This is a generalisation of Bongard Problems that allows them to have any number of sides. There is a sense in which this problem is about valid vs. invalid ways of partitioning a set of examples into equivalence classes.

https://en.wikipedia.org/wiki/Equivalence_class

Adjacent-numbered pages:
BP1148 BP1149 BP1150 BP1151 BP1152  *  BP1154 BP1155 BP1156 BP1157 BP1158

abstract, teach, meta (see left/right), miniproblems, infodense, structure, rules, miniworlds

zoom in left

Leo Crabbe

This Problem is mostly concerned with categorising BPs whose examples aren't necessarily formatted as traditional Bongard Problems.

Adjacent-numbered pages:
BP1149 BP1150 BP1151 BP1152 BP1153  *  BP1155 BP1156 BP1157 BP1158 BP1159

meta (see left/right), links

visualbp [smaller | same | bigger]

Leo Crabbe

Adjacent-numbered pages:
BP1150 BP1151 BP1152 BP1153 BP1154  *  BP1156 BP1157 BP1158 BP1159 BP1160

abstract, unwordable, creativeexamples, right-unknowable, traditional, finishedexamples, rules

Leo Crabbe

Adjacent-numbered pages:
BP1151 BP1152 BP1153 BP1154 BP1155  *  BP1157 BP1158 BP1159 BP1160 BP1161

precise, minimal, boundingbox, left-finite, left-full, perfect, pixelperfect, finishedexamples, preciseworld, absoluteposition

Leo Crabbe

Operations depicted in right-sorted examples are called "commutative".

"Order matters" here means that if the objects in the top half were to switch places, the output would look different.

https://en.wikipedia.org/wiki/Commutative_property

Adjacent-numbered pages:
BP1152 BP1153 BP1154 BP1155 BP1156  *  BP1158 BP1159 BP1160 BP1161 BP1162

nice, abstract, unwordable, notso, structure, rules, miniworlds

Leo Crabbe

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

In the typical "rules" Bongard Problem, it is possible to come up with many convoluted rules that fit each example, but the intended interpretation is the only simple and obvious one.

Since it is difficult to communicate a rule with little detail, "rules" Bongard Problems are usually infodense.

Typically, each example is itself a bunch of smaller examples that all obey the rule. It is the same as how a Bongard Problems relies on many examples to communicate rules; likely just one example wouldn't get the answer across.

On the other hand, in BP1157 for example, each intended rule is communicated by just one example; these rules have to be particularly simple and intuitive, and the individual examples have to be complicated enough to communicate them.

Often, each rule is communicated by showing several examples of things satisfying it. (See keywords left-narrow and right-narrow.) Contrast Bongard Problems, which are more communicative, by showing some examples satisfying the rule and some examples NOT satisfying the rule.

A "rules" Bongard Problem is often collective. Some examples may admit multiple equally plausible rules, and the correct interpretation of each example only becomes clear once the solution is known. The group of examples together improve the solver's confidence about having understood each individual one right.

It is common that there will be one or two examples with multiple reasonable interpretations due to oversight of the author.

All meta Bongard Problems are "rules" Bongard Problems.

Many other Bongard-Problem-like structures seen on the OEBP are also about recognizing a pattern. (See keyword structure.)

"Rules" Bongard Problems are abstract, although the individual rules in them may not be abstract. "Rules" Bongard Problems also usually have the keyword creativeexamples.

Adjacent-numbered pages:
BP1153 BP1154 BP1155 BP1156 BP1157  *  BP1159 BP1160 BP1161 BP1162 BP1163

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

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 an image of a circle, but they fit left because nothing indicates that they are not an image of a circle. A more pedantic solution to this Bongard Problem would be "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

Note that most traditional Bongard Problems don't sort an all black-panel at all.

See BP567 (left-null versus right-null) for the version about all-white panels, which is more often applicable.

Adjacent-numbered pages:
BP1155 BP1156 BP1157 BP1158 BP1159  *  BP1161 BP1162 BP1163 BP1164 BP1165

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

Leo Crabbe

Adjacent-numbered pages:
BP1156 BP1157 BP1158 BP1159 BP1160  *  BP1162 BP1163 BP1164 BP1165 BP1166

unwordable, notso, arbitrary, handed, leftright, updown, stretch, blackwhite, creativeexamples, right-null, perfect, pixelperfect, help

Leo Crabbe

Bongard Problems sorted left obtain the keyword "viceversa" on the OEBP.

Contrast the keyword notso.

"Viceversa" BPs are often dual.

The solution to a less-than/greater-than quantity comparison Bongard Problem (keyword spectrum) where the two sides divide the spectrum in half can be phrased as "closer to left end of spectrum than right end vs. vice versa." Whether this is a natural way to phrase the solution depends on the kind of quantity being compared.

Here are some examples of spectra for which the "vice versa" phrasing tends to seem natural: left vs. right, up vs. down, black vs. white, higher quantity of [thing type 1] vs. higher quantity of [thing type 2].

Adjacent-numbered pages:
BP1157 BP1158 BP1159 BP1160 BP1161  *  BP1163 BP1164 BP1165 BP1166 BP1167

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

Aaron David Fairbanks