Left examples are quantity-comparison Problems in which the dividing point on the spectrum separating the sides lands between them. Right examples are quantity-comparison Problems in which the dividing point is the entirety of one of the sides (always the left side, for clarity).

Only less-than vs. greater-than Problems may have imprecise (BP876^right) dividing point between sides.

Adjacent-numbered pages:
BP872 BP873 BP874 BP875 BP876  *  BP878 BP879 BP880 BP881 BP882

hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes_quantity_soln [smaller | same | bigger]

Aaron David Fairbanks

Left Bongard Problems do not have to sort all relevant examples; if they would leave some border cases unsorted, it just has to be clear precisely which examples those would be.

Often a precise divide between values on a spectrum comes from intuitively "crossing a threshold." For example, there is an intuitive threshold between acute and obtuse angles. Two sides of a Bongard Problem on opposite ends of a threshold, coming close to it, are interpreted as having precise divide between sides, right up against that threshold.

See BP508 for the version with links to pages on the OEBP instead of images of Bongard Problems.

Adjacent-numbered pages:
BP871 BP872 BP873 BP874 BP875  *  BP877 BP878 BP879 BP880 BP881

hard, notso, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes [smaller | same | bigger]
zoom in left (bpimage_shapes_exact_sort)

Aaron David Fairbanks

Left examples partition a pool of objects cleanly into two classes.

See BP509 (keyword "allsorted") for the version with links to pages on the OEBP instead of images of Bongard Problems.

The left side implies BP876^left.

Adjacent-numbered pages:
BP870 BP871 BP872 BP873 BP874  *  BP876 BP877 BP878 BP879 BP880

hard, challenge, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes [smaller | same | bigger]
zoom in left | zoom in right

Aaron David Fairbanks

See BP873 for comparisons based on discrete quantities vs. comparisons based on continuous quantities. All examples in that Bongard Problem fit left here.

Similar to BP200 with sides flipped. (However, "Bongard Problem based on quantity" is a more general criterion than "Bongard Problem based on discrete counting.")

See BP507 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP869 BP870 BP871 BP872 BP873  *  BP875 BP876 BP877 BP878 BP879

meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes [smaller | same | bigger]
zoom in left (bpimage_shapes_quantity_soln)

Aaron David Fairbanks

All examples in this Bongard Problem fit left in BP874.

See BP351 for the version with sequences of constant change instead of Bongard Problems.

See BP1152 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP868 BP869 BP870 BP871 BP872  *  BP874 BP875 BP876 BP877 BP878

meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, presentationinvariant

bpimage_shapes_quantity_soln [smaller | same | bigger]

Aaron David Fairbanks

See BP553 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP867 BP868 BP869 BP870 BP871  *  BP873 BP874 BP875 BP876 BP877

hard, challenge, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure

bpimage_shapes [smaller | same | bigger]

Aaron David Fairbanks

In particular, horizontal reflections work in all left examples.

An image of this Bongard Problem would fit on the left.

See BP552 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Adjacent-numbered pages:
BP866 BP867 BP868 BP869 BP870  *  BP872 BP873 BP874 BP875 BP876

hard, abstract, challenge, meta (see left/right), miniproblems, creativeexamples, presentationmatters, infodense, assumesfamiliarity, structure

bpimage_shapes [smaller | same | bigger]

Aaron David Fairbanks

This fits on its own left side.

See BP821 for the version with links to pages on the OEBP (instead of images of Bongard Problems), of which this fits on the left side.

Adjacent-numbered pages:
BP863 BP864 BP865 BP866 BP867  *  BP869 BP870 BP871 BP872 BP873

notso, meta (see left/right), miniproblems, example, left-finite, left-full, impossible, experimental, funny, presentationinvariant

bpimage [smaller | same | bigger]

Aaron David Fairbanks

Left-sorted BPs have the keyword "notso" on the OEBP.

This meta Bongard Problem is about Bongard Problems featuring two rules that are conceptual opposites.

Sometimes both sides could be seen as the "not" side: consider, for example, two definitions of the same Bongard Problem, "shape has hole vs. does not" and "shape is not filled vs. is". It is possible (albeit perhaps unnatural) to phrase the solution either way when the left and right sides partition all possible relevant examples cleanly into two groups (see the allsorted keyword).

When one property is "positive-seeming" and its opposite is "negative-seeming", it usually means the positive property would be recognized without counter-examples (e.g. a collection of triangles will be seen as such), while the negative property wouldn't be recognized without counter-examples (e.g. a collection of "non-triangle shapes" will just be interpreted as "shapes" unless triangles are shown opposite them).

BP513 (keyword left-narrow) is about Bongard Problems whose left side can be recognized without the right side. When a Bongard Problem is left-narrow and not "right-narrow that usually makes the property on the left seem positive and the property on the right seem negative.

The OEBP by convention has preferred the "positive-seeming" property (when there is one) to be on the left side.

All in all, the keyword "notso" should mean:

1) If the Bongard Problem is "narrow" on at least one side, then it is left-narrow.

2) The right side is the conceptual negation of the left side.

If a Bongard Problem's solution is "[Property A] vs. not so", the "not so" side is everything without [Property A] within some suitable context. A Bongard Problem "triangles vs. not so" might only include simple shapes as non-triangles; it need not include images of boats as non-triangles. It is not necessary for all the kitchen sink to be thrown on the "not so" side (although it is here).

See BP1001 for a version sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP. (This version is a little different. In BP1001, the kitchen sink of all other possible images is always included on the right "not so" side, rather than a context-dependent conceptual negation.)

Contrast keyword viceversa.

"[Property A] vs. not so" Bongard Problems are often allsorted, meaning they sort all relevant examples--but not always, because sometimes there exist ambiguous border cases, unclear whether they fit [Property A] or not.

Adjacent-numbered pages:
BP862 BP863 BP864 BP865 BP866  *  BP868 BP869 BP870 BP871 BP872

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

everything [smaller | same]
zoom in left

Aaron David Fairbanks

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

Be encouraged to contribute new interesting examples to Bongard Problems with this keyword.

There is much overlap with the keyword hardsort.

This is what it usually means to say examples fit on (e.g.) the left of a Bongard Problem in various creative ways: there is no (obvious) general method to determine a left-fitting example fits left.

There is a related idea in computability theory: a "non recursively enumerable" property is one that cannot in general be checked by a computer algorithm.

But keep in mind the tag "creativeexamples" is supposed to mean something less formal. For example, it requires no ingenuity for a human being to check when a simple shape is convex or concave (so BP4 is not labelled "creativeexamples"). However, it is not as if we use an algorithm to do this, like a computer. (It is not even clear what an "algorithm" would mean in this context, since it is ambiguous both what class of shapes the Bongard Problem sorts and how that would be encoded into a computer program's input. There are usually many options and ambiguities like this whenever one tries to formalize the content of a Bongard Problem.)

Adjacent-numbered pages:
BP861 BP862 BP863 BP864 BP865  *  BP867 BP868 BP869 BP870 BP871

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

bp [smaller | same | bigger]

Aaron David Fairbanks