See BP953, BP902.

Adjacent-numbered pages:
BP954 BP955 BP956 BP957 BP958  *  BP960 BP961 BP962 BP963 BP964

meta (see left/right), miniproblems, left-finite, right-finite, left-full, right-full, right-null, perfect, infinitedetail, finished, experimental, funny

zoom in left | zoom in right (blank_image)

Aaron David Fairbanks, Leo Crabbe

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

Many things might be called "creating a picture". For example, drawing a path in a maze. However, use this keyword to indicate a Bongard Problem requires the solver to create something totally new "on a separate piece of paper" (whether mentally or physically), beyond just annotating the existing picture.

A "visualimagination" BP will likely be hardsort.

"Visualimagination" BPs are abstract.

"Visualimagination" BPs are are often about deciding whether some potential thing exists. (See BP634 for Bongard Problems featuring the concept ofexistence.) One can demonstrate it exists by constructing it.

Adjacent-numbered pages:
BP955 BP956 BP957 BP958 BP959  *  BP961 BP962 BP963 BP964 BP965

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

Aaron David Fairbanks

Some examples are Bongard Problems with this solution.

Adjacent-numbered pages:
BP956 BP957 BP958 BP959 BP960  *  BP962 BP963 BP964 BP965 BP966

nice, precise, dual, handed, leftright, perfect, infinitedetail, both, neither, preciseworld

Aaron David Fairbanks

Adjacent-numbered pages:
BP957 BP958 BP959 BP960 BP961  *  BP963 BP964 BP965 BP966 BP967

precise, allsorted, minimal, dual, blackwhite, gap, left-finite, right-finite, left-full, right-full, left-null, finished, preciseworld, unstableworld

[smaller | same | bigger]
zoom in left (blank_image) | zoom in right (black_image)

Leo Crabbe

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

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

For the purposes of this Bongard Problem, "small change" means adding to or removing from an arbitrarily small portion of the image. Other kinds of small change could be explored, such as making changes in multiple small places, translating, rotating, scaling, or deforming the whole image slightly (see also keywords deformunstable vs. deformstable), or even context-dependent small changes (e.g., changing the shadings slightly in BP196, or making small 3d changes to the represented 3d objects in BP333), but they are not considered here.

In a "stable" Bongard Problem, no small change should outright flip an example's sorting. It is allowed for a small change to make an example sorted slightly more ambiguously.

Small changes that make an example no longer even fit in with the format of a Bongard Problem are not considered. (Otherwise, far fewer Bongard Problems would be called "stable".)

For whether small changes make an example no longer fit in with the Bongard Problem, see unstableworld vs. stableworld.

If a Bongard Problem is shown with imperfect hand drawings (keyword ignoreimperfections), it is fine to apply the keyword "unstable" ignoring this. For instance, a hand-drawn version of BP344 would still be tagged "unstable", even though it would show examples wrong by small amounts.

(Note: a BP would only be tagged "ignoreimperfections" in the first place if the underlying idea were such that several small changes could make an example switch sides, no longer fit in with the format of the Bongard Problem, or otherwise be ambiguously sorted.)

Stable Bongard Problems are generally perfect and pixelperfect.

Gap (technically) implies stable. (However, in practice it has seemed unnatural to tag BPs "stable" when ALL small changes render certain examples unsortable, as is sometimes the case in "gap" BPs.)

Unstable Bongard Problems are often precise.

Stable Bongard Problems tend to either be fuzzy or otherwise either have a gap or be not allsorted.

See BP1144, which is about all small changes making all examples unsortable rather than some small change making some example switch sides.

See BP1140, which is about any (perhaps large) additions of detail instead of small changes.

Adjacent-numbered pages:
BP958 BP959 BP960 BP961 BP962  *  BP964 BP965 BP966 BP967 BP968

BP1 is unstable because it's possible to change nothing slightly by adding a pixel to end up with something.

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

Aaron David Fairbanks

Right-sorted BPs have the keyword "gap" on the OEBP.

A Bongard Problem with a gap showcases two completely separate classes of objects.

For example, the Bongard Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there is a space of partially filled black-and-white images between them, or any number of other ambient contexts.

Bongard Problems about comparing quantities on a spectrum should not usually be considered "gap" BPs. (Discrete spectra perhaps.) A spectrum establishes a shared context, with examples on both sides of the BP landing somewhere on it. (However, if it is reasonable to imagine getting the solution without noticing a spectrum in between, it could be a gap, since the ambient context is unclear.)

Bongard Problems with gaps may seem particularly arbitrary when the two classes of objects are particularly unrelated.

If a Bongard Problem has a "gap" it is likely precise: it will likely be clear on which side any potential example fits.

"Gap" implies stable. (This technically includes cases in which ALL small changes make certain examples no longer fit in with the Bongard Problem, as is sometimes the case in "gap" BPs. See also BP1144.)

See also preciseworld. "Gap" Bongard Problems would be tagged "preciseworld" when the two classes of objects are each clear; it is then apparent that there is no larger shared context and that no other types of objects besides the two types would be sorted by the Bongard Problem.

See BP1140, which is about any (perhaps large) additions instead of repeated small changes.

Adjacent-numbered pages:
BP959 BP960 BP961 BP962 BP963  *  BP965 BP966 BP967 BP968 BP969

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

Aaron David Fairbanks

Rotations are allowed. To avoid confusion about whether reflections are allowed, no examples are included on the right that require reflections to match up with themselves locally but not globally; no examples are included on the left that can match up with themselves locally but not globally using a reflection.

Only parts of ellipses are used, and only one type of ellipse per image, to make everything easier to read and reason about.

See BP1246 for a variation on this idea where instead of lining the image up with itself along arbitrarily small regions, you line the image up with itself along individual separate objects.

Adjacent-numbered pages:
BP960 BP961 BP962 BP963 BP964  *  BP966 BP967 BP968 BP969 BP970

hard, precise, distractingworld, perfect

Aaron David Fairbanks

See BP889 for the version in which the background doesn't count.

Adjacent-numbered pages:
BP961 BP962 BP963 BP964 BP965  *  BP967 BP968 BP969 BP970 BP971

nice, boundingbox, number, right-null, perfect, pixelperfect, traditional, bordercontent

Aaron David Fairbanks

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

See also the keyword presentationmatters.

Adjacent-numbered pages:
BP962 BP963 BP964 BP965 BP966  *  BP968 BP969 BP970 BP971 BP972

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

keyword [smaller | same | bigger]

Aaron David Fairbanks

"Invalid Bongard Problems" are images that look sort of like Bongard Problems but aren't actually Bongard Problems.

With many examples included, this Problem might be placed somewhere to nonverbally show someone the subtler rules about what is allowed and what isn't allowed in Bongard Problems.

See BP829 for the Bongard Problem about Bongard Problems with no clear solution.

See BP522 (flipped) for a version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

See BP829 (flipped) for a near exact copy of this Bongard Problem idea but that does not include images with two of the same boxes on either side.

Also see BP1080, which includes various different formats of Bongard Problems, distinguishing them from arbitrary images that are not Bongard Problems.

Adjacent-numbered pages:
BP963 BP964 BP965 BP966 BP967  *  BP969 BP970 BP971 BP972 BP973

teach, meta (see left/right), miniproblems, assumesfamiliarity, structure

Jago Collins