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

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

Users are not able to add or remove examples from Problems tagged "finished." (This is unusual; most Bongard Problems on the OEBP can be expanded indefinitely by users.)

A "finished" Bongard Problem will always admit the alternate, convoluted solution "is [left example 1] OR is [left example 2] OR . . . OR is [last left example] vs. is [right example 1] OR is [right example 2] OR . . . OR is [last right example]".

Bongard's original Problems are tagged "finished."

Adjacent-numbered pages:
BP499 BP500 BP501 BP502 BP503  *  BP505 BP506 BP507 BP508 BP509

meta (see left/right), links, keyword, oebp, presentationmatters, left-finite, right-finite, instruction

bppage [smaller | same | bigger]

Aaron David Fairbanks

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 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 examples have the keyword "help" on the OEBP.

BPs should be marked "help" when the OEBP wants most examples (at least on one side) to be helpful (not when just one or two uploaded examples are helpful).

Helpfulness can be a spectrum; most Bongard Problems are helpful to some degree just by not using the most convoluted unintelligible examples possible.

Examples that are helpful to people are often not particularly helpful to computers.

Any helpful Bongard Problem has a harder, not helpful version. For example, BP384 (square number of dots versus non-square number of dots) would be much harder if all examples had hundreds of dots that weren't arranged recognizably. Instead, the dots in the examples are always arranged in shapes that make the square-ness or non-square-ness of the numbers easy to check without brute counting.

When all examples in a Bongard Problem are helpful, it may become unclear whether the helpfulness is part of the Bongard Problem's solution.

E.g.: Is the left-hand side of BP384 "square number of dots", or is it "square number of dots that are arranged in a helpful way so as to communicate the square-ness"?

See seemslike, where examples being helpful is an irremovable aspect of the Bongard Problem's solution.

Adjacent-numbered pages:
BP925 BP926 BP927 BP928 BP929  *  BP931 BP932 BP933 BP934 BP935

anticomputer, meta (see left/right), links, keyword, oebp, instruction

bppage [smaller | same | bigger]
zoom in left (help_bp)

Aaron David Fairbanks

Left-sorted Bongard Problems are tagged with the keyword "preciseworld" on the OEBP.

The keyword "preciseworld" basically means: if a new Bongard Problem were created to sort whether or not examples fit in the pool of examples in the original Bongard Problem, it would be tagged precise.

For a Bongard Problem fitting left, the intended class of examples sorted by the Bongard Problem is clear-cut.

For a Bongard Problem fitting right, there isn't any obvious boundary to take as delimiting the pool of potential examples. There is an imprecise fading of relevancy rather than a natural cutoff point.

Sometimes there are specific notable cases of potential examples for which there is ambiguity about whether they belong.

For example, the empty square (zero dots) has been left out of BP989. This is perhaps the only obvious example that is ambiguous as to whether it should be considered as belonging to the pool of examples shown in the Bongard Problem (or any similar dot-counting Bongard Problem).

(There would be no ambiguity if it were actually included in the Bongard Problem.)

(Whether or not zero seems like an obvious example also has a cultural component (see culture); someone who is not accustomed think of zero as a number might not see this as ambiguous at all.)

Larger pools of examples make the absence of notable border cases like this more conspicuous and intentional-seeming. (See also discussion at left-narrow.) But expanding the pool of examples cannot resolve certain border cases: if the rule of the Bongard Problem by nature leaves unsorted a potential example that is a border case for even fitting in with the rest of the examples, its absence doesn't communicate anything; whether it belongs with the pool of examples remains ambiguous.

It is tempting to make another another "allsortedworld" analogous to allsorted. But the pool of relevant examples fitting in a Bongard Problem is like a Bongard Problem with only one side: a collection satisfying some rule. Would there be any difference between precise and allsorted for a Bongard Problem with only one side?

Adjacent-numbered pages:
BP1185 BP1186 BP1187 BP1188 BP1189  *  BP1191 BP1192 BP1193 BP1194 BP1195

Bongard Problems featuring generic shapes ( https://oebp.org/search.php?q=world:fill_shape ) have not usually been labelled "preciseworld". (What counts as a "shape"? Can the shapes be fractally complicated, for example? What exactly are the criteria?) Nonetheless, these Bongard Problems are frequently precise.

meta (see left/right), links, keyword

Aaron David Fairbanks