Yet Again: Intelligence of the Gaps. Part III

NAID Granville Sewell has been caught up in
 the dualistic bandwagon which contrasts physical
laws against divine agency 

In the third part of this series I continue to examine the thinking of  Granville Sewell who argues that the second law of thermodynamics theoretically undermines evolution. Granville is part of the North American Intelligent Design (NAID) community who not only specialise in promoting a God an Intelligence-of-the-Gaps paradigm (which they will strongly deny) but they also veer toward a right-wing political stance. Strong evidence of this politics is seen in that the unwoke political animal Chris Rufo was a one time director of the Intelligent Design think-tank, The Discovery Institute. 

See the following links for the two previous two parts...

Quantum Non-Linearity: Yet Again: Intelligence of the Gaps. Part 1

Quantum Non-Linearity: Yet Again: Intelligence of the Gaps. Part II

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GRANVILLE: You can argue that a few billion years ago a simple self-replicator formed by natural chemical processes, and that over the millions of years natural selection was able to organize the duplication errors made by these self-replicators into intelligent, conscious, humans, who were able to build rockets that could reach the moon and return safely. 

MY COMMENT: Ah, at last Granville is asking the right question: It's not about the evolution of junkyard computers, rather it's a question of bio-molecular evolution. If one assumes OOL has occurred (by no means a trivial assumption) those duplication errors that Granville refers to, as we will see below, play a crucial role. 

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GRANVILLE:  I would counter that we with all our advanced technology are still not close to designing any self-replicating machine; that is still pure science fiction. When you add technology to such a machine, to bring it closer to the goal of reproduction, you only move the goal posts, as now you have a more complicated machine to reproduce. So how could we believe that such a machine could have arisen by pure chance? 

MY COMMENT: Yet again, I repeat: We are not dealing with pure chance; instead we are dealing with conditional probability. and at that conditions created by an Omnigod. Therefore, we can not yet eliminate from the inquiry the possibility that the requisite physical pre-conditions needed for OOL-development have been contrived by a God for whom all (logically contingent) things are possible. So, given this relationship:

 I <= S + Log T

1.0

....it may be that without sufficient starting information, S, about how to construct a general molecular self-replicator, the computation time, T, required to arrive at this information, I, is humanly speaking prohibitive; but really we don't know the answer to that question. The best humanity has done, however, is create replicators in the virtual world of computer memory. Evolution itself, however, poses a far more abstruse meta-question: Is it possible to invent a regime of laws, constants and diffusive momenta which, given enough time, will result in an OOL natural history....that is, to arrive at simple self-replicating structures...and then on to highly complex replicators? I'm not aware that this has been achieved even within a computer memory (*2). In fact this problem could be computationally irreducible. If Granville is looking for gaps, then this is the mother of all gaps. Trouble is, given the intellectual resources of an Omnigod we don't know whether He has filled that gap with a physical regime where OOL is possible.

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GRANVILLE: And suppose we did somehow manage to design, say, a fleet of cars with fully automated car-building factories inside, able to produce new cars, and not just normal new cars, but new cars with fully automated car-building factories inside them. Who could seriously believe [!Gut-reaction!] that if we left these cars alone for a long time, the accumulation of duplication errors made as they reproduced themselves would result in anything other than devolution, and eventually could even be organized by selective forces into more advanced automobile models? So I would claim that we don’t really understand [!Yes we do!] how living things are able to pass their complex structures on to their descendants without significant degradation, generation after generation, much less how they evolve even more complex structures.  [Concession: may be!]

MY COMMENT: OK, so leaving aside the somewhat misleading subject of self-replicating cars, the core question Granville is really asking here is this: Assuming the existence of molecular self-replicators how is it that the information needed to breed biological replicators from generation to generation isn't slowly but surely being corrupted by random noise? There is a plausible answer to this particular problem and that answer also shows us why Granville's insistence that the second law is a mathematical block to evolution is fallacious.  I will be dealing with this question in the finale. 

