SIMON AND THE MYTH OF THE GREAT PREDICTOR   A representation of Newcombe's Paradox Steve Davis   With an additional note by Rudi Borth

The computer was undoubtedly the largest and fastest ever built. Whether its purpose merited such awesome power is debatable. It had, in fact, been built to predict. This was not an altogether novel idea, since computers designed to predict the weather, for example, had been around for ages. The computer was similar to one of these. Weather computers store information about small packets of atmosphere: temperature, humidity, pressure, movement, and so on. Based on this information, they are able to calculate how these packets of atmosphere will change over time. Further, they collect all these individual predictions into a global prediction of how the weather will behave The Great Predictor, known as Simon. was to do the same thing,only this time using information about groups of molecules in the human brain, rather than packets of air. By plotting their future movements, it should he able to predict the future actions of any individual. Incidentally, the computer was named after Simon de Laplace, the French philosopher and mathematician, who first proposed that any entity that knew the position and trajectory of all the molecules in the universe would know its future.  Of course, it wasn't as easy as that. Laplace had been writing in the Seventeenth Century, three hundred years before the discovery of chaos. Chaotic systems become unpredictable because they are so sensitive to their starting conditions. The weather is such a system. If you don't take your starting measurements precisely enough, or your packets of air are too large, then after a while the measuring errors you made at the beginning mount up and your prediction goes haywire. Most natural systems tend to be chaotic, so Simon the computer's predictions about human actions are just as fallible. In fact, it was reckoned that Simon would only be 90% correct within twenty four hours of his prediction. For this reason, he acquired the perhaps uncharitable nickname of Simple Simon. He could equally well have been called Simplistic Simon, since many argued that the human psyche was not like the weather, and human actions could not be predicted simply by plotting the movements of all the chemical and electrical impulses around the brain.  The day came for the test, to see if Simon could live up to the claims of its designers. In order to ensure that the day achieved maximum publicity, volunteers to take part in the trial were given the opportunity of winning over £1,000,000. This not only ensured publicity, but also ensured several volunteers who were willing to undergo the gruelling, and possibly unsafe ordeal of having their brains physically probed and measured by Simon. All came through this part successfully, and Simon pronounced himself satisfied. He was then connected to a trolley with an artificial arm and a large bag of money. the test could begin.  Each contestant was to be assigned a pair of boxes - one transparent and one opaque - and asked to select either the opaque box or both boxes. The transparent box would be seen to contain £1000 Twenty four hours before this event, Simon was asked to predict each trialist's choice, and signal it in the following way. If he predicted that the volunteer would pick only the opaque box, he was to put £1,000,000 in it. If he predicted that the volunteer would pick both boxes, he was to leave the opaque box empty. Working alone, Simon did this. He was then taken off the trolley and removed from the building: he could have no further control over the experiment. In due course the test took place. Simon was, in fact right 9 times out of 10, just as his makers said he would be. We reach the final contestant who argues as follows......  In the contest the choice made by the contestants produces an outcome. If I believe the predictor is mostly right - and his track record tends to suggest this - then I can work out what the outcomes of the choices will be.  If I choose the opaque box alone I will receive £1, 000, 000. If I choose both boxes I receive £1000, since Simon, in this case, leaves the opaque box empty. The choice seems obvious: the opaque box However, the choice is not as obvious as it seems. After all, Simon has made his prediction a day ago and left the building. 'There is now no mechanism available to change the money in the boxes. There is either a million in the opaque box or not. So why not take both boxes, and at least be sure of the thousand? But if Simon has predicted this train of thought, then all I will get is the thousand Hmmm ......what do I do?  There would be no problem in choosing if there was a direct causal link between choice and box contents: if the opaque box were automatically filled if it alone was chosen. Unfortunately, the link between the choice and its content is indirect*. The choice is reflected by the prediction, which also enables the outcome by deciding on the placing of the money. Now if this link were totally reliable or acceptable there would still not be a problem. But it is neither. It is unreliable because it only works 90% of the time. Worse, it is unacceptable because it is counter-intuitive. To believe that actions today affect actions yesterday is, to say the least, contrary to our accepted views of causality. Put more simply, I think we would all agree that to choose two boxes is an act of reason, to choose one box is an act of faith.  