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

Right-sorted Bongard Problems have the keyword "less." They are not necessarily "bad," but we do not want more like them.

Adjacent-numbered pages:
BP498 BP499 BP500 BP501 BP502  *  BP504 BP505 BP506 BP507 BP508

subjective, meta (see left/right), links, keyword, oebp, right-finite, left-it, feedback, time

bp [smaller | same | bigger]

Aaron David Fairbanks

BPs sorted left are tagged with the keyword "abstract" on the OEBP. The solution is not an easily-checked or concretely-defined geometrical or numerical property in pictures.

Adjacent-numbered pages:
BP507 BP508 BP509 BP510 BP511  *  BP513 BP514 BP515 BP516 BP517

abstract, meta (see left/right), links, keyword, left-self, sideless

bp [smaller | same | bigger]

Aaron David Fairbanks

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).

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

dual, meta (see left/right), links, keyword, side

bp [smaller | same | bigger]

Aaron David Fairbanks

Left examples have the keyword "math" on the OEBP.

Although everything is arguably related to math, these BP solutions include content that people don't inherently understand without learning at least some mathematics.

Left examples do not technically have "culturally-dependent" content (keyword culture), but knowledge and previous learning plays a role in how easy they are to solve.

Adjacent-numbered pages:
BP566 BP567 BP568 BP569 BP570  *  BP572 BP573 BP574 BP575 BP576

fuzzy, meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks

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

Be encouraged to contribute new interesting examples to Bongard Problems with this keyword.

There is much overlap with the keyword hardsort.

This is what it usually means to say examples fit on (e.g.) the left of a Bongard Problem in various creative ways: there is no (obvious) general method to determine a left-fitting example fits left.

There is a related idea in computability theory: a "non recursively enumerable" property is one that cannot in general be checked by a computer algorithm.

But keep in mind the tag "creativeexamples" is supposed to mean something less formal. For example, it requires no ingenuity for a human being to check when a simple shape is convex or concave (so BP4 is not labelled "creativeexamples"). However, it is not as if we use an algorithm to do this, like a computer. (It is not even clear what an "algorithm" would mean in this context, since it is ambiguous both what class of shapes the Bongard Problem sorts and how that would be encoded into a computer program's input. There are usually many options and ambiguities like this whenever one tries to formalize the content of a Bongard Problem.)

Adjacent-numbered pages:
BP861 BP862 BP863 BP864 BP865  *  BP867 BP868 BP869 BP870 BP871

notso, meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP913 BP914 BP915 BP916 BP917  *  BP919 BP920 BP921 BP922 BP923

meta (see left/right), links, metaconcept

bp [smaller | same | bigger]

Leo Crabbe

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

In the typical "rules" Bongard Problem, it is possible to come up with many convoluted rules that fit each example, but the intended interpretation is the only simple and obvious one.

Since it is difficult to communicate a rule with little detail, "rules" Bongard Problems are usually infodense.

Typically, each example is itself a bunch of smaller examples that all obey the rule. It is the same as how a Bongard Problems relies on many examples to communicate rules; it likely wouldn't get the answer across with just one example.

Often, each rule is communicated just by showing some examples of things satisfying it placed next to each other. (See keywords left-narrow and right-narrow.) Contrast Bongard Problems, which are more communicative, by showing some examples satisfying the rule and some examples NOT satisfying the rule.

BP1157 is an example of a "rules" Bongard Problem in which each intended rule is communicated by just one example of its application; these rules have to be particularly simple and intuitive, and the individual examples have to be complicated enough to communicate them.

A "rules" Bongard Problem is often collective. Some examples may admit multiple equally plausible rules, and the correct interpretation of each example only becomes clear once the solution is known. The group of examples together improve the solver's confidence about having understood each individual one right.

It is common that there will be one or two examples with multiple reasonable interpretations due to oversight of the author.

All meta Bongard Problems are "rules" Bongard Problems.

Many of the other Bongard-Problem-like structures seen on the OEBP are also about recognizing a pattern. (See keyword structure.)

"Rules" Bongard Problems are abstract, although the individual rules in them may not be abstract. "Rules" Bongard Problems also usually have the keyword creativeexamples.

Adjacent-numbered pages:
BP1153 BP1154 BP1155 BP1156 BP1157  *  BP1159 BP1160 BP1161 BP1162 BP1163

fuzzy, meta (see left/right), links, keyword, left-self, rules

Aaron David Fairbanks

Left-sorted Problems have the keyword "miniworlds" on the OEBP.

All examples in this Problem are visual Bongard Problems with multiple objects in most panels. This is key as an intuitive set of allowable objects needs to be communicated by any one sorted image.

There is a decent degree of overlap between rules and "miniworlds", but BP1049 is an example of a "miniworlds" problem where the rule is constant across examples, and BP1155 is an example of a "rules" Problem that would not be tagged "miniworlds".

Although this Problem does sort any BP whose examples are images of Bongard Problems left, it is probably best not to consider them to avoid clutter and more unnecessary keywords being attached to them.

Adjacent-numbered pages:
BP1175 BP1176 BP1177 BP1178 BP1179  *  BP1181 BP1182 BP1183 BP1184 BP1185

meta (see left/right), links, keyword

visualbp [smaller | same | bigger]

Leo Crabbe

Bongard Problems sorted left have the keyword "dithering" on the OEBP.

Bongard's original Problems never involved shades of gray. They were just black and white drawings.

Adjacent-numbered pages:
BP1193 BP1194 BP1195 BP1196 BP1197  *  BP1199 BP1200 BP1201 BP1202 BP1203

meta (see left/right), links, keyword

Aaron David Fairbanks