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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

BP518 Keywords on the OEBP vs. other Bongard Problem pages.
BP501
BP503
BP504
BP506
BP507
BP508
BP509
BP510
BP511
BP512
BP513
BP514
BP515
BP516
BP517
BP518
BP519
BP520
BP521
BP522
BP534
BP535
BP537
BP539
BP546
BP547
BP549
BP550
BP552
BP553
BP554
BP556
BP563
BP565
BP566

. . .

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COMMENTS

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

CROSSREFS

Adjacent-numbered pages:
BP513 BP514 BP515 BP516 BP517  *  BP519 BP520 BP521 BP522 BP523

KEYWORD

meta (see left/right), links, keyword, oebp, left-self, left-it, feedback, funny

WORLD

bppage [smaller | same | bigger]
zoom in left (keyword)

AUTHOR

Aaron David Fairbanks

BP520 Bongard Problems whose sorting of examples depends on subjective opinion vs. not so.
BP237
BP501
BP503
BP506
BP550
BP801
BP812
BP864
BP865
BP869
BP882
BP894
BP939
BP1000
(edit; present; nest [left/right]; search; history)
COMMENTS

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


Subjective Bongard Problems are fuzzy.

CROSSREFS

Adjacent-numbered pages:
BP515 BP516 BP517 BP518 BP519  *  BP521 BP522 BP523 BP524 BP525

KEYWORD

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP537 Meta Bongard Problems vs. other Bongard Problems.
BP200
BP501
BP503
BP504
BP506
BP507
BP508
BP509
BP510
BP511
BP512
BP513
BP514