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BP504 BP pages on the OEBP in need of more examples vs. BP pages with a list of examples that should not be altered.
BP860
BP865
BP928
BP954
BP969
BP970
BP981
BP988
BP989
BP993
BP994
BP999
BP1001
BP1082
BP1085
BP1091
BP1098
BP1137
BP1206
BP1207
BP1208
BP1209
BP1210
BP1211
BP1213
BP1214
BP1215
BP1216
BP1217
BP1218
BP1220
BP1221
BP1222
BP1223
BP1224

. . .

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
BP32
BP33
BP34
BP35
BP36

. . .

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COMMENTS

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

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


Users are not able to add or remove examples from Problems tagged "finished." (This is unusual; most Bongard Problems on the OEBP can be expanded indefinitely by users.)


A "finished" Bongard Problem will always admit the alternate, convoluted solution "is [left example 1] OR is [left example 2] OR . . . OR is [last left example] vs. is [right example 1] OR is [right example 2] OR . . . OR is [last right example]".

CROSSREFS

Bongard's original Problems are tagged "finished."

Adjacent-numbered pages:
BP499 BP500 BP501 BP502 BP503  *  BP505 BP506 BP507 BP508 BP509

KEYWORD

meta (see left/right), links, keyword, oebp, presentationmatters, left-finite, right-finite, instruction

WORLD

bppage [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP507 Bongard Problems about comparison of quantity vs. other Bongard Problems.
BP2
BP11
BP12
BP28
BP29
BP34
BP36
BP37
BP38
BP53
BP62
BP65
BP67
BP79
BP173
BP176
BP196
BP211
BP292
BP338
BP501
BP565
BP869
BP882
BP915
BP971
BP972
BP978
BP1044
BP1046
BP1208
BP1
?
BP6
(edit; present; nest [left/right]; search; history)
COMMENTS

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


In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"). Then, to determine whether an object fits left or right in the Bongard Problem, its value is compared with a fixed threshold value.


Spectra can be continuous or discrete.


A "spectrum" Bongard Problem is usually arbitrary, since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary. And in BP2, the spectrum of values ("size") is vague, so much that the fuzzy threshold, of about half the size of the bounding box, does not seem arbitrary.


A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of the latter two typically only makes sense when the condition before it is true.


If a spectrum Bongard Problem obeys 1) and 2), then it will usually be precise.

For example:

"Angles less than 90° vs. angles greater than 90°" is "precise".


If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be allsorted.

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".


Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there isn't one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)


In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just the threshold value. For example, "right angles vs. obtuse angles." In certain cases like this the threshold is an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." Cases like this might not even be understood as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword notso.)


Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".


After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

REFERENCE

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

CROSSREFS

See BP874 for the version sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

Adjacent-numbered pages:
BP502 BP503 BP504 BP505 BP506  *  BP508 BP509 BP510 BP511 BP512

KEYWORD

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

WORLD

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

AUTHOR

Aaron David Fairbanks

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
BP813
BP847
BP865
BP894
BP895
BP939
BP1002
BP1111
BP1158
(edit; present; nest [left/right]; search; history)
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

BP672 Bongard Problem with solution relating to concept: number (countable quantity of feature or object) vs. Bongard Problem unrelated to this concept.
BP6
BP10
BP23
BP27
BP28
BP29
BP53
BP85
BP86
BP87
BP88
BP89
BP90
BP91
BP96
BP98
BP107
BP110
BP114
BP122
BP126
BP127
BP141
BP143
BP144
BP145
BP151
BP156
BP159
BP160
BP164
BP166
BP167
BP169
BP181

. . .

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

Adjacent-numbered pages:
BP667 BP668 BP669 BP670 BP671  *  BP673 BP674 BP675 BP676 BP677

KEYWORD

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

CONCEPT This MBP is about BPs that feature concept: "number"

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP769 Bongard Problem with solution relating to concept: triangle vs. Bongard Problem unrelated to this concept.
BP6
BP25
BP26
BP36
BP37
BP38
BP46
BP47
BP54
BP75
BP79
BP80
BP82
BP103
BP111
BP117
BP121
BP132
BP146
BP151
BP160
BP171
BP178
BP193
BP194
BP243
BP272
BP283
BP287
BP891
BP897
BP898
BP934
BP969
BP970

. . .

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

Adjacent-numbered pages:
BP764 BP765 BP766 BP767 BP768  *  BP770 BP771 BP772 BP773 BP774

KEYWORD

meta (see left/right), links, metaconcept

CONCEPT This MBP is about BPs that feature concept: "triangle"

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP983 Bongard Problem with solution relating to concept: comparison of multiple quantities (within one example) vs. Bongard Problem unrelated to this concept.
BP7
BP27
BP28
BP29
BP36
BP37
BP38
BP53
BP969
BP970
BP1208
BP1214
BP1217
(edit; present; nest [left/right]; search; history)
COMMENTS

"More," "fewer," "greater than," "less than."

See BP752 and BP749 for equality.

CROSSREFS

Adjacent-numbered pages:
BP978 BP979 BP980 BP981 BP982  *  BP984 BP985 BP986 BP987 BP988

KEYWORD

meta (see left/right), links, metaconcept

CONCEPT This MBP is about BPs that feature concept: "quantity_comparison"
Searchable synonyms: "more", "less", "greater", "lesser", "greater than", "less than", "fewer".

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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