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Topic: The Eccentric Ornithologist (Read 1165 times) |
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ThudnBlunder
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The Eccentric Ornithologist
« on: Apr 9th, 2003, 3:57am » |
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An eccentric ornithologist has a new project. He has decided to find out if all ravens are black. So every morning he sets off and checks that every raven that he sees is black. And sure enough, every raven he sees is black.
One day he tells his logician colleague of his project. The logician says, "Hmm... I know how to make things much easier for you." And he outlines the following idea:
Let R = the statement 'an object is a Raven'
Let B = the statement 'an object is Black'
All Ravens are Black becomes R => B
But this is logically equivalent to ~B => ~R (contrapositive)
In other words, every non-Black object that he sees that is not a Raven is a confirming instance of his theory that all Ravens are Black. This means that, instead of getting up early every morning and looking for elusive ravens, he can merely sit in his office or stroll down the street - and every non-Black thing he espys that is not a Raven will support his hypothesis that all Ravens are Black.
What do you think of this idea?
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| « Last Edit: Oct 27th, 2003, 8:43pm by ThudnBlunder » |
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towr
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Re: The Eccentric Ornithologist
« Reply #1 on: Apr 9th, 2003, 8:06am » |
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Well, it really depends on several things.
Formost is the domain of objects closed.
There's much more to say, but I allready know the problem, so I'll let someone else have a go first..
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aero_guy
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Re: The Eccentric Ornithologist
« Reply #2 on: Apr 10th, 2003, 4:08am » |
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It would seem that every time he sees and non-black object and confirms it is not a raven supports his claim, but unless he identifies ALL non-black objects it does not prove his claim. As there are many more non-black objects than ravens, it is more efficient, if not more correct, to go looking for ravens.
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ThudnBlunder
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Re: The Eccentric Ornithologist
« Reply #3 on: Apr 10th, 2003, 10:30am » |
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Quote:| ...but unless he identifies ALL non-black objects it does not prove his claim |
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He is not seeking to absolutely prove his hypothesis. In the real world, all we can do is collect information which may objectively support our hypotheses.
Quote:| As there are many more non-black objects than ravens, it is more efficient, if not more correct, to go looking for ravens. |
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More efficient? But it will require a lot more of his energy to find just one Raven than to find various non-Black objects. 
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| « Last Edit: Apr 10th, 2003, 11:56am by ThudnBlunder » |
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towr
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Re: The Eccentric Ornithologist
« Reply #4 on: Apr 10th, 2003, 10:41am » |
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Well, philosphy of science comes into play here, and there are really tons of ways to evaluate a hypothesis, none of which are objectively 'the best'.
Bayes might be a good choice, if you like statistics. In this case because there are many non-raven objects, these would each bring much less weight to the hypothesis that black ravens.
Of course it'd be much easier to falsify the claim, and just paint a raven white and be done with it..
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aero_guy
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Re: The Eccentric Ornithologist
« Reply #5 on: Apr 10th, 2003, 11:01am » |
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Lets consider it as percentage towards being proven. If he examines all ravens or all non-black objects he is at 100%. Lets say there are 2 million ravens out there and (on the earth only as that is all that needs to be proven) 1E1000 non-black objects. Each raven he sees, assuming it is a different raven, brings him 5E-5% closer to proof. Each non-black object brings him 1E-900% closer. So, he may be able to find more non-black objects around, but he would need to find 2E894 non-black objects to equal one raven. Thus, it is inefficient.
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prince
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Re: The Eccentric Ornithologist
« Reply #6 on: Apr 10th, 2003, 11:18am » |
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on Apr 10th, 2003, 10:30am, THUDandBLUNDER wrote:
He is not seeking to absolutely prove his hypothesis. In the real world, all we can do is collect information which objectively supports our hypotheses. |
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Well, then he will never find out if all ravens are black, which is what he decided to do, according to the original riddle. This statement is much easier to disprove (find 1 non-black raven) than to prove. As aeroguy points out, to prove it he has to find all ravens, or all non-black objects.
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James Fingas
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Re: The Eccentric Ornithologist
« Reply #7 on: Apr 14th, 2003, 1:45pm » |
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Looking at it from the perspective of trying to disprove the theory, we can see that the theory will be disproven only when we find a non-black raven.
So to be fair, if we go out looking for non-black items, we will have to find a raven before we're done anyways.
