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I'm answering questions from the 'hardest exam in the world'

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Re: I'm answering questions from the 'hardest exam in the world'

#21

Post by joe_the_user »

Scanning the exam's questions, I really can't see them as "hard" in the conventional sense.

Hard would be a question in math, physics or some other field which has a very difficult to discover objective answer. There's no limit to hard here but these essay questions are different. "Should wealth be inheritable?" just doesn't have an objective answer and one's answer could only be judged based on whatever the exam grader thinks is a good answer (well written, clever, whatever). In fact, considering one can choose three out of twenty seven, the exam doesn't seem much harder than some essay exams I've taken that were supposed to be extremely easy (CBest, for example). Some of the essays would be require to marshal facts in a given field (classics or economics) but we can hope the writers have some expertise in something.

I think the only way the questions could be considered hard would be if someone taking it thought they needed to settle one or another of these debatable questions. There you have might the situation where geeks and humanities majors each think the other has "really hard exams"...

Edit: And that's "are there objective probabilities" - an English major could take half an hour to answer without worrying about whether they'd really objectively established their answer. We geeks will stop and aim for an "objective" answer. But while one can establish whatever model one wants in the realm of math, one isn't going to pin down the concept of "objective" and "probability" as used by English speaking humans today.

Re: I'm answering questions from the 'hardest exam in the world'

#22

Post by mcarvin »

eru wrote: post #17
mcarvin wrote: post #14

Earlier quoted context omitted.

Certain irony about saying that a LAW of physics is not deterministic. Conceded though that determinism does not hold up at the quantum level. Disagree though that quantum non-determinism translates to non-determinism at the scale we experience [1]. Have never seen a Feynman diagram for a soccer ball. Which is why I feel comfortable saying that if you believe the macro world is deterministic then you cannot also beli…

Determinism does hold up at the quantum level. Quantum mechanics is completely deterministic. Collapsing the wave function to a classic state, is the probabilistic aspect, if any.

Admittedly beyond at the limits of what this armchair quantum mechanic can say with confidence but to borrow from Hawkings... probabilities in quantum mechanics "reflect a fundamental randomness in nature" [The Grand Design]. So while quantum theories are testable, they are not always predictive (necessary for determinism).

Re: I'm answering questions from the 'hardest exam in the world'

#23

Post by aplusbi »

joe_the_user wrote: post #21

Scanning the exam's questions, I really can't see them as "hard" in the conventional sense. Hard would be a question in math, physics or some other field which has a very difficult to discover objective answer. There's no limit to hard here but these essay questions are different. "Should wealth be inheritable?" just doesn't have an objective answer and one's answer could only be judged based on whatever the exam gra…

It sounds like people are [mis-]using the word "hard" to mean "selective".

Re: I'm answering questions from the 'hardest exam in the world'

#24

Post by pcrh »

mcarvin wrote: post #6

I understand the question quite differently. The question of objective probabilities is a question of whether the world is deterministic. If you believe the world is governed by physical laws and you further believe you understand those laws (physics), you consequently must believe that with sufficient information about the past you can predict the future (determinism). So if I was to throw a dart at a dartboard, wit…

There are alternative uses of probability. For example, you might measure the weight of 50 people eating one of two diets, and determine an average weight for each group. You want to know if the different diets affect weight. It is highly unlikely that the average weight will be exactly identical for each group, so now you use statistical methods to determine the probability that the diet caused the observed difference in weight. You now assign a "probability" to the hypothesis that diet influenced weight -- is that probability objective?

Re: I'm answering questions from the 'hardest exam in the world'

#25

Post by tallanvor »

kstenerud wrote: post #16

Intuition 1 is incorrect. The probability of the marble being under the box during that period of time was 1 because its state never changed. It was merely your incomplete knowledge that encouraged you to (incorrectly) assign a probability of 0.5. You've become confused over WHAT is the subject of your test. If, however, you were to change the experiment such that there were two boxes, one with a marble and one witho…

You're making assumptions when you say that "the probability that you will CHOOSE TO LIFT the box containing the marble is 0.5".

Consider that there may be 3 boxes, and the person setting up the experiment flipped a coin for each box. If the coin landed heads up, a marble was placed in the box. If the coin landed tails up, no marble was placed. This means there may be 0 - 3 marbles total. Until you know the actual state of the box, the probability remains 0.5.

Re: I'm answering questions from the 'hardest exam in the world'

#26

Post by BCM43 »

kstenerud wrote: post #16

Intuition 1 is incorrect. The probability of the marble being under the box during that period of time was 1 because its state never changed. It was merely your incomplete knowledge that encouraged you to (incorrectly) assign a probability of 0.5. You've become confused over WHAT is the subject of your test. If, however, you were to change the experiment such that there were two boxes, one with a marble and one witho…

This would then go down to theoretical physics and whether or not it was already defined which box you would choose. I think something closer to the Schrödinger's cat experiment, and whether the cat will die. In this case, I think you could objectively say the probability is 50/50.

Re: I'm answering questions from the 'hardest exam in the world'

#28

Post by snowwrestler »

I would say yes, there are objective probabilities. For instance a path integral in quantum mechanics sums all possible paths for a particle along with each path's probability; if the calculations are done correctly, the numbers for a particular calculation will come out the same every time, even if different people perform the calculations. Since the facts and outcomes are observably equal for different people, I would say this fits the definition of objective knowledge. It is what makes quantum mechanics testable and useful.

There are plenty of other examples, like the Monty Hall problem, where many different people have confirmed the objective truth of a probability through direct testing.

The problem I see with this question is that it is couched as a philosophy question, not math or physics. That's what makes it "hard".

Re: I'm answering questions from the 'hardest exam in the world'

#29

Post by Natsu »

mcarvin wrote: post #15
JumpCrisscross wrote: post #12

Earlier quoted context omitted.

Heisenberg uncertainty principle and the entire field of quantum mechanics?

Well played and conceded. So do we need two sets of rules? One for 'our world' and one for the subatomic world?

Good question. My best guess is that the law of large numbers averages out the weirdness so that you never spontaneously tunnel through the floor or whatever, but that's only a guess. And there's a lot of weirdness to deal with.
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