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 examples have the keyword "leftright" on the OEBP.

See updown.

All "leftright" Bongard Problems are handed.

Adjacent-numbered pages:
BP530 BP531 BP532 BP533 BP534  *  BP536 BP537 BP538 BP539 BP540

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

handed_visualbp [smaller | same | bigger]

Aaron David Fairbanks

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

Meta Bongard Problems are Bongard Problems that sort Bongard Problems. Sometimes abbreviated MBPs.

The first meta Bongard Problem was BP200.

Some meta BP pages sort images of Bongard Problems (keyword miniproblems), while other meta BP pages sort other BP pages (keyword links).

BPs that sort meta-BPs are labelled metameta.

Adjacent-numbered pages:
BP532 BP533 BP534 BP535 BP536  *  BP538 BP539 BP540 BP541 BP542

meta (see left/right), links, keyword, world, left-self, sideless, metameta, left-full, feedback

bp [smaller | same | bigger]
zoom in left (linksbp)

Aaron David Fairbanks

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

If mirroring any example along the any axis can change its sorting the BP is "handed."

Note that BPs about comparing orientation between multiple things in one example fit on the right side.

See BP871 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

The keyword leftright is specifically about flipping over the vertical axis, while the keyword updown is specifically about flipping over the horizontal axis.

Bongard Problems tagged rotate are usually "handed", since any rotation can be created by two reflections. Not necessarily, however, since the reflected step in between might not be sorted on either side by the Bongard Problem.

Adjacent-numbered pages:
BP547 BP548 BP549 BP550 BP551  *  BP553 BP554 BP555 BP556 BP557

meta (see left/right), links, keyword, invariance, wellfounded

visualbp [smaller | same | bigger]
zoom in left (handed_visualbp)

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 "structure" on the OEBP.

Examples of "structures": Bongard Problem, Bongard Problem with extra unsorted panel ("Bongard's Dozen"), 4-panel analogy grid, sequence of objects with a quantity changing by a constant amount.

If the solver hasn't become familiar with the featured structure, the Bongard Problem's solution may seem convoluted or inelegant. (See keyword assumesfamiliarity.) Once the solver gets used to seeing a particular structure it becomes easier to read that structure and solve Bongard Problems featuring it.

A Bongard Problem can non-verbally teach someone how a particular structure works, showing valid examples of that structure versus non-examples. E.g., BP968 for the structure of Bongard Problems and BP981 for the structure of analogy grids.

Adjacent-numbered pages:
BP784 BP785 BP786 BP787 BP788  *  BP790 BP791 BP792 BP793 BP794

meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks

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 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