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BP508 |
| Bongard Problems with precise definitions vs. Bongard Problems with vague definitions. |
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COMMENTS
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Bongard Problems sorted left have the keyword "precise" on the OEBP.
Bongard Problems sorted right have the keyword "fuzzy" on the OEBP.
In an precise Bongard Problem, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted.
(All relevant examples clearly sorted either left or right is the keyword allsorted.)
How can it be decided whether or not a rule is precise? How can it be decided whether or not a rule classifies all "examples that are relevant"? There needs to be another rule to determine which examples the original rule intends to sort. Bongard Problems by design communicate ideas without fixing that context ahead of time. The label "precise" can only mean a Bongard Problem's rule seems precise to people who see it. (This "precise vs. fuzzy" Bongard Problem is fuzzy.)
In an precise "less than ___ vs. greater than ___" Bongard Problem (keyword spectrum), the division between the sides is usually an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles (see e.g. BP292).
As a rule of thumb, do not consider imperfections of hand drawn images (keyword ignoreimperfections) when deciding whether a Bongard Problem is precise or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be labelled fuzzy; similar vagueness arises in all hand-drawn Bongard Problems. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword perfect.)
Sometimes the way a Bongard Problem would sort certain examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a precise criterion that has been used to verify each sorted example fits where it fits (some kind of mathematical proof); however, where some examples fit is still unknown. Whether or not such a Bongard Problem should be labelled "precise" might be debated.
(Technical note: some properties are known to be undecidable, and sometimes the decidability itself is unknown. See https://en.wikipedia.org/wiki/Decision_problem .)
(See the keyword proofsrequired.)
One way to resolve this ambiguity is to define "precise" as meaning that once people decide where an example belongs for a reason, they will all agree about it.
Sometimes the class of all examples in a Bongard Problem is imprecise, but, despite that, the rule sorting those examples is precise. Say, for some potential new example, it is unclear whether it should be included in the Bongard Problem at all, but, if it were included, it would be clear where it should be sorted (or that it should be left unsorted). A Bongard Problem like this can still be tagged "precise".
(If all examples are clearly sorted except for some example for which it is unclear whether it belongs to the class of relevant examples, the situation becomes ambiguous.)
On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword preciseworld.)
There is a subtle distinction to draw between Bongard Problems that are precise to the people making them and Bongard Problems that are precise to the people solving them. A Bongard Problem (particularly a non-allsorted one) might be labeled "precise" on the OEBP because the description and the listed ambiguous examples explicitly forbid sorting certain border cases; however, someone looking at the Bongard Problem without access to the OEBP page containing the definition would not be aware of this. It may or may not be obvious that certain examples were intentionally left out of the Bongard Problem. A larger collection of examples may make it more clear that a particularly blatant potential border case was left out intentionally. |
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CROSSREFS
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See BP876 for the version with pictures of Bongard Problems instead of links to pages on the OEBP.
See both and neither for specific ways an example can be classified as unsorted in an "precise" Bongard Problem.
Adjacent-numbered pages:
BP503 BP504 BP505 BP506 BP507  *  BP509 BP510 BP511 BP512 BP513
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KEYWORD
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fuzzy, meta (see left/right), links, keyword, right-self, sideless
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WORLD
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bp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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BP509 |
| Bongard Problems that sort all relevant examples vs. Bongard Problems that would leave some unsorted. |
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COMMENTS
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Left-sorted Bongard Problems have the keyword "allsorted" on the OEBP.
A Bongard Problem is labelled "allsorted" when the type of thing it sorts is partitioned unambiguously and without exception into two groups.
Similarly to using the precise and fuzzy keywords, calling a Bongard Problem "allsorted" is a subjective/intuitive judgment. The collection of all relevant potential examples is not clearly delineated anywhere.
(Sometimes it's ambiguous whether to consider certain examples that are ambiguously sorted relevant.)
The solution to an "allsorted" Bongard Problem can usually be re-phrased as "___ vs. not so" (see the keyword notso).
But not every "___ vs. not so" Bongard Problem should be labelled "allsorted"; there could be ambiguous border cases in a "___ vs. not so" Bongard Problem.