Granville goes onto criticise infinite multiverse attempts at explaining away the high improbabilities of our highly ordered world. I am at one with Granville in rejecting multiverse theory and won't publish his comments here, but here are links to some of my comments on the subject:

Quantum Non-Linearity: Many Worlds Theory: A theory devoid of meaning, goals and purpose

Quantum Non-Linearity: Science and the Multiverse

Quantum Non-Linearity: Middlebrow Atheism. Part 5 (Final Part)

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GRANVILLE:  Conclusions: There are various ways to argue that what has happened on Earth does not violate the more general statements of the second law as found in physics texts. The “compensation” argument, which says that “entropy” can decrease in an open system as long as the decrease is compensated by equal or greater increases outside, so that the total entropy of any isolated system containing this system still increases, is perhaps the most widely used. Since in this context “entropy” is just used as a synonym for “disorder,” [i.e. high statistical weight and not high improbability] the compensation argument, as I paraphrased it in Physics Essays, essentially says that extremely improbable things can happen in an open system as long as things are happening outside which, if reversed, would be even more improbable! This compensation argument is not valid even when applied just to thermal entropy, as the decrease in an open system is limited not by increases outside, but by the amount exported through the boundary, as I’ve shown. Since tornados derive their energy from the sun, the compensation argument could equally well be used to argue that a tornado running backward, turning rubble into houses and cars, would not violate the second law either.

MY COMMENT: Once again Granville is trying to stretch credibility in evolution by ludicrous examples whose probability is all but nil. Once again, as we saw in Part II, in lieu of giving proper cognizance to conditional probabilities and a rigorous definition of entropy Granville is using our gut-feelings about known improbabilities such as tornadoes reconstructing houses and junk yards evolving computers and then exploiting those feeling to throw doubt on bio-evolution.... not a very satisfactory way to argue.

For my purposes there is no need to get involved with this compensation argument: We know from the process of crystallisation that highly improbable things (in the unconditional sense) do happen in isolated systems given the right conditions.  Also, Granville fails to make clear that entropy is not the same as randomness and therefore a system of maximum entropy is not necessarily highly random; a system of maximum entropy is a system whose macrostate has the highest statistical weight given the physical constraints on the system. Since maximum statistical weight can't be equated with randomness, then high order in a system constrained by physics is not necessarily to be equated with high improbability, although it can be equated with high unconditional improbability. 

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GRANVILLE:  Conclusions: But there is really only one logically valid way to argue that what has happened on Earth does not violate the fundamental principle underlying the second law — the one principle from which every application and every statement of this law draws its authority. And that is to say that it only seems impossibly improbable, but it really is not, that under the right conditions, [Ahh! What about conditions created by an Omnigod?] the influx of stellar energy into a planet could cause atoms there to rearrange themselves into nuclear power plants and digital computers and encyclopedias and science texts, and spaceships that could travel to tother planets and back safely. [Granville is appealing to his gut reactions again!]

And although the second law is all about probability, very few Darwinists are willing to make such an argument; they prefer to avoid the issue of probability altogether.

MY COMMENT: Although Granville gives no cognizance to conditional probabilities and the high unconditional improbability of crystallisation, this failure certainly doesn't mean that evolutionary mechanisms, as currently understood, are the engine driving natural history; all we can say at this juncture is that Granville's line of reasoning is fallacious and as an attempt to logically falsify evolution it has failed. Instead he has fallen-back on hand waving and gut-reaction-responses to ludicrous ideas about computers, encyclopaedias, science texts and spaceships popping out of an unconditional vacuum. No, Granville, the second law isn't all about probability, rather it is all about probability and the physical constraints on that probability. Think probability envelopes! But the form of those envelopes is a vexed question (see below) and that question is as much of a poser to so-called "Darwinists" (sic) as it is to the NAIDs.

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FINALE: Concerning Duplication Errors: In his post Granville raises the question about replicator duplication errors. Why doesn't random noise corrupt the information which needs to be passed from generation to generation to preserve the integrity of the replicator configuration? An answer is to be found in an equation I've often cited on Quantum Non-Linearity: Viz: the multiplying diffusion equation.....

2.0

....where: Y represents the count of replicators diffusing through configuration space, D is the diffusion constant and the "house" operator is a multidimensional version of the 3-dimensional "Del" operator. The intelligent information which has the potential to preserve the configurational status quo of replicators is incorporated into the VY term; The value of V is assumed to be coordinate dependent and will be dependent on the creation's physical regime. This term, depending on whether V is positive or negative, respectively describes either an exponential growth or an exponential decay of the replicator population at the coordinate concerned. The result, depending on how V varies over configuration space, is that at some points in configuration space the replicator population grows and at other points it decays. 

