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.

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

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

bp [smaller | same | bigger]

Aaron David Fairbanks

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.

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

fuzzy, meta (see left/right), links, keyword, right-self, sideless, right-it, feedback

bp [smaller | same | bigger]

Aaron David Fairbanks

Left-sorted BPs have the keyword "noisy" on the OEBP. Right-sorted examples have the keyword "minimal."

Noisy Bongard Problems include extra details varying between examples that distract from the solution property; more specifically noise is properties independent of the solution property that vary between examples. Minimalist Bongard Problems only vary details absolutely necessary to communicate the solution.

"Noisy" is different than the kind of distraction mentioned at distractingworld, which means the class of examples is distractingly specific, irrelevant to the solution, rather than that there are extra distracting properties changing between examples.

Bongard Problems have varying degrees of noisiness. Only include here BPs that are very noisy or very minimal.

See BP827 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

See BP845 for noise in sequences of quantity increase.

Adjacent-numbered pages:
BP506 BP507 BP508 BP509 BP510  *  BP512 BP513 BP514 BP515 BP516

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

bp [smaller | same | bigger]

Harry E. Foundalis, 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 examples have keyword "distractingworld" on the OEBP.

This is different than the kind of distraction mentioned at noisy, which means there are details that are irrelevant to the solution changing between examples.

To label a BP "distractingworld" is to judge that the type of examples are more specific than should have been necessary to communicate the same general solution idea--this involves separating out which ideas are the nice ideas the BP really ought to have been about, and which ideas seem unimportant and irrelevant. On the other hand, to label a BP "noisy" is just to notice there are extra properties varying that are independent of the solution property.

Distractingworld BPs are often arbitrary.

Adjacent-numbered pages:
BP860 BP861 BP862 BP863 BP864  *  BP866 BP867 BP868 BP869 BP870

BP1105 was created as an extreme example of this. All images in that BP show the same distractingly detailed background, irrelevant to the solution.

stub, fuzzy, abstract, subjective, meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks

One left and one right example with each solution are shown for help.

This BP is fuzzy for multiple reasons. How obvious it is that an example fits a rule is subjective. Also, somebody could read the simplicity of all included examples as part of a Bongard Problem's solution. For example, the more obvious version of "square number of dots vs. non-square number of dots" could be interpreted as "square small number of dots arranged in easy-to-read way vs. non-square small number of dots arranged in easy-to-read way."

Whether this Bongard Problem solution would categorize an image of itself left or right depends on the difficulty of the solutions of the mini-Problems.

See keyword help.

See keyword hardsort.

Adjacent-numbered pages:
BP889 BP890 BP891 BP892 BP893  *  BP895 BP896 BP897 BP898 BP899

fuzzy, abstract, notso, subjective, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, contributepairs

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

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

Right-sorted Bongard Problems have the keyword "presentationinvariant" on the OEBP.

Meta Bongard problems that sort Bongard Problems purely based on their solutions usually have two versions in the database: one that sorts images of Bongard Problems and one that sorts links to pages on the OEBP. If both versions exist, users should make them cross-reference one another. (Meta Bongard Problems that sort images of Bongard Problems have the keyword miniproblems, whereas meta Bongard Problems that sort links to OEBP pages have the keyword links.)

For meta-pages on the OEBP that sort other pages on the OEBP (keyword links), "presentationmatters" means factoring in content like the BP number, the currently uploaded examples, the wording of the title, the description, and so on, rather than just the solution (that is, how the page would sort all potential examples). This is unusual.

"One solution vs. multiple solutions" (BP828) seems like a border-case. - Aaron David Fairbanks, Aug 01 2020

See BP1010 (projectionmatters versus 3d) for a similar idea: there 2D representations are to 3D objects as here Bongard Problems are to Bongard Problem solutions.

Adjacent-numbered pages:
BP890 BP891 BP892 BP893 BP894  *  BP896 BP897 BP898 BP899 BP900

fuzzy, meta (see left/right), links, keyword, right-self, sideless, metameta, right-it, dependence, presentationinvariant

metabp [smaller | same | bigger]

Jago Collins

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

Sometimes all the examples in a Bongard Problem need to be interpreted a certain way for the Bongard Problem to make sense. Only once the representation is understood, the idea seems simple.

For example, all meta Bongard Problems (Bongard Problems sorting other Bongard Problems) assume the solver interprets the examples as Bongard Problems.

TO DO: Maybe it is best to stop putting the label "assumesfamiliarity" on all meta-Bongard Problems. There are so many of them. It may be better to only use the "assumesfamiliarity" keyword on meta-BPs for a further assumption than just that all examples are interpreted as Bongard Problems. - Aaron David Fairbanks, Feb 11 2021

Many Bongard Problems in which all examples take the same format (keyword structure) assume the solver already knows how to read that format.

Some Bongard Problems assume the solver will be able to understand symbolism that is consistent between examples (keyword consistentsymbols).

Bongard Problems tagged math often assume the solver is familiar with a certain representation of a math idea.

Adjacent-numbered pages:
BP1106 BP1107 BP1108 BP1109 BP1110  *  BP1112 BP1113 BP1114 BP1115 BP1116

BP1032: The solution should really read "Assuming all images are Bongard Problems sorting each natural number left or right ..." This Bongard Problem makes sense to someone who has been solving a series of similar BPs, but otherwise there is no reason to automatically read a collection of numbers as standing for a larger collection of numbers.

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

bp [smaller | same | bigger]

Aaron David Fairbanks

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; likely just one example wouldn't get the answer across.

On the other hand, in BP1157 for example, each intended rule is communicated by just one example; these rules have to be particularly simple and intuitive, and the individual examples have to be complicated enough to communicate them.

Often, each rule is communicated by showing several examples of things satisfying it. (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.

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 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