May 242014

This video brought me back to Newcomb’s paradox:

The Janken robot, built at the Ishikawa Oku Laboratory in Japan, anticipates whether the human hand is playing Rock, Paper or Scissors. As it does it quicker than it takes the hand to complete the action, it has a 100% win rate.

Think of Janken as Dr Wise. To parallel Newcomb’s problem, imagine that you are given 1,000 dollars just to play the game. Then, if Janken plays Paper (say), you get a million dollars. If it wins – because you played Rock – you get the million but have to return the 1,000. If it loses – because you played Scissors – you get the million and get to keep the grand. If it draws – because you also played Paper – the game is repeated. On the other hand, if Janken plays Rock or Scissors, you only get 1,000 dollars, whatever you played.

What do you play? Rock, obviously. Do that and you get a million. Do anything else and you get 1,000. There is no problem and no paradox. Why?

Let’s assume that Dr Wise is also infallible, i.e. 100% accurate, and remember why Newcomb’s problem appears to be a paradox. There is certainly 1,000 dollars in the Green box. Then Dr Wise will either put a million in the Red box, if he thinks you will only open the Red box, or he will put nothing in it, if he thinks you will open both boxes. So there you are. Dr Wise has decided. The Red box contains either a million dollars or nothing. Now it is your turn to decide: do you just open the Red box or both boxes? Both, of course – says the devil on your left shoulder – in either case you will be 1,000 dollars ahead! Don’t be silly – says the angel on your right shoulder – everybody who did that ended up with just a grand, while all of those who just opened the Red box got a million! Why on earth do you think your chances should be any different?

Don’t listen to him – says the devil. Think about it: the Wise Guy has already decided. If he thought you were a Chuck, he put a million in the Red box; if he thought you were a Dominic, he put nothing. He can’t step back. So if you choose to open both boxes you will be a grand ahead for sure!

Ok, ok, do that – says the angel –like all the other fools who listened to the devil. Join them and throw away a sure million for a zero chance of an extra grand!

With all due respect, my dear angel – you reply – I must say the devil has a point. Dr Wise cannot know what I will do, for the simple reason that I haven’t decided it yet. If I don’t know what I will do, how can he?

True – says the angel – you are free to choose whether to open one or both boxes, and there is nothing that Dr Wise can do to influence your choice. But you are not free to choose whether you are a Dominic – who agrees with the devil – or a Chuck, who agrees with me. You are either one or the other. Dr Wise is just very good – nay, infallible – at figuring it out. You may wonder how he does it, but that is irrelevant: he just does it, and he is never wrong. So you can be sure that he won’t be wrong in your case either.

Spooky – you say – but that means that I am not free after all: if I am a Chuck I will open one box, if I am a Dominic I will open both. That’s preposterous. I am free, and I’ll tell you what: I choose to open both boxes, which, as the devil points out, is the most rational thing to do.

Are you sure? – asks Dr Wise. Yes – you say, defiantly. Of course – says Dr Wise – you are a typical Dominic. Here is your grand. Enjoy it. There is nothing in the Red box. You can’t say you weren’t warned.

Shit shit shit SHIT! – you cry, head banging the wall – what an idiot! I made the wrong choice. Or was it a choice?

Welcome to the thorny problem of Free Will, which has kept people banging their heads since time immemorial, and still does.

Now let’s go back to Janken. Why is there no paradox in that version of Newcomb’s problem? It is because we understand why Janken is 100% accurate. After you have decided what to play, moving your hand to produce the intended shape takes some time. It is a very short time, but it is not zero. What Janken does is amazing but fully understandable. Janken does not predict your decision: it sees what you have decided to do while you are doing it and quickly reacts to it, before you complete the action. Hence it would be obviously wrong for you to play anything but Rock.

Dr Wise, on the other hand, does nothing at all after your decision. He has already decided, before you did. It is as if Janken produced its shape before you decided to produce yours. What would you do in that case? The devil would tell you to play Scissors, which gets you 1,000 if Janken played Rock, a repeat if it played Scissors and 1.001 million if it played Paper. That is better than playing Rock, which would get you a repeat, 1,000 and one million respectively; and much better than playing Paper, which would get you 1,000, 1,000 and a repeat. But, again, the angel would remind you of Jenken’s accuracy and implore you to play Rock. And again your hesitation would hinge on your refusal to concede that Jenken has figured out what you will do, in advance of your decision. You are aware of Jenken’s accuracy but, since you can’t explain it, you find it difficult to acknowledge it. This has little to do with Janken being a clump of metal. You have the same difficulty with Dr Wise’s accuracy – whence Newcomb’s paradox.

Acknowledging something requires an explanation: understanding why it happened. And the answer to why is be-cause: what caused it to be. But while we have no problem appreciating that our decisions can be influenced by many external factors, we can’t avoid perceiving them as absolutely free: caused by nothing but our will. Is such perception illusory? It must be, if you take the view that nothing can happen out of nowhere and everything must have a cause, including our will and its ensuing decisions. Not so, if you take the opposite view (as I do).

Expecting something, on the other hand, does not require an explanation: the only requirement is experience. Expecting the sun to rise tomorrow does not require understanding why it will, but only that it has unfailingly done so until now. That’s why we are certain that the sun will rise tomorrow – and would take any bet to the contrary. Likewise, we do not need an explanation for Dr Wise’s accuracy to expect that he will predict our decision. If his accuracy is truly 100%, it is as foolish to try to outsmart him as it is foolish to bet against sunrise. Who decides first is irrelevant. If Dr Wise is infallible, Newcomb’s problem is not a paradox.

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