
I'm answering questions from the 'hardest exam in the world' - nqureshi
http://blog.nabeelqu.com/2012/05/all-souls-questions-are-there-objective.html
======
kstenerud
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 without, you now have the ability to engage in real
probability. The probability that a marble is present under each box is either
1 or 0. However, the probability that you will CHOOSE TO LIFT the box
containing the marble is 0.5. This is not a probability of presence or absence
of a marble; it's the probability that YOU will choose to look under a
particular box.

Probability requires the possibility of change, and the probability of change
in a marble's presence under a box (such as by teleporting from one box to
another) is small indeed.

~~~
tallanvor
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.

~~~
kstenerud
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.

------
mcarvin
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, with sufficient
information about arm speed, humidity, wind etc you could perfectly predict
where on the dartboard it would land. The problem is that the mathematical /
computational complexity necessary to achieve that is still beyond our means.
Enter Probability, which we use to reduce the computational burden of
predicting the future. As probability will always be model dependant (ie
subject to someone's view of the world and necessarily wrong some % of the
time) - it follows that an objective probability cannot be consistent with a
deterministic world.

So is the world deterministic?

~~~
alphaBetaGamma
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>

~~~
mcarvin
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 believe there are objective
probabilities (unless, as you indicated you are talking about the subatomic
world).

~~~
eru
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.

~~~
pron
I think that quantom mechanics makes us think differently about probability
and determinism by giving the mathematical (human created) concept of
probability a physical meaning. Similar to the example in intuition 2, a coin
toss could be considered determinstic even if we do not try to predict the
result. It is pre-determined that given a large enough number of coin tosses,
very close to 50% of them would come out heads. Qunatom mechanics makes us
consider probability as a physical property inherent in all physical objects.
This way of thinking helps reasoning about genetic predisposition as well
(which is always probabilistic). Just like any coin is "free" to make a
choice, and yet it is certain that they would (almost) precisely split down
the middle, so too can genetic predisposition can be said to be both
constraining and not constraining at all at the same time.

------
ackien
>To sum up: probabilities are (a) true or false, (b) regardless of what I
believe about this probabilities. Estimated probabilities (c) depend on the
prior knowledge of the mind in question. Moreover, (d) the fact that the
probability is X is a fact about my mind.

I'm not sure why you then go on to say that probability is neither objective
nor subjective, and that probability has traits of both (which seems somewhat
like a contradiction), rather than conclude that there are two different kinds
of probability: objective probability and subjective probability
('probabilities' and 'Estimated probabilities' as you even differentiate
yourself). (And then there is the other interpretation of the question of
whether objective probability even exists at all or wether the world is
deterministic.)

------
fragsworth
On "Intuition 2":

> At time t, if it is true that the probability of the marble being under a
> given box is 0.5, then if I guessed randomly, I would be correct one out of
> two times on average.

> The fact that the probability is 0.5 is completely independent of whether or
> not any particular mind believes that it is 0.5. But this is the definition
> of an objective truth. Therefore, probability must be objective.

This is begging the question. The two things combined is like saying "At time
t, if it is true that probability is objective... therefore probability must
be objective."

~~~
nqureshi
Saying p=0.5 necessarily implies the 1/2 thing. Neither implies any stance on
whether it's subjective/objective so far. The 'objective' conclusion there
requires the further fact of mind-independence, which is based on 'you can't
change the odds that a fair coin comes up heads just by thinking about it'
type arguments. So it's not circular/question-begging, IMO.

~~~
mcarvin
When a fair coin is tossed it will either come up heads or it wont. Put
another way, the probability of getting heads is 1 or 0, unless you believe
that something magical happens to the coin while it is in mid-air that somehow
makes it impossible to predict what will happen when it lands (given a
complete set of data).

So the outcome of the coin-toss is knowable, it just happens to be complex
enough that it is not known (to us). To bridge the gap between the knowable
and the not known we introduce a margin of error in our calculations, called
Probability. Probability then, only exists as man-made mathematical spackle -
and is by definition subjective.

To prove me wrong find an event that has an outcome that cannot be known in
advance. That's why this question is on a philosophy exam.

~~~
JumpCrisscross
Heisenberg uncertainty principle and the entire field of quantum mechanics?

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

~~~
JumpCrisscross
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.

------
habitatforus
Upvote, because I didn't know the 'hardes exam in the world' existed, and I
now think it's awesome. Good luck.

~~~
nqureshi
Thanks. Did you check out the link to the general paper? One of my favourite
questions from there: "Does the moral character of an orgy change when the
participants are wearing Nazi uniforms?"

~~~
mturmon
Engaging in an orgy while clothed is certainly more perverted than doing so
while naked.

------
dfan
The question is inherently crippled, because there have to be objective
probabilities, otherwise quantum mechanics wouldn't work.

I guess the question really is "if the universe operated according to
classical principles, would there be objective probabilities?" And that is an
interesting question, but it's a hypothetical alternate-universe one.

------
bazzargh
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.

~~~
pcrh
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.

------
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.

~~~
pcrh
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.

~~~
joe_the_user
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.

~~~
pcrh
From the perspective of All Souls, they do want exams that only a few can
pass. The goal of this kind of exam is to identify original and insightful
thinkers.

I presume that it is hoped that those who enter All Souls will make original
and long-lasting contributions to their field of endeavor.

In the natural sciences, a similar effort is supported by the Howard Hughes
Foundation at Janelia Farms, as described here:
[http://www.nature.com/news/research-at-janelia-life-on-
the-f...](http://www.nature.com/news/research-at-janelia-life-on-the-
farm-1.9373)

------
ravintpillai
Borrowing from the physics nomenclature, I guess you'd say Probability has
"Subjective Objective Duality"

------
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".

