The sheer complexity of natural organisms is often cited as a “scientific” reason why evolution must be false – as here for instance (though when this fallacy of the argument is pointed out the poster resorts to attacking people for being ‘ungodly’, therefore giving the game away) – it is simply too much to expect such random arrangements to come into being.

Reading Herbert A. Simon‘s classic 1962 paper “The Architecture of Complexity” we can see this argument get taken down using, perhaps mischievously, an analogy long favoured by creationists, that of a watchmaker.

Simon’s argument runs as follows: imagine we had two watchmakers making watches of equal quality, each with 1000 separate parts. But the two use two different methods. Watchmaker A’s watches are hierarchical in nature, she makes the watches out of hierarchies of ten pieces, which are then assembled into another hierarchy of 10 pieces, and then these 10 pieces are assembled together to make the watch. Watchmaker B takes a different approach, assembling all 1000 pieces in one ‘flat’ system.

Now when either watchmaker gets a telephone call from a potential customer they must put the piece they are working on down and restart work on it from scratch when they put the phone down.

This means when B gets a call he has to start building the whole watch again from scratch, while when A gets a call she only has to restart the piece in the hierarchy. What are the outcomes for their businesses?

Well, let us say they can add a piece every minute. Then, obviously B takes 1000 minutes to make a watch.

But A takes more time: she makes 100 pieces of 10 pieces – 1000 minutes and then a further 100 minutes to assemble these into 10 pieces and another 10 minutes to put these 10 pieces together – a total of 1110 minutes – more than 11% longer.

But, in fact, A is far more productive than B. Because every time a call comes through, A is only set back 5 minutes (plus the call time) on average (ie half an assembly), whereas B is likely to lose much more time.

Let us us say both watchmakers get a call on average every 100 minutes of manufacturing time – so the probability of getting a call in any minute is 0.01. Then A will get an average of 11.1 calls during each watch manufacture – adding 55.5 minutes (for ease of exposition we ignore that this extra time increases the chances of getting a call). So A produces a new watch every 1166 minutes or so (not enough to keep up with demand, we note, but that’s another issue).

What of B? The chances that B will complete a watch are very low indeed. The chances that B can complete a watch are in fact – the probability that a call will not come through in 1000 minutes – roughly a 0.00004 chance. So for every 8 hours of the working day (480 minutes), on average A will output watches and B will output – in other words A will be more than 21,000 times more productive than B.

The relevance to evolution is that the creationists are arguing that natural selection follows the path of B, when obviously it follows A. Living things are hierarchies – and as they evolve they do not have to start from scratch every time.

Indeed the example shows that repeatable natural processes in general will tend to generate hierarchies because otherwise they will not be repeatable.

The paper contains a lot of other fascinating insights about the natures of hierarchies – some of which have been confounded by recent experience of social media. I may blog about some of them too in coming days.

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