Bongard Problems in which the two sides are so different that there is no middle ground between them (keyword gap) are sometimes still labelled "allsorted", since the intuitive pool of all relevant examples just amounts to the two unrelated sides. But some "gap" Bongard Problems are not like that; for example sometimes there are more related classes of examples besides the two shown.
Sometimes the class of all examples in a Bongard Problem is imprecise, but, despite that, the rule sorting those examples is precise. Say, for some potential new example, it is unclear whether it should be included in the Bongard Problem at all, but, if it were included, it would be clear where it should be sorted. A Bongard Problem like this can still be tagged "allsorted".
On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword preciseworld.)
In deciding where to sort an example, we think about it until we come to a conclusion; an example isn't here considered ambiguous just because someone might have a hard time with it (keyword hardsort).
However, sometimes the way a Bongard Problem would sort certain examples is an unsolved problem in mathematics, and it may be unknown whether there is even a solution. Whether or not such a Bongard Problem should be labelled "allsorted" might be debated.
(See the keyword proofsrequired.)
One way to resolve this ambiguity is to redefine "allsorted" as meaning that once people decide where an example belongs, it will be on one of the two sides, and they will all agree about it.
There is a distinction to be made between a non-"allsorted" Bongard Problem that could be made "allsorted" by making (finitely many) more examples sorted (thereby modifying or clarifying the solution of the Bongard Problem) and one such that this is not possible while maintaining a comparably simple solution. The former kind would often be labelled precise, in particular when these border cases have been explicitly forbidden from being sorted in the Bongard Problem's definition.
For instance, discrete Bongard Problems that are not allsorted usually fall into the former category. |
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CROSSREFS
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See BP875 for the version with pictures of Bongard Problems instead of links to pages on the OEBP.
"Allsorted" implies precise.
"Allsorted" and both are mutually exclusive.
"Allsorted" and neither are mutually exclusive.
Adjacent-numbered pages:
BP504 BP505 BP506 BP507 BP508  *  BP510 BP511 BP512 BP513 BP514
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KEYWORD
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fuzzy, meta (see left/right), links, keyword, right-self, sideless, right-it, feedback
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WORLD
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bp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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BP512 |
| Abstract Bongard Problems vs. concrete visual Bongard Problems. |
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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. |
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COMMENTS
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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 BP can be narrow, e.g. BP6.
Even a rule and its conceptual opposite can be narrow, e.g. BP20.
What seems like a typical example depends on expectations. If one is expecting there to be triangles, the absence of triangles will be noticeable. (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".)
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). |
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CROSSREFS
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See BP830 for a version with pictures of Bongard Problems (miniproblems) instead of links.
Adjacent-numbered pages:
BP508 BP509 BP510 BP511 BP512  *  BP514 BP515 BP516 BP517 BP518
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KEYWORD
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dual, meta (see left/right), links, keyword, side
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WORLD
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bp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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BP514 |
| Bongard Problems whose right examples could stand alone vs. the left side is necessary to communicate what the right side is. |
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BP550 |
| Experimental Bongard Problems vs. traditional-style Bongard Problems. |
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COMMENTS
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Left examples have the keyword "experimental" on the OEBP.
Right examples have the keyword "traditional" on the OEBP.
Experimental BPs push the boundaries of what makes Bongard Problems Bongard Problems.
Traditional BPs show some simple property of black and white pictures. The OEBP is a place with many wild and absurd Bongard Problems, so it is useful to have an easy way to just find the regular old Bongard Problems. |
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CROSSREFS
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Adjacent-numbered pages:
BP545 BP546 BP547 BP548 BP549  *  BP551 BP552 BP553 BP554 BP555
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KEYWORD
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subjective, meta (see left/right), links, keyword, left-it
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WORLD
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bp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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BP567 |
| Visual Bongard Problems that would sort a blank panel on the left vs. visual Bongard Problems that would sort a blank panel on the right. |
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BP571 |
| Bongard Problems that require mathematical understanding to solve vs. other Bongard Problems. |
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