Monday, May 19, 2008

When small changes make big differences

Artist's conception of  a supernova explosion
Image credit: NASA/CXC/M. Weiss

When dealing with predictions, sometimes some very minor changes to your input can make drastic changes in the output.

For example, a colleague of mine is running several simulations of stars about ten times more massive than the sun. He's making minor tweaks in between simulations. Sometimes the star loses matter a little faster, sometimes a little slower, sometimes the star is spinning faster, and sometimes slower. At the end of the simulation, the star dies. Sometimes it explodes as a spectacular supernova, which rips the entire star apart (like in the artist's conception above), and sometimes it forms a white dwarf, a pile of glowing ashes that slowly fades away. Very minor tweaks to the inputs make a big effect at the end -- either a big explosion, or a fading whimper.

These differences aren't because we don't understand physics. We understand it quite well. In fact, these very small differences to the inputs make very small differences in the star throughout its entire life, up until the very end. But the star is straddling a fine line dividing two very different fates, and we don't know which set of inputs is correct, because we haven't measured them accurately in real stars. Or maybe they are all correct, so that in the real Universe, some stars ten times more massive than the sun will explode, and some won't.

My point is that we understand the structure and the evolution of stars very well, with some points we aren't sure about (like how fast stars lose matter as they age, or how fast they spin). Astronomers will have giant arguments at conferences and in papers over these uncertain points, but if you look at the entire lifetime of a star, these uncertainties make very small differences. Eventually, though, there comes a point where the difference becomes huge.

We see the same thing in our daily lives here on Earth with regard to the weather. If you compare forecasts coming from different computer models that treat the inputs slightly differently, the forecasts will often agree quite well in the short term, even up to a few days. Beyond that, the models start to show differences. And if you run detailed weather forecasts months into the future, they will completely disagree. This isn't because we don't understand the basics of weather forecasting; it's because the small details can make a big difference over time.

So, when you see scientific studies coming out with widely different conclusions, we need to be careful on how we interpret those results. Some people claim that different conclusions mean we don't understand anything about physics or medicine or climate. That idea is wrong. Mostly, we have a pretty good understanding of the big picture, but the details remain to be filled in. And while those details can make a big difference far down the road, it doesn't mean that our theories are useless in the meantime.

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