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

Call a rule "narrow" if it is likely to be noticed in a large collection of examples, without any counterexamples provided.

A collection of triangles will be recognized as such; "triangles" is a narrow rule. A collection of non-triangular shapes will just be seen as "shapes"; "not triangles" is not narrow.

Intuitively, a narrow rule seems small in comparison to the space of other related possibilities. Narrow rules tend to be phrased positively ("is [property]"), while non-narrow rules opposite narrow rules tend to be phrased negatively ("is not [property]").

Both sides of a BP can be narrow, e.g. BP6.

Even a rule and its conceptual opposite can be narrow, e.g. BP20.

What seems like a typical example depends on expectations. If one is expecting there to be triangles, the absence of triangles will be noticeable. (See the keyword assumesfamiliarity for Bongard Problems that require the solver to go in with special expectations.)

A person might notice the absence of triangles in a collection of just polygons, because a triangle is such a typical example of a polygon. On the other hand, a person will probably not notice the absence of 174-gons in a collection of polygons.

Typically, any example fitting a narrow rule can be changed slightly to no longer fit. (This is not always the case, however. Consider the narrow rule "is approximately a triangle".)

It is possible for a rule to be "narrow" (communicable by a properly chosen collection of examples) but not clearly communicated by a particular collection of examples satisfying it, e.g., a collection of examples that is too small to communicate it.

Note that this is not just BP514 (right-narrow) flipped.

Is it possible for a rule to be such that some collections of examples do bring it to mind, but no collection of examples unambiguously communicates it as the intended rule? Perhaps there is some border case the rule excludes, but it is not clear whether the border case was intentionally left out. The border case's absence would likely become more conspicuous with more examples (assuming the collection of examples naturally brings this border case to mind).

See BP830 for a version with pictures of Bongard Problems (miniproblems) instead of links.

Adjacent-numbered pages:
BP508 BP509 BP510 BP511 BP512  *  BP514 BP515 BP516 BP517 BP518

dual, meta (see left/right), links, keyword, side

bp [smaller | same | bigger]

Aaron David Fairbanks

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

This sorts Bongard Problems based on how BP513 (left-narrow) would sort them if they were flipped; see that page for a description.

Adjacent-numbered pages:
BP509 BP510 BP511 BP512 BP513  *  BP515 BP516 BP517 BP518 BP519

dual, meta (see left/right), links, keyword, side

bp [smaller | same | bigger]

Aaron David Fairbanks

Left-sorted BPs have the keyword "left-finite" in the OEBP.

How to distinguish between different examples depends on the Bongard Problem. For example, in BPs about little black dots, examples may be considered the same when they have the same number of dots in all the same positions.

Note that this is not just BP516 (right-finite) flipped.

"Left-finite" implies left-narrow.

See left-listable, which is about an infinite left side that can be organized into a neverending list versus infinite left side that cannot be organized into a neverending list.

"Left-finite" BPs are typically precise.

See BP1032 for a version that sorts images of Bongard Problems (miniproblems) instead of links, and which only sorts images of Bongard Problems about numbers.

Adjacent-numbered pages:
BP510 BP511 BP512 BP513 BP514  *  BP516 BP517 BP518 BP519 BP520

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

bp [smaller | same | bigger]
zoom in right (bp_infinite_left_examples)

Aaron David Fairbanks

Left-sorted BPs have the keyword "right-finite" in the OEBP.

BPs are sorted based on how BP515 (left-finite) would sort them were they flipped; see that page for a description.

"Right-finite" implies right-narrow.

See right-listable, which is about an infinite right side that can be organized into a neverending list versus infinite right side that cannot be organized into a neverending list.

"Right-finite" BPs are typically precise.

See BP1041 for a version that sorts images of Bongard Problems (miniproblems) instead of links, and which only sorts images of Bongard Problems about numbers.

