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BP949 |
| Two unique distances between points vs. three unique distances between points. |
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BP950 |
| Arbitrarily specific BP included in the OEBP database as a representative of a larger class of similar BPs vs. not. |
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COMMENTS
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Left-sorted Bongard Problems have the keyword "arbitrary" on the OEBP.
Arbitrary BPs often communicate non-arbitrary ideas. M. M. Bongard's original "A vs. Б" Problem (BP100) is about recognizing letters. A choice of some such arbitrary letters was necessary.
Most Bongard Problems are at least slightly arbitrary. Almost any Bongard Problem could be changed in a number of ways to make slightly different Bongard Problems. When a Bongard Problem is labeled as "arbitrary", that means there is one especially obvious class of similar Bongard Problems, with none of them particularly more interesting or special than any other.
The self-referential (invalid) Bongard Problems BP538, BP545, BP902, BP1073 fit this definition (the solution involves the arbitrary detail of being that specific Bongard Problem instead of any other). On the other hand, the solution idea is not arbitrary when phrased with "this Bongard Problem".
Many "arbitrary" Bongard Problems are of the form "Detail X has arbitrary value A vs. not so" or "Detail X has arbitrary value A vs. detail X has arbitrary value B". Other "arbitrary" Bongard Problems feature arbitrary details that are not the distinction between the sides, e.g. BP545.
It is unclear whether or not we should label a Bongard Problem "arbitrary" if the arbitrarily fixed detail is a notable special case. For example, BP1024 could have been made using any number, but the number 1 is a non-arbitrary number, so the Bongard Problem does not seem so arbitrary. |
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CROSSREFS
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Similar to thespecificity concept BP (BP773), which is more general, including Bongard Problems relating conceptually in any way to arbitrary specificity.
Adjacent-numbered pages:
BP945 BP946 BP947 BP948 BP949  *  BP951 BP952 BP953 BP954 BP955
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KEYWORD
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meta (see left/right), links, keyword, right-self, sideless
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WORLD
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bp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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BP951 |
| Process described leaves some inputs invariant vs. no output will resemble its input. |
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COMMENTS
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There are many ambiguities here. The solver is expected to determine what things are "allowed" to be inputs for each process. To avoid confusion examples should not be sorted differently if you consider inputting nothing.
In each example there is at least some overlap between the set of possible inputs and the set of possible outputs for each process. If we did not apply this constraint, an easy example to be sorted right would be a process that turns blue shapes red.
A harder-to-read but more clearly defined version of this Problem could include within each example a mini Bongard Problem sorting left all allowed inputs for the process. |
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REFERENCE
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https://en.wikipedia.org/wiki/Fixed_point_(mathematics) |
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CROSSREFS
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Adjacent-numbered pages:
BP946 BP947 BP948 BP949 BP950  *  BP952 BP953 BP954 BP955 BP956
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KEYWORD
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structure, rules, miniworlds
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CONCEPT
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function (info | search)
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AUTHOR
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Leo Crabbe
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BP952 |
| Images of Bongard Problems about images of Bongard Problems about images of Bongard Problems vs. images of Bongard Problems not including images of Bongard Problems including images of Bongard Problems. |
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BP953 |
| Image of this Bongard Problem vs. empty image. |
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COMMENTS
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"Image of Bongard Problem with solution X vs. empty image" where X is the phrase in quotes. |
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CROSSREFS
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See BP959, BP902.
Adjacent-numbered pages:
BP948 BP949 BP950 BP951 BP952  *  BP954 BP955 BP956 BP957 BP958
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KEYWORD
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nice, precise, meta (see left/right), miniproblems, overriddensolution, right-full, right-null, perfect, infinitedetail, experimental, funny
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CONCEPT
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fractal (info | search), recursion (info | search), self-reference (info | search)
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WORLD
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zoom in left (bp953_image) | zoom in right (blank_image)
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AUTHOR
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Leo Crabbe
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BP954 |
| Solution could appear in a Bongard Problem that has itself as a panel vs. not so. |
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COMMENTS
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Loosely speaking, examples on the left are "Bongard Problems that can be self-similar". However, Bongard Problems with images of themselves deeply nested in boxes or rotated/flipped are not here considered "self-similar"; the Bongard Problem must use itself, as-is (allowing downward scaling and allowing infinite detail, ignoring pixelation--see keyword infinitedetail), as a panel.
