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

Bongard Problems sorted left have the keyword "discrete" on the OEBP.

Bongard Problems sorted right have the keyword "continuous".

All examples are spectrum Bongard Problems.

See BP873 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

Adjacent-numbered pages:
BP1147 BP1148 BP1149 BP1150 BP1151  *  BP1153 BP1154 BP1155 BP1156 BP1157

meta (see left/right), links, keyword

Aaron David Fairbanks

This was created as an example for BP1073 (left-it versus right-it).

Adjacent-numbered pages:
BP1145 BP1146 BP1147 BP1148 BP1149  *  BP1151 BP1152 BP1153 BP1154 BP1155

less, meta (see left/right), links, oebp, example, left-self, presentationmatters, right-it, experimental, left-listable, right-listable

Aaron David Fairbanks

Inspired by BP1148.

Adjacent-numbered pages:
BP1144 BP1145 BP1146 BP1147 BP1148  *  BP1150 BP1151 BP1152 BP1153 BP1154

nice, precise, unwordable, notso, handed, leftright, left-narrow, sequence, preciseworld, left-listable, right-listable

Aaron David Fairbanks

Left-sorted Problems usually have a very specific collection of examples, where the only images sorted all show the same type of object.

See unstable vs. stable, which is about examples switching sides upon small changes instead of being rendered unsortable.

See unstableworld vs. stableworld, which is about SOME small change to SOME example making it no longer fit in.

See BP1142 for the version only about additions of detail (no erasures), and with no restriction on them being slight additions.

Adjacent-numbered pages:
BP1139 BP1140 BP1141 BP1142 BP1143  *  BP1145 BP1146 BP1147 BP1148 BP1149

meta (see left/right), links, problemkiller

Aaron David Fairbanks

Any Bongard Problem that allows a fully black box fits right.

Another version of this Bongard Problem could be made about adding white (erasure of detail) instead of black (addition of detail).

Another version could be made about adding one of either white or black (but not both).

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

Bongard Problems tagged finishedexamples will fit right.

Adjacent-numbered pages:
BP1138 BP1139 BP1140 BP1141 BP1142  *  BP1144 BP1145 BP1146 BP1147 BP1148

meta (see left/right), links

visualbp [smaller | same | bigger]

Aaron David Fairbanks

The description in terms of rectangles was noted by Sridhar Ramesh when he solved this.

All examples in this Bongard Problem feature arced line segments connected at endpoints; these segments do not cross across one another and they are nowhere vertical; they never double back over themselves in the horizontal direction.

Furthermore, in each example, there is a single leftmost point and a single rightmost point, and every segment is part of a path bridging between them. So, there is a topmost total path of segments and bottommost total chain of segments.

Any picture on the left can be turned into a subdivided rectangle by the process of expanding points into vertical lines.

Here is another answer:

"Right examples: some junction point has a single line coming out from either the left or right side."

If there is some junction point with only a single line coming out from a particular side, the point cannot be expanded into a vertical segment with two horizontal segments bookending its top and bottom (as it would be if this were a subdivision of a rectangle).

And this was the original, more convoluted idea of the author:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. The string may only enter a region when it fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Only in left images can this process be done so that no segment of the string ever hesitates."

Quite convoluted when spelled out in detail, but not terribly complicated to imagine visually. (See the keyword unwordable.)

The string-sweeping answer is the same as the rectangle answer because a rectangle represents the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string stay still as the string sweeps down.

The principle that horizontal lines subdividing the original rectangle become the segments in the final picture corresponds to the idea that the string must enter or exit a single region all at once.

BP1129 started as an incorrect solution for this Bongard Problem. Anything fitting right in BP1130 fits right in BP1129.

Adjacent-numbered pages:
BP1125 BP1126 BP1127 BP1128 BP1129  *  BP1131 BP1132 BP1133 BP1134 BP1135

hard, unwordable, solved

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Aaron David Fairbanks

This was an unintended solution for BP1130.

In category theory lingo, left examples are built by repeated horizontal composition and vertical composition. (Making horizontal lines as 0-ary vertical compositions is here forbidden.)

Anything fitting right in BP1130 fits right here.

Adjacent-numbered pages:
BP1124 BP1125 BP1126 BP1127 BP1128  *  BP1130 BP1131 BP1132 BP1133 BP1134

hard, less, convoluted, solved, inductivedefinition

[smaller | same | bigger]

Aaron David Fairbanks

Bongard Problems sorted left have the keyword "inductivedefinition" on the OEBP.

An inductive definition is like, "Call certain basic objects 'blurps', and call combinations of blurps 'blurps' too."

Adjacent-numbered pages:
BP1123 BP1124 BP1125 BP1126 BP1127  *  BP1129 BP1130 BP1131 BP1132 BP1133

meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks

Other ways of phrasing this:

"Local" vs. "global" properties of collections: to check a collection satisfies a "local" property, it is only necessary to check each individual thing in it satisfies some property.

The rule all collections satisfy is just "every object is a ___" vs. the rule is something more.

Adjacent-numbered pages:
BP1122 BP1123 BP1124 BP1125 BP1126  *  BP1128 BP1129 BP1130 BP1131 BP1132

abstract, creativeexamples, left-unknowable, rules, miniworlds

[smaller | same | bigger]

Aaron David Fairbanks