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BP513 Bongard Problems whose left examples could stand alone vs. the right side is necessary to communicate what the left side is.
BP1
BP31
BP50
BP328
BP334
BP345
BP356
BP373
BP384
BP386
BP559
BP569
BP850
BP856
BP902
BP922
BP932
BP935
BP937
BP988
BP989
BP999
BP1004
BP1005
BP1006
BP1011
BP1049
BP1080
BP1086
BP1093
BP1098
BP1109
BP1110
BP1145
BP1147

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BP544
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COMMENTS

Left-sorted Bongard Problems have the the keyword "left-narrow" on the OEBP.


Call a rule "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.


A collection of triangles will be recognized as such; "triangles" is a narrow rule. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.


Intuitively, a narrow rule seems small in comparison to the space of other related possibilities. Narrow rules tend to be phrased positively ("is [property]"), while non-narrow rules opposite narrow rules tend to be phrased negatively ("is not [property]").


Both sides of a Bongard Problem can be narrow, e.g. BP6.

Even a rule and its conceptual opposite can be narrow, e.g. BP20.

A Bongard Problem such that one side is narrow and the other side is the non-narrow opposite reads as the narrow side being a subset of the other. See BP881.


What seems like a typical example depends on expectations. (See the keyword assumesfamiliarity for Bongard Problems that require the solver to go in with special expectations.)

A person might notice the absence of triangles in a collection of just polygons, because a triangle is such a typical example of a polygon. On the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.


Typically, any example fitting a narrow rule can be changed slightly to no longer fit. (This is not always the case, however. Consider the narrow rule "is approximately a triangle".) See the keyword stable.


It is possible for a rule to be "narrow" (communicable by a properly chosen collection of examples) but not clearly communicated by a particular collection of examples satisfying it, e.g., a collection of examples that is too small to communicate it.


Note that this is not just BP514 (right-narrow) flipped.



Is it possible for a rule to be such that some collections of examples do bring it to mind, but no collection of examples unambiguously communicates it as the intended rule? Perhaps there is some border case the rule excludes, but it is not clear whether the border case was intentionally left out. The border case's absence would likely become more conspicuous with more examples (assuming the collection of examples naturally brings this border case to mind).

CROSSREFS

See BP830 for a version with pictures of Bongard Problems (miniproblems) instead of links.

Adjacent-numbered pages:

AUTHOR

Aaron David Fairbanks

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