Good hair day for mathematicians

Fermat’s last theorem and the Poincaré conjecture – just two of the great mathematical problems that have tested and teased humanity’s love affair with numbers for generations. And it is a love affair that has given us so much.

Our ever increasing fluency in what many regard as the language of the universe permeates all of our modern technology. It has become the very bedrock of modern science.

Yet, on the Science Lite desk we have what could be regarded as an ‘uneasy relationship’ with mathematics – in the way that a wildebeest has an ‘uneasy relationship’ with a lion. It frightens us – if we stumble upon an equation our fight or flight response kicks in and we inevitably end up cowering in a corner trying to avoid its toothy jowls. Safe to say that the language of the universe is one that we have failed to successfully acquire – as such deep mathematical insight holds an almost romantic reverence for us. At once unknowable, enchanting and mysterious – for us it’s as if mathematicians are wise sages dealing in the mystically abstract.

Yet even we are aware of the very real importance and truth held within mathematical equations. As such we were surprised that such an important one had skipped us by. Back in 2012 there was an announcement that a problem which has being playing on the mind of number crunchers since the times of Da Vinci had finally been cracked. That we missed it wasn’t the only surprising thing here – there was another peculiarity…

The problem solved doesn’t really seem worthy of the sages we hold in such esteem. You see the problem that has so entranced them, that has caused many scratched heads and chewed pens, does not deal with the quantum mechanics of particle collision, or the topology of curved spacetime – rather it deals with the shape of a ponytail. Research published in Physical Review Letters provides the first – and, dare we say it, probably the last – quantitative understanding of the distribution of hairs in a ponytail. To derive the Ponytail Shape Equation, the mathematicians took account of the stiffness of the hairs, the effects of gravity and the presence of the random curliness or waviness that is ubiquitous in human hair.

Together with a new quantity described in the article – the Rapunzel Number – the equation can, they say, be used to predict the shape of any ponytail. Ponytail Shape Equation? Rapunzel Number? What an earth has happened to the sacrosanct word of mathematics we found so worthy? This isn’t mysterious – it’s plain bizarre. Just how much of a bad hair day did the researchers involved suffer to inspire them to finally crack this pesky problem?

In fact Professor Raymond Goldstein from the University of Cambridge and Professor Robin Ball from the University of Warwick – the hair heroes behind the equation – argue that theirs is a solution that encapsulates all that it is to be a physicist. “To be able to reduce this problem to a very simple mathematical form which speaks immediately to the way in which the random curliness of hair swells a ponytail is deeply satisfying. Physicists aim to find simplicity out of complexity, and this is a case in point.”

Hmm – perhaps we are splitting hairs (…we are truly, deeply sorry for that) but would their satisfaction not have been even deeper if they had aimed their sage-like talents at a more worthy cause? Not so, it turns out this has important implications for understanding the structure of many materials made up of random fibres, such as wool and fur. And that is just a start – once an equation is born it can end up in all manner of scrapes and adventures. Just ask Pythagoras (you can’t, obviously – but you catch our drift), his famous equation (a2 + b2 = c2) ended up being vital in the construction of the theory of relativity and in doing so re-shaped the way we understand the universe.

Time, we think, to set the Ponytail Shape Equation free and see what it gets up to…