Tuesday, June 11, 2013

Discarded cicada shells

Another cicada photo. Albert sent this one of their discarded shells in New Zealand. He says “I thought the empty shells were actually critters that could jump up at me. It was only later that I learnt that what I had been photographing were nothing more scary than empty cicada shells!” The shells’ owners were not necessarily dead. After emerging from underground the cicadas molt (shed their skins) on a nearby plant for the last time and emerge as adults. The abandoned exoskeleton remains, still clinging to the bark of trees, as here.  More about their life-cycle in Wikipedia.

Cicada shells

Monday, June 10, 2013

Can cicadas calculate prime numbers?

Photo: Tom Wildoner
In the US the 17-year cicada hatch of 2013 is in full bloom. Millions of crimson-eyed critters and their otherworldly din, I've seen them described as. They showed up yesterday in Carbon County, Pennsylvania – the photo comes from EarthSky. These 17-year cicadas live out most of their long lives as nymphs underground, but, each 17 years, they crawl out of the ground for a three-to-four-week festival of singing and mating. Afterwards, they die. Why every 17 years? Because they are mathematicians, that’s why. They recognise 17 as a prime number and they use it to elude their predators. 

It works this way. Cicadas are easy prey for birds and wasps. Now it turns out that predators commonly have 2-to-10-year population cycles. Imagine a cicada species with a 12-year cycle: it would be a feast for any predator with a 2-, 3-, 4-, or 6-year cycle (factors of 12).

On the other hand, Stephen J Gould reasoned in a famous essay that a cicada that emerges every 17 years and has a predator with a 5-year population cycle will only face a peak predator population once every 85 (5 x 17) years.

Advantage of prime numbers 

This gives an enormous advantage to cicadas that know how to calculate prime numbers.  Some biologists however claim that advanced number theory is well beyond the cicadas insect-sized brain and suggest instead that the pattern emerged as a result of Darwinian natural selection: cicadas that matured in easily divisible years were gobbled up by predators, and simply didn’t live long enough to produce as many offspring. Those who, by chance, had long, prime-numbered life spans fared best, survived longest, and left the most offspring, becoming the dominant variation of the species. It seems there are now at least fifteen distinct populations of periodical cicadas. Cicada emergence is tightly timed, with the bulk of the insects emerging within a span of a few weeks. Any cicada that tries to break the pattern is highly likely to have her offspring gobbled up.

I first became aware of this cicada prime number behaviour a few years ago through an In Our Time episode on prime numbers which I highly recommend. It included my guru Marcus du Sautoy.

In another radio programme I heard the biologist Simon Conway Morris pour cold water on cicadas and prime numbers, but he didn't elaborate his reasons.

Sunday, June 9, 2013

Half a dozen obvious propositions

The English common law consists of about half a dozen obvious propositions, but unfortunately nobody knows what they are. 

Why does this aphorism, which I've just stumbled on, tickle me? It's known to us through Harold Chaloner Dowdall (1868-1955), a high court judge. Whilst he didn't invent it, he was sufficiently impressed by it to record it for posterity in the following letter to The Times in 1932, relating a remark he heard many years earlier when a junior barrister. 

Lord Sterndale [another high court judge] once said, “The common law consists of about half a dozen obvious propositions, but unfortunately nobody knows what they are.” He was reading a case I had looked up for him, and I did not know whether he was speaking to himself or enlightening a junior barrister in the mysteries of the law, and as his clerk immediately called him into Court the matter dropped. He was a leader at the time, and I think it was not long after he had taken silk. The observation is so witty and true that, unless it is already familiar, it deserves record; but as the number of those who knew Lord Sterndale diminishes, it would be interesting if any of your readers ever heard him make a similar observation.

The clerk immediately calling Lord Sterndale into court puts one in mind of the person from Porlock. Harold Chaloner Dowdall besides being a judge was also a regular commentator on ecclesiastical affairs, and in 1908-9 served as lord mayor of his native Liverpool. 

The phrase “taken silk” referred to a barrister becoming a Senior Counsel. I know all this from the Quote Investigator, who has additional information with citations if you want it.