Adjacent-numbered pages:
BP818 BP819 BP820 BP821 BP822  *  BP824 BP825 BP826 BP827 BP828

notso, math, left-couldbe

Aaron David Fairbanks

This is solvable; it was solved by Sridhar Ramesh.

A full turn is considered "the same angle" as no turns; likewise for adding and subtracting full turns from any angle. All sequences of angles shown start at the rightmost tick.

It doesn't matter whether the angle is measured clockwise or counterclockwise, as long as the choice is consistent.

Adjacent-numbered pages:
BP820 BP821 BP822 BP823 BP824  *  BP826 BP827 BP828 BP829 BP830

hard, convoluted, notso, math, solved

Aaron David Fairbanks

Note this is not actually the limit of each infinitesimal pixel assembled into an image. For example in a sequence of halvings the limit value is never reached, so the bottom pixel would never change color and thus its limit would not would not either.

Sequences progress from left to right (and there is not usually a way to intuitively extend the sequence in the other direction).

Adjacent-numbered pages:
BP847 BP848 BP849 BP850 BP851  *  BP853 BP854 BP855 BP856 BP857

notso, creativeexamples, perfect, infinitedetail, assumesfamiliarity, structure, contributepairs, rules

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

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

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 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

One left and one right example with each solution are shown.

This BP is fuzzy for multiple reasons. How obvious it is that an example fits a rule is subjective. Also, somebody could read the simplicity of all included examples as part of a Bongard Problem's solution. For example, the more obvious version of "square number of dots vs. non-square number of dots" could be interpreted as "square small number of dots arranged in easy-to-read way vs. non-square small number of dots arranged in easy-to-read way."

Whether this Bongard Problem solution would categorize an image of itself left or right depends on the difficulty of the solutions of the mini-Problems.

See keyword help.

See keyword hardsort.

Adjacent-numbered pages:
BP889 BP890 BP891 BP892 BP893  *  BP895 BP896 BP897 BP898 BP899

fuzzy, abstract, notso, subjective, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, contributepairs

boxes_bpimage_three_per_side [smaller | same | bigger]

Aaron David Fairbanks

Another way to phrase this solution is that right examples can be folded down flat onto one isosceles triangle while left examples cannot.

All examples in this Problem feature four isosceles triangles connected by corners and/or edges.

This was conceived as a false solution for BP898.

Adjacent-numbered pages:
BP892 BP893 BP894 BP895 BP896  *  BP898 BP899 BP900 BP901 BP902

nice, precise, allsorted, notso, traditional, preciseworld

[smaller | same | bigger]

Molly C Klenzak, Aaron David Fairbanks

Which two sides are the long sides and which side is the short side, or equivalently which angles are the wider angles and which angle is the narrower angle, is the only relevant information to consider for each triangle. Triangles are all assumed isosceles and congruent to one another.

All examples in this Problem feature four of these triangles connected by corners and/or edges.

BP897 was conceived as a false solution for this.

Adjacent-numbered pages:
BP893 BP894 BP895 BP896 BP897  *  BP899 BP900 BP901 BP902 BP903

hard, precise, allsorted, notso, math, preciseworld

[smaller | same | bigger]

Molly C Klenzak