Adjacent-numbered pages:
BP511 BP512 BP513 BP514 BP515  *  BP517 BP518 BP519 BP520 BP521

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

bp [smaller | same | bigger]
zoom in right (bp_infinite_right_examples )

Aaron David Fairbanks

Left-sorted BPs have the keyword "left-self" on the OEBP. Right-sorted BPs have the keyword "right-self."

These keywords are added to pages automatically.

Rhetorical questions: Where does this BP sort itself? Where does this BP sort the flipped version of itself?

See BP793 for the version sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

See BP1075 for an example of a BP that is tagged "left-self" but would still be tagged "left-self" after the sides in the title were flipped. (This is unusual; a "left-self" BP after being flipped is typically "right-self" and vice versa.)

Adjacent-numbered pages:
BP512 BP513 BP514 BP515 BP516  *  BP518 BP519 BP520 BP521 BP522

nice, dual, meta (see left/right), links, keyword, side, metameta, feedback

Multiple options:
linksbp [smaller | same | bigger],
bp_in_own_world [smaller | same | bigger]
zoom in left | zoom in right

Aaron David Fairbanks

This is the "it" Problem.

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

Right-sorted Bongard Problems have the keyword "right-it" on the OEBP.

Left-it or right-it implies feedback.

Adjacent-numbered pages:
BP1068 BP1069 BP1070 BP1071 BP1072  *  BP1074 BP1075 BP1076 BP1077 BP1078

nice, meta (see left/right), links, keyword, side, metameta, feedback, time, experimental, funny, presentationinvariant

linksbp [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1074 BP1075 BP1076 BP1077 BP1078  *  BP1080 BP1081 BP1082 BP1083 BP1084

meta (see left/right), links, side, wellfounded

recursive_boxes_bp [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP1076 BP1077 BP1078 BP1079 BP1080  *  BP1082 BP1083 BP1084 BP1085 BP1086

meta (see left/right), links, side, wellfounded

outline_or_fill_circle_bp_clear_set_of_ratios [smaller | same | bigger]

Aaron David Fairbanks

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

Right-sorted Bongard Problems have the keyword "right-unknowable".

Think of searching for needles in endless haystacks. You can be sure a haystack has a needle by finding it, but you can never be sure a haystack does not have a needle.

When a Bongard Problem is "left-unknowable", individual examples cannot be determined for certain to fit left, by any means. The author of the Bongard Problem just chooses some examples that seem to fit left. (See also the noproofs keyword.)

It is very extreme for this to apply to all examples without exception. Often a Bongard Problem is close to being purely left-unknowable, but a few examples spoil it by being obviously disqualified from the right side for some reason.

It is natural for a person to guess the solution to an unknowable Bongard Problem before actually understanding all the knowable examples, taking some of them on faith.

As a prank, take a left- or right- unknowable Bongard Problem and put an example that actually belongs on the unknowable side on the knowable side. The solver will have to take it on faith there is some reason it fits there they are not seeing.

(The property of having this kind of sorting mistake is unknowable for left- or right- unknowable Bongard Problems.)

One interpretation of topology (a subject of mathematics -- see https://en.wikipedia.org/wiki/Topology ) is that a topology describes the observability of various properties. (The topological "neighborhoods" of a point are the subsets one could determine the point to be within using a finite number of measurements.) The analogue of a property that is nowhere directly observable is a "subset with empty interior". Furthermore, the fact that the negation of the property is observable corresponds to the subset being "closed".

Left- or right- unknowable Bongard Problems are generally notso Bongard Problems: an example fits on one side just in case it cannot be observed to fit on the other.

Although the descriptions of left-couldbe and right-couldbe sound similar to "left-unknowable" and "right-unknowable", they are not the same. It is the difference between a clear absence of information and perpetual uncertainty about whether there is more information to be found. For any example sorted on a "could be" side, there is a clear (knowable) absence of information whose presence would justify the example being on the other side.

