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

The archetypal example is "rhombuses vs. rectangles".

Notice "rhombuses vs. rectangles" could alternatively be interpreted as "not rectangles vs. not rhombuses"; by this less natural interpretation, a square would fit on neither side (keyword neither) rather than both.

In fact, for any Bongard Problem solution "A vs. B", there are three alternative solution descriptions: "A vs. not A", "not B vs. B", and "not B vs. not A". These are not necessarily just different wordings of the same answer. For example, "rhombuses vs. not rhombuses" and "not rectangles vs. rectangles" differ on where they would sort a square. (This discrepancy between "A vs. not A" and "B vs. not B" occurs whenever "A vs. B" does not sort all relevant cases. See the keyword allsorted.)

"Is a rhombus" and "is a rectangle" are what are on the OEBP called "narrow" patterns, while "is not a rectangle" and "is not a rhombus" are not. (See keywords left-narrow and right-narrow for more explanation.)

The keywords both and allsorted are mutually exclusive.

Adjacent-numbered pages:
BP1183 BP1184 BP1185 BP1186 BP1187  *  BP1189 BP1190 BP1191 BP1192 BP1193

meta (see left/right), links, keyword

Aaron David Fairbanks

Left-sorted Bongard Problems have the keyword "neither" on the OEBP.

This keyword is for Bongard Problems for which some obviously relevant case, in the same class as the shown examples, clearly would not fit in with either of the two sides.

An example falling in the threshold between a less-than/greater-than comparison (keyword spectrum) is a special case; it is easy to view such an example as belonging on both sides (keyword both) as well as neither side.

NOTE: It might be nice to have a separate keyword for tracking these special-case spectrum-based ambiguities (because they don't quite suit the keywords "both" or "neither"). - Aaron David Fairbanks, Apr 16 2022

See also both.

The keywords "neither" and allsorted are mutually exclusive.

Usually, Bongard Problems with a case that fits neither side in a clear-cut way are precise.

Adjacent-numbered pages:
BP1184 BP1185 BP1186 BP1187 BP1188  *  BP1190 BP1191 BP1192 BP1193 BP1194

meta (see left/right), links, keyword

Aaron David Fairbanks

Left-sorted Bongard Problems are tagged with the keyword "preciseworld" on the OEBP.

The keyword "preciseworld" basically means: if a new Bongard Problem were created to sort whether or not examples fit in the pool of examples in the original Bongard Problem, it would be tagged precise.

For a Bongard Problem fitting left, the intended class of examples sorted by the Bongard Problem is clear-cut.

For a Bongard Problem fitting right, there isn't any obvious boundary to take as delimiting the pool of potential examples. There is an imprecise fading of relevancy rather than a natural cutoff point.

Sometimes there are specific notable cases of potential examples for which there is ambiguity about whether they belong.

For example, the empty square (zero dots) has been left out of BP989. This is perhaps the only obvious example that is ambiguous as to whether it should be considered as belonging to the pool of examples shown in the Bongard Problem (or any similar dot-counting Bongard Problem).

(There would be no ambiguity if it were actually included in the Bongard Problem.)

(Whether or not zero seems like an obvious example also has a cultural component (see culture); someone who is not accustomed think of zero as a number might not see this as ambiguous at all.)

Larger pools of examples make the absence of notable border cases like this more conspicuous and intentional-seeming. (See also discussion at left-narrow.) But expanding the pool of examples cannot resolve certain border cases: if the rule of the Bongard Problem by nature leaves unsorted a potential example that is a border case for even fitting in with the rest of the examples, its absence doesn't communicate anything; whether it belongs with the pool of examples remains ambiguous.

It is tempting to make another another "allsortedworld" analogous to allsorted. But the pool of relevant examples fitting in a Bongard Problem is like a Bongard Problem with only one side: a collection satisfying some rule. Would there be any difference between precise and allsorted for a Bongard Problem with only one side?