At the same time random perturbations (Granville's "duplication errors") ensure that replicator configurations are diffusing through multidimensional configuration space; if replicator configurations diffuse into configurational areas where V is negative the population decays and dies; if they move into areas where V is positive the population grows. Thus, for example, if a replicator's configuration has become corrupt due to duplication errors and this corruption adversely impacts the replicator's ability to self-perpetuate and replicate, then in that area of configuration space V will be negative and the population will die. Alternatively, if V is positive the population will increase. The value of V is the selecting mechanism which ensures that regions of successful replication will prosper and regions with negative V entail decaying population. Thus V has the potential to not only preserve configurational integrity but to enhance configurational survival. This is standard evolutionary theory expressed in an abstracted mathematical form. There is here a similarity with language changes. Languages are subject to incremental drifting all the time, but only those increments that ensure the language remains comprehensible and useful are selected. 

But and this is the big But it all depends on the given form of V and its layout in configuration space. As I've made clear in previous posts, if standard evolution is to work V must superimpose on configuration space a network of channels constraining the diffusion and forming a connected set I call that the "spongeam". For OOL and subsequent evolution to work the spongeam network must have connections all the way back from complex replicators to lifeless soups of chemicals.

Quantum Non-Linearity: Necessary Conditions for Evolution: The Spongeam

However, given the physics of our world it is by no means clear whether or not V traces out a spongeam facilitating evolution from scratch. For example if the functionality that organic life requires to survive occurs in isolated islands then there is an unsurmountable problem for conventional evolution; trouble is, proving this one way or the other is very problematic and the cognitive gaps here tend to get filled with the tribal gut-reactions of the woke and the unwoke. 

Equation 2.0 is, however, clear on one thing; namely, that Granville's NAID tribal belief that increasing entropy necessarily contradicts evolution is wrong. The spongeam, if it exists given our physical regime, is a networked domain of possibility in configuration space defined by the form of V. This networked space is also a domain of diffusion with the diffusion being a consequence of random walk. In elementary random walk the transition rate between any pair of points in space is the same both ways because it is only dependent on the distance separating pairs of points. This sets up the condition needed for the H-theorem to hold, and if the H-theorem holds it means that in configuration space the total entropy is always increasing. This constantly increasing entropy is true even though the presumed tight constraints imposed by the spongeam on configuration space may mean that as evolution progresses highly organised configurations appear for the simple reason they are on one of diffusion routes. The irony is that the random motions of entropy are actually the motive force which drives the system toward the complex organization encoded in V, just as the random motions of the molecules of a gas create a pressure which drives the gas through a network of conduits.

Equation 2.0 is notional and no doubt a simplistic town-toy model of a possible evolutionary scenario. But although it may not bear a strong resemblance to the complexities of an actual evolutionary scenario (if such exists) what it does show, by a mathematical example, is that Granville's assertion that the second law necessarily contradicts evolution is false.

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Repeating what I said in the last part: The NAID community have sold out to anti-evolutionism, and a God an intelligence-of-the-gaps model, although that will be denied by them. I propose that they subliminally hold on to this model because the deism of the enlightenment still plagues the thoughts of many. For should the completeness of science as a descriptive system be adequately demonstrated then the subliminal intuitions of both NAID and atheist alike quietly prompts them to view the cosmos as a kind enlightenment automata capable of working unattended; no deity needed. It is then a short step to eliminating deity altogether. Anxious to avoid this conclusion the NAID community have put all their eggs into the anti-evolution basket in their determination to find evidence that God does after all demonstrate His presence in overt interventions in natural history. This has prompted them to invent the bogus category they call "blind natural forces"; not something I would use to refer to God's creation and what He has encoded into it.

Of course conversely their atheist antagonists have put all their eggs in the evolutionary basket and concluded therefore that no God is needed to drive the machinery & mechanisms of natural history. 

