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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
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
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°" 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

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
(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

BP662 Bongard Problem with solution relating to concept: light / dark vs. Bongard Problem unrelated to this concept.
BP196
BP236
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP657 BP658 BP659 BP660 BP661  *  BP663 BP664 BP665 BP666 BP667

KEYWORD

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

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP762 Bongard Problem with solution relating to concept: texture of area vs. Bongard Problem unrelated to this concept.
BP95
BP196
BP236
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP757 BP758 BP759 BP760 BP761  *  BP763 BP764 BP765 BP766 BP767

KEYWORD

meta (see left/right), links, metaconcept

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

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

BP1162 Bongard Problem with solution that can be naturally phrased as "___ vs. vice versa" vs. not so.
BP28
BP29
BP36
BP37
BP38
BP43
BP45
BP46
BP47
BP48
BP49
BP53
BP63
BP65
BP67
BP68
BP76
BP79
BP196
BP211
BP565
BP830
BP971
BP972
BP1124
BP1159
BP1254
BP1
BP170
BP331
BP1004
BP1044
BP1046
BP1162
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COMMENTS

Bongard Problems sorted left obtain the keyword "viceversa" on the OEBP.

CROSSREFS

Contrast the keyword notso.


"Viceversa" BPs are often dual.


The solution to a less-than/greater-than quantity comparison Bongard Problem (keyword spectrum) where the two sides divide the spectrum in half can be phrased as "closer to left end of spectrum than right end vs. vice versa." Whether this is a natural way to phrase the solution depends on the kind of quantity being compared.

Here are some examples of spectra for which the "vice versa" phrasing tends to seem natural: left vs. right, up vs. down, black vs. white, higher quantity of [thing type 1] vs. higher quantity of [thing type 2].

Adjacent-numbered pages:
BP1157 BP1158 BP1159 BP1160 BP1161  *  BP1163 BP1164 BP1165 BP1166 BP1167

KEYWORD

notso, meta (see left/right), links, keyword, right-self

AUTHOR

Aaron David Fairbanks

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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