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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'

#31

Post by alphaBetaGamma »

mcarvin wrote: post #14
alphaBetaGamma wrote: post #9

Earlier quoted context omitted.

Your premises are wrong: you can believe in physics, but the laws of physics could not deterministic. To the best of our knowledge this is the case[1], and we have strong indications [2] that this is a fundamental feature of nature: the non deterministic aspects do not come from our lack of understanding and knowledge. [1] http://en.wikipedia.org/wiki/Quantum_mechanics [2] http://en.wikipedia.org/wiki/EPR_paradox

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…

Chaotic macroscopic system + non-determinism at atomic scale = non-determinism at macroscopic scale.

So, e.g., the temperature at the tip of the Eiffel tower on Jan 1, 2014 1pm is non-deterministic.

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

#33

Post by JumpCrisscross »

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?

Just because relativity showed Newtonian physics to be wrong about how the universe worked doesn't mean we can't use the latter as a decent approximation under appropriate constraints. Similarly, we don't really need to calculate the probability of the Sun teleporting over Wall Street when valuing Facebook's IPO.

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

#34

Post by [deleted] »

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…

[deleted]

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

#35

Post by kstenerud »

tallanvor wrote: post #25
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 st…

Probability is temporal. You need to specify timeframe.

If you are talking about before the coins were flipped to decide whether a marble was to be placed into the box, then at that time BEFORE the coin was flipped, the probability would be 0.5 per box.

If you are talking about AFTER the coin has been flipped, the probability for each box goes to either 0 or 1. This is regardless of whether an outside observer is aware of the state or not.

If you were to now enter the room, having no knowledge of what boxes (if any) have had a marble placed in them, the probability of a marble being in a particular box has not changed. It is STILL either 1 or 0. There are only two ways to induce probability at this point: Pick a single, random box to open, in which case you are measuring the probability that you will choose a box with a marble in it (you are measuring yourself, not the marbles). The other is to guess whether a particular box has a marble in it, and then open it, in which case you are measuring whether your guess is correct or not (once again, measuring yourself, not the marble).

Most people go wrong here because they think they are measuring one thing but are actually measuring something else.

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

#36

Post by pcrh »

bazzargh wrote: post #27

I parse this question differently. Most commenters seem to be answering 'can ALL priors be objective' when the question is only asking if any exist. For people not sitting this exam, the probability of passing it is zero.

The goal of the exam is not to determine what knowledge you have assimilated, but how likely you are to generate new knowledge. Hence the very open nature of the question.

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

#37

Post by kstenerud »

BCM43 wrote: post #26
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.

The Schrödinger's cat experiment is flawed, as pointed out by Niels Bohr and explained here: http://web.archive.org/web/20061130173850/http://www.ensmp.f...

The wave function collapses as you induce probabilistic action. And once again, to speak of probability one must speak temporally. Lack of observation of the change does not negate the change in probability.

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

#38

Post by pcrh »

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…

Some of the most pressing problems in society don't have answers that fit into the mindset of the more mathematically-minded among us.

They are problems nonetheless, for example: should free speech exist? You can't answer that question using science, yet we need people to think about that kind of thing.

For what it's worth, the reputation of All Souls College (which does not have students) is strongest in the humanities.

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

#39

Post by celer »

mcarvin wrote: post #14
alphaBetaGamma wrote: post #9

Earlier quoted context omitted.

Your premises are wrong: you can believe in physics, but the laws of physics could not deterministic. To the best of our knowledge this is the case[1], and we have strong indications [2] that this is a fundamental feature of nature: the non deterministic aspects do not come from our lack of understanding and knowledge. [1] http://en.wikipedia.org/wiki/Quantum_mechanics [2] http://en.wikipedia.org/wiki/EPR_paradox

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…

From a practical approach, the physical world can seem fairly deterministic. If you drop something in a vacuum and nothing hits it, you can say with a great deal of accuracy how long it will take to hit the ground. I don't think that this practical determinism translates to a philosophical determinism.

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

#40

Post by joe_the_user »

pcrh wrote: post #38
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…

Some of the most pressing problems in society don't have answers that fit into the mindset of the more mathematically-minded among us. They are problems nonetheless, for example: should free speech exist? You can't answer that question using science, yet we need people to think about that kind of thing. For what it's worth, the reputation of All Souls College (which does not have students ) is strongest in the humani…

Saying the exam wasn't "hard" as such wasn't intended to slight All Souls College or the humanities.

It seems like what makes a question part of the humanities is that many if not most humans have some sort of answer to the question. For that reason, I imagine the humanities might be better served not conjuring up images of super-hard exams only a few can pass.

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