Some thoughts about William Dembski’s Law of the Conservation of Information

Following a suggestion from Tom English I am taking the whole of this comment which was in the form a Word document and putting it on this blog.

Professors William Dembksi and Robert Marks have written a number of papers suggesting that there is a “Law of the Conservation of Information” and this law proves that life cannot have evolved through entirely natural processes (e.g. Dembski and Marks II 2009).  Roughly speaking their argument is:

(a)    There are outcomes in the universe – including many aspects of living things – that have “intrinsic targets”. E.g the intrinsic target of a protein might be the ability to carry oxygen in the bloodstream (variants of haemoglobin); the target of a whole genome might be the ability to develop a viable organism.

(b)    Producing outcomes that meet these targets can be considered as a search for the target in the space of all possible outcomes e.g a search for a viable genome in the space of all DNA sequences of that size.

(c)    The “endogenous information” content of the target is a way of referring to the improbability of finding that target using a “blind search” (more precisely – Dembski measures exogenous information as –log ₂  of the probability). A blind search is selecting a configuration at random to see if it meets the target.  The lower the probability of a blind search succeeding, the higher the information content of an outcome that meets the target.

(d)    The probability of a blind search succeeding is calculated using Bernoulli’s Principle of Indifference (BPoI) which is controversial way of coming up with a probability “with no additional information”. So without further information there is no reason to prefer one base pair rather than another in any sequence of DNA and using BPoI the probability of any base pair in any position is equally likely.

(e)    The probability of a search succeeding can be increased (and the information content of the target lowered) by using a better search. 

(f)     However, to do this it is necessary to find a better search and the difficulty (improbability) of finding a better search will always more than balance the gain in probability over a blind search. In terms of information – the loss of information from using the better search is at least compensated for (and may be exceeded) by the gain in information from finding the better search. This is the law of conservation of information.

(g)    Therefore, no natural mechanism can ever increase the overall probability of finding a target over the probability of using a blind search i.e. the amount of information in the observed outcome can never be decreased – any apparent decrease has to be compensated for by an increase elsewhere.

(h)    Only processes involving intelligence can increase information.

(i)      Many of the successful searches in life, are so improbable using a blind search (have such high information content) they could not have been reasonably accomplished in the lifetime of the universe.  So no natural mechanism can possibly have accounted for the success in meeting the target and intelligence must been involved.

The Dembski and Marks papers have been subjected to much criticism.  Most of this has focussed on the mathematics of (f) i.e. the law itself.  That is not my concern.  I am more concerned about (a) and (b):  the propositions that life contains intrinsic targets, and that a process that produces life is equivalent to a search for those targets.  The LCI makes a kind of sense when we are talking about a literal search for a target. For example, suppose you are confronted with a pack of playing cards face down. You know nothing about how they are ordered. You are allowed to turn over up to five cards one card at a time and want to turn up the ace of spades.  You can choose from an almost infinite number of search strategies for deciding which cards to turn over, for example:

• start nearest the top and work systematically from left to right;
• turn over one card and, if it is a spade, turn over another card next to it, otherwise choose at random;
• turn over the card corresponding to the day of the month and then every third card.  

The LCI may or may not be mathematically correct, but at least in this context it is somewhat plausible.  The chances of finding a search strategy that does better than just picking cards at random are probably very low and may well be lower than the increase in chances of success from using that strategy. But evolution is nothing like this. There is no target and no one is choosing a search strategy. 

Let’s look first at the concept of an “intrinsic target”.  In the case of the playing cards I had a target – I wanted to reveal the ace of spades.  Dembski would call this an external target.  It comes from outside and cannot be deduced just by inspecting the playing cards. Life does not have an external target; but Dembski claims that it has an “intrinsic” target. The problem is that he does not enlarge on this and it is hard to know what he means other than there are some outcomes that are alive and some that are not.  There is no sense in which anything or anybody has planned those outcomes or is striving to make them happen.  The word “target” seems misleading.  They are just those outcomes which are viable.

Even more misleading is the idea that someone or something is selecting a strategy to find these results.  In the case of the cards it made some kind of sense to talk of the probability of finding a search strategy.  Dembski and Mark’s proof of LCI does this by identifying various ways of enumerating possible strategies and making liberal use of BPoI to assign a probability to each strategy.  But this is just not what is happening in the case of evolution.  It makes no sense to even list the possible search strategies for finding life, much less to talk of the probability of one of them being used.