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As I've said before the right-wing political stance of NAID is really no surprise: The negative and even hostile reaction of the academic establishment who regard NAID as a purveyor of pseudo-science goes down like a dog-dirt sandwich with the NAID community; they know that they are being classified as the rejected other. But the NAID community have fallen in with politically powerful friends such as Trump, Kennedy and Steven Miller et al. Perhaps these powerful friends can teach the "woke" academic establishment a lesson or two! Such is the degeneration of a community who propose otherwise interesting questions about the ultimate origins of the cosmos.

Footnotes and notes

1. See this link for more on my reaction to the woke and the unwoke

Views, News and Pews: Review of Sharon James Book , "The LIES...."

*2. But see this: Did Google Researchers Just Create a Self-Replicating Computer Life Form?

3. Evolution and Human Technology:  

Quantum Non-Linearity: From Spears to Aircraft

And Again: Where North American ID goes wrong

                    Time for another critique of North American ID

North American ID tends to veer toward political partisanship
Picture from: https://www.discovery.org/

On several counts I can give a cautious endorsement to the North American Intelligent Design (NAID) movement. But this is a very qualified endorsement as I have criticisms of both their intellectual position and their cultural & political posturing (*3). See for example my criticism of Casey Luskin in this series. Moreover, my acceptance of the intelligent design argument for God is very cautious compared to NAID culture; for given that we are extrapolating from our experience with the works of human and animals (& aliens?) who act within the created context, to the works of a very Alien Totalizing Being who is postulated to be The Context of creation, it seems a bit of a stretch to claim that we can uncritically use what we observe of human and animal intelligence as a model for the intelligence of God. However, I would certainly concede that given the remarkable and irreducible organization of our cosmos, which for me most forcibly emerges in the descriptive effectiveness of the elegant algorithms of physics, there is a compelling intuition that by analogy the cosmos itself has its origins in an all embracing intelligence. This feeling is further reinforced when set against the arguments of arrogant atheist blowhard Richard Carrier who deludes himself with his misconceptions about probability theory as he attempts to account for physics as an aspect of randomness. 

However, as I have suggested in this short paper, I nevertheless take a rather reserved attitude toward the simple extrapolation of design arguments for God using Bayesian ideas. For me a faithful & personal God is an a-priori feature of my world view (Hebs 11:6), a feature which not only promotes a successful epistemology but also makes ultimate sense of a seemingly senseless world, a world whose irreducibly contingent organization is otherwise destined to remain an enigma. On this account God is not a simple inductive extrapolation from observation but rather the initial step in an abductive approach which gives anthropic meaning and purpose to the world (*1). Without this sense making world view one is left with little but a bleak absurdity where nothing makes sense (see Brian Cox). So, whilst I'm in sympathy with the general thrust of the NAID movement (but not their politics) I would nevertheless want to point out that they have over invested in the following points of view.....

1. The so called explanatory filter: When applied to human, animal and even alien activity, activity which takes place within the creation this filter works. But it all too easily leads to naive "God of the Gaps" thinking when applied to divine activity. This has mislead NAIDs to commit to needless subliminal "God-of-the-gaps" thinking as evidenced by their total commitment to anti-evolutionism.

3. Anti-evolutionism: OK, I can accept that some theists, from a theological point of view, might find evolution difficult to stomach. But we cannot rule out evolution on the basis of the category mistake that it classifies as a "blind natural force". If the Divine is as totalizing as Christian theology suggests then there is no such thing as "blind natural forces" incapable of filling explanatory gaps which according to NAID otherwise need filling with the interventions of divine design. If the process of evolution as commonly conceived has taken place in relatively short cosmic times then it is itself a remarkable work of creation. If you are going to argue against evolution it must be from empirical grounds not on the basis of God-of-the-gaps intuitions about the inability of "blind natural forces" (sic) to fill a gap that can only be filled with divine hocus-pocus. 

2. Anti-Junk DNA: There is no obliging need for theists to commit themselves one way or the other on this question; again, it must be on empirical grounds that this dispute is settled. Who can tell just what a contextually totalizing Being would or would not want to do with redundant/random coding in his DNA. My own uncompiled computer code is usually littered with the developmental legacy of historical but now redundant coding, so who knows what the Great Unknown of the Divine Mind might do. 

