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BP501 Easy Bongard Problems vs. hard Bongard Problems.
BP1
BP2
BP3
BP4
BP5
BP6
BP7
BP8
BP9
BP10
BP23
BP31
BP97
BP98
BP100
BP194
BP196
BP211
BP363
BP374
BP812
BP839
BP882
BP911
BP956
BP1002
BP1015
BP1017
BP1022
BP1087
BP1095
BP1104
BP1105
BP1255
BP1260

. . .

BP112
BP162
BP344
BP383
BP394
BP559
BP564
BP793
BP795
BP796
BP801
BP825
BP831
BP842
BP849
BP860
BP871
BP872
BP875
BP876
BP877
BP878
BP898
BP899
BP927
BP934
BP944
BP954
BP965
BP998
BP1011
BP1038
BP1040
BP1055
BP1123

. . .

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COMMENTS

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

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


"Easy" means easy for human beings to solve, not computers.

CROSSREFS

Adjacent-numbered pages:
BP496 BP497 BP498 BP499 BP500  *  BP502 BP503 BP504 BP505 BP506

KEYWORD

spectrum, subjective, meta (see left/right), links, keyword, sideless

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP503 "Nice" Bongard Problems vs. Bongard Problems the OEBP does not need more like.
BP1
BP2
BP3
BP4
BP5
BP6
BP7
BP8
BP9
BP11
BP12
BP15
BP16
BP20
BP23
BP30
BP32
BP33
BP50
BP51
BP57
BP59
BP62
BP70
BP71
BP72
BP74
BP76
BP77
BP85
BP97
BP98
BP100
BP106
BP108

. . .

BP213
BP214
BP221
BP231
BP237
BP262
BP538
BP545
BP548
BP555
BP570
BP801
BP862
BP882
BP915
BP920
BP941
BP1000
BP1008
BP1042
BP1043
BP1129
BP1150
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COMMENTS

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

Right-sorted Bongard Problems have the keyword "less." They are not necessarily "bad," but we do not want more like them.

CROSSREFS

Adjacent-numbered pages:
BP498 BP499 BP500 BP501 BP502  *  BP504 BP505 BP506 BP507 BP508

KEYWORD

subjective, meta (see left/right), links, keyword, oebp, right-finite, left-it, feedback, time

WORLD

bp [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
BP1271
BP1
?
BP6
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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°."


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°."


In a discrete spectrum Bongard Problem, even if it is precise, 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 of 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

BP534 Bongard Problems such that potential left examples can intuitively be put in bijection with potential right examples vs. other Bongard Problems.
BP7
BP8
BP19
BP36
BP43
BP45
BP54
BP55
BP63
BP64
BP67
BP95
BP106
BP109
BP157
BP158
BP180
BP196
BP197
BP211
BP234
BP278
BP279
BP286
BP313
BP337
BP357
BP363
BP372
BP513
BP514
BP515
BP516
BP517
BP793

. . .

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COMMENTS

This is the keyword "dual" on the OEBP.

Given an example there is some way to "flip sides" by altering it. The left-to-right and right-to-left transformations should be inverses.


It is not required that there only be one such transformation. For example, for many handed Bongard Problem, flipping an example over any axis will reliably switch its sorting.


It is not required that every left example must have its corresponding right example uploaded on the OEBP nor vice versa. See the keyword contributepairs for the BPs the OEBP advises users upload left and right examples for in pairs.

CROSSREFS

Adjacent-numbered pages:
BP529 BP530 BP531 BP532 BP533  *  BP535 BP536 BP537 BP538 BP539

KEYWORD

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

WORLD

bp [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
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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

BP676 Bongard Problem with solution relating to concept: outlined / filled vs. Bongard Problem unrelated to this concept.
BP3
BP25
BP26
BP27
BP28
BP41
BP45
BP48
BP56
BP58
BP79
BP90
BP93
BP94
BP128
BP157
BP180
BP189
BP190
BP211
BP244
BP261
BP282
BP283
BP284
BP288
BP301
BP337
BP341
BP1223
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CROSSREFS

Adjacent-numbered pages:
BP671 BP672 BP673 BP674 BP675  *  BP677 BP678 BP679 BP680 BP681

KEYWORD

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

CONCEPT This MBP is about BPs that feature concept: "outlined_filled"
Searchable synonyms: "color", "filled".

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP696 Bongard Problem with solution relating to concept: size of objects or features vs. Bongard Problem unrelated to this concept.
BP2
BP14
BP21
BP22
BP34
BP38
BP76
BP126
BP140
BP211
BP248
BP256
BP286
BP295
BP301
BP969
BP970
BP1014
BP1214
BP1217
BP1222
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP691 BP692 BP693 BP694 BP695  *  BP697 BP698 BP699 BP700 BP701

KEYWORD

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

CONCEPT This MBP is about BPs that feature concept: "size"
Searchable synonyms: "large", "small", "big".

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP763 Bongard Problem with solution relating to concept: texture vs. Bongard Problem unrelated to this concept.
BP3
BP9
BP25
BP26
BP27
BP28
BP34
BP35
BP41
BP45
BP48
BP56
BP58
BP63
BP79
BP90
BP93
BP94
BP95
BP107
BP128
BP157
BP180
BP184
BP185
BP189
BP190
BP196
BP211
BP212
BP216
BP217
BP221
BP236
BP244

. . .

