This refers to all Bongard Problem solution ideas. No need to be a particularly well-made or well-defined Bongard Problem.

Adjacent-numbered pages:
BP536 BP537 BP538 BP539 BP540  *  BP542 BP543 BP544 BP545 BP546

notso, meta (see left/right), links, world, left-self, right-null, left-it, feedback

everything [smaller | same]
zoom in left (bp)

Aaron David Fairbanks

Adjacent-numbered pages:
BP537 BP538 BP539 BP540 BP541  *  BP543 BP544 BP545 BP546 BP547

notso, meta (see left/right), links, oebp, world, left-self, right-null, left-it, feedback

everything [smaller | same]
zoom in left (bppage)

Aaron David Fairbanks

All ideas and things, with no limits.

Adjacent-numbered pages:
BP539 BP540 BP541 BP542 BP543  *  BP545 BP546 BP547 BP548 BP549

notso, meta (see left/right), links, world, left-self, right-finite, right-full, left-null, left-it, feedback, experimental, funny

everything [smaller | same]
zoom in left (everything) | zoom in right (nothing)

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

Although this Bongard Problem is self-referential, it's only because of the specific phrasing of the solution. "BP902 vs. anything else" would also work. The number 902 could have been chosen coincidentally.

See BP953, BP959.

Adjacent-numbered pages:
BP897 BP898 BP899 BP900 BP901  *  BP903 BP904 BP905 BP906 BP907

notso, meta (see left/right), links, left-self, left-narrow, left-finite, left-full, right-null, right-it, invalid, experimental, funny

everything [smaller | same]
zoom in left (bp902)

Leo Crabbe

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

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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

[smaller | same | bigger]

Aaron David Fairbanks