4. Information can't be created by "blind natural forces"? This is false: See here. Grumpy atheist PZMyers has recently & rightly taken NAID Stephen Myer to task on this one - see here: I have to roll my eyes when a creationist says information! Behind the NAID view on information generation is their subliminal "God-of-the-gaps" mentality; for them any sophisticated information becomes a "gap" incapable of being filled with "blind natural forces" and therefore demands deity intelligence to fill it. (*2)

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The notion that only enigmatic intelligence can create information may be based on the idea that somehow human intelligence should be categorized as a mysterious incomprehensible and transcendent process. To support this NAIDs may point to Roger Penrose's ideas about intelligence making use of non-computable processes.

I have critiqued Penrose's work here.  This work appears to have its origin in the fact that no finite system can fully be "self-aware". Full "self-awareness", for finite systems, opens up the potential for self-referencing contradictions. However, an outside perspective of an ontology external to a subject intelligence can be fully aware of the processes of that subject intelligence. 

Apart from my criticisms above, the following post on Science and Culture is much more to my liking than NAID knee-jerk anti-evolutionism....

Inscrutable Dice, Hitchcock’s Beans, and Cosmological Fine-Tuning | Science and Culture Today

However. I suspect some of the issues this writer raises can be short cut once we get a handle on the concept if randomness.  Theorems around randomness have no bounds as to the sizes of the sets to which they apply. 

Footnotes
*1 Christianity has a strong existential component in its evidences; that is, Christianity is partly dependent on the testimony of personal experiences. This slant toward anecdotal evidence, of course, cannot qualify as being on the same footing as the formal and sharable evidences of our science which depends on an a-priori high organization. 

*2 What I would concede however is that there is a cosmic sized "gap" everywhere and everywhen in as much as the descriptive nature of science is incapable of furnishing logical closure on the ultimate question of existence. 

*3 I also look askance at the mutual backslapping tribal culture that is the NAID community. This culture is not conducive to independent interest-free thinking;  it creates conflicts of interest.  It is probably true to say however that the gelling of their tribal culture has been encouraged by the vociferous and unfair opposition they have received from some quarters. See here

Bill Dembski's Information Conservation Thesis Falls Over

NAID's Stephen Meyer interviewed by Unwoke Right Wing Republican Dan Crenshaw. 
Evidence that NAID has become part of the  politicized culture war

I see that William "Bill" Dembski has done a post on Evolution News on the subject of the "Conservation of Information". The article is for the most part an interesting history of that phrase and goes to show that "information" has a number of meanings dependent on the discipline where it is being used, with Bill Dembski having his own proprietary concerns tied up with his support of the North American Intelligent Design (NAID) community.  See here for the article:

Conservation of Information: History of an Idea | Evolution News

Bill's particular information interest seems to lie with the so called "No Free Lunch Theorems". These theorems were about the mathematical limits on computer algorithms purposed to search for (and/or generate) configurations with properties of particular interest. Bill's focus on the "No Free Lunch Theorems" is bound up with the NAID community's challenge to standard evolution, a process which they see as a threat to their self-inflicted XOR creation dichotomy; viz: either "God Intelligence did it" XOR "Blind unguided natural forces did it" . 

But Bill gets full marks for spotting the relevance of these theorems to evolutionary theory: Evolution does have at least some features isomorphic with computer searches; in particular these theorems do throw some light on evolution's "search", reject and select mechanism which locks in organic configurations. So, the least I can say is that Bill's interest in the "No free lunch theorems" is based on what looks to be a potentially fruitful avenue of study. However, although it is true that the "No free lunch theorems" reveal interesting mathematical limits on computer searches, as we will see Bill has gone too far in trying co-opt these theorems for his concept of information conservation; in fact, to the contrary I would say that these theorems prove that Bill is wrong about the conservation of information.

                                                                                             ***

We can get a gut feeling for the No free lunch theorems with the impressionistic & informal mathematical analysis in this post. 

(Note: I arrived at similar conclusions in these two essays...

GeneratingComplexity2c.pdf - Google Drive

CreatingInformation.pdf - Google Drive 

These essays are more formal and cover the subject in more detail)

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We imagine that we have a set of computer programs executing in parallel with the intention of finding out if at some point in their computations they generate examples of a particular class of configuration. These configurations are to be found somewhere in an absolutely huge domain of possible configurations that I shall call D and which numbers D members, where D is extremely large.  It is a well known fact that most of the members of D will likely be highly disordered. 