I am a rational person. Why is it, then, that every time I read this scenario, I have a nagging feeling that I ought to choose the one box I believe it is because I am not entirely happy with the simple view of causality - 'this then that'. The above paradox could be construed more simply in terms of a conversation I had with someone once, who told me she used the more expensive and less well-stocked corner shop because 'sometime we might need it'. This does not, on the face of it, seem to be a rational statement. After all, one person using the corner shop will make no difference one way or the other to its chances of survival. The statement does make sense, however, if the person sees herself as representative of the views of a number of people. The act of using the corner shop, in a way, caused it to be widely used; not causes it directly, but causes it indirectly through this mitigating factor of representability. So representability stands in the same relationship to this scenario as the prediction stands to Simon's story; it is a third factor which is the causal link relating two otherwise unrelated events.  These mitigating factors are of greater importance in our thinking than we usually realise, and are only noticed when we actually consider the sort of stark representation of them that Newcombe's Paradox provides. As a further illustration of mitigating factors, suppose we are told that scientists are 90% certain that tooth decay is not a product of eating sweet things, but is the product of a certain gene, which also gives us a craving for sweet things. In other words, tooth decay is linked indirectly to eating sweets by a third factor. In these circumstances, if you were offered a sweet, and had a longing to eat it, would you actually take it? If you hesitate on the choice, then you are in exactly the same position as the person who hesitates over the choice of boxes in Simon's story. You are effectively saying that by manipulating the result, the desire for a sweet, you will in some way, affect the cause, the gene, which will in turn affect the other result, the tooth decay. Again, like the person who uses the comer shop, you have committed yourself to a non-intuitive example of causality.  And so we could go on.  Calvinists believe that they are predestined to be saved or not. So why act virtuously, since no matter how you act your thread is already spun, measured and cut? We act virtuously because, it is argued, our actions betoken, or represent our fate. So acting virtuously indicates salvation. The choice to act in this way can be seen as a nice combination of the 'use-the- corner-shop' and 'refuse-to-eat-sweet-things' argument.  Why bother to vote in a parliamentary election, when your single vote will never decide; anything? After all, 'elections are never that close. Again, voting; makes sense if you see your vote as representative of a whole trend in voting. In this sense, your vote is actualising this trend.  In Gone With The Wind, Melanie looks after destitute Northern soldiers trekking North, because she hopes some Northern matriarch will treat her Ashley in the same way.  All of these are examples of what we might refer to as 'one-box' thought. I would also contend that we see them as perfectly natural and rational ways to think. But if we follow this belief to its conclusion, we have, nevertheless, to see them, as we saw one box thought in Simon's story, as an act of faith. Is faith, therefore, an integral part of reason?  Or is that another paradox? A Note by Rudi Borth on 'Simon and the myth of the Great Predictor'  The above article strikes the rational part of my mind as a typical example of the philosophical shadow-boxing made possible by the approximate and imprecise nature of language which permits nonsensical or unreal or illogical statements as long as they are grammatically correct. Poetic or mystical texts can be wonderful, but not in the context of this thought-experiment.  The real situation faced by all contestants, not just the last one, has four possible outcomes and is easily summarized in a two-by-two table [Ed. ... except on the Internet, where a list may be easier].  =========================================================== . . . . . . . . . . : Simon's prediction having resulted in . . . . . . . . . . : ------------------------------------- Contestant's choice : . . .opaque box. . . : .opaque box. . . . . . . . . . . . : containing 1 million : . . empty. . . =========================================================== Opaque box. . . . . : . Win = 1 million. . : . .Win = 0 . . --------------------:----------------------:--------------- Both boxes. . . . . :Win = 1 million + 1000: .Win = 1000. . ===========================================================  Weird notions or doubts about causality or prediction are a factor only to the extent that they may influence a susceptible contestant's choice in this betting set-up.  Mathematical statistics should not come into it because its results (based, by the way, on assumptions sometimes not fully borne out in reality) refer to averages and distribution widths rather than single cases.  Further thoughts on this to: Rudi Borth, D.Sc., Professor Emeritus [University of Toronto] Stratford, Ontario, Canada email: rborth@orc.ca