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Search: keyword:invariance
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BP510 Bongard Problems that can change the way they sort examples over time vs. other Bongard Problems.
BP503
BP546
BP826
BP943
BP1073
BP1174
BP1194
BP1243
BP1
BP507
(edit; present; nest [left/right]; search; history)
COMMENTS

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

CROSSREFS

"Time" implies the culture keyword.

"Time" Bongard Problems tend to be invalid Bongard Problems.

Adjacent-numbered pages:
BP505 BP506 BP507 BP508 BP509  *  BP511 BP512 BP513 BP514 BP515

EXAMPLE

BP504 (the page for the stub keyword) will change the way it sorts Bongard Problem pages over time.

KEYWORD

meta (see left/right), links, keyword, invariance, left-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
(edit; present; nest [left/right]; search; history)
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

BP539 Meta Bongard Problems such that if the sides of an example Bongard Problem are switched its sorting within the meta Problem may switch vs. meta Bongard Problems that always sort flipped versions on the same side.
BP513
BP514
BP515
BP516
BP517
BP567
BP1073
BP1079
BP1081
BP1124
BP1159
BP1160
BP501
BP506
BP507
BP508
BP509
BP511
BP512
BP520
BP521
BP522
BP534
BP535
BP537
BP539
BP561
BP895
BP950
BP964
BP1010
BP1139
BP1140
BP1142
BP1167
BP1171
(edit; present; nest [left/right]; search; history)
COMMENTS

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

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


Here "flipping the sides" of a Bongard Problem does not flip the sides of the example BPs.

CROSSREFS

Metaconcept implies "sideless".

Adjacent-numbered pages:
BP534 BP535 BP536 BP537 BP538  *  BP540 BP541 BP542 BP543 BP544

KEYWORD

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

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

BP553 Rotation-dependent Bongard Problems vs. rotation-independent visual Bongard Problems.
BP7
BP19
BP36
BP65
BP95
BP106
BP152
BP158
BP199
BP273
BP523
BP551
BP971
BP1014
BP1086
BP1087
BP1213
BP1215
BP1216
BP1218
BP1245
BP16
BP54
BP1122
(edit; present; nest [left/right]; search; history)
COMMENTS

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


If rotating an example about the center can change its sorting the BP is a left example here.


Note that BPs about relative rotation comparisons fit on the right side.

CROSSREFS

See BP872 for the version with pictures of Bongard Problems instead (miniproblems) of links to pages on the OEBP.


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:
BP548 BP549 BP550 BP551 BP552  *  BP554 BP555 BP556 BP557 BP558

KEYWORD

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

WORLD

visualbp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP554 Size-dependent Bongard Problems vs. size-independent visual Bongard Problems.
BP2
BP14
BP1122
BP38
(edit; present; nest [left/right]; search; history)
COMMENTS

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


If applying a scaling to the whole of any example can change its sorting the BP fits on the left side here. (For BPs with bounding boxes means scaling an object appearing in a box within the bounding box.)


Note that BPs about relative size comparisons of multiple objects fit on the right side.

CROSSREFS

Adjacent-numbered pages:
BP549 BP550 BP551 BP552 BP553  *  BP555 BP556 BP557 BP558 BP559

KEYWORD

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

WORLD

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

BP964 Bongard Problems such that making repeated small changes can switch an example's sorting vs. Bongard Problems in which the two sides are so different that it is impossible to cross the gap by making successive small changes to examples while staying within the class of examples sorted by the Bongard Problem (there is no middle-ground between the sides; there is no obvious choice of shared ambient context both sides are part of).
BP2
BP4
BP8
BP9
BP3
BP16
BP23
BP363
BP962
BP1219
BP1253
(edit; present; nest [left/right]; search; history)
COMMENTS

Right-sorted BPs have the keyword "gap" on the OEBP.


A Bongard Problem with a gap showcases two completely separate classes of objects.


For example, the Bongard Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there is a space of partially filled black-and-white images between them, or any number of other ambient contexts.


Bongard Problems about comparing quantities on a spectrum should not usually be considered "gap" BPs. (Discrete spectra perhaps.) A spectrum establishes a shared context, with examples on both sides of the BP landing somewhere on it. (However, if it is reasonable to imagine getting the solution without noticing a spectrum in between, it could be a gap, since the ambient context is unclear.)


Bongard Problems with gaps may seem particularly arbitrary when the two classes of objects are particularly unrelated.

CROSSREFS

If a Bongard Problem has a "gap" it is likely precise: it will likely be clear on which side any potential example fits.


"Gap" implies stable. (This technically includes cases in which ALL small changes make certain examples no longer fit in with the Bongard Problem, as is sometimes the case in "gap" BPs. See also BP1144.)


See also preciseworld. "Gap" Bongard Problems would be tagged "preciseworld" when the two classes of objects are each clear; it is then apparent that there is no larger shared context and that no other types of objects besides the two types would be sorted by the Bongard Problem.


See BP1140, which is about any (perhaps large) additions instead of repeated small changes.

Adjacent-numbered pages:
BP959 BP960 BP961 BP962 BP963  *  BP965 BP966 BP967 BP968 BP969

KEYWORD

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

AUTHOR

Aaron David Fairbanks

BP974 "Bounding-box-dependent" Bongard Problems vs. Bongard Problems in which the bounding box can be extended arbitrarily in any direction (in white space) without switching the sorting of any examples.
BP8
BP157
BP209
BP210
BP243
BP257
BP312
BP321
BP525
BP818
BP942
BP966
BP971
BP972
BP1008
BP1014
BP1089
BP1093
BP1104
BP1122
BP1132
BP1156
BP1245
?
BP2
(edit; present; nest [left/right]; search; history)
COMMENTS

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


Slightly different: sliding the content in a box around without letting it cross the bounding box and without changing the size of the bounding box. (See keyword absoluteposition.)


Expanding the boxes of BP2 ("big vs. small") makes the contents smaller in comparison to the box, but not smaller in an absolute sense. Hence the situation is ambiguous.

CROSSREFS

If a Bongard Problem has the keyword absoluteposition, then it likely has the keyword boundingbox.

If a Bongard Problem has the keyword boundingbox and does not have the keyword bordercontent, then it likely has the keyword absoluteposition.

Adjacent-numbered pages:
BP969 BP970 BP971 BP972 BP973  *  BP975 BP976 BP977 BP978 BP979

KEYWORD

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

AUTHOR

Aaron David Fairbanks

BP1009 Visual Bongard Problems such that flipping over horizontal axis (up/down) can switch an example's side vs. visual Bongard Problems whose examples' sorting does not change under such a transformation.
BP36
BP199
BP286
BP313
BP337
BP363
BP551
BP896
BP972
BP1008
BP1014
BP1161
BP1213
BP1215
BP1216
BP1217
BP1218
BP1122
(edit; present; nest [left/right]; search; history)
COMMENTS

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

CROSSREFS

See leftright.

All "updown" Problems are handed.

Adjacent-numbered pages:
BP1004 BP1005 BP1006 BP1007 BP1008  *  BP1010 BP1011 BP1012 BP1013 BP1014

KEYWORD

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

WORLD

handed_visualbp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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