Sometimes an unknowable BP can be turned into a couldbe BP by explicitly restricting the amount of available information. For example, if there were a hypothetical Bongard Problem with infinitely detailed pictures, using a low resolution for all pictures could simplify the issue of detecting some properties that would be "unknowable". Many fractal-based BPs are this way (e.g. BP1122). See keyword infinitedetail.

Right-unknowable Bongard Problems are generally left-narrow (and left-unknowable Bongard Problems are generally right-narrow).

A Bongard Problem with examples on both sides cannot be tagged both proofsrequired and left- or right- unknowable.

Many Bongard Problems are about finding rules (keyword rules)--in each panel a rule is to be found, and there are no specified limits about what kind of rule it can be or how abstract it can be. (Just like a Bongard Problem.) "There is a rule vs. there isn't" (resp. vice versa) are right- (resp. left-) unknowable. (That is, disregarding cases that obviously do not define a rule because of some trivial disqualifying reason.)

Actually, I think there is something more to be said about this. It is possible to design examples that signal there is no rule to be found. See for example EX9138 in BP1127 and EX6829 in BP829. (Related: keyword help.) Each of these examples communicates a clear rule that "doesn't count". And there is so little information shown that a person can feel confident they've noticed all the relevant details. So, contrary to how they are currently tagged, these Bongard Problems aren't strictly "unknowable"; there are some exceptional knowable cases. But being too strict about the definition of "unknowable" makes it so there aren't any examples of unknowable Bongard Problems, so it's probably better to be a bit loose. - Aaron David Fairbanks, Apr 20 2022

Adjacent-numbered pages:
BP1119 BP1120 BP1121 BP1122 BP1123  *  BP1125 BP1126 BP1127 BP1128 BP1129

The perfect example is BP1163.

Interesting example of a Bongard Problem that is neither left-unknowable nor right unknowable in particular, but for which it is impossible to know whether any example fits on either side: BP1229 (translational symmetry vs. not) made with examples that can be expanded to any larger finite region the solver wants to look at. In this case, examples could only be sorted based on what they seem like (see seemslike), trusting they appear in a way that hints psychologically at what they actually are (see help).

dual, meta (see left/right), links, keyword, side, viceversa

Aaron David Fairbanks

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

Right-sorted Bongard Problems have the keyword "right-couldbe".

In a "couldbe" Bongard Problem, some relevant information is left out by the way objects are displayed. Solutions to "left-couldbe" BPs sound like "Could be a ___ vs. definitely not a ___" (and vice versa for "right-couldbe" BPs.)

To put it in mathematical jargon, there is a "projection" function from objects to pictures, such that objects satisfying property X are mapped to the same picture as objects not satisfying property X. Sorted on the "couldbe" side is the image (under projection) of the collection of objects satisfying property X.

Furthermore, usually X is a relatively narrow criterion, so that most objects do not satisfy it (see keywords left-narrow and right-narrow), and all pictures are in the image (under projection) of the collection of objects not satisfying property X.

Consider BP525, "Cropped image of a circle vs. not so." None of the left-hand examples are definitely a cropped image of a circle, but they fit left because nothing indicates that they are not a cropped image of a circle. A more pedantic solution to this Bongard Problem would be "Could be a cropped image of a circle vs. is definitely not" or "There is a way of cropping a circle that gives this image vs. there isn't."

See also the keyword seemslike, where neither side can be confirmed.

Either "left-couldbe" or "right-couldbe" implies notso.

Although the descriptions of "left-couldbe" and "right-couldbe" sound similar to left-unknowable and right-unknowable, they are not the same. It is the difference between a clear absence of information and perpetual uncertainty about whether there is more information to be found.

"Left-couldbe" is usually left-narrow and "right-couldbe" usually right-narrow.

Adjacent-numbered pages:
BP1154 BP1155 BP1156 BP1157 BP1158  *  BP1160 BP1161 BP1162 BP1163 BP1164

dual, meta (see left/right), links, keyword, side, viceversa

Leo Crabbe