CRUNCHING THE NUMBERS
PHOTO: JOHN MCDERMOTT
GEOFF NICHOLLS SHEDS LIGHTS ON THE ARTS.
Ingenio May 2003
Arts graduates may think themselves lucky that they escaped university without having to grapple with mathematics. But maths is now grappling with the humanities and shedding light on such subjects as linguistics and archaeology. Dr Geoff Nicholls, a senior lecturer in the subject most feared by non-scientists, has a passion for bringing mathematical theory to bear on thorny problems in the humanities, and coming up with practical solutions.
"Here is an example of an amazing fact," he says.
"When you look at all the languages in the world, it really
is possible that they contain common words of essentially arbitrary
age. Look at the word for the number 5. The same word for 5 can
be recognised in a great many Indo-European languages. How does
that work? It's because they're all descended from ancient common
languages."
Nicholls takes the idea further to look at the ancient languages
of Australia or Papua New Guinea. It may seem improbable that
languages which separated from European languages so long ago
would have words in common with them. But maths can tell the linguist
about the probability that these diverse languages contain common
words.
"Just a very simple back-of-the envelope calculation shows it is quite likely these languages contain words descended from a common ancestor." The idea that maths can be useful in the humanities is something that particularly appeals to Nicholls. "When people talk about applied maths, they tend to mean in the physical sciences. It's particularly fun when you can make a contribution in humanities," he says.
Often questions relate to dating: an archaeologist may want to know when people occupied a particular site or a geneticist may ask whether two people have a common ancestor. "That is the real thing all my collaborations have in common they are dating problems. But the actual mathematical models you use are dictated by the application."
Nicholls has collaborated with an archaeologist on radiocarbon dating and with a geneticist on DNA sequences of the HIV virus, seeking to pin down when patients became infected. That research has led to what Nicholls describes as a Jurassic Park scenario the recent notion that fossil DNA can be obtained and used for dating.
The method can be used alongside radiocarbon dating which is far less reliable in marine environments and one of Nicholls' students has applied genetics work to penguin fossils dug up in Antarctica. The technique might also shed light on the controversy in New Zealand history over the date of the arrival of Maori. "I would love to have a go at dating some old Polynesian rat DNA," he says.
Nicholls, who has taught maths at Auckland since 1995, moved into applied maths because of his interest in arts, languages, archaeology and history, combined with his conviction that maths could assist the humanities. "You can contrast the kind of applied maths I'm doing with pure maths. I'm letting the biologist or anthropologist or whatever tell me what mathematical structures I should be dealing with. That almost always leads to an interesting mathematical problem," he says. "It's important to me that it's useful, but it's also important that it's a mathematical problem. I'm not interested in just cranking the handle and solving everyone else's problems. I'm not that virtuous." CATRIONA MACLENNAN