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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

BP684 Bongard Problem with solution relating to concept: ratio vs. Bongard Problem unrelated to this concept.
BP288
BP306
BP505
BP1044
BP1045
BP1046
BP1047
BP1048
BP1050
BP1051
BP1052
BP1053
BP1054
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CROSSREFS

Adjacent-numbered pages:
BP679 BP680 BP681 BP682 BP683  *  BP685 BP686 BP687 BP688 BP689

KEYWORD

meta (see left/right), links, metaconcept, primitive

CONCEPT This MBP is about BPs that feature concept: "ratio"
Searchable synonyms: "fraction", "percentage".

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP1081 Left is an open subset of the rational numbers vs. not so.
BP1047↔
BP1048↔
BP1050↔
BP1053↔
BP1044
BP1045
BP1046
BP1052
BP1044↔
BP1045↔
BP1046↔
BP1051↔
BP1052↔
BP1054↔
BP1047
BP1048
BP1050
BP1051
BP1053
BP1054
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CROSSREFS

Adjacent-numbered pages:
BP1076 BP1077 BP1078 BP1079 BP1080  *  BP1082 BP1083 BP1084 BP1085 BP1086

KEYWORD

meta (see left/right), links, side, wellfounded

CONCEPT semidecidable (info | search),
finite_infinite (info | search)

WORLD

outline_or_fill_circle_bp_clear_set_of_ratios [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1190 BPs with a precisely defined pool of examples vs. BPs with an imprecisely defined pool of examples.
BP3
BP6
BP13
BP103
BP292
BP312
BP329
BP334
BP376
BP384
BP386
BP390
BP391
BP557
BP558
BP560
BP569
BP576
BP788
BP856
BP891
BP897
BP898
BP905
BP922
BP932
BP942
BP945
BP949
BP956
BP961
BP962
BP988
BP989
BP993

. . .

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COMMENTS

Left-sorted Bongard Problems are tagged with the keyword "preciseworld" on the OEBP.


The keyword "preciseworld" basically means: if a new Bongard Problem were created to sort whether or not examples fit in the pool of examples in the original Bongard Problem, it would be tagged precise.


For a Bongard Problem fitting left, the intended class of examples sorted by the Bongard Problem is clear-cut.

For a Bongard Problem fitting right, there isn't any obvious boundary to take as delimiting the pool of potential examples. There is an imprecise fading of relevancy rather than a natural cutoff point.



Sometimes there are specific notable cases of potential examples for which there is ambiguity about whether they belong.


For example, the empty square (zero dots) has been left out of BP989. This is perhaps the only obvious example that is ambiguous as to whether it should be considered as belonging to the pool of examples shown in the Bongard Problem (or any similar dot-counting Bongard Problem).

(There would be no ambiguity if it were actually included in the Bongard Problem.)

(Whether or not zero seems like an obvious example also has a cultural component (see culture); someone who is not accustomed think of zero as a number might not see this as ambiguous at all.)

Larger pools of examples make the absence of notable border cases like this more conspicuous and intentional-seeming. (See also discussion at left-narrow.) But expanding the pool of examples cannot resolve certain border cases: if the rule of the Bongard Problem by nature leaves unsorted a potential example that is a border case for even fitting in with the rest of the examples, its absence doesn't communicate anything; whether it belongs with the pool of examples remains ambiguous.



It is tempting to make another another "allsortedworld" analogous to allsorted. But the pool of relevant examples fitting in a Bongard Problem is like a Bongard Problem with only one side: a collection satisfying some rule. Would there be any difference between precise and allsorted for a Bongard Problem with only one side?

CROSSREFS

Adjacent-numbered pages:
BP1185 BP1186 BP1187 BP1188 BP1189  *  BP1191 BP1192 BP1193 BP1194 BP1195

EXAMPLE

Bongard Problems featuring generic shapes ( https://oebp.org/search.php?q=world:fill_shape ) have not usually been labelled "preciseworld". (What counts as a "shape"? Can the shapes be fractally complicated, for example? What exactly are the criteria?) Nonetheless, these Bongard Problems are frequently precise.

KEYWORD

meta (see left/right), links, keyword

AUTHOR

Aaron David Fairbanks

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