# It’s official: size does matter (yes, the size of that)

Yes, we are talking about penis size.

(Photo credit: Wikipedia)

Last week the US Academy of Sciences published a peer reviewed paper based on a study of the attractiveness to young women of various images of naked men.

The abstract for the paper reads:

Compelling evidence from many animal taxa indicates that male genitalia are often under postcopulatory sexual selection for characteristics that increase a male’s relative fertilization success. There could, however, also be direct precopulatory female mate choice based on male genital traits. Before clothing, the nonretractable human penis would have been conspicuous to potential mates. This observation has generated suggestions that human penis size partly evolved because of female choice. Here we show, based upon female assessment of digitally projected life-size, computer-generated images, that penis size interacts with body shape and height to determine male sexual attractiveness. Positive linear selection was detected for penis size, but the marginal increase in attractiveness eventually declined with greater penis size (i.e., quadratic selection). Penis size had a stronger effect on attractiveness in taller men than in shorter men. There was a similar increase in the positive effect of penis size on attractiveness with a more masculine body shape (i.e., greater shoulder-to-hip ratio). Surprisingly, larger penis size and greater height had almost equivalent positive effects on male attractiveness. Our results support the hypothesis that female mate choice could have driven the evolution of larger penises in humans. More broadly, our results show that precopulatory sexual selection can play a role in the evolution of genital traits.

If you need help with that, what it is saying is:

• We already know that larger male genitalia are a good indication of how likely young are to survive – so evolution pushes towards larger genitalia;
• But now we have evidence that women prefer large genitalia also;
• That female choice probably contributed to humans having bigger penises than other primates;
• Very big penises are not any more attractive than big penises;
• The taller you are the more important it is to have a large penis (or alternatively, if you are short then a larger penis is not much help);
• If you are more muscular you can get away with a smaller penis.

Update: Here’s a handy measuring chart from the paper:

Me? I’m going to spend even more time down at the gym.

# Watchmakers for evolution

Watchmaker, from Wikipedia

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 $0.99^{1000}$ – 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 $\frac{480}{1166}$ watches and B will output $\frac{480}{1000} \times 0.00004$ – 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.

# And on to “The Selfish Gene”

English: Richard Dawkins at New York City’s Cooper Union to discuss his book The Greatest Show on Earth: The Evidence for Evolution (Photo credit: Wikipedia)

So, having completed (listening to) Kevin Mitnick’s Ghost In The Wires: My Adventures as the World’s Most Wanted Hacker I decided that the idea – of listening to a book while pounding away on the exercise equipment at the gym – is a good one and I would pick another book, but not a novel (it now seems lazy to listen to a novel but not to a non-fiction work).

I picked The Selfish Gene. Richard Dawkins has taken a lot of flack in the UK of late, adding opponents of private university education to his traditional enemies in the world of religion, after he supported plan for a private university college in Bloomsbury. But the prefaces to the book make it clear that he’s been dealing with wider political interpretations of his work for some time.

In fact, he seems very defensive about them all. Yet it is difficult to disagree with the comment of Stephen Jay Gould, quoted at the start, that the theories in the book will be seen as part of an ideological flow to the right in the 1970s. But then again, as Dawkins makes clear, the theories themselves are about the truth, not politics.

Promises to be an interesting ride…

# Evolution and the second law of thermodynamics

Image via Wikipedia

When I wrote my first piece about Roger Penrose‘s Cycles of Time – one of the links offered to me was to a Christian fundamentalist blogger who claimed that the second law of thermodynamics showed evolution could not have taken place:

E. Evolution contradicts the Second law of Thermodynamics

In the Theory of Evolution it is proposed that “simple life” evolved into more complex life forms by Spontaneous Generation. Both Darwin’s Theory of Evolution and the Spontaneous Generation model both directly contravene the Law of Biogenesis.

The Second Law Of Thermodynamics

The Second Law of Thermodynamics states that the disorder in a system increases, rather than decreases.

The problem for this argument’s advocates is that Penrose demolishes it in brilliant style. I won’t quote from him directly, but I will try to summarise his argument.

Penrose begins by actually restating the fundamentalist argument in a much wider sense – it is life itself that on a naive view would appear to violate the second law – after all our bodies do not melt away (so long as we live), but remain highly ordered and as we grow (eg our hair or nails) appear to create order out of disorder.

The key to this is the Sun. The first thing a secondary school science student is taught is that the Sun supplies the Earth with energy but, in fact, this is not true in the sense that the Sun does not provide a net increase in energy on Earth – if it did then our planet would continually heat up until it reached an equilibrium. The Earth re-radiates the Sun’s energy back into space at a equal rate to which it is recieved.

What the Sun is, though, is much hotter than surrounding space and so it sends the Earth a number of high energy (yellow light) photons. When the Earth re-radiates the Sun’s energy it does so at a lower temperature than the Sun – essentially at infra-red frequencies – so many more photons are radiated back into space than are received. More photons means a greater phase space and hence it means a higher entropy. So the Sun continually supplies the Earth with low entropy energy which processes on the Earth – including life – convert into high entropy energy.

For instance when we eat food we convert that low entropy food source (eg an egg) into high entropy heat energy. The food source itself ultimately derived its energy from the low entropy energy source that is the Sun, and so on.

Of course, all the time, the Sun’s own entropy is increasing, but we don’t need to worry about the consequences of that for a few billion more years.

It’s a brilliant, beautiful, argument though it is also one that is seldom, if ever, taught in schools.