4 min and 12 sec to read, 1050 words

Predictions are about the future, but that is about as much as we can be sure about — there seems to be many different dimensions to predictions that create a whole taxonomy of them for us to consider as we think about how to understand their role in society.

First, there is something we can call resolution. A prediction can be targeted in time and space in such a way that it is highly precise. If I predict you will die at 22.34, at a certain longitude and latitude, on a certain date and in a certain way, I have made a very different prediction than if I predict that one day you will die.

One way to think about the former kind of prediction is to say that it is not just more precise, but also more complex in that it combines, in itself, several different variables in state space, so it divides state space into a smaller set than the latter one does. The latter prediction merely states that state space is divided into one part where you live and one where you do not, and at one point you will be in the part of state space where you do not live.

The former prediction, however, sections out a much more precise chunk of state space and states that you will find yourself in that chunk.

This raises the interesting question of how precise a prediction can be: can a prediction be complete in some sense? If there is such a thing as a completely defined prediction and all others are just partial predictions, then partial and complete predictions are end points in this particular dimensions. So this give is a first candidate dimension:

(I) Resolution – complete -partial predictions of systems

Are there other relevant dimensions?

We can play around with a toy model in which we put three balls into three slots lined up in a single line, and we randomly change the configuration every hour. The balls are blue, black and red, and our job is to predict in what state this system will be in the future. If we only have to predict that there will be a blue ball in the line-up at some point in time, our job is easy – we can do that with high probability of being right. If we have to predict the probability that the balls will appear in some given order, like red / blue / black at some point in time, our task is harder, but the longer the time window, the easier it gets. Predicting the sequence of ball configurations is harder than predicting a single state of the system – and so on.

But this toy model fails us in thinking about systems that are teleonomic, so here there seems to be a different dimension for us to explore. Systems that are intentional or intentionally configured seem harder to predict because they respond to predictions and change with that response.

Let’s assume the balls are placed by an opponent who is rewarded when we predict the wrong order of the balls, and that we now are locked in a prediction game — here the nature of the prediction is dependent on the legibility of our actions by an opponent. Or many opponents!

Predictions can, then, be agonistic. They can be adversarial games where we are trying to predict what someone else predicts and then act accordingly. These kinds of predictions seem different, because they include the prediction as a part of the system predicted, and need to find some kind of depth to make sense. It is easy to imagine a world in which I predict that you predict that I predict…and so on, but time sets natural boundaries to the prediction depth we deal with (although there is a fun short story here about two eternal and omnipotent beings trying to play chess, predicting endlessly what the other would do and so never playing that first move — and this raises the question of if there is an end to such reciprocal prediction loops or if they are truly infinite in some sense (how infinite can an infinite regress really be?).

This is, of course, a kind of prediction game, and we should recognise that most prediction games will be n-person and not just 2–person games. This adds another layer of complexity that enriches the question of what we need to work with.

We could say that predictions are exogenous to some systems and endogenous to others – in that predicting some systems change them, but predicting others do not. If I communicate my prediction about the stock market this prediction is absorbed to some degree determined by my credibility etc. But if I predict the weather or the solar system, the predicted system does not change because of my prediction.

This gives us a second dimension or category to work with:

(II) Competition – n-person predictions vs single person predictions (akin to game theory / decision theory).

Predictions can be high or low resolution, they can be games or decisions. Are there other categories here we should explore? We could look at things like temporal dimensions (but that is sort of included in the first version), complexity of the system predicted (hinting at the fact that some systems are chaotic and some deterministic and some in between in a state of uncertainty of some kind) — but for now these two dimensions seem to capture something important.

The issue of system complexity – and the resulting predictability – is interesting. It raises issues like if the stock market is more or less complex than the weather because of its ability to react to the predictions made about it – or if this actually can make it more stable in some ways?

So, we would say that self-reflexive systems are more complex in some way than non-reflexive system, but is that necessarily a complexity that make the former harder to predict? Our folk-psychology says no: this is why we have the concept of the self-fulfilling prophecy, and this is why my prediction of other people’s behavior and norms will necessarily make me act in conformance and so further make those norms likely in the overall system.

Something to get back to.