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

Bongard Problems that break the rules or spirit of Bongard Problems but are interesting enough to keep in the database.

See BP829 and BP968 (flipped) for versions with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

Adjacent-numbered pages:
BP517 BP518 BP519 BP520 BP521  *  BP523 BP524 BP525 BP526 BP527

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

bp [smaller | same | bigger]

Aaron David Fairbanks

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

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

Here "flipping the sides" of a Bongard Problem does not flip the sides of the example BPs.

Metaconcept implies "sideless".

Adjacent-numbered pages:
BP534 BP535 BP536 BP537 BP538  *  BP540 BP541 BP542 BP543 BP544

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

Aaron David Fairbanks

This is about BP pages on the OEBP.

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

Adjacent-numbered pages:
BP541 BP542 BP543 BP544 BP545  *  BP547 BP548 BP549 BP550 BP551

meta (see left/right), links, keyword, oebp, right-self, feedback, time

bppage [smaller | same | bigger]

Aaron David Fairbanks

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

Right examples have the keyword "anticomputer" on the OEBP.

Easy abstract Bongard Problems are typically anticomputer Bongard Problems.

See keyword help for Bongard Problems that can be made easier for humans to solve by the selection of helpful examples.

Adjacent-numbered pages:
BP560 BP561 BP562 BP563 BP564  *  BP566 BP567 BP568 BP569 BP570

spectrum, anticomputer, meta (see left/right), links, keyword, right-self, viceversa

bp [smaller | same | bigger]

Leo Crabbe

"Impossible Bongard Problem" is a loose term, but it roughly means the Bongard Problem can't be displayed as an image.

BP868, the version of this whose examples are images of Bongard Problems (miniproblems), rather than links to pages on the OEBP, is impossible. - Aaron David Fairbanks, Jul 29 2020

See overriddensolution for Problem solutions that Bongard Problems can have, but that will not be chosen by a reasonable person as the best solution.

Adjacent-numbered pages:
BP816 BP817 BP818 BP819 BP820  *  BP822 BP823 BP824 BP825 BP826

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

bp [smaller | same | bigger]

Leo Crabbe

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. It is about solutions, but it only makes sense for images of Bongard Problems with particular examples. - 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 examples have the keyword "contributepairs" on the OEBP.

When this keyword is added to a Problem, OEBP users are advised to add a corresponding right example for every left example they add and vice versa.

It is common for Bongard Problems to present left examples on the left side and corresponding altered versions of those examples on the right side, tweaked only slightly, to highlight the difference and make the solution easier to see (see keyword help).

This is common in more abstract Bongard Problems that admit a wide range of examples, a variety of different styles or types (e.g. BP360). Showing two versions of the same thing, one on the left and one on the right, helps a person interpret what that thing is meant to be in the context of the Bongard Problem; whatever qualities vary between the two in the pair must be relevant.

If a person cannot sort an example according to the solution property without seeing its corresponding opposite example, the Bongard Problem is invalid (see https://www.oebp.org/invalid.php ). There is no one rule dividing the sides; the solution is not a method to determine whether an arbitrary example fits left or right. See also Bongard Problems with the keyword collective, which are similarly borderline-invalid.

A BP in which each left example corresponds to a right example and vice versa could be remade as a Bongard Problem in which the left examples are the pairs. For example BP360 would turn into "a pair consisting of the ordered version of something and the chaotic version of the same thing vs. a pair of things not satisfying this relationship." This process would turn a Bongard Problem that is invalid in the sense described above into a valid one.

(See keyword orderedpair.)

In some "contributepairs" Bongard Problems there really is a natural choice of left version for every right example and vice versa (see keyword dual); in others the choice is artificially imposed by the Bongard Problem creator.

When "contributepairs" Bongard Problems are laid out in the format with a grid of boxes on either side of a dividing line, the boxes may be arranged so as to highlight the correspondence: either

A B | A B

E F | E F

G H | G H

or

A B | B A

E F | F E

G H | H G.

Adjacent-numbered pages:
BP914 BP915 BP916 BP917 BP918  *  BP920 BP921 BP922 BP923 BP924

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

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

Aaron David Fairbanks

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

Arbitrary BPs often communicate non-arbitrary ideas. M. M. Bongard's original "A vs. Б" Problem (BP100) is about recognizing letters. A choice of some such arbitrary letters was necessary.

Most Bongard Problems are at least slightly arbitrary. Almost any Bongard Problem could be changed in a number of ways to make slightly different Bongard Problems. When a Bongard Problem is labeled as "arbitrary", that means there is one especially obvious class of similar Bongard Problems, with none of them particularly more interesting or special than any other.

The self-referential (invalid) Bongard Problems BP538, BP545, BP902, BP1073 fit this definition (the solution involves the arbitrary detail of being that specific Bongard Problem instead of any other). On the other hand, the solution idea is not arbitrary when phrased with "this Bongard Problem".

Many "arbitrary" Bongard Problems are of the form "Detail X has arbitrary value A vs. not so" or "Detail X has arbitrary value A vs. detail X has arbitrary value B". Other "arbitrary" Bongard Problems feature arbitrary details that are not the distinction between the sides, e.g. BP545.

It is unclear whether or not we should label a Bongard Problem "arbitrary" if the arbitrarily fixed detail is a notable special case. For example, BP1024 could have been made using any number, but the number 1 is a non-arbitrary number, so the Bongard Problem does not seem so arbitrary.

Similar to thespecificity concept BP (BP773), which is more general, including Bongard Problems relating conceptually in any way to arbitrary specificity.

Adjacent-numbered pages:
BP945 BP946 BP947 BP948 BP949  *  BP951 BP952 BP953 BP954 BP955

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

bp [smaller | same | bigger]

Aaron David Fairbanks