Wednesday, April 16, 2008

Monte Hall Problem - bad interpretation.

Scott Adams talked about the Monte Hall Problem in his blog yesterday... and I don't know if I actually agree with his interpretation of what the problem implies.

That is interesting enough on its own. (I’ll give a link later that explains the math of it.) But here is the freaky part. You only improve your odds by switching doors if Monte Hall knows what is behind each door. If he simply got lucky and opened a door with a goat behind it, your odds are unchanged. In other words, your odds are changed by Monte’s knowledge, and your knowledge that Monte has that knowledge.

I don't know which definition of subjective he is using... Let's say he uses: "influenced by personal opinion." then fine... I would easily interpret it as some shade of causality, its obviously a choice Montel made, and his internal state is unknown... Still that definition does not particularly apply well with reality, as it is a definition which strictly applies to sentient beings and does not in any way cross with causality, and statistics as an objective study of outcomes due to limited knowledge.

Blah, this guys use of logic is just a disastrous ostentatious minefield... Lets go on with this definition: "Philosophy. relating to or of the nature of an object as it is known in the mind as distinct from a thing in itself.". Good, lets also asume that when he means reality is subjective he means that there exists no object beyond the mind.

Yet, the same article he points to states:

When the problem and the solution appeared in Parade, approximately 10,000 readers, including several hundred mathematics professors, wrote to the magazine claiming the published solution was wrong. Some of the controversy was because the Parade statement of the problem fails to fully specify the host's behavior and is thus technically ambiguous. However, even when given completely unambiguous problem statements, explanations, simulations, and formal mathematical proofs, many people still meet the correct answer with disbelief.

What does the fact that simulations agree? Is this facet of reality subjective if it can be reproduced outside of minds?

To me, as always, he lives in a contrived, self contradicting, albeit theatrical and entertaining to the less-dull witted.
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