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Comment by rmc | Hacker News Reader

Science has several rules of thumb, Occams Razor says that the simpliest is usually the more likely, and the assumption that the universe operates according to universal, consistant mathematical rules means that you should favour theories that match every other part of observable reality, the rule of thumb that extraordinary claims require extraordinary evidence is like occam's razor and means, again, choose the simpliest explaination that matches your evidence.

Hence, you can sort theories, and then try to devise tests to falsify each one to differenciate between them.

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The problem with Occam's Razor is that it requires you to identify the simplest explanation. In fields like for example molecular biology deciding what is 'the simplest' often is difficult and debatable.

The author didn't name Occam's Razor, but she did touch on the idea that simplicity can be an unhelpful or ambiguous criteria to apply:

"Usually when you are asked to continue a pattern the assumption is that you are supposed to choose the simplest way. But sometimes it is difficult to decide what the testers think the simplest way is. Can you replace the question mark with a number in the following sequence: 31, ?, 31, 30, 31, 30, 31, … You might say that the answer is 30 as the numbers alternate; or, you might say that the answer is 28 as these are the days of the month."

This isn't to say that Occam's Razor isn't helpful -- it often is, if for no other reason than the fact that model/theory with fewer "moving parts" is simply easier to work with than another with more (and a similar level of explanatory power). Just that simplicity sometimes can't help or that it can be a value judgment.

I think in this case simplicity does reveal the answer. I would put 30 because the sequence becomes a repeating sequences of 31, 30. Answering 28 requires making the assumption that the sequence of numbers represent days of the month, which has a higher information entropy making the sequence less simple.

29 would be more valid in a leap year - so calendar days is far from simple and unambiguous.

Could you develop on how to mesure the information entropy in an absolute way?

http://en.wikipedia.org/wiki/Kolmogorov_complexity

Given the incomputability of Kolmogorov complexity, this concept is not usable as an absolute mesure.

In a lot of modern biology however you will have tens or hundreds of thousands of equally simple competing hypotheses. Biologist have had to adapt to this by using multiple hypothesis testing methods, but Prisig was working well before this became standard, so perhaps this was the barrier he was running up against.

Pirsig actually came up with an entire metaphysical system in response to this. It's in his book "Lila". Basically it deals with what "good" (as in a good theory, or answer) is, and the different kinds of goodness or Quality, as he calls it, there are.

It's quite detailed, but his first distinction is between 'static' and 'dynamic' good. A test-writer values static good more highly than dynamic, and while this is justifiable in the circumstances, in the big picture, dynamic good is the real deal.

Interesting, that sounds worth checking out.

Don't bother with bloodless synopses online, or Zen and the Art of Motorcycle Maintenance.

http://coinread.com/lila_an_inquiry_into_morals.503624.html

The essence of Dynamic Quality is that you click on the link now :)

I think that Occam's razor says, that if we have several theories that describe reality with the same accuracy, we should chose the most succint (least redundant).

That's a good way to put it. If you want to be mathematically rigorous about it, you could phrase it as a statement about probabilities: for any A and B, P(A and B) <= P(A).

Being simple could more useful than being succinct e.g.:

  aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

is simpler than

  d9$lLsi

because the first is just 45a

http://en.wikipedia.org/wiki/Kolmogorov_complexity

The first one is more succint in a sense, because normally it wouldn't be represented in this literal, long form.

I don't think of it in terms of redundancy, but of introduced entities. That is, if two theories have equal explanatory power, but one theory requires ten new concepts, but the other one requires one new concept, prefer the latter. This interpretation is, I think, the spirit of what he intended: http://en.wikipedia.org/wiki/Occams_razor#Ockham

And if more than one theory is more-or-less equally probable, simple, and in accord with observed reality then you test all of them to see which you can eliminate. Repeat.

Yes. The context that has to be taken into account includes the social context, ie. 'I am sitting in a room taking a test, I cannot request clarification of the question, the person who wrote this test may be far less intelligent than me, etc'.

By making an effort to choose the possible answer that I perceive as the most boring and conformist, rather than one I might find brilliant, funny, novel, and suggestive of further even more interesting ideas, I am pursuing a strategy of "favouring theories that match every other part of observable reality", as you put it.

My 6yo daughter was upset because she couldn't understand the first clue in one of those kids' word puzzle books.

    "My first letter is in TOAST but not in ROAST".

Sometimes, dear daughter, you're just smarter than the guy who wrote the book.

Is there any reason that in this case and in the case of the parent comment, there's a tendency to jump to conclusions about the intelligence level of the test/puzzle writer? Do truly intelligent people never write lousy questions?

When I was young, I was furious at "Skip the first letter, keep every other letter, and what does it spell?" Data was something like "ghfeklmlto", and my answer was "hfeklmlto", of course.

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