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BP949 Two unique distances between points vs. three unique distances between points.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP944 BP945 BP946 BP947 BP948  *  BP950 BP951 BP952 BP953 BP954

KEYWORD

nice, precise, allsorted, stretch, perfect, traditional, preciseworld

CONCEPT two (info | search),
three (info | search)

WORLD

3_or_4_points [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP950 Arbitrarily specific BP included in the OEBP database as a representative of a larger class of similar BPs vs. not.
BP100
BP121
BP158
BP170
BP197
BP230
BP231
BP232
BP839
BP911
BP920
BP1008
BP1027
BP1048
BP1058
BP1063
BP1068
BP1074
BP1075
BP1102
BP1105
BP1161
BP1168
BP1183
BP1192
BP1193
BP1226
BP1255
BP1260
BP1
BP950
?
BP538
?
BP545
?
BP902
?
BP1024
?
BP1073
?
BP1076
(edit; present; nest [left/right]; search; history)
COMMENTS

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.

CROSSREFS

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

KEYWORD

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP951 Process described leaves some inputs invariant vs. no output will resemble its input.
?
?
?
(edit; present; nest [left/right]; search; history)
COMMENTS

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.

REFERENCE

https://en.wikipedia.org/wiki/Fixed_point_(mathematics)

CROSSREFS

Adjacent-numbered pages:
BP946 BP947 BP948 BP949 BP950  *  BP952 BP953 BP954 BP955 BP956

KEYWORD

structure, rules, miniworlds

CONCEPT function (info | search)

AUTHOR

Leo Crabbe

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.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See BP547 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

Any left example in this BP will be a left example for BP1084.

Adjacent-numbered pages:
BP947 BP948 BP949 BP950 BP951  *  BP953 BP954 BP955 BP956 BP957

KEYWORD

meta (see left/right), miniproblems, funny, presentationinvariant

CONCEPT recursion (info | search)

WORLD

[smaller | same | bigger]
zoom in left

AUTHOR

Leo Crabbe

BP953 Image of this Bongard Problem vs. empty image.
(edit; present; nest [left/right]; search; history)
COMMENTS

"Image of Bongard Problem with solution X vs. empty image" where X is the phrase in quotes.

CROSSREFS

See BP959, BP902.

Adjacent-numbered pages:
BP948 BP949 BP950 BP951 BP952  *  BP954 BP955 BP956 BP957 BP958

KEYWORD

nice, precise, meta (see left/right), miniproblems, overriddensolution, right-full, right-null, perfect, infinitedetail, experimental, funny

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

WORLD

zoom in left (bp953_image) | zoom in right (blank_image)

AUTHOR

Leo Crabbe

BP954 Solution could appear in a Bongard Problem that has itself as a panel vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

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.

CROSSREFS

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

KEYWORD

hard, abstract, challenge, meta (see left/right), miniproblems, infinitedetail, presentationinvariant, visualimagination

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

AUTHOR

Leo Crabbe

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.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See also BP957 for the other two evident possibilities.

Adjacent-numbered pages:
BP950 BP951 BP952 BP953 BP954  *  BP956 BP957 BP958 BP959 BP960

KEYWORD

abstract, dual, handed, leftright, solved, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, experimental

CONCEPT self-reference (info | search)

WORLD

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)

AUTHOR

Leo Crabbe

BP956 Nested pairs of brackets vs. other arrangement of brackets (some open brackets are not closed or there are extra closing brackets).
(edit; present; nest [left/right]; search; history)
COMMENTS

Examples on the left are also known as "Dyck words".

REFERENCE

https://en.wikipedia.org/wiki/Dyck_language

CROSSREFS

Adjacent-numbered pages:
BP951 BP952 BP953 BP954 BP955  *  BP957 BP958 BP959 BP960 BP961

KEYWORD

easy, nice, precise, allsorted, unwordable, notso, sequence, traditional, inductivedefinition, preciseworld, left-listable, right-listable

CONCEPT recursion (info | search)

AUTHOR

Aaron David Fairbanks

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.
(edit; present; nest [left/right]; search; history)
CROSSREFS

See also BP955 for the other two evident possibilities.

Adjacent-numbered pages:
BP952 BP953 BP954 BP955 BP956  *  BP958 BP959 BP960 BP961 BP962

KEYWORD

nice, abstract, solved, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, experimental

CONCEPT self-reference (info | search)

WORLD

oblong_panels_bpimage_sorts_both_sides_balanced [smaller | same | bigger]
zoom in left (oblong_panels_bpimage_sorts_both_sides_stay) | zoom in right (oblong_panels_bpimage_sorts_both_sides_swap)

AUTHOR

Leo Crabbe

BP958 Visual Bongard Problems about examples being read with infinite detail vs. other visual Bongard Problems.
BP529
BP530
BP531
BP532
BP533
BP543
BP852
BP953
BP954
BP959
BP961
BP1058
BP1059
BP1060
BP1061
BP1062
BP1063
BP1065
BP1066
BP1067
BP1068
BP1069
BP1070
BP1071
BP1077
BP1084
BP1098
BP1107
BP1108
BP1114
BP1115
BP1116
BP1118
BP1119
BP1120

. . .

(edit; present; nest [left/right]; search; history)
COMMENTS

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.

CROSSREFS

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

KEYWORD

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

WORLD

visualbp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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