wedrifid comments on Open Thread: April 2010 - Less Wrong

4 Post author: Unnamed 01 April 2010 03:21PM

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Comment author: wedrifid 07 April 2010 10:15:32PM *  -1 points [-]

not as an exercise for solving

...and yet...

Can the teacher fulfill his announcement?

Probably.

p(teacher provides a surprise test) = 1 - x^3
Where:
x = 'improbability required for an event to be surprising'

If a 50% chance of having a test that day would leave a student surprised he can be 87.5% confident in being able to fullfil his assertion.

However, if the teacher was a causal decision agent then he would not be able to provide a surprise test without making the randomization process public (or a similar precommitment).

Comment author: Amanojack 08 April 2010 12:23:28AM 1 point [-]

The problem with choosing at day at random is, what if it turns out to be Friday? Friday would not be a surprise, since the test will be either Monday, Wednesday or Friday, and so by Thursday the students would know by process of elimination that it had to be Friday.

Comment author: RobinZ 07 April 2010 10:30:12PM 0 points [-]

How do you get that result while requiring that the test occur next week? It is that assumption that drives the 'paradox'.

Comment author: wedrifid 07 April 2010 10:51:19PM -1 points [-]

The answer to the question 'Can the teacher fulfill his announcement?' is 'Probably'. The answer to the question 'Is there a 100% chance that the teacher fulfills his announcement?' is 'No'.

Comment author: RobinZ 07 April 2010 11:44:20PM *  1 point [-]

You misunderstand me - I maintain that an obvious unstated condition in the announcement is that there will be a test next week. Under this condition, the student will be surprised by a Wednesday test but not a Friday test, and therefore

p(teacher provides a surprise test) = 1 - x^2

and, if I guess your algorithm correctly,

p(teacher provides a surprise lack of test) = x^2 * (1 - x)

[edit: algebra corrected]

Comment author: wedrifid 08 April 2010 01:24:49AM *  1 point [-]

I maintain that an obvious unstated condition in the announcement is that there will be a test next week.

The condition is that there will be a surprise test. If the teacher were to split 'surprise test' into two and consider max(p(surprise | p(test) == 100)) then yes, he would find he is somewhat less likely to be making a correct claim.

You misunderstand me

I maintain my previous statement (and math):

The answer to the question 'Can the teacher fulfill his announcement?' is 'Probably'. The answer to the question 'Is there a 100% chance that the teacher fulfills his announcement?' is 'No'.

Something that irritates me with regards to philosophy as it is often practiced is that there is an emphasis on maintaining awe at how deep and counterintuitive a question is rather than extract possible understanding from it, disolve the confusion and move on.

Yes, this question demonstrates how absolute certainty in one thing can preclude uncertainty in some others. Wow. It also demonstrates that one can make self defeating prophecies. Kinda-interesting. But don't let that stop you from giving the best answer to the question. Given that the teacher has made the prediction and given that he is trying to fulfill his announcement there is a distinct probability that he will be successful. Quit saying 'wow', do the math and choose which odds you'll bet on!

Comment author: RobinZ 08 April 2010 02:51:11AM 0 points [-]

I never intended to dispute that

The answer to the question 'Can the teacher fulfill his announcement?' is 'Probably'. The answer to the question 'Is there a 100% chance that the teacher fulfills his announcement?' is 'No'.

only the specific figure 87.5%.

It's a minor point. Your logic is good.

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