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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

BP535 Visual Bongard Problems such that flipping over the vertical axis (left/right) can switch an example's side vs. visual Bongard Problems whose examples' sorting doesn't change under such a transformation.
BP8
BP43
BP67
BP109
BP207
BP234
BP278
BP279
BP313
BP337
BP357
BP363
BP372
BP793
BP795
BP796
BP805
BP830
BP881
BP931
BP955
BP961
BP971
BP1008
BP1014
BP1024
BP1025
BP1027
BP1028
BP1029
BP1030
BP1031
BP1032
BP1033
BP1034

. . .

BP199
BP839
BP896
BP972
BP986
BP1122
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COMMENTS

Left examples have the keyword "leftright" on the OEBP.

CROSSREFS

See updown.

All "leftright" Bongard Problems are handed.

Adjacent-numbered pages:
BP530 BP531 BP532 BP533 BP534  *  BP536 BP537 BP538 BP539 BP540

KEYWORD

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

WORLD

handed_visualbp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP537 Meta Bongard Problems vs. other Bongard Problems.
BP200
BP501
BP503
BP504
BP506
BP507
BP508
BP509
BP510
BP511
BP512
BP513
BP514
BP515
BP516
BP517
BP518
BP519
BP520
BP521
BP522
BP526
BP534
BP535
BP537
BP539
BP541
BP542
BP544
BP546
BP547
BP549
BP550
BP552
BP553

. . .

BP1
BP2
BP3
BP4
BP5
BP6
BP7
BP8
BP9
BP10
?
BP1080
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COMMENTS

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


Meta Bongard Problems are Bongard Problems that sort Bongard Problems. Sometimes abbreviated MBPs.


The first meta Bongard Problem was BP200.


Some meta BP pages sort images of Bongard Problems (keyword miniproblems), while other meta BP pages sort other BP pages (keyword links).

CROSSREFS

BPs that sort meta-BPs are labelled metameta.

Adjacent-numbered pages:
BP532 BP533 BP534 BP535 BP536  *  BP538 BP539 BP540 BP541 BP542

KEYWORD

meta (see left/right), links, keyword, world, left-self, sideless, metameta, left-full, feedback

CONCEPT recursion (info | search)

WORLD

bp [smaller | same | bigger]
zoom in left (linksbp)

AUTHOR

Aaron David Fairbanks

BP552 Orientation-dependent Bongard Problems vs. orientation-independent visual Bongard Problems.
BP7
BP8
BP16
BP36
BP43
BP54
BP55
BP63
BP67
BP106
BP109
BP199
BP207
BP234
BP278
BP279
BP286
BP313
BP337
BP363
BP372
BP793
BP795
BP796
BP805
BP830
BP881
BP896
BP931
BP955
BP961
BP971
BP972
BP1008
BP1014

. . .

BP1
BP2
BP3
BP4
BP5
BP6
BP986
BP1197
BP1199
BP1200
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COMMENTS

Left examples have the keyword "handed" on the OEBP.


If mirroring any example along the any axis can change its sorting the BP is "handed."


Note that BPs about comparing orientation between multiple things in one example fit on the right side.

CROSSREFS

See BP871 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.


The keyword leftright is specifically about flipping over the vertical axis, while the keyword updown is specifically about flipping over the horizontal axis.


Bongard Problems tagged rotate are usually "handed", since any rotation can be created by two reflections. Not necessarily, however, since the reflected step in between might not be sorted on either side by the Bongard Problem.

Adjacent-numbered pages:
BP547 BP548 BP549 BP550 BP551  *  BP553 BP554 BP555 BP556 BP557

KEYWORD

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

WORLD

visualbp [smaller | same | bigger]
zoom in left (handed_visualbp)

AUTHOR

Aaron David Fairbanks

BP571 Bongard Problems that require mathematical understanding to solve vs. other Bongard Problems.
BP171
BP203
BP319
BP326
BP327
BP333
BP334
BP335
BP339
BP340
BP341
BP344
BP369
BP370
BP378
BP380
BP381
BP382
BP384
BP505
BP560
BP562
BP563
BP569
BP576
BP788
BP790
BP791
BP797
BP801
BP806
BP809
BP810
BP811
BP813

. . .

