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BP567 Visual Bongard Problems that would sort a blank panel on the left vs. visual Bongard Problems that would sort a blank panel on the right.
BP1
BP137
BP384
BP525
BP544
BP569
BP904
BP905
BP915
BP945
BP962
BP1056
BP1219
BP1260
BP1261
BP1262
BP211
BP334
BP364
BP541
BP542
BP902
BP953
BP959
BP966
BP988
BP989
BP1008
BP1080
BP1089
BP1093
BP1108
BP1141
BP1151
BP1161
BP1220
BP1249
BP1252
BP1263
(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted BPs have the keyword "left-null" on the OEBP.

Right-sorted BPs have the keyword "right-null" on the OEBP.

CROSSREFS

See BP796 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

See BP1160 for the version about an all-black panel instead of all-white.

Adjacent-numbered pages:
BP562 BP563 BP564 BP565 BP566  *  BP568 BP569 BP570 BP571 BP572

KEYWORD

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

WORLD

visualbp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP566 Meta Bongard Problems of the form "[transformation] applied to some examples switch their sorting vs. sorting is invariant under [transformation]" vs. other meta Bongard Problems.
BP510
BP535
BP539
BP552
BP553
BP554
BP556
BP964
BP974
BP1009
BP1112
BP1140
BP1195
?
BP575
(edit; present; nest [left/right]; search; history)
COMMENTS

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


Bongard Problems labelled "invariance" are usually (but not always) about transformations that can be undone by other transformations of the same class. (The technical term for this kind of transformation is an "isomorphism".)


When the transformations used in a "invariance" Bongard Problem vary continuously, there could usually be made a corresponding stability Bongard Problem. Stability Bongard Problems are like "invariance" Bongard Problems but for arbitrarily small applications of [transformation] affecting examples' sorting.


Potentially, stability Bongard Problems could be considered "invariance" Bongard Problems. On one hand, they are different, since checking whether arbitrarily small transformations switch an example's sorting is different from checking whether a particular transformation switches an example's sorting; the former is infinitely many conditions. On the other hand, there is actually only finitely much detail in any of the examples, and in practice a stability Bongard Problem generally just amounts to "a small application of [transformation] switches an example's sorting vs. not".

(The keyword gap is another example of a Bongard Problem currently labelled with "invariance" that arguably does not technically fit.)


Also, dependence Bongard Problems could be considered "invariance" Bongard Problems, where the relevant kind of transformation is swapping the example out for any other example that shares the relevant property.

CROSSREFS

"Invariance" Bongard Problems are notso Bongard Problems.

"Invariance" Bongard Problems are often keywords (keyword keyword) on the OEBP.


See keyword problemkiller, which is about transformations making all sorted examples unsortable.

Adjacent-numbered pages:
BP561 BP562 BP563 BP564 BP565  *  BP567 BP568 BP569 BP570 BP571

KEYWORD

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

WORLD

linksbp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP565 Bongard Problems that are hard for humans to solve but easier for computers to solve vs. Bongard Problems that are hard for computers to solve but easier for humans to solve.
BP112
BP558
BP941
BP1008
BP1055
BP100
BP170
BP190
BP193
BP197
BP199
BP235
BP237
BP252
BP331
BP349
BP373
BP382
BP524
BP551
BP565
BP812
BP839
BP844
BP862
BP869
BP882
BP930
BP939
BP1002
BP1004
BP1092
BP1110
BP1260
(edit; present; nest [left/right]; search; history)
COMMENTS

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

Right examples have the keyword "anticomputer" on the OEBP.


Easy abstract Bongard Problems are typically anticomputer Bongard Problems.

CROSSREFS

See keyword help for Bongard Problems that can be made easier for humans to solve by the selection of helpful examples.

Adjacent-numbered pages:
BP560 BP561 BP562 BP563 BP564  *  BP566 BP567 BP568 BP569 BP570

KEYWORD

spectrum, anticomputer, meta (see left/right), links, keyword, right-self, viceversa

WORLD

bp [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP563 Bongard Problems such that there is a way of making an infinite list of all relevant possible left-sorted examples vs. Bongard Problems where there is no such way of listing all left-sorted examples.
BP386
BP394
BP904
BP922
BP926
BP931
BP956
BP997
BP1057
BP1072
BP1146
BP1147
BP1148
BP1149
BP1150
BP1197
BP1199
BP1200
BP1201
BP319
BP345
BP351
BP559
BP818
?
BP329
(edit; present; nest [left/right]; search; history)
COMMENTS

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


All the possible left examples for the BPs on the left side of this problem could be listed in one infinite sequence. Right examples here are Problems for which no such sequence can exist.


This depends on deciding what images should be considered "the same thing", which is subjective and context-dependent.


All examples in this Bongard Problem have an infinite left side (they do not have the keyword left-finite).


The mathematical term for a set that can be organized into an infinite list is a "countably infinite" set, as opposed to an "uncountably infinite" set.

Another related idea is a "recursively enumerable" a.k.a. "semi-decidable" set, which is a set that a computer program could list the members of.

The keyword "left-listable" is meant to be for the more general idea of a countable set, which does not have to do with computer algorithms.


Note that this is not just BP940 (right-listable) flipped.


It seems in practice, Bongard Problems that are left-listable are usually also right-listable because the whole class of relevant examples is listable. A keyword for just plain "listable" may be more useful. Or instead keywords for left- versus right- semidecidability, in the sense of computing. - Aaron David Fairbanks, Jan 10 2023

REFERENCE

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

CROSSREFS

See left-finite, which distinguishes between a finite left side and infinite left side.


"Left-listable" BPs are typically precise.

Adjacent-numbered pages:
BP558 BP559 BP560 BP561 BP562  *  BP564 BP565 BP566 BP567 BP568

KEYWORD

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

WORLD

bp_infinite_left_examples [smaller | same | bigger]
zoom in right (left_uncountable_bp)

AUTHOR

Leo Crabbe

BP561 Meta Bongard Problems fitting in their own world vs. other meta Bongard Problems.
BP561
(edit; present; nest [left/right]; search; history)
COMMENTS

This prompts thinking about left-self and right-self keywords.

CROSSREFS

Adjacent-numbered pages:
BP556 BP557 BP558 BP559 BP560  *  BP562 BP563 BP564 BP565 BP566

KEYWORD

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

WORLD

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

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

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

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

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

BP550 Experimental Bongard Problems vs. traditional-style Bongard Problems.
BP195
BP200
BP300
BP359
BP538
BP544
BP545
BP548
BP555
BP570
BP793
BP795
BP797
BP801
BP812
BP813
BP844
BP854
BP859
BP862
BP868
BP902
BP911
BP915
BP920
BP939
BP941
BP942
BP953
BP955
BP957
BP959
BP1008
BP1056
BP1073

. . .

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

. . .

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

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

Right examples have the keyword "traditional" on the OEBP.


Experimental BPs push the boundaries of what makes Bongard Problems Bongard Problems.


Traditional BPs show some simple property of black and white pictures. The OEBP is a place with many wild and absurd Bongard Problems, so it is useful to have an easy way to just find the regular old Bongard Problems.

CROSSREFS

Adjacent-numbered pages:
BP545 BP546 BP547 BP548 BP549  *  BP551 BP552 BP553 BP554 BP555

KEYWORD

subjective, meta (see left/right), links, keyword, left-it

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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