Psychic octopodes?
Monday, July 12, 2010 at 12:54PM 
There are two possibilities: either the octopus is guessing, or it is psychic. Statisticians call these the null and alternative hypotheses. The null hypothesis is the position you take before you examine the evidence and it is often the status quo position: since no octopus has ever been scientifically demonstrated to be psychic, it is my null hypothesis in this case. The alternative hypothesis is the position you're willing to move to if the evidence is strong enough.
We then consider what would happen if the null hypothesis is true. If the octopus is guessing then it has a fifty:fifty, or one half, chance of guessing correctly each time it is asked to predict the outcome of a world cup match. In fact, it was asked to predict the outcome of eight world cup matches. The probability that it would correctly guess the outcome of all eight matches is one half times one half times one half ... [eight times in total] . . . in other words one half to the power eight, which is 1/256.
This number is called the significance probability or p-value. It is the likelihood that, if the null hypothesis is true, we would get an outcome as extreme (or more extreme) than the one we got. In this case, you cannot get more than eight out of eight correct, so it is simply the probability of guessing all eight matches correctly.
We now have a choice to make. Which of these explanations do we prefer: either the octopus is psychic or it has been extremely lucky and done something that only happens one time in over two hundred and fifty. If we go with the first choice we are said to reject the null hypothesis; if we go with the second we do not reject the null hypothesis. (You should never say that you "accept the null hypothesis" because there may be other null hypotheses that are equally consistent with the data and you have no ground for preferring one of these over any of the others.)
To help us decide which explanation to choose we consider the consequences of being wrong. If the octopus is not psychic but we conclude that it is, we have committed a Type I error: that is, we have rejected the null hypothesis when it is in fact true. What are the consequences of this? We may erroneously rely on the octopus, now that we believe it is psychic, and suffer loss as a result of basing decisions on its predictions. (More generally, we may make claims based on the data that will subsequently be shown to be wrong. This can be very damaging to the public's confidence in the scientific method and it may also result in public humiliation.)
On the other hand if the octopus really is psychic but conclude that it is not, we have committed a Type II error: that is, we have failed to reject the null hypothesis when it is in fact false. What are the consequences of this? We have lost the opportunity to profit from the reliable predictions of the octopus. (More generally, we have missed an opportunity to expand our understanding of the world. This holds back progress and no-one wins any Nobel prizes.)
Ultimately it's up to you. Do you think a one in over two hundred and fifty chance is so small that you'd rather believe the octopus is psychic? Or do you think that the idea of a psychic octopus is so outlandish that you'd need very much more evidence before you're persuaded? If it's the latter, you're in good company. One of the principles of the scientific method is replication. The experiment should be repeated, ideally by another team of researchers. If they get the same results, our conclusions are strengthened. If they do not, they are weakened and we may be forced to abandon our original belief altogether.
We should also be careful to limit our conclusions to those circumstances surrounding our actual experiment. On the basis of the data we currently have, we cannot conclude that all octopodes are psychic; indeed, we cannot even actually conclude that the world cup octopus is psychic. The best we can say is that it can predict the outcomes of matches in the 2010 World Cup. In fact, setting aside its prediction for the final, it can predict the outcomes of matches involving Germany in the 2010 World Cup: its prediction for the final may have been a guess. We call these limitations on our conclusions the scope of inference. Bad science results when conclusions are generalised too widely.
One last point: the plural of octopus is octopodes. Octopus comes from the Greek (octo eight + pous foot) and not the Latin. If it were Latin then octopi might be its plural, but it is not.
As for this one octopus: psychic or not?
Reader Comments (1)
Psychic or straight forward predictable?
How about the octopus is not psychic and there is no 50:50 chance? To make matters a bit more complicated we don't deal with an automaton here. The octopus is an animal and as such at least a Skinnerian creature that makes real (unconscious) decisions; whether or not it is a sentient being.
If we analyse a possible stimulus for each experiment, i.e. the countries flags, we can see that the flag of the country Paul went for each match had distinctly bright colours, especially yellow and red. Although an octopus does not necessarily have colour vision, it has eyes (the transducer) that are sensitive to polarised light, which can play a role in the detection and recognition of an object.
This may be an accidental regularity but certainly would aid an explanation by introducing an underlying law of nature which would skew the otherwise 50:50 probability of a Darwinian creature or an inanimate object.
How would one test this hypothesis? Simply feed him more images of various patterns and colours (making them increasingly more indistinguishable in patterns and colours), or use polarised light, or change or invert colours on the England flag and see what he comes up with in each case.
How about the Germany vs Spain game then? - both flags contain red and yellow. Possibly two options here:
1. the sensitivity of the octopus' (polarised) vision was the clincher, and maybe the black in the German flag had a discriminatory effect or
2. if the visional sensitivity is not as developed, this one game was really governed by a (near) 50:50 chance.
Ultimately it's up to the biologist to find a suitable experiment, but I personally doubt that Paul is psychic or that he had a 50:50 chance to get it right. There is surely more to it, and he is likely to reacts as a consequence of his own ocular input data. As Dennett would put it, the explanation for Paul's behaviour can be found by adopting the physical stance.