to the organization of the system from the outset. Thus an observer who understands the physical regime is less surprised by evolutionary outcomes because information has shifted from these outcomes to his knowledge of the organization of the underlying mechanics.

There is one final question here that really takes me onto the next stages of this investigation. What is it that raises the weighting of certain configurational forms well above an even handed “Copernican” treatment? In Avida the weighting was effectively put in by hand. However in natural evolution this weighting it is undoubtedly bound up with the possibility of cybernetic structures that, given the context of the natural physical regime, have a self perpetuating/self maintaining structure. This subject will in due time take me onto the knotty issue of irreducible complexity and Dembski’s infamous concept of “Complex Specified Information”.

Coming soon… Active information and Intelligent Design

The authors of the Avida program analysed the XNOR function and broke it down into a hierarchical structure of components, sub-components and sub-sub-components. The XNOR function was then subsequently evolved by building into the software a “ratchet” using a scoring system that assigned a fitness value to the components and sub-components of XNOR. Hence, the software can, in stages, arrive at the top of XNOR’s structural hierarchy because the “ratchet” suppresses the tendency to slip back down the component hierarchy if during the random shuffling of components a “higher” component happens to come together. The Avida program works, in effect, by incorporating a stratified stability into its “search”

If the dynamic in morphospace is simply that of an isotropic and homogenous diffusion, then ultimately no particular configuration is statistically weighted; for any given boundary condition the end result is that in time probability spreads itself evenly over all configurations in a light uniform grey. Thus, isotropic homogeneous diffusion is extremely unlikely to evolve any complex organized structures because these structures constitute such a small class of possibility. In any case if in the remote chance they did make an appearance they would not persist and would soon melt back into the background sea of randomness.

To get the Avida category of evolution to work the required members of the class of complex organized structures must have probabilities weighted in their favour. There is more than one way of doing this but the Avida program builds in this weighting using a “configurational ratchet”; that is, the algorithmic regime of Avida is such that should perchance a required complex ordered configuration come into existence it has a high chance of persisting and will not quickly dissolve back into its surroundings. Moreover, although the system is suppressed from going “backwards”, it is, nevertheless allowed to go “forwards” in the sense that “higher” components are allowed to be formed from assemblages of sub-components. The higher components which once formed are themselves “fixed” by the ratchet.

In terms of random walk the introduction of a configurational ratchet into the system is the equivalent of giving the random walk a directional bias; there is then a greater chance of stepping in one direction than the other because a particular configuration is more likely to be assembled than disassembled. This has the effect of introducing a directional drift in the diffusion created by the random walk.

Did I just say “directional drift”? Isn’t it the height of scientific incorrectness to say that evolutionary change has direction? Have the Avida builders committed a “scientific heresy”? It is, in fact, possible to drop an anisotropic random walk and instead introduce heterogeneity in the walk by allowing the step size of the walk to vary from place to place in morphospace. The random walk is then isotropic, but the step size is contrived to be very small around the area of certain complex organized configurations (like XNOR and its components), thus endowing them with a degree of persistence. However, my own mathematical work shows that the effect on the morphological diffusion equation of a varying step size of this sort is that it still introduces a directional drift toward the persisting configurations. Another way of favouring the required complex organized configurations is to introduce a term into the morphological diffusion equation that is analogous to the potential term in the Schrödinger equation of quantum mechanics. Yet another method is by weighting the probabilities in morphospace in favour of organized complexity by applying some kind of constraint that eliminates the enormous numbers pathways in morphospace leading to disordered configurations. However this effectively reintroduces anisotropy into morphospace.

However one cuts it, somehow those required complex organized configurations must be awarded a probability weighting that compensates for the highly atypical nature of their class. If the above considerations port to the evolution of biological configurations then it really does give the lie to the idea that complex organized configurations do not have a favoured status; clearly they must have a favoured status otherwise evolution simply cannot happen. Thus, within the visible cosmos, generalized Copernicanism, in the sense that no point is has a preferred status, does not apply to morphology; this is apparent because in morphospace, where the overwhelming numbers of configurations are disordered, complex organized configurations must be favoured with extraordinarily high probability weightings in order to compensate for their very sparse representation in the class of all possible configurations.

