In the curious case of the brain-download it is not enough to create a computer model that is similar to a human brain. For a successful download of your brain we need to recreate, to a high-level of accuracy, 'Your' exact brain. Your unique and wonderful brain, with all its imperfections and hard-won connections which you’ve trained and pruned your whole life. The computer model has to be exactly the same as your biological brain in terms of how it behaves, otherwise it simply doesn't count. A half-baked, inaccurate model would not really be ‘You’, or at least would cease to behave as ‘You’ would after a short amount of time. And who wants to live forever as an approximation of their former self?
The issue then is not whether we will ever have the technology to reproduce your brain digitally, but whether a digital copy of your brain could ever be good enough to be indistinguishable from your real brain. We might almost dismiss the notion on principle because a computer model is, by necessity, a summary of a real scenario. Since a summary could never contain the same amount of information as the original (otherwise it would not be a summary), the premise is necessarily false. However it would be foolish to suggest that a model cannot meaningfully represent reality. After all, we use models all the time. The map on your phone, for example, is a digital model of your surrounding geography. The important information, the roads and place names, are contained in the map, but everything else is ignored. The textures and smells of the real world aren’t needed for the map to be useful, so they are ignored. This reduces the amount of information in the model while preserving its behaviour. Theoretically we should also be able to reduce the amount of information we need to represent in our computer-brain-model while still preserving your brain’s behaviour. However, the behaviour in this case is vastly more complex, meaning that the more information we leave out, the higher the chance of producing a bad model.
Models of relatively simple systems can afford to be superficial. A simulation of a snooker game, for example, doesn’t need to take into account the effect every hair on the snooker table has on the moving ball. It can afford to ‘zoom out’ and represent the net contribution of all the hairs with a summary variable, such as 'Friction'. Because the system is simple, our model will be able to make accurate predictions of the ball’s trajectory despite summarising reality to a great extent, and ignoring all the tiny variations between the individual hairs on the table. Despite this blunt approach, our model will still be a true representation of the real system.
In reality, of course, those little hairs do have an effect on the snooker ball’s trajectory, but their contribution is so infinitesimally small that within the confines of our snooker table the effect is completely unnoticeable. If we had a long enough snooker table though, and a perpetually moving ball, these tiny effects would eventually become very relevant. In other words, on an infinite table if we plucked a single hair from the ball’s path and re-struck the ball in the exact same way, the new trajectory would noticeably diverge from the original given enough time.
Modelling simple systems is relatively easy because we can afford to be inaccurate. That is why you can play snooker right now on your phone for 59p if you wished. For complex systems like the brain however, the situation is very different. Complex systems are determined by lots of different factors, each of which might be influenced by many others. The number of possible interactions means that complex systems are very hard to model accurately, because an error in any one of these factors will lead to bigger and bigger errors with every interaction. Like a virulent sneeze on a train, the single error infects all factors it comes in contact with, and eventually blights the whole model.
And speaking of colds, we all know first-hand how futile it is to try to model complex systems. In fact, there is one particular chaotic system that we talk about pretty much every day…