In logical terms, finding a black raven is completely worthless (there's no "contribution" towards proof), and finding a non-black non-raven is likewise worthless.
Unless you have all the ravens in front of you to examine, you can't definitively answer the question. So I guess the ornithologist was doomed from the start, trying to prove an unprovable hypothesis.
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Icarus
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Re: The Eccentric Ornithologist
« Reply #8 on: Apr 14th, 2003, 6:26pm » |
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In mathematical terms, no he cannot prove his hypothesis without examining either every raven, or every non-black object.
But this is not about mathematical proof. Our researcher knows that there is no way he can see every raven, or every non-black object. Instead he is trying to justify his hypothesis scientifically. This is an entirely different matter. As I have stated in other threads (very hot button issue for me), science is not about proof, and the only "scientific facts" are direct observations - without any interpretation. (You can carry this to extremes - is what I perceive real or just an illusion? - so any science does come with an unsaid provisio that all results are assuming the observations reflect reality.) Everything else is theory. Mathematics is learning by codified deduction. Science is learning by codified induction. That is, looking for patterns and assuming those patterns will still hold in new situations.
While this is puzzle is simple-minded, the problem in scientific justification it points out is one that actually occurs with regularity. It is one of the ways in which people misuse scientific reasoning to back up fallacious claims. It is also a variation of the same problem which occurs in the Willywutang has STDs? puzzle.
In this case, aero_guy is right. If there are N ravens in the world and M non-black objects, the strength of the "all ravens are black" hypothesis increases by about 1/N for each black raven observed, and by about 1/M for each non-black non-raven observed. Since M dwarfs N, it takes incredibly many more observations of non-black items than of ravens to increase the observed strength of the theory.
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towr
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Re: The Eccentric Ornithologist
« Reply #9 on: Apr 14th, 2003, 11:18pm » |
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yes.. because if you've seen 75% M and 75% N you have 150% evidence..
wait that doesn't seem right.. 
But all joking aside, there a many, many ways to look at this problem..
In evaluating hypothesis it makes a lot of sense to compare hypotheses, rather than just say if it is good in itself. Once you have a bunch of hypothesis you can look at what they predict about the state of the real world, and try to observe the differences.
So if you have "all ravens are black" an obvious null-hypothesis (for lack of other competitors) is "not all ravens are black", the difference, there is at least one raven that is not black, so look for it. Try to find an experiment where that non-black raven would be likely to be observed, and do that experiment.
Of course it works better for hypotheses that predict more about the world.. Like relativity's bending of light due to gravity. Since it was deemed an unlikely prediction it gave relativity a smashing victory over other theories when it was observed during a solar exclipse (when the stars next to to the sun were visible, and clearly appeared closer to the sun thatn they were, by the exact amount predicted by relativity)
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James Fingas
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Re: The Eccentric Ornithologist
« Reply #10 on: Apr 21st, 2003, 12:34pm » |
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towr,
In this case, we are given the fact that the eccentric ornothologist wants to prove that "all ravens are black". This is a logical statement, not a scientific statement, and the approach given is a logical, rather than a scientific one.
If I were scientifically interested in the colour of ravens, then I might try to approach it this way:
1) Suppose I really want to know that "all ravens are black" with a 99% certainty level, then:
2) I determine the total population of ravens.
3) I sample the population randomly, controlling for all variables that might affect colour, finding N black ravens and no non-black ravens.
4) I calculate the probability that there are one or more non-black ravens, given that a random sampling of ravens found only black ravens.
5) If the probability is less than 1% that there is a single non-black raven out there, then I am done. Otherwise, I keep sampling.
6) The problem with this is that our calculations in part 3 will only give us less than 1% probability when we have sampled more than 99% of the ravens! This is just as impossible as sampling all the ravens, of course.
Scientifically, we do no better than the ornithologist did in the first place!
The problem that I see is this: yes, we are making fun of non-scientific people, when they try to prove logically un-provable statements using logical analysis. We laugh at them from our scientific standpoint, in which we don't try to prove things like this. But until we discard the statement "all ravens are black", and accept that scientific observation can only work when you use probability, confidence, and acknowledgement of assumptions, we are stuck in the same puddle as they are.
The problem is not in the method. All methods of "proof" that "all ravens are black" are flawed. You can scientifically demonstrate that "if you find a raven, you can be 99.9% sure it will be black", but you can't partially prove that "all ravens are black". To find an answer, we must fix the question.
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