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BP508 Bongard Problems with precise definitions vs. Bongard Problems with vague definitions.
BP1
BP3
BP4
BP6
BP13
BP23
BP31
BP67
BP72
BP103
BP104
BP210
BP292
BP312
BP321
BP322
BP324
BP325
BP329
BP334
BP344
BP348
BP367
BP368
BP376
BP384
BP386
BP389
BP390
BP391
BP523
BP527
BP557
BP558
BP559

. . .

BP2
BP9
BP10
BP11
BP12
BP14
BP62
BP119
BP148
BP364
BP393
BP505
BP508
BP509
BP511
BP524
BP571
BP812
BP813
BP847
BP865
BP894
BP895
BP939
BP1002
BP1111
BP1158
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COMMENTS

Bongard Problems sorted left have the keyword "precise" on the OEBP.

Bongard Problems sorted right have the keyword "fuzzy" on the OEBP.


In an precise Bongard Problem, any relevant example is either clearly sorted left, clearly sorted right, or clearly not sorted.

(All relevant examples clearly sorted either left or right is the keyword allsorted.)


How can it be decided whether or not a rule is precise? How can it be decided whether or not a rule classifies all "examples that are relevant"? There needs to be another rule to determine which examples the original rule intends to sort. Bongard Problems by design communicate ideas without fixing that context ahead of time. The label "precise" can only mean a Bongard Problem's rule seems precise to people who see it. (This "precise vs. fuzzy" Bongard Problem is fuzzy.)


In an precise "less than ___ vs. greater than ___" Bongard Problem (keyword spectrum), the division between the sides is usually an apparent threshold. For example, there is an intuitive threshold between acute and obtuse angles (see e.g. BP292).


As a rule of thumb, do not consider imperfections of hand drawn images (keyword ignoreimperfections) when deciding whether a Bongard Problem is precise or fuzzy. Just because one can draw a square badly does not mean "triangle vs. quadrilateral" (BP6) should be labelled fuzzy; similar vagueness arises in all hand-drawn Bongard Problems. (For Bongard Problems in which fine subtleties of drawings, including small imperfections, are meant to be considered, use the keyword perfect.)


Sometimes the way a Bongard Problem would sort certain examples is an unsolved problem in mathematics. (See e.g. BP820.) There is a precise criterion that has been used to verify each sorted example fits where it fits (some kind of mathematical proof); however, where some examples fit is still unknown. Whether or not such a Bongard Problem should be labelled "precise" might be debated.

(Technical note: some properties are known to be undecidable, and sometimes the decidability itself is unknown. See https://en.wikipedia.org/wiki/Decision_problem .)

(See the keyword proofsrequired.)

One way to resolve this ambiguity is to define "precise" as meaning that once people decide where an example belongs for a reason, they will all agree about it.


Sometimes the class of all examples in a Bongard Problem is imprecise, but, despite that, the rule sorting those examples is precise. Say, for some potential new example, it is unclear whether it should be included in the Bongard Problem at all, but, if it were included, it would be clear where it should be sorted (or that it should be left unsorted). A Bongard Problem like this can still be tagged "precise".

(If all examples are clearly sorted except for some example for which it is unclear whether it belongs to the class of relevant examples, the situation becomes ambiguous.)

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword preciseworld.)


There is a subtle distinction to draw between Bongard Problems that are precise to the people making them and Bongard Problems that are precise to the people solving them. A Bongard Problem (particularly a non-allsorted one) might be labeled "precise" on the OEBP because the description and the listed ambiguous examples explicitly forbid sorting certain border cases; however, someone looking at the Bongard Problem without access to the OEBP page containing the definition would not be aware of this. It may or may not be obvious that certain examples were intentionally left out of the Bongard Problem. A larger collection of examples may make it more clear that a particularly blatant potential border case was left out intentionally.

CROSSREFS

See BP876 for the version with pictures of Bongard Problems instead of links to pages on the OEBP.

See both and neither for specific ways an example can be classified as unsorted in an "precise" Bongard Problem.

Adjacent-numbered pages:
BP503 BP504 BP505 BP506 BP507  *  BP509 BP510 BP511 BP512 BP513

KEYWORD

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP509 Bongard Problems that sort all relevant examples vs. Bongard Problems that would leave some unsorted.
BP1
BP3
BP31
BP103
BP312
BP321
BP322
BP329
BP334
BP376
BP384
BP386
BP389
BP390
BP527
BP557
BP559
BP560
BP564
BP569
BP576
BP788
BP820
BP856
BP863
BP891
BP897
BP898
BP905
BP922
BP934
BP935
BP937
BP945
BP949

. . .

BP292
BP508
BP509
BP961
BP1073
BP1208
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COMMENTS

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


A Bongard Problem is labelled "allsorted" when the type of thing it sorts is partitioned unambiguously and without exception into two groups.


Similarly to using the precise and fuzzy keywords, calling a Bongard Problem "allsorted" is a subjective/intuitive judgment. The collection of all relevant potential examples is not clearly delineated anywhere.

(Sometimes it's ambiguous whether to consider certain examples that are ambiguously sorted relevant.)