Bongard Problems fitting left evidently come in three categories: 1) the Bongard Problem could only appear on its own left side, 2) the Bongard Problem could appear on its own right side, or 3) the Bongard Problem could appear on its own left or the right side. See BP987.
Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit left here.
All examples here are in the conventional format, i.e. white background, black vertical dividing line, and examples in boxes on either side. (A more general version of this Bongard Problem might allow many formats of Bongard Problems, sorting an image left if a self-similar version is possible having the same solution and format. This more general version would no longer be tagged presentationinvariant, since sorting would not only depend on solution, but also format.)
It would hint at the solution (keyword help) to only include images of Bongard Problems that, as it stands, are already clearly categorized on one side by themselves. (That is, images of Bongard Problems that belong on one of the two sides of BP793.) It is tricky to come up with images that are categorized by themselves as it stands but that could NOT be recursively included within themselves. EX7967, EX7999, EX7995, and EX6574 are some examples. |
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CROSSREFS
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See BP987 which narrows down the left-hand side of this BP further based on whether or not the BP could contain itself as a panel on both sides.
Adjacent-numbered pages:
BP949 BP950 BP951 BP952 BP953  *  BP955 BP956 BP957 BP958 BP959
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KEYWORD
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hard, abstract, challenge, meta (see left/right), miniproblems, infinitedetail, presentationinvariant, visualimagination
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CONCEPT
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fractal (info | search), recursion (info | search), self-reference (info | search)
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AUTHOR
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Leo Crabbe
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BP955 |
| Images of Bongard Problems that sort an image of their left side on their left and an image of their right side on their left vs. images of Bongard Problems that sort an image of their left side on their right and an image of their right side on their right. |
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CROSSREFS
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See also BP957 for the other two evident possibilities.
Adjacent-numbered pages:
BP950 BP951 BP952 BP953 BP954  *  BP956 BP957 BP958 BP959 BP960
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KEYWORD
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abstract, dual, handed, leftright, solved, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, experimental
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CONCEPT
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self-reference (info | search)
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WORLD
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oblong_boxes_bpimage_sorts_both_sides_skewed [smaller | same | bigger] zoom in left (oblong_boxes_bpimage_sorts_both_sides_left) | zoom in right (oblong_boxes_bpimage_sorts_both_sides_right)
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AUTHOR
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Leo Crabbe
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BP956 |
| Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets). |
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COMMENTS
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Examples on the left are also known as "Dyck words". |
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REFERENCE
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https://en.wikipedia.org/wiki/Dyck_language |
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CROSSREFS
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Adjacent-numbered pages:
BP951 BP952 BP953 BP954 BP955  *  BP957 BP958 BP959 BP960 BP961
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KEYWORD
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easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable
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CONCEPT
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recursion (info | search)
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AUTHOR
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Aaron David Fairbanks
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BP957 |
| Images of Bongard Problems that sort an image of their left side on their left and an image of their right side on their right vs. images of Bongard Problems that sort an image of their left side on their right and an image of their right side on their left. |
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BP958 |
| Visual Bongard Problems about examples being read with infinite detail vs. other visual Bongard Problems. |
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COMMENTS
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Left examples have the keyword "infinitedetail" on the OEBP.
Image files on the OEBP do not really have infinite detail. For a panel to be intuitively read as having infinite detail, there usually needs to be some apparent self-similarity, or perhaps a sequence of objects following an easy to read pattern getting smaller and smaller with increasing pixelation.
Usually in "infinitedetail" Bongard Problems, not only is it a puzzle to figure out the solution, but it is another puzzle to find self-similarities and understand the intended infinite detail in each example. |
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CROSSREFS
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BPs tagged with the keyword "infinitedetail" usually feature pixelated images that give the closest approximation of the intended infinite structure up to pixelation. This means they should be tagged with the keyword perfect, but should not be tagged with the keyword pixelperfect.
Just because a Bongard Problem has "infinitedetail" does not necessarily make it infodense. Some fractal images might be encoded by a small amount of information (just the information about which places within itself it includes smaller copies of itself) and may be recognized quickly.
Adjacent-numbered pages:
BP953 BP954 BP955 BP956 BP957  *  BP959 BP960 BP961 BP962 BP963
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KEYWORD
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notso, meta (see left/right), links, keyword, wellfounded
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WORLD
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visualbp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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