But Avida leaves us with another point to ponder. In Avida it is clear that the XNOR function cannot be assembled without passing through the “lower levels” of the component hierarchy; that is certain sub-components must precede “higher” components. If the initial boundary condition is that we start with a soup of basic atomic NAND gates, then Avida evolution has to proceed by first traversing the “lower” levels of the structural hierarchy and then work its way “up” the hierarchy. Once again Avida challenges “generalized Copernicanism” in the sense that the structures of morphospace don’t stand in symmetrical relationship to one another; in order to arrive at the “higher structures” certain antecedents must necessarily be realized first, but the converse is untrue: the “lower” structures need not be necessarily be preceded by the “higher” structures. In a word, the formation of the “lower” structures are necessary to the formation of the “higher” structures, but not vice versa.

The hierarchical structure of Avida’s logical components crudely echoes the hierarchal structure of biological components: Viz: atoms, organic molecules, cells, and multicell organisms. Hence biological evolution also has imposed on it a necessary sequence of events, although the real picture is complicated by the likely hood that in actual evolution the different levels of the hierarchy probably evolve in parallel.

All this, however, doesn’t tell us anything we don’t already know in a more general form: namely that some problems are intrinsically more difficult to “solve” than others because they require more steps, more time, and more resources in general. It is therefore no surprise if some structures are more complex than others in the sense that they demand more computational resources, or stand in a hierarchal relation to other less complicated structures that serve as necessary precursors. Therefore when discussing evolved structures it is difficult not to use such terms like “higher”, “lower”, “complex”, “simple”, “progress”, “developed”. These terms arise out of a natural way of describing the mathematical necessities of computation, necessities telling us that certain outcomes put a greater demand on computational resources than others. Even the word “solve” is a problem, in that it carries a goal seeking intentionality, but the fact is that evolution is a consequence of a world in morphological disequilibrium, just as it is in thermodynamic disequilibrium, and thus there is an asymmetry between beginnings and endings.

But terms like “higher”, “lower”, “progress” and “more complex” sit uneasily with an instinctive hyper Copernicanism which is inclined feel that preferred frames smack of theism and creationism; generalized cosmic mediocrity, the feeling goes, is ever the evidence of the absence of deity. But the fact is that if evolution is to work certain structures have a “preferred” status in that their probability must be elevated by the algorithmic regime to be considerably above that implied by a bland random walk. Nevertheless it has to be admitted that such terms as “preferred”, “higher”, “lower”, and “progress” have associations linked to our system of values, and religiously sensitive people, whether believers or atheists, pick up the signals immediately along with any implicit attack or corroboration of their views. This makes a detached discussion of the subject all but impossible. See for example this post on Sandwalk where I was involved in a discussion on the subject of the dynamics of evolution with an atheist who was reluctant to admit the presence of asymmetries in morphospace, perhaps because he felt this somehow threatened his world view.

If the Avida experiment has anything to tell us about real evolution, it does, as Dembksi suggests, show that a workable evolution must make use of active information. In this case intrinsic active information built into the mechanics of the system. This means that the actual outcomes of evolution have an elevated probability which in turn depresses their information value on occurrence because the information is intrinsic to the organization of the system from the outset. Thus an observer who understands the physical regime is less surprised by evolutionary outcomes because information has shifted from these outcomes to his knowledge of the organization of the underlying mechanics.

There is one final question here that really takes me onto the next stages of this investigation. What is it that raises the weighting of certain configurational forms well above an even handed “Copernican” treatment? In Avida the weighting was effectively put in by hand. However in natural evolution this weighting it is undoubtedly bound up with the possibility of cybernetic structures that, given the context of the natural physical regime, have a self perpetuating/self maintaining structure. This subject will in due time take me onto the knotty issue of irreducible complexity and Dembski’s infamous concept of “Complex Specified Information”.

Coming soon… Active information and Intelligent Design

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