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 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 examples have the keyword "pixelperfect" on the OEBP.

All examples here are perfect Bongard Problems. That is, subtle imperfections in images are meant to be considered.

When a Problem is tagged with "pixelperfect", users are reminded to make sure they do not upload images such that taking the pixelation into account would affect the sorting of that example. That is, the zoomed-in jagged blocky version of the picture should still fit the solution.

For example, in the examples of BP335, which is about tessellation, the pixels interlock properly.

Stable Bongard Problems are generally pixelperfect.

Adjacent-numbered pages:
BP942 BP943 BP944 BP945 BP946  *  BP948 BP949 BP950 BP951 BP952

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

perfect_bp [smaller | same | bigger]

Leo Crabbe

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

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