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COMMENTS

Left examples have the keyword "math" on the OEBP.


Although everything is arguably related to math, these BP solutions include content that people don't inherently understand without learning at least some mathematics.


Left examples do not technically have "culturally-dependent" content (keyword culture), but knowledge and previous learning plays a role in how easy they are to solve.

CROSSREFS

Adjacent-numbered pages:
BP566 BP567 BP568 BP569 BP570  *  BP572 BP573 BP574 BP575 BP576

KEYWORD

fuzzy, meta (see left/right), links, keyword

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP789 Bongard Problems in which all examples have the same format, a specific multi-part structure vs. other Bongard Problems.
BP200
BP324
BP325
BP339
BP346
BP350
BP351
BP352
BP353
BP354
BP355
BP356
BP357
BP361
BP362
BP372
BP548
BP790
BP791
BP793
BP795
BP796
BP802
BP803
BP805
BP827
BP828
BP829
BP831
BP832
BP833
BP834
BP835
BP836
BP843

. . .

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COMMENTS

Left examples have the keyword "structure" on the OEBP.


Examples of "structures": Bongard Problem, Bongard Problem with extra unsorted panel ("Bongard's Dozen"), 4-panel analogy grid, sequence of objects with a quantity changing by a constant amount.


If the solver hasn't become familiar with the featured structure, the Bongard Problem's solution may seem convoluted or inelegant. (See keyword assumesfamiliarity.) Once the solver gets used to seeing a particular structure it becomes easier to read that structure and solve Bongard Problems featuring it.


A Bongard Problem can non-verbally teach someone how a particular structure works, showing valid examples of that structure versus non-examples. E.g., BP968 for the structure of Bongard Problems and BP981 for the structure of analogy grids.

CROSSREFS

Adjacent-numbered pages:
BP784 BP785 BP786 BP787 BP788  *  BP790 BP791 BP792 BP793 BP794

KEYWORD

meta (see left/right), links, keyword

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP895 Meta Bongard Problems that sort Bongard Problems based on other information than just their solutions (e.g. what format the Bongard Problem is, or what specific examples are shown in it) vs. Meta Bongard Problems that sort Bongard Problems purely based on solution.
BP504
BP793
BP795
BP802
BP803
BP827
BP831
BP834
BP871
BP872
BP894
BP1150
BP200
BP796
BP829
BP830
BP832
BP833
BP835
BP836
BP868
BP873
BP874
BP875
BP876
BP877
BP878
BP879
BP880
BP881
BP895
BP927
BP944
BP948
BP952
BP954
BP987
BP1024
BP1025
BP1026
BP1027
BP1028
BP1029
BP1030
BP1031
BP1032
BP1033

. . .

?
BP828
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COMMENTS

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

Right-sorted Bongard Problems have the keyword "presentationinvariant" on the OEBP.


Meta Bongard problems that sort Bongard Problems purely based on their solutions usually have two versions in the database: one that sorts images of Bongard Problems and one that sorts links to pages on the OEBP. If both versions exist, users should make them cross-reference one another. (Meta Bongard Problems that sort images of Bongard Problems have the keyword miniproblems, whereas meta Bongard Problems that sort links to OEBP pages have the keyword links.)


For meta-pages on the OEBP that sort other pages on the OEBP (keyword links), "presentationmatters" means factoring in content like the BP number, the currently uploaded examples, the wording of the title, the description, and so on, rather than just the solution (that is, how the page would sort all potential examples). This is unusual.


"One solution vs. multiple solutions" (BP828) seems like a border-case. - Aaron David Fairbanks, Aug 01 2020

CROSSREFS

See BP1010 (projectionmatters versus 3d) for a similar idea: there 2D representations are to 3D objects as here Bongard Problems are to Bongard Problem solutions.