A computer "search" starts with its initial algorithmic information  usually coded in the form of a character string or configuration S of length S. This configurational string contains the information informing the computing machinery how to generate a sequence of configurations C1, C2,.....,C_n,.... etc. The software creates this sequence by modifying the current configuration C_n in order to create the next configuration C_n+1. A crucial operational characteristic of algorithms is that they are capable of making if-then-else type decisions which means that the modifications leading to C_n+1 will be dependent on configurational features found in C_n. It is this decisional feature of executed algorithms which gives them their search, reject and select character, not unlike evolution. This means that their trajectory through configuration space is often very difficult to predict without actually executing the algorithm. This is because the conditional decision-making of algorithms means that we can't predict what direction an algorithm will take at any one point in the computation until the conditions it is responding to have actually been generated by the algorithm. The concept of computational irreducibility is relevant here. 

In his article Bill is careful to describe the components of search algorithms, components which give them their search, reject & select character. But for my purposes we can simplify things by ignoring these components and only give cognizance to the fact that an algorithm takes its computer along what is possibly a non-linear trajectory in configuration space. We can also drop Bill's talk of the algorithm aiming for a specified target and then stopping since in general an algorithm can go on indefinitely moving through configuration space endlessly generating configurations as does conventional evolution. All we need to be concerned about here is the potentiality for algorithms to generate a class of configs of interest in a  "time" T where T is measured in algorithmic steps. 

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If we have an algorithm with a string length of S then the maximum number of possible algorithms that can be constructed given this string length is A^s where A is the number of characters in the character set used to write the algorithm.

We now imagine that we have these possible A^s algorithms all executing in parallel for T steps. It then follows that the maximum number of configurations C which potentially can be generated by these possible algorithms of length S will be no greater than the limits set by the following relationship....

C <= A^s x  T

 Relation 1.0

...where C is the number of configurations that can be created in time T if the set of algorithms are run in parallel and assuming that a) T is measured in algorithmic steps and that b) the computing machinery is only capable of one step at a time and generates one configuration per step per algorithm.  

If the class of configurations we are interested in exist somewhere in a huge domain D consisting of D configurations and where for practically realistic execution times T:

                                     D >>> C

Relation 2.0

...then the relatively meager number of configurations our algorithm set can generate in realistic times like T are a drop in the ocean when compared to the size of the set of configurational possibilities that comprise D.  If relationship 2.0 holds then it is clear that given realistic times T, our "searches" will be unable to access the vast majority of configurations in D. 

With the above relationships in mind no free lunch starts to make some sense: If we are looking for algorithms which generate members of a particular class of configuration of interest (e.g. organic-like configurations) then for the algorithmic search to have a chance of succeeding in a reasonable time we require one of the following two conditions to be true...

1. Assuming that such exists then an algorithm of reasonable length S has to be found which is able to generate the targeted class of configurations within a reasonable time T.  However, if relationship 2.0 holds then it is clear that this option will not work for the vast majority of configurations in D.

2.  The alternative is that we invalidate relationship 2.0 by either a) allowing the algorithms of length S to be large enough so that A^s ~ D, or b) allowing the execution time T of these algorithms to be sufficiently large so that T ~ D,  or c) allowing that T and A^s when combined invalidate relationship  2.0. 

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So, with the foregoing in mind we can see that if an algorithm is to generate a stipulated class of solution in domain D in a reasonable time T it either a) has to be logically possible to code the algorithmic solution in a starting string S of reasonable length S or b) we have to code the required information into a long string S of length S such that A^s ~ D. 

In case a) both S and T are of a practically reasonable magnitude from which it follows that given relationship 1.0 then little of the domain D  can be generated by such algorithms and therefore the majority of configurations that could possibly be designated as of interest in D (especially if they are complex disordered configurations) can not be found by these case-a algorithms. In case b) the starting string S, in terms of the number of possible algorithms that can be constructed, is commensurate with the size of D and therefore could possibly generate configurations of stipulated interest in a reasonable time. 

Therefore it follows that if we are restricted to relatively short algorithm strings of length S then these algorithms will only have a chance of reaching the overwhelming majority of configurations in D after very long execution times. If our configurations of designated interest are in this long execution time region in D these configurations will demand large values of T to generate. Long execution time algorithms, absent of any helpful starting strings which provide "short cut" information are I think what Bill calls "blind search algorithms". That emphasis on the word "blind" is a loaded misnomer which appeals to the NAID community for reasons which I hope will become clear. 

