The Science of Discworld IV Judgement Da - By Terry Pratchett, Ian Stewart Page 0,32

our inability to model observations in quantum mechanics in a way that corresponds to actual experimental apparatus. Instead of admitting that we can’t say what happens when we observe the world, and find just one state out of many potential ones, we insist that the entire universe must keep splitting into pieces that include all possible outcomes. This is just like insisting that the entire universe revolves round a stationary Earth, instead of accepting that maybe the Earth spins instead.

Since many things did not happen when you came into being, what about those that did? Were lots of them random rolls of the genetic dice, in which one sperm carrying these genes got there and the other 200 million missed out? Or a specific cannonball took an arm off and missed all the rest … or killed other people? Were other – perhaps all – events strictly determined by what had happened the instant before, which in turn was determined by the instant before that? Do we have to choose between everything that happens being the luck of the draw, or everything being strictly causal and determinate, from the Big Bang onward, through now into the infinite future? So that only one future was ever possible?

The opening chapters of Daniel Dennett’s Freedom Evolves show conclusively that we can’t – ever – decide between these options. They aren’t real choices: determinate/indeterminate isn’t the way to go, because we can’t ever know which applies. The distinction makes sense only in a thought-experiment where we rerun the entire universe again, starting from an identical state, and check whether the same events occur both times. It is a valid distinction for how we think about our world, for the kinds of model we propose, but it’s not a meaningful statement about the world itself.

We could take examples of events from anywhere and anything, and discuss their provenance: what makes them happen. Here we will look at three. The first example shows how difficult it is to demonstrate a cause in the real physical world, because tiny events can have tremendous outcomes. The second shows how, in our cultural world, small events – or the absence of such events – can take over a social universe and bias it away from the desirable outcome. Finally, we’ll show how meddling by humans can completely change biological systems – and we’re not thinking of dodos.

In the 1960s Edward Lorenz, a mathematician and meteorologist, discovered that tiny differences in computer input for (a toy model of) weather prediction could lead to large differences in the resulting forecast. From this discovery, together with a variety of other inputs, came the mathematics of deterministic chaos. We have all heard how the flapping of a butterfly’s wings in Tokyo can cause a tornado in Texas a month later. This is a fine, dramatic example, but it considerably misrepresents causality. It suggests that only that butterfly is needed for the tornado, when actually it’s the difference made by that butterfly that changes the circumstances just slightly, and flips the balance of causality into another path, a different trajectory on the same attractor. In reality, our world is full of butterflies.

Weather is a dynamic path through the attractor that we call climate. As long as the climate stays the same, the attractor doesn’t change, but the path through it can. We then experience the same kind of weather, but in a different order. Climate change is more drastic: it alters the attractor. Now the entire range of possible weather-trajectories is different. Nonetheless, much of it still looks like plausible weather from the original attractor, because the attractor may not undergo any radical change – it need not encounter a tipping point. It can get a bit bigger, a bit smaller, or move around a little. We can’t observe attractors directly, but we can reconstruct them mathematically from observations, processed in the right way. The simplest way to detect change in the attractor is to observe data such as long-term averages of temperature, size and frequency of hurricanes, likelihood of flooding etc. Many objections to ‘climate change’ confuse climate with weather.

We wrote a long piece in The Science of Discworld III about causality, and don’t want to repeat that here. Enough to say that there is not any single cause of any event; it is almost always truer to declare that all of the preceding events contribute, than to point to one cause. However, stories do have a linear structure: A causes B causes