Adjacent-numbered pages:
BP890 BP891 BP892 BP893 BP894  *  BP896 BP897 BP898 BP899 BP900

KEYWORD

fuzzy, meta (see left/right), links, keyword, right-self, sideless, metameta, right-it, dependence, presentationinvariant

WORLD

metabp [smaller | same | bigger]

AUTHOR

Jago Collins

BP1111 Bongard Problem requires solver to already be interpreting all examples in a specific way for the answer to seem simple vs. not so.
BP200
BP361
BP362
BP793
BP795
BP796
BP802
BP803
BP827
BP828
BP829
BP831
BP832
BP833
BP834
BP835
BP836
BP852
BP871
BP872
BP873
BP874
BP875
BP876
BP877
BP878
BP879
BP880
BP881
BP894
BP955
BP957
BP968
BP987
BP1024

. . .

BP1
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COMMENTS

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


Sometimes all the examples in a Bongard Problem need to be interpreted a certain way for the Bongard Problem to make sense. Only once the representation is understood, the idea seems simple.


For example, all meta Bongard Problems (Bongard Problems sorting other Bongard Problems) assume the solver interprets the examples as Bongard Problems.


TO DO: Maybe it is best to stop putting the label "assumesfamiliarity" on all meta-Bongard Problems. There are so many of them. It may be better to only use the "assumesfamiliarity" keyword on meta-BPs for a further assumption than just that all examples are interpreted as Bongard Problems. - Aaron David Fairbanks, Feb 11 2021

CROSSREFS

Many Bongard Problems in which all examples take the same format (keyword structure) assume the solver already knows how to read that format.

Some Bongard Problems assume the solver will be able to understand symbolism that is consistent between examples (keyword consistentsymbols).

Bongard Problems tagged math often assume the solver is familiar with a certain representation of a math idea.

Adjacent-numbered pages:
BP1106 BP1107 BP1108 BP1109 BP1110  *  BP1112 BP1113 BP1114 BP1115 BP1116

EXAMPLE

BP1032: The solution should really read "Assuming all images are Bongard Problems sorting each natural number left or right ..." This Bongard Problem makes sense to someone who has been solving a series of similar BPs, but otherwise there is no reason to automatically read a collection of numbers as standing for a larger collection of numbers.

KEYWORD

fuzzy, meta (see left/right), links, keyword

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1126 Meta Bongard Problems in which examples are pages on the OEBP vs. meta Bongard Problems in which examples are pictures of Bongard Problems.
BP501
BP503
BP504
BP506
BP507
BP508
BP509
BP510
BP511
BP512
BP513
BP514
BP515
BP516
BP517
BP518
BP519
BP520
BP521
BP522
BP526
BP534
BP535
BP537
BP539
BP541
BP542
BP544
BP546
BP547
BP549
BP550
BP552
BP553
BP554

. . .

BP200
BP793
BP795
BP796
BP802
BP803
BP827
BP828
BP829
BP830
BP831
BP832
BP833
BP834
BP835
BP836
BP868
BP871
BP872
BP873
BP874
BP875
BP876
BP877
BP878
BP879
BP880
BP881
BP894
BP948
BP952
BP953
BP954
BP955
BP957

. . .

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

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

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


The keyword "links" is automatically added to a Bongard Problem on the OEBP if a BP number is added as an example.


Meta Bongard problems that sort Bongard Problems purely based on their solutions (keyword presentationmatters) usually have two versions in the database: one that sorts images of Bongard Problems and one that sorts links to pages on the OEBP. If both versions exist, users should make them cross-reference one another.

CROSSREFS

All the examples of miniature Bongard Problems within any meta Bongard Problem tagged "miniproblems" would fit left on BP1080 (which is a showcase of the various formats for images of Bongard Problems).

Adjacent-numbered pages:
BP1121 BP1122 BP1123 BP1124 BP1125  *  BP1127 BP1128 BP1129 BP1130 BP1131

KEYWORD

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

WORLD

metabp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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