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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

BP1112 "Stretch-dependent" Bongard Problems vs. Bongard Problems in which examples can be stretched (or compressed) along any axis without being sorted differently.
BP7
BP11
BP12
BP13
BP33
BP50
BP62
BP76
BP77
BP80
BP103
BP152
BP250
BP289
BP328
BP329
BP333
BP335
BP336
BP523
BP525
BP536
BP557
BP559
BP812
BP813
BP816
BP860
BP920
BP924
BP942
BP949
BP1011
BP1086
BP1145

. . .

BP1
BP5
BP15
BP31
BP45
BP98
BP157
BP240
BP322
BP327
BP330
BP331
BP332
BP348
BP363
BP367
BP368
BP369
BP389
BP809
BP810
BP851
BP853
BP911
BP966
BP977
BP992
BP1022
BP1094
BP1131
BP1135
BP1136
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COMMENTS

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


If applying a scaling along one particular axis to the whole of any example can change its sorting the BP fits on the left side here. (For BPs with bounding boxes this means scaling and cropping, but without cutting out any detail.)

CROSSREFS

Adjacent-numbered pages:
BP1107 BP1108 BP1109 BP1110 BP1111  *  BP1113 BP1114 BP1115 BP1116 BP1117

KEYWORD

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

WORLD

[smaller | same | bigger]

AUTHOR

Leo Crabbe

BP1159 Bongard Problems where examples are only sorted left if nothing indicates that they would be sorted right vs. vice-versa.
BP250
BP333
BP525
BP823
BP1230
BP1183
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COMMENTS

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

Right-sorted Bongard Problems have the keyword "right-couldbe".


In a "couldbe" Bongard Problem, some relevant information is left out by the way objects are displayed. Solutions to "left-couldbe" BPs sound like "Could be a ___ vs. definitely not a ___" (and vice versa for "right-couldbe" BPs.)



To put it in mathematical jargon, there is a "projection" function from objects to pictures, such that objects satisfying property X are mapped to the same picture as objects not satisfying property X. Sorted on the "couldbe" side is the image (under projection) of the collection of objects satisfying property X.


Furthermore, usually X is a relatively narrow criterion, so that most objects do not satisfy it (see keywords left-narrow and right-narrow), and all pictures are in the image (under projection) of the collection of objects not satisfying property X.

REFERENCE

Consider BP525, "Cropped image of a circle vs. not so." None of the left-hand examples are definitely an image of a circle, but they fit left because nothing indicates that they are not an image of a circle. A more pedantic solution to this Bongard Problem would be "There is a way of cropping a circle that gives this image vs. there isn't."

CROSSREFS

See also the keyword seemslike, where neither side can be confirmed.


Either "left-couldbe" or "right-couldbe" implies notso.


Although the descriptions of "left-couldbe" and "right-couldbe" sound similar to left-unknowable and right-unknowable, they are not the same. It is the difference between a clear absence of information and perpetual uncertainty about whether there is more information to be found.


"Left-couldbe" is usually left-narrow and "right-couldbe" usually right-narrow.

Adjacent-numbered pages:
BP1154 BP1155 BP1156 BP1157 BP1158  *  BP1160 BP1161 BP1162 BP1163 BP1164

KEYWORD

dual, meta (see left/right), links, keyword, side, viceversa

AUTHOR

Leo Crabbe

BP1194 Bongard Problems listed in Harry E. Foundalis's collection vs. not.
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

. . .

BP501
BP503
BP504
BP505
BP506
BP507
BP508
BP509
BP510
BP1194
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COMMENTS

Alternatively, BP pages on the OEBP with number less than or equal to 394 vs. other BP pages.

REFERENCE

https://www.foundalis.com/res/bps/bpidx.htm

CROSSREFS

Adjacent-numbered pages:
BP1189 BP1190 BP1191 BP1192 BP1193  *  BP1195 BP1196 BP1197 BP1198 BP1199

EXAMPLE

Foundalis's collection includes all Bongard Problems by Bongard.

KEYWORD

meta (see left/right), links, right-self, time

AUTHOR

Aaron David Fairbanks

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