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

Adjacent-numbered pages:
BP758 BP759 BP760 BP761 BP762  *  BP764 BP765 BP766 BP767 BP768

KEYWORD

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

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP913 Bongard Problems in which fine subtleties of images may be considered with respect to the solution (no slightly wrong hand-drawings) vs. other visual Bongard Problems.
BP1
BP160
BP199
BP210
BP211
BP213
BP216
BP217
BP223
BP312
BP321
BP324
BP325
BP335
BP341
BP344
BP348
BP367
BP368
BP386
BP523
BP529
BP530
BP531
BP532
BP533
BP551
BP557
BP559
BP564
BP816
BP852
BP859
BP860
BP861

. . .

BP5
BP6
BP72
BP91
BP136
BP148
?
BP119
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COMMENTS

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

Right examples have the keyword "ignoreimperfections".


Consider the difference in style between BP344 and BP24.


Hand-drawn figures in BPs are typically imperfect. A "circles vs. squares" BP may only show what are approximately circles and approximately squares. A pedant might append to the solutions of all Bongard Problems the caveat "...when figures are interpreted as the most obvious shapes they approximate."

This is the meaning of the label "ignoreimperfections". On the other hand, the label "perfect" means even the pedant would drop this caveat; either all the images are precise, or precision doesn't matter (see also keyword stable).


Even in BPs tagged "perfect", the tiny rough edges caused by image pixelation are not expected to matter. If the OEBP would indeed prefer users only upload pixel-perfect examples, a BP can be tagged with the stricter keyword pixelperfect.

E.g., for BPs having to do with smooth curves and lines, "perfect" only requires images offer the best possible approximation of those intended shapes given the resolution.


Most Bongard Problems involving small details at all would be tagged "perfect". However, this is not always so; sometimes the small details are intended to be noticed, but certain imperfections are still intended to be overlooked.


BP119 ("small correction results in circle vs. not") is an interesting example: imperfections matter with respect to the outline being closed, but imperfections do not matter with respect to circular-ness.


If a Bongard Problem on the OEBP is tagged "ignoreimperfections" -- i.e., it has imperfect hand drawings -- then other keywords are generally applied relative to the intended idea, a corrected version sans imperfect hand drawings. (For example, this is how the keywords precise and stable are applied. Alternative versions of these keywords, which factor in imperfect hand drawings, could be made instead, but that would be less useful.)




It may be better to change the definition of "perfect" so it only applies to Bongard Problems such that small changes can potentially switch an example's side / remove it from the Bongard Problem. That would cut down on the number of Bongard Problems to label "perfect". There isn't currently a single keyword for "small changes can potentially switch an example's side / remove it from the Bongard Problem", but this is basically captured by unstable or unstableworld. There is also deformunstable which uses a different notion of "small change". - Aaron David Fairbanks, Jun 16 2023

CROSSREFS

See BP508 for discussion of this topic in relation to Bongard Problems tagged precise.


Stable Bongard Problems are generally "perfect".

Pixelperfect implies "perfect".


The keywords proofsrequired and noproofs (BP1125) have a similar relationship: "noproofs" indicates a lenience for a certain kind of imperfection.

Adjacent-numbered pages:
BP908 BP909 BP910 BP911 BP912  *  BP914 BP915 BP916 BP917 BP918

EXAMPLE

Many Bongard Problems involving properties of curves (e.g. BP62) really are about those wiggly, imperfect curves; they qualify as "perfect" problems. On the other hand, Bongard Problems involving polygons, (e.g. BP5) often show only approximately-straight lines; they are not "perfect" problems.

KEYWORD

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

WORLD

visualbp [smaller | same | bigger]
zoom in left (perfect_bp)

AUTHOR

Aaron David Fairbanks

BP947 BPs where users are advised to only upload images in which the pixelation is not misleading vs. other "perfect" Bongard Problems that use pixelated images to closely approximate the actual intended shapes.
BP1
BP31
BP210
BP211
BP217
BP279
BP321
BP324
BP325
BP335
BP341
BP367
BP386
BP523
BP548
BP859
BP860
BP861
BP892
BP920
BP934
BP935
BP966
BP1008
BP1088
BP1089
BP1090
BP1093
BP1104
BP1131
BP1156
BP1161
BP1168
BP1183
BP344
BP559
BP564
BP912
BP937
BP949
BP965
(edit; present; nest [left/right]; search; history)
COMMENTS

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


All examples here are perfect Bongard Problems. That is, subtle imperfections in images are meant to be considered.


When a Problem is tagged with "pixelperfect", users are reminded to make sure they do not upload images such that taking the pixelation into account would affect the sorting of that example. That is, the zoomed-in jagged blocky version of the picture should still fit the solution.


For example, in the examples of BP335, which is about tessellation, the pixels interlock properly.

CROSSREFS

Stable Bongard Problems are generally pixelperfect.

Adjacent-numbered pages:
BP942 BP943 BP944 BP945 BP946  *  BP948 BP949 BP950 BP951 BP952

KEYWORD

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

WORLD

perfect_bp [smaller | same | bigger]

AUTHOR

Leo Crabbe

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