The solution to an "allsorted" Bongard Problem can usually be re-phrased as "___ vs. not so" (see the keyword notso).

But not every "___ vs. not so" Bongard Problem should be labelled "allsorted"; there could be ambiguous border cases in a "___ vs. not so" Bongard Problem.


Bongard Problems in which the two sides are so different that there is no middle ground between them (keyword gap) are sometimes still labelled "allsorted", since the intuitive pool of all relevant examples just amounts to the two unrelated sides. But some "gap" Bongard Problems are not like that; for example sometimes there are more related classes of examples besides the two shown.


Sometimes the class of all examples in a Bongard Problem is imprecise, but, despite that, the rule sorting those examples is precise. Say, for some potential new example, it is unclear whether it should be included in the Bongard Problem at all, but, if it were included, it would be clear where it should be sorted. A Bongard Problem like this can still be tagged "allsorted".

On the other hand, sometimes the class of all examples is very clear, with an obvious boundary. (Keyword preciseworld.)



In deciding where to sort an example, we think about it until we come to a conclusion; an example isn't here considered ambiguous just because someone might have a hard time with it (keyword hardsort).

However, sometimes the way a Bongard Problem would sort certain examples is an unsolved problem in mathematics, and it may be unknown whether there is even a solution. Whether or not such a Bongard Problem should be labelled "allsorted" might be debated.

(See the keyword proofsrequired.)

One way to resolve this ambiguity is to redefine "allsorted" as meaning that once people decide where an example belongs, it will be on one of the two sides, and they will all agree about it.



There is a distinction to be made between a non-"allsorted" Bongard Problem that could be made "allsorted" by making (finitely many) more examples sorted (thereby modifying or clarifying the solution of the Bongard Problem) and one such that this is not possible while maintaining a comparably simple solution. The former kind would often be labelled precise, in particular when these border cases have been explicitly forbidden from being sorted in the Bongard Problem's definition.

For instance, discrete Bongard Problems that are not allsorted usually fall into the former category.

CROSSREFS

See BP875 for the version with pictures of Bongard Problems instead of links to pages on the OEBP.

"Allsorted" implies precise.

"Allsorted" and both are mutually exclusive.

"Allsorted" and neither are mutually exclusive.

Adjacent-numbered pages:
BP504 BP505 BP506 BP507 BP508  *  BP510 BP511 BP512 BP513 BP514

KEYWORD

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP556 Visual Bongard Problems such that if black and white are switched some examples switch sides vs. visual Bongard Problems that would always sort two switched versions the same way.
BP157
BP196
BP211
BP337
BP859
BP962
BP971
BP972
BP1008
BP1161
BP1249
BP1252
BP170
BP359
BP524
BP1089
BP1093
BP1210
BP1230
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COMMENTS

Left-sorted examples have the keyword "blackwhite" on the OEBP.

Right-sorted examples have the keyword "blackwhiteinvariant" on the OEBP.


All examples are visual Bongard Problems that allow black to touch the bounding box (keyword bordercontent).

CROSSREFS

Adjacent-numbered pages:
BP551 BP552 BP553 BP554 BP555  *  BP557 BP558 BP559 BP560 BP561

KEYWORD

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

CONCEPT black_white_inversion (info | search)

WORLD

visualbp [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP867 Bongard Problem with solution that can be naturally expressed as "___ vs. not so" vs. not so.
BP32
BP77
BP82
BP127
BP243
BP257
BP274
BP288
BP323
BP344
BP376
BP381
BP385
BP390
BP506
BP507
BP515
BP516
BP538
BP541
BP542
BP544
BP545
BP553
BP559
BP569
BP576
BP812
BP816
BP818
BP823
BP825
BP852
BP866
BP867

. . .

BP6

Qat

blimp

notso

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COMMENTS

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).

CROSSREFS

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

KEYWORD

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

WORLD

everything [smaller | same]
zoom in left

AUTHOR

Aaron David Fairbanks

BP1196 Bongard Problems with content touching the border of some examples vs. Bongard Problems with a lip of whitespace around the border of all examples.
BP157
BP210
BP211
BP321
BP806
BP966
BP971
BP972
BP1008
BP1014
BP1089
BP1093
BP1228
BP1230
BP1245
BP1249
BP1252
BP1
BP2
BP3
BP4
BP5
BP6
BP7
BP8
BP9
BP10
BP11
BP12
BP13
BP14
BP15
BP16
BP17
BP18
BP19
BP20
BP21
BP22
BP23
BP24
BP25
BP26
BP27
BP28
BP29
BP30
BP31
BP32
BP33
BP34
BP35

. . .

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COMMENTS

Bongard Problems sorted left have the keyword "bordercontent" on the OEBP.


All of Bongard's original Problems have whitespace around the border of all examples.

CROSSREFS

Adjacent-numbered pages:
BP1191 BP1192 BP1193 BP1194 BP1195  *  BP1197 BP1198 BP1199 BP1200 BP1201

KEYWORD

meta (see left/right), links, keyword

AUTHOR

Aaron David Fairbanks

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