To demonstrate this it helpful to consider two different types of things that Dembski and Marks might mean by a search strategy for life.  Most simply they might just mean the process or processes which lead to life i.e. they consider all the different factors that lead from a lifeless planet 4 billion years ago to a viable genome now – the formation of replicating molecules, the variation in those molecules, the environment which selects the variations etc.  A “search strategy for an intrinsic target” in this sense just means a process that causes a distinctive outcome. To enumerate all possible causes and then apply BPoI to them appears hopeless. But if it was possible and the LCI held for such causes it would have the most bizarre consequences.  Consider almost any case where there is a distinctive outcome and a cause. For example, when molten lava solidifies at mid-ocean ridges, iron-containing minerals in the lava align themselves with Earth’s active magnetic field. The alignment of the minerals is a distinctive outcome and has as much right to be called an intrinsic target as a genome that is viable. If we knew nothing about the cause then all directions would appear to be equal and using BPoI the chances of these minerals all being aligned in same direction by chance are negligible.  The alignment is very high in “information”. Now applying the LCI and treating the cause (the earth’s magnetic field) as a search strategy, let us use some of Dembski and Mark’s notation.

Let p be the probability of the minerals being aligned by chance using BPoI. Then the information content of those minerals is called the endogenous information I_Ω = -log(p).

Let q be the probability of the minerals being aligned given a magnetic field. The information content of the minerals in this case is called the exogenous information I_S =-log(q).

The active information I₊ is defined as I_Ω – I_S = log(q/p).

The LCI says that the search strategy must contain at least as much information as the active information. i.e. the probability of the earth having a magnetic field cannot exceed p/q.  The probability of the minerals being aligned given a magnetic field is close to 1 i.e. q is approx 1. So we conclude that the probability of the earth having a magnetic field cannot be greater than the probability of the minerals being aligned by chance: two events which are entirely disconnected. Furthermore, the value of p depends very much on the number of minerals that are aligned: the more minerals the lower the maximum probability of the earth having a magnetic field. I think this is sufficient to act as a reduction ad absurdum for the LCI in this case.

It may be that Dembski and Marks mean something slightly different when they refer to a search strategy for the “target” of life.  Perhaps they are referring to a particular aspect of the way evolution causes life. They take the infrastructure of a replicating molecule such as DNA or RNA for granted and are referring specifically to the way variation produces candidates for life. Intuitively this feels more like a search. The mental model of evolution trying different variations at each replication until it reaches its target is attractive.  The reason is that the link between variation in DNA and a viable genome is not as clear as the link between the earth’s magnetic field and the alignment of minerals.  Given the magnetic field it is almost inevitable that minerals will be aligned.  Given undirected variation it is far from inevitable that the result will be life.  This perhaps where LCI has something to contribute?

This leads to a familiar topic in the discussion of intelligent design. If the range of viable genomes was completely unstructured so that even a small change was no more likely to lead to a viable genome than throwing all the base pairs in the pot and choosing any DNA string of the same length – then it hardly needs the LCI to tell us that evolution would not lead to life.  But life is not like that.  Starting from a viable genome, the common variations (point mutation, chromosome duplication etc) are far more likely to lead to another viable genome than selecting a string of DNA at random.  Such variations are happening every time an organism reproduces and the results are viable more often that not. The search space of possible genomes is highly structured in the sense that viable genomes are “close” to each other.  Given this, it follows that variation and selection is likely to lead to viable life forms. It may (or may not) need extraordinary luck to get started – to stumble on the first viable replicating molecule – but once the process is underway the structure makes further life plausible.  The claim of Dembski and Marks is presumably that this structure provides “information”. But given their definition of information this is the same as claiming that that the probability of the structure existing must be very low.    But now exactly the same logic applies to the structure as applied to the earth’s magnetic field. The probability of such a structure is hard to define, much less estimate (it does not seem that surprising that a small change to something that works is more likely to continue working than a big change, but it is hard to prove).  But whatever that probability, it is hard to see how it can be limited by the overall frequency of viable genomes in the space of DNA sequences.

The application of LCI to evolution appears to be based on a false invalid analogy between the probability of choosing a search strategy and the probability of a cause existing.

Bibliography

Dembski, William A, and Robert J Marks II. “Conservation of Information in Search: Measuring the Cost of Success.” IEEE Transactions on Systems, Man and Cybernetics A, Systems & Humans. 2009. 1051-1061.