Adjacent-numbered pages:
BP1185 BP1186 BP1187 BP1188 BP1189  *  BP1191 BP1192 BP1193 BP1194 BP1195

Bongard Problems featuring generic shapes ( https://oebp.org/search.php?q=world:fill_shape ) have not usually been labelled "preciseworld". (What counts as a "shape"? Can the shapes be fractally complicated, for example? What exactly are the criteria?) Nonetheless, these Bongard Problems are frequently precise.

meta (see left/right), links, keyword

Aaron David Fairbanks

Alternatively, BP pages on the OEBP with number less than or equal to 394 vs. other BP pages.

https://www.foundalis.com/res/bps/bpidx.htm

Adjacent-numbered pages:
BP1189 BP1190 BP1191 BP1192 BP1193  *  BP1195 BP1196 BP1197 BP1198 BP1199

Foundalis's collection includes all Bongard Problems by Bongard.

meta (see left/right), links, right-self, time

Aaron David Fairbanks

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

The repositioned content has to stay within the box. If an example in a Bongard Problem features content touching a border (keyword bordercontent), then that prevents the contents from being shifted in that direction.

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:
BP1190 BP1191 BP1192 BP1193 BP1194  *  BP1196 BP1197 BP1198 BP1199 BP1200

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

Aaron David Fairbanks

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

All of Bongard's original Problems have whitespace around the border of all examples.

Adjacent-numbered pages:
BP1191 BP1192 BP1193 BP1194 BP1195  *  BP1197 BP1198 BP1199 BP1200 BP1201

meta (see left/right), links, keyword

Aaron David Fairbanks

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

Bongard's original Problems never involved shades of gray. They were just black and white drawings.

Adjacent-numbered pages:
BP1193 BP1194 BP1195 BP1196 BP1197  *  BP1199 BP1200 BP1201 BP1202 BP1203

meta (see left/right), links, keyword

Aaron David Fairbanks

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

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

In a "stableworld" Bongard Problem, no small change should outright make an example outright no longer fit in with the others in the Bongard Problem. It is allowed for a small change to make an example slightly less like all the others.

The meaning of "stableworld" is close to "examples have no particular format at all", but not quite the same.

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

See BP1144, which is about ALL small changes to ALL examples making them unsortable.

Adjacent-numbered pages:
BP1198 BP1199 BP1200 BP1201 BP1202  *  BP1204 BP1205 BP1206 BP1207 BP1208

meta (see left/right), links, keyword

Aaron David Fairbanks

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

For any "stability" Bongard Problem there could usually be made a corresponding invariance Bongard Problem ("[transformation] applied to some examples switch their sorting vs. sorting is invariant under [transformation]").

Potentially, "stability" Bongard Problems could be considered invariance Bongard Problems. On one hand, they are different, since checking whether arbitrarily small transformations switch an example's sorting is different from checking whether a particular transformation switches an example's sorting; the former is infinitely many conditions. On the other hand, there is actually only finitely much detail in any of the examples, and in practice a "stability" Bongard Problem generally just amounts to "a small application of [transformation] switches an example's sorting vs. not".

Adjacent-numbered pages:
BP1199 BP1200 BP1201 BP1202 BP1203  *  BP1205 BP1206 BP1207 BP1208 BP1209

meta (see left/right), links, keyword

Aaron David Fairbanks

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

Right examples have the keyword "deformstable" on the OEBP.

For the purposes of this Bongard Problem, a "slight deformation" is a way of dragging the details of an image around which is relatively uniform in any local area and moves each point at most an arbitrarily small distance. More precise definitions could be made using mathematics.

In a "deformstable" Bongard Problem, no slight deformation should outright flip an example's sorting. It is allowed for a slight deformation to make an example sorted slightly more ambiguously.

See unstable vs. stable for changing content within a small area.

Adjacent-numbered pages:
BP1200 BP1201 BP1202 BP1203 BP1204  *  BP1206 BP1207 BP1208 BP1209 BP1210

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

Aaron David Fairbanks