Predicting the Future

Arguably the greatest contribution of computing to the total of human knowledge is that relatively simple results from theoretical models of computation show that the future is an inherently unknowable place — not just in principle, but for fundamental reasons.
A Turing machine is a simple model of computation with two parts: an infinite row of memory elements, each able to contain a single character; and a state machine, a simple device that is positioned at one of the memory elements, and makes moves by inspecting the single character in the current element and using a simple transition table to decide what to do next. Possible next moves include changing the current character to another one (from a finite alphabet) or moving one element to the right or to the left, or stopping and turning off.
A Turing machine is a simple device; all of its parts are straightforward; and many real-world simulators have been built. But it is hypothesised that this simple device can compute any function that can be computed by any other computational device, and so it contains within its simple structure everything that can be found in the most complex supercomputer, except speed.
It has been suggested that the universe is a giant Turing machine, and everything we know so far about physics continues to work from this perspective, with the single exception that it requires that time is quantized rather than continuous — the universe ticks rather than runs.
But here’s the contribution of computation to epistemology: Almost nothing interesting about the future behaviour of a Turing machine is knowable in any shortcut way, that is in any way that is quicker than just letting the Turing machine run and seeing what happens. This includes questions like: will the Turing machine ever finish its computation? Will it revisit this particular memory element? Will this symbol ever again contain the same symbol that it does now? and many others. (These questions may be answerable in particular cases, but they can’t be answered in general — that is you can’t inspect the transitions and the storage and draw conclusions in a general way.)
If most of the future behaviour of such a simple device is not accessible to “outside” analysis, then almost every property of more complex systems must be equally inaccessible.
Note that this is not an argument built from limitations that might be thought of as “practical”. Predicting what will happen tomorrow is not, in the end, impossible because we can’t gather enough data about today, or because we don’t have the processing power to actually build the predictions — it’s a more fundamental limitation in the nature of what it means to predict the future. This limitation is akin (in fact, quite closely related) to the fact that, within any formal system, there are some theorems that we know to be true but cannot prove.

There are other arguments that also speak to the problem of predicting the future. These aren’t actually needed, given the argument above, but they are often advanced, and speak more to the practical difficulties.

The first is that non-linear systems are not easy to model, and often have unsuspected actions that are not easy to infer even when we have a detailed understanding of them. Famously, bamboo canes can suddenly appear from the ground and then grow more than 2 feet in a day.

The second is that many real-world systems are chaotic, that is infinitesimal differences in their conditions at one moment in time can turn into enormous differences at a future time. This is why forecasting the weather is difficult: a small error in measurement at one  weather station today (caused, perhaps by a butterfly flapping its wings) can completely change tomorrow’s weather a thousand miles away. The problem with predicting the future here is that the current state cannot be measured to sufficient accuracy.

So if the future is inherently, fundamentally impossible to predict, what do we mean when we talk about prediction in the context of knowledge discovery? The answer is that predictive models are not predicting a previously unknown future, but are predicting the recurrence of patterns that have existed in the past. It’s desperately important to keep this in mind.

Thus when a mortgage prediction system (should this new applicant be given a mortgage?) is built, it’s built from historical data: which of a pool of earlier applicants for mortagages did, and did not, repay those loans. The prediction for a new mortgage applicant is, roughly speaking, based on matching the new applicant to the pool of previous applicants and making a determination from what the outcomes were for those. In other words, the prediction assumes an approximate rerun of what happened before — “now” is essentially the same situation as “then”. It’s not really a prediction of the future; it’s a prediction of a rerun of the past.

All predictive models have (and must have) this historical replay character. Trouble starts when this gets forgotten, and models are used to predict scenarios that are genuinely in the future.  For example, in mortgage prediction, a sudden change in the wider economy may be significant enough that the history that is wired into the predictor no longer makes sense. Using the predictor to make new lending decisions becomes foolhardy.

Other situations have similar pitfalls, but they are a bit better hidden. For example, the dream of personalised medicine is to be able to predict the outcome for a patient who has been diagnosed with a particular disease and is being given a particular treatment. This might work, but it assumes that every new patient is close enough to some of the previous patients that there’s some hope of making a plausible prediction. At present, this is foundering on the uniqueness of each patient, especially as the available pool of existing patients for building the predictor is often quite limited. Without litigating the main issue, models that attempt to predict future global temperatures are vulnerable to the same pitfall: previous dependencies of temperatures on temperatures at earlier times do not provide a solid epistemological basis for predicting future temperatures based on temperatures now (and with the triple whammy of fundamental unpredictability, chaos, and non-linear systems).

All predictors should be built so that predictions all pass through a preliminary step that compares them to the totality of the data used to build the predictor. New records that do not resemble records used for training cannot legitimately be passed to the predictor, since the result has a strong probability of being fictional. In other words, the fact that a predictor was build from a particular set of training data must be preserved in the predictor’s use. Of course, there’s an issue of how similar a new record must be to the training records to be plausibly predicted. But at least this question should be asked.

So can we predict the future? No, we can only repredict the past.

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