Editor’s note: We are delighted to present a new series by William Dembski, adapted from his Substack. This is the 11th post. Find the full series so far here, “My Personal History with Information.”
To understand what conservation of information means today, I need to turn to an example from The Blind Watchmaker. It was this example that set me on a path to understanding conservation of information in its general form (not just with respect to specified complexity). In The Blind Watchmaker, Richard Dawkins describes a computer program that generates the phrase METHINKS IT IS LIKE A WEASEL from a random sequence of capital letters and spaces. Starting from a random sequence and then by making random changes, as intermediate sequences are rewarded for being, letter by letter, closer to the target sequence METHINKS IT IS LIKE A WEASEL, Dawkins shows how these letter sequences can converge (“evolve”) to the target in short order (roughly 40 steps) whereas it would take something like 10^40 steps on average to get this target sequence by pure chance. The much faster convergence to the target in the first scenario, Dawkins argues, demonstrates the power of natural selection.
A Moment’s Reflection
Yet even the smallest reflection reveals that the target sequence was built into the algorithm that generates it, for how else could the algorithm determine proximity to the target sequence or reward increasing proximity? It became clear that Dawkins was engaged in a subterfuge, and that he had in fact smuggled in the information that he claimed to be getting out for free. The outputted sequence was made to seem like it had been produced for free. But in fact, the information outputted merely disguised the information inputted, building it into the algorithm. This, it seemed to me, was a perfectly general phenomenon with evolutionary computing, and so there would be no way for such algorithms to create novel information in the way Dawkins was claiming.
At the time I came to this conclusion in 1997, I was sharing office space with Paul Nelson in Evanston, Illinois. Paul is incredibly well read and keeps up with a wide range of literature relevant to intelligent design. As I was explaining to him the fallacy in Dawkins’s example, he recalled seeing a then recent paper by William Macready and David Wolpert on No Free Lunch theorems. These were information-theoretic results for searches in evolutionary computing (thus covering Dawkins’s example) showing that no search, on average across fitness landscapes, outperforms blind search. It was not a result that many wanted to hear at the time, especially those who thought evolutionary computing provided confirmation for biological evolution. But the math was solid, and there seemed no way around these results.
A Hill-Climbing Algorithm
The No Free Lunch theorems, however, didn’t go far enough for me. It’s one thing to say that any search on average does not outperform blind search. The fact is, however, that for specific problems, some searches do outperform blind search. Dawkins’s algorithm generated METHINKS IT IS LIKE A WEASEL quickly with high probability because it was in effect a hill-climbing algorithm where the hill ascended with smooth gradients and the top of the hill corresponded to this sequence. And yet, any other sequence could likewise have been designated as the top of some hill. So the question, left unanswered by No Free Lunch, is what makes a search better than another, especially better than a baseline search that is purely random.
In Dawkins’s example, the difference maker that improved the search for METHINKS IT IS LIKE A WEASEL over blind search is the information inputted into the algorithm that directed it to reward sequences that, letter by letter, were closer to the target sequence. But was this smuggling in of information specific to Dawkins’s example and thus something that could be avoided in search more generally, or was it a property of any search that, if it improved on the probability of success in finding a target, it did so by incorporating novel information over and above what was available in a baseline search that had a low probability of success. I suspected this was a general phenomenon, and in practice I could find no counterexample to it. I called that phenomenon “displacement” — the success of the search was displaced or offloaded to some item of information that was itself unaccounted for.
Alice, Bob, and the Million Dollars
To illustrate this point, imagine trying to explain how Alice came into possession of $1,000,000. It would be one thing to say of Alice that, based on her own skills and effort, she earned $1,000,000. This would be like a baseline search, based on its inherent resources, achieving a target with high probability. But what if instead Alice’s $1,000,000 resulted from Bob giving her that amount? In that case, the natural question becomes where did Bob get the $1,000,000. The explanation of the $1,000,000 in Alice’s pocket is thus displaced and left unresolved. Likewise, if a baseline search gets supplanted by one that has much higher probability of successfully locating a target, where did it get the information to make itself so much more powerful a search?
Next, “Evolutionary Computing: An Audit of Smuggled Information.”