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# dspeyer comments on The Fallacy of Gray - Less Wrong

73 07 January 2008 06:24AM

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Comment author: 17 November 2011 03:38:19AM 8 points [-]

Then there's the fallacy of shades of gray: that every space can be reasonably modeled as 1-dimensional.

Comment author: 20 April 2012 06:30:24PM *  0 points [-]

I'm trying to imagine the other dimension we could add to this. If we have "more right" and "less right" along one axis, what's orthogonal to it?

I initially felt this comment was silly (the post isn't saying every space can be reasonably modeled as one-dimensional, is it?), but my brain is telling me we actually could come up with a more precise way to represent the article's concept with a Cartesian plane... but I'm not actually able to think of one. False intuition based on my experience with the "Political Compass" graph, perhaps.

Comment author: 20 April 2012 06:50:42PM 1 point [-]

Direction of divergence?

Neither (1, 5) nor (5, 1) may be "more wrong" when the answer is (2, 2), but may still be quite meaningfully distinct for some purposes.

Comment author: 20 April 2012 07:39:15PM *  0 points [-]

That's true. They could be wrong in different ways (or "different directions", in our example), which could be important for some purposes. But as you say, that depends on said purposes; I'm still uncertain as to the fallacy that dspeyer refers to. If our only purpose is determining some belief's level of correctness, absent other considerations (like in which way it's incorrect), isn't the one dimension of the "shades of grey" model sufficient?

Although -- come to think of it, I could be misunderstanding his criticism. I took it to mean he had an issue with the original post, but he could just be providing an example of how the shades-of-grey model could be used fallaciously, rather than saying it is fallacious, as I initially interpreted.

Comment author: 26 April 2012 05:25:55AM *  2 points [-]

I meant my comment more as a warning to readers than as a criticism of the article. When you've upgraded your mental model, don't stop and be satisfied -- see if there are more low-hanging upgrades. This is especially important if having recently improved your model biases you toward overconfidence (which I suspect is common).

To address your actual challenge...

Probability of correctness may actually be one dimensional. Though in practice it's worth keeping around what the big hunks of uncertainty are so you can update them easily if needed (i.e. P(my_understanding) = P(I_understood_what_I_read) * P(the_author_was_honest) * ... is easier to update if you later learn the author was a troll).

Degrees of correctness are more complex. "The geography of the Earth is as shown on a Mercator map" and "The geography of the Earth is as shown on a Peters map" are both false. They are both useful approximations. Is one more useful than the other? That depends on what you want to do with it.

There were other examples in the article besides correctness. "Every society imposes some of its values on those raised within it, but the point is that some societies try to maximize that effect, and some try to minimize it" and some maximize it with regard to their perspective on murder and minimize it with regard to their perspective on shellfish. "No one is perfect, but some people are less imperfect than others" and some people are imperfect in different ways from others, which are more or less harmful in different circumstances.