Chaotic universe
Do we finally have a handle on chaos theory – and how it influences the world around us?
Have we finally got a handle on the theory that governs the cosmos and everyday life?
When it comes to surviving in space, the tiniest things can be the difference between life and death. As Canadian astronaut Chris Hadfield said: “An astronaut who doesn’t sweat the small stuff is a dead astronaut.” That may be the case for human space travel, but astronomers are increasingly suspecting the same mantra also applies to the wider universe. When it comes to the cosmos, it seems chaos theory is king.
Chaos theory traces its origins way back to the 19th century. French polymath Henri Poincaré was attempting to win a prize of 2,500 crowns – a third of a professor’s yearly salary – offered up by King Oscar II of Sweden and Norway to celebrate his 60th birthday. To win you had to predict the orbits of the planets. Isaac Newton’s work on gravity allows you to foretell the future positions of two gravitationally intertwined objects with clockwork precision. Yet throw a third object into the mix and that ability vanishes. Poincaré failed to solve this ‘three-body problem’, but was awarded the prize nonetheless for important insights into why it is such a thorny conundrum to crack.
Russian mathematician Sofya Kovalevskaya also carried out important work on the problem. The puzzle is difficult because even the smallest changes in a system with many moving parts can lead to huge differences later down the line. That, in a nutshell, is the essence of chaos theory. “We wouldn’t have chaos theory if we didn’t study planetary orbits,” says Dr Paul Sutter of the Flatiron Institute in New York.
American mathematician and meteorologist Edward Lorenz compared it to the flap of a seagull’s wing affecting the weather. He later switched his metaphorical creature to a butterfly, and to this day it is still known as the ‘butterfly effect’. In the 1960s Lorentz was using computers to try and predict weather patterns on Earth, but he found that the outcome was wildly different even though it looked as if he was modelling the same situation each time. Further investigation revealed that tiny rounding errors in the values fed into the computer blew up into major differences in the predicted forecast.
Today Lorenz gets the lion’s share of the credit, but Mary Cartwright and John Littlewood analysed chaotic patterns in radio signals during World War Two. To this day chaos theory places a limit on how far into the future we can accurately predict the weather. Chaos theory makes meteorology an imperfect science.
Mathematicians have been studying chaos theory ever since Lorenz’s insights. Somewhat counterintuitively, they have found that chaotic systems are not as unpredictable as they first seem. “It helps us to identify patterns, key elements, hidden rhythms and orders in systems that are not normally apparent,” says Sutter. Period doubling is just one example. In a chaotic system, the time it takes for a pattern of behaviour to repeat increasingly grows to twice as long as before. Eventually the behaviour takes so long to replicate itself that the system appears lacking in an underlying order – it looks
chaotic. However, there is method in the madness if you know where to look. In 1975 American mathematician Mitchell Feigenbaum, one of the pioneers of chaos theory, discovered that the ratio of the points at which the period doubles increasingly approach the number 4.6692… as the system becomes more chaotic. This number is now known as the Feigenbaum constant in his honour.
Applying chaos theory to the cosmos could help us to explain how the Earth came to be the life-hosting planet it is today. The Sun was one of many stars formed when a vast cloud of interstellar gas and dust collapsed around 5 billion years ago. “Tiny little changes in that gas cloud can lead to very big changes in the population of stars that form,” says Sutter. An extra little clump of dust here, a tiny bit of extra spin there and the Sun could have been a very different star, or even not have formed at all. Star formation may look like a chaotic system, but there could be an underlying mathematical order that reveals the likelihood of forming the kind of stars suitable for sustaining habitable planets. In turn that could point us to the appropriate corners of the nearby universe to search for alien life. The creation of new stars is often studied by creating very complex computer simulations. “Chaos theory gives us a mathematical tool to help us get a handle on what’s going on,” says Sutter.
Why is our Solar System a good place for life to emerge, evolve and thrive? Our cosmic backyard looks serene today, with planets neatly drifting around the Sun in well-behaved orbits and relatively few unstable asteroids left to careen into them.
Yet today’s peace and quiet belies a tumultuous youth. “We suspect that a lot more planets formed around the Sun and some of them were on chaotic orbits,” says Sutter. Tiny changes in their speed
“It helps us to identify patterns, key elements, hidden rhythms and orders in systems”
Paul Sutter