"More," "fewer," "greater than," "less than."

See BP752 and BP749 for equality.

Adjacent-numbered pages:
BP978 BP979 BP980 BP981 BP982  *  BP984 BP985 BP986 BP987 BP988

meta (see left/right), links, metaconcept

bp [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP977 BP978 BP979 BP980 BP981  *  BP983 BP984 BP985 BP986 BP987

meta (see left/right), links, metaconcept

bp [smaller | same | bigger]

Aaron David Fairbanks

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

Consider the amount of data a person has to consciously unpack in each example in the process of determining how it should be sorted. In BP3, it is only necessary to notice the color of the shape. In BP871, however, it is important to read various qualities of every tiny shape shown.

Images of Bongard Problems that are "infodense" typically need to include a large number of examples in order to communicate the solution clearly without admitting unintended solutions. With so much data packed in each example, it becomes more likely that some of the random patterns in the data will happen to distinguish between the two sides in an unintended way. A similar issue appears in convoluted Bongard Problems.

Contrast "infodense" Problems to hardsort Bongard Problems, in which examples are difficult to sort, but perhaps that difficulty does not stem from reading a high amount of information; perhaps there is a small amount of information extracted from the examples, but it is hard to determine whether or not that information fits a rule.

Adjacent-numbered pages:
BP973 BP974 BP975 BP976 BP977  *  BP979 BP980 BP981 BP982 BP983

abstract, spectrum, meta (see left/right), links, keyword

Aaron David Fairbanks

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

Slightly different: sliding the content in a box around without letting it cross the bounding box and without changing the size of the bounding box. (See keyword absoluteposition.)

Expanding the boxes of BP2 ("big vs. small") makes the contents smaller in comparison to the box, but not smaller in an absolute sense. Hence the situation is ambiguous.

If a Bongard Problem has the keyword absoluteposition, then it likely has the keyword boundingbox.

If a Bongard Problem has the keyword boundingbox and does not have the keyword bordercontent, then it likely has the keyword absoluteposition.

Adjacent-numbered pages:
BP969 BP970 BP971 BP972 BP973  *  BP975 BP976 BP977 BP978 BP979

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

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

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

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

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

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 examples have the keyword "infinitedetail" on the OEBP.

Image files on the OEBP do not really have infinite detail. For a panel to be intuitively read as having infinite detail, there usually needs to be some apparent self-similarity, or perhaps a sequence of objects following an easy to read pattern getting smaller and smaller with increasing pixelation.

Usually in "infinitedetail" Bongard Problems, not only is it a puzzle to figure out the solution, but it is another puzzle to find self-similarities and understand the intended infinite detail in each example.

BPs tagged with the keyword "infinitedetail" usually feature pixelated images that give the closest approximation of the intended infinite structure up to pixelation. This means they should be tagged with the keyword perfect, but should not be tagged with the keyword pixelperfect.

Just because a Bongard Problem has "infinitedetail" does not necessarily make it infodense. Some fractal images might be encoded by a small amount of information (just the information about which places within itself it includes smaller copies of itself) and may be recognized quickly.

Adjacent-numbered pages:
BP953 BP954 BP955 BP956 BP957  *  BP959 BP960 BP961 BP962 BP963

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

visualbp [smaller | same | bigger]

Aaron David Fairbanks