The first Bongard Problem.

All examples in this Bongard Problem are line drawings (one or more connected figures made up of curved and non-curved lines).

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

Adjacent-numbered pages:
  *  BP2 BP3 BP4 BP5 BP6

A circle fits on the right because it is not nothing.

easy, nice, precise, allsorted, unstable, world, left-narrow, left-finite, left-full, left-null, perfect, pixelperfect, finished, traditional, stableworld, deformstable, bongard

zoom in left (blank_image) | zoom in right (curves_drawing)

Mikhail M. Bongard

Adjacent-numbered pages:
BP1071 BP1072 BP1073 BP1074 BP1075  *  BP1077 BP1078 BP1079 BP1080 BP1081

meta (see left/right), links, metameta

linksbp [smaller | same | bigger]

Aaron David Fairbanks

This is an example of a meta Bongard Problem that sorts itself left, and would still sort itself left after the sides in the title were switched.

That is, this BP is tagged the keyword left-self and so would its flipped version be.

See also the keyword feedback for chains of meta Bongard Problems that eventually form loops.

Adjacent-numbered pages:
BP1070 BP1071 BP1072 BP1073 BP1074  *  BP1076 BP1077 BP1078 BP1079 BP1080

notso, arbitrary, meta (see left/right), links, left-self, experimental

Aaron David Fairbanks

See also BP1056, "blank image vs. nothing".

BP1 is also a (less specific) solution to this.

BP1209 (flipped) is also a (less specific) solution to this.

Adjacent-numbered pages:
BP1214 BP1215 BP1216 BP1217 BP1218  *  BP1220 BP1221 BP1222 BP1223 BP1224

minimal, gap, left-narrow, right-narrow, left-finite, right-finite, left-full, right-full, left-null, funny, unstableworld

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