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For Bill this what no free lunch means to him...

Because no-free-lunch theorems assert that average performance of certain classes of search algorithms remain constant at the level of blind search, these theorems have very much a conservation of information feel in the sense that conservation is strictly maintained and not merely that conservation is the best that can be achieved, with loss of conservation also a possibility

It's true that unless primed with the right initial information by far and away the majority of algorithms will reach most targets of an arbitrarily designated interest only after very long execution times involving laborious searching.....ergo, upfront information that lengthens S is needed to shorten the search; in fact this is always true by definition if we are wanting to generate configurations of interest that are also random configurations. 

So, the following is my interpretation of what Bill means by the conservation of information; namely, that to get the stipulated class of garbage out in reasonable time you have to put the right garbage in from the outset. The "garbage in" is a starting string S of sufficient length to tip the algorithm off as to where to look. The alternative is to go for searches with very long execution times T. So, paraphrasing Bill, we might say that his conservation of information can be expressed by this caricatured equation:

G_in = G_out

Relation 3.0

....where G_in represents some kind of informational measure of the "garbage" going in and G_out is the informational measure of the garbage coming out of the computation. But the following is the crucial point which as we will see invalidates Bill's conservation of information: Although relationship 3.0 gives Bill his conservation of information feel, it is an approximation which only applies to reasonable execution times.....it neglects the fact that the execution of an algorithm does create information if only slowly. That Bill has overlooked the fact that what he calls "blind searches" nevertheless slowly generate information becomes apparent from the following analysis.

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If we take the log of relation 1.0 we get:

                                                         Log (C) <= S Log (A) + Log(T)

relation 4.0

The value C is the number of configurations that A^s algorithms will generate in time T and this will be less than or equal to the righthand side of the above relation. The probability of one these C configurations being chosen at random will be 1/C. Converting this probability to a Shannon information value, I, gives:

I = - Log (1/C) = Log (C)

relation 5.0

Therefore substituting I into 4.0 gives:

I <= S Log (A) + Log(T)

relation 6.0

Incorporating Log (A) into a generalized measure of string length, S gives....

I <= S + Log(T)

relation 7.0

From this relationship we can see that parallel algorithms do have the potential to generate Shannon Information with time T, and the information is not just incorporated from the outset in a string of length S. However, we do notice that because the information generated by execution time is the log function of T, that information is generated very slowly. This is what Bill has overlooked: What he derisively refers to as a "blind search" (sic) actually has the potential to generate information, if slowly. Bill's view is expressed further in the following quote from his article (With my emphases and with my insertions in red).....

With the no-free-lunch theorems, something is clearly being conserved [No, wrong] in that performance of different search algorithms, when averaged across the range of feedback information, is constant and equivalent to performance of blind search.[Log(T) is the "blind search" component] The question then arises how no free lunch relates to the consistent claim in the earlier conservation-of-information literature about output information not exceeding input information. In fact, the connection is straightforward. The only reason to average performance of algorithms across feedback information is if we don’t have any domain-specific information to help us find the target in question.[The "domain-specific" information is implicit in the string S of length S in relation 7.0] 

Consequently, no free lunch tells us that without such domain-specific information, we have no special input information to improve the search, and thus no way to achieve output information that exceeds the capacities of blind search. When it comes to search, blind search is always the lowest common denominator — any search under consideration must always be able to do at least as good as blind search because we can always execute a blind search.[Oh no we can't Bill, at least not practically quickly enough under the current technology; we still await the technological sophistication to implement the expanding parallelism needed for "blind search" to be effective, the holy grail of computing. "Blind search" is a much more sophisticated idea than our Bill and his NAID mates are making out!] With no free lunch, it is blind search as input and blind search as output. The averaging of feedback information treated as input acts as a leveler, ensuring parity between information input and output. No free lunch preserves strict conservation [Tough, not true!] precisely because it sets the bar so low at blind search.

By distilling its findings into a single fundamental relation of probability theory, this work provides a definitive, fully developed, general formulation of the Law of Conservation of Information, showing that information that facilitates search cannot magically materialize out of nothing but instead must be derived from pre-existing sources.[False; information derives not just from S, but can also creep in from an algorithm's  execution time T ]

Blind search, blind search, blind search, blind, blind, blind,...... the repeated mantra of NAID culture which with its subliminal gnosto-dualism repeatedly refers to the resources of God's creation as a place of "blind natural forces". Sometimes you will also hear them talk about "unguided natural forces". But in one sense I would maintain the cosmos is far from "natural", and this is evidenced by the  sense of wonder its highly contingent form engenders among theists and atheists alike, all of whom can advance no logically obliging reason as to its highly organised configuration (accept perhaps Richard Carrier whose arrogance on this score would do Zaphod Beeblebrox  proud)

Bill's last sentence above is clearly false, as false can be; he's overlooked the slowly growing information term in relation 7.0. Information is not conserved during a search because the so-called "blind search" (sic) term is slowly, almost undetectably creating information. There is therefore no "strict conservation of information" (sic). That the so-called "blind search" (sic) is being understated by Bill and the NAID culture he represents becomes very apparent as soon as we realize that equation 7.0 has been derived on the assumption that we are using parallel processing; that is, a processing paradigm where the number of processors doing the computation is constant. But if we start thinking about the exponentials of a process which utilizes expanding parallelism the second term on the righthand side of 7.0 has the potential to become linear in T and therefore highly significant. This is why so much effort and cash is being put into quantum computing; Quantum computers clearly create information at a much more rapid rate and it is the monumental resources being invested in this line of cutting edge research which gives the lie to Bill's contention that information is conserved during computation and that somehow "blind search" rates as a primitive last resort. 

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As far as the big evolution question is concerned I regard this matter with studied detachment. God as the sovereign author of the cosmic story could introduce information into the cosmic configuration generator using either or both terms in relation 7.0; in particular if unlike primitive humanity at our current technological juncture God has at his finger tips the power of expanding parallelism to crack the so called blind search problem the second term on the righthand side of 7.0 has the potential to become significant. Accordingly, I reject NAID's wrongly identified "blind natural forces" category when those forces are in fact highly sophisticated because they are in the hands of Omniscient Omnipotence. The trouble is that the NAID community have heavily invested in an anti-evolution culture and it looks like they've past the point of no return, such is their huge social and tribal identification with anti-evolutionism. Ironically, even if bog-standard evolution is true (along with features like junk DNA) we are still faced with the Intelligent Design question. As for myself I have no indispensable intellectual investment in either the evolutionist or anti-evolutionist positions.

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As I have remarked so many times before, what motivates NAID (& YEC) culture's aversion to the idea that information can be created by so-called "blind natural forces" is this culture's a priori anti-evolution stance. Underlying this stance, I propose, is a subliminal gnosto-dualist mindset, and this mindset in this subliminal form afflicts Western societies across the board, from atheism to authoritarian & touchy feely expressions of Christianity; in fact Western religious expression in general. But that's another story. (See for example my series on atheist Don Cupitt - a series yet to be completed)

What's compounded my problem with NAID & YEC nowadays is their embrace of unwoke political culture, a culture which automatically puts them at odds with the academic establishment. I'll grant that that establishment and its supporters have often (or at least sometimes) subjected outsiders (like Bill for example) to verbal abuse and cancellation (e.g. consider Richard Dawkins & the Four Horseman, RationalWiki etc.). This has help urge them to find friends among the North American far-right academia hating tribes and embrace some of their political attitudes (See here). As I personally by and large support academia (but see here) it is therefore likely that I too would be lumped together by the NAID & YEC communities as a "woke" sympathizer, even though I reject any idea that the problems of society can be finally fixed by social engineering initiated centrally, least of all by Marxist social engineering. But then I'm also a strong objector to far-right libertarian social engineering which seeks a society regulated purely by a community's use of their purses (and then be pray to the chaotic non-linearities of market economics and power grabbing by plutocratic crony capitalists). In today's panicked and polarized milieu the far-right would see even a constitutional Royalist like myself who is also in favour of a regulated market economy, as at best a diluted "socialist" and at worst a far-left extremist, ripe for the woke-sin-bin!

NOTE: An article on "Conservation of Information" has recently popped up on Panda's Thumb. See here: Conservation of arguments