Fast-forwarding reality

In the film the Matrix, the world is simulated in a vast computer allowing the humans to experience the world in all its detail even though it's not there. Of course if all you are trying to do is model the world as it happens then it's easy. You only have to go at the speed of reality.

Real scientists want to do better than that. They want to see what happens in the future. That means the computers have got to go faster than reality!

This is done using what is called abstraction by computer scientists. It is essentially just the idea of losing detail that doesn't matter. Think of a road map. It represents reality, just not all of it. To have a fully accurate map, it would need to be the same size as the area it mapped. Instead it shows only the detail that matters to the task in hand, getting from here to there. That means it can be vastly smaller than the area it maps.

When computers are used to simulate some aspect of reality, the same idea holds. You don't need the whole of reality, just the things that matter. They are based on a "mathematical model" - a mathematical description of how the things that matter change over time. By focussing on those aspects and jumping time forwards in suitable intervals, accurate predictions of what will happen in reality can be obtained.

Take the weather. We take it for granted that the weather reports will give us a rough idea of what the weather will be like tomorrow. Lots of sophisticated science, maths and computing go into seeing that little bit of the future as accurately as we do. Mathematical models of the way weather systems change are used to simulate the weather. Data about what the weather is like now are collected, not just here but all around. From that information of the current state, the computer steps the model forward in time to predict what happens in the future. The faster the computers, the more data that can be number-crunched and so the more accurate the predictions. Well, maybe.

Turns out though that there are limits to what is possible. We may never be able to accurately predict the weather more than 4 or 5 days ahead, however fast the computers become. Reality contains a sting in the tail that means it can be more complicated than we might have hoped.

This was seen most dramatically in October 1987 when the BBC weather forecast suggested the worst of the coming storms would miss Britain heading up the North Sea instead.

...Britain woke up to the worst storms in three hundred years!

The problem is that weather systems have a property that mathematicians call 'chaotic'. Chaotic Systems aren't random. From step to step they are predictable. It is when you try to take too many steps into the future in one go that the problems arise. In chaotic systems, tiny differences in the current state lead eventually to widely different future states. That means if your measurements of the current state are not totally accurate your long-term predictions will probably be wrong.

What that means for weather forecasting is that if your observations are not accurate enough then the computer model will appear to be fine to start with. It will get the weather right tomorrow perhaps, or even the day after, but then after a few days the real weather will start to drift off, doing its own unexpected thing until eventually the model's prediction will be way off track predicting something totally different. You can see this if you track how the long term weather forecasts are changed each day. The replacements each day are slight adjustments to the previous days predictions.

In 1987 the computer predicted the storm would head off to the East but it 'changed' direction: it drifted off the prediction. The model looked like it was doing fine, but actually it wasn't. The critical difference was just too small to see until it was too late. Oops.

'We can predict the weather accurately provided it doesn't do anything unexpected', as Mathematician Ian Stewart was told by one weather forecaster.

Computer simulations based on mathematical models now routinely fast-forward reality so we can see into the future. With models such as climate models which aren't looking at the detail we can even get a good idea of what the future will be like decades away. Don't expect the whole of reality ever to be fast-forwarded accurately on a computer though. There will always be some things we can't see when our computers use their mathematical model looking glasses to see into the murky swirls of the future. Chaos wins hands down when it comes to reality.