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quintopia comments on Where to Draw the Boundary? - Less Wrong

36 Post author: Eliezer_Yudkowsky 21 February 2008 07:14PM

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Comment author: quintopia 26 April 2012 06:58:23AM *  0 points [-]

I disagree. When I hear 'natural joint', I imagine the process a university professor uses to decide where the breakpoints between letter grades fall ("setting the curve") in such a way to minimize requests by students to change their letter grade. One way I have seen is to sort the grades, then look for large gaps in the distribution. "No one has a final grade between 86.6 and 87.9, so I'll set 87.9 as the minimum grade needed for an A." This gap in the distribution is a 'natural joint'.

Note that this way of dividing up concept-space is much less well-defined than a straightforward Voronoi-diagram-with-concept-prototypes-as-cell-centers, in the sense that it is more memory-intensive when explicitly computed. However, I also think it more accurately reflects the intuitive sort of categories that humans actually produce.

That is, humans don't just ask "Is this thing more similar to the A prototype or the B prototype (with respect to the particular properties I am interested in)?" when trying to decide is something should be best called an A or a B, but rather, "Is this thing more similar to X and Y from category A or P and Q from category B (with respect to the particular properties I am interested in)?" If X and Y are far from P and Q in concept space, there is a 'natural joint' between A and B.

This gap could close up if enough things are added to both A and B that there is an X in A and a P in B that are very close to one another; at this point we consider combining the categories into a single category, or seeking out new properties that further separate them. Sometimes, though, we have good reason to keep different categories to describe concepts that are hopelessly intermingled, and in this and only this case, I would agree that "There is no 'natural joint'."