Are fananciers really stupid?

The New Scientist (30 March 2013) has the following question, under the heading ‘Stupid is as stupid does’:

Jack is looking at Anne but Anne is looking at George. Jack is married but George is not. Is a married person looking at an unmarried person?

Possible answers are: “yes”, “no” or “cannot be determined”.

You might want to think about this before scrolling down.

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It is claimed that while ‘the vast majority’ (presumably including financiers, whose thinking is being criticised) think the answer is “cannot be determined”,

careful deduction shows that the answer is “yes”.

Similar views are expressed at  a learning blog and at a Physics blog, although the ‘careful deductions’ are not given. Would you like to think again?

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Now I have a confession to make. My first impression is that the closest of the admissible answers is ‘cannot be determined’, and having thought carefully for a while, I have not changed my mind. Am I stupid? (Based on this evidence!) You might like to think about this before scrolling down.

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Some people object that the term ‘is married’ may not be well-defined, but that is not my concern. Suppose that one has a definition of marriage that is as complete and precise as possible. What is the correct answer? Does that change your thinking?

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Okay, here are some candidate answers that I would prefer, if allowed:

  1. There are cases in which the answer cannot be determined.
  2. It is not possible to prove that there are not cases in which the answer cannot be determined. (So that the answer could actually be “yes”, but we cannot know that it is “yes”.)

Either way, it cannot be proved that there is a complete and precise way of determining the answer, but for different reasons. I lean towards the first answer, but am not sure. Which it is is not a logical or mathematical question, but a question about ‘reality’, so one should ask a Physicist. My reasoning follows … .

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Suppose that Anne marries Henry who dies while out in space, with a high relative velocity and acceleration. Then to answer yes we must at least be able to determine a unique time in Anne’s time-frame in which Henry dies, or else (it seems to me) there will be a period of time in which Anne’s status is indeterminate. It is not just that we do not know what Anne’s status is; she has no ‘objective’ status.

If there is some experiment which really proves that there is no possible ‘objective’ time (and I am not sure that there is) then am I not right? Even if there is no such experiment, one cannot determine the truth of physical theories, only fail to disprove them. So either way, am I not right?

Enlightenment, please. The link to finance is that the New Scientist article says that

Employees leaving logic at the office door helped cause the financial crisis.

I agree, but it seems to me (after Keynes) that it was their use of the kind of ‘classical’ logic that is implicitly assumed in the article that is at fault. Being married is a relation, not a proposition about Anne. Anne has no state or attributes from which her marital status can be determined, any more than terms such as crash, recession, money supply, inflation, inequality, value or ‘the will of the people’ have any correspondence in real economies.  Unless you know different?

Dave Marsay

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About Dave Marsay
Mathematician with an interest in 'good' reasoning.

2 Responses to Are fananciers really stupid?

  1. adv says:

    Either Anne is married, or she is not. If the former, the answer is yes, because she is looking at George. If the latter, the answer is also yes, because Jack is looking at her. Pretty obvious really.

    • Dave Marsay says:

      Thanks. I guess the point of my post is that while it is obvious that ‘either Anne is married, or she is not’, it may not be true. To convince me that it is true you would seem to me to need to define ‘is married’ and a rule for determining when someone is married that can be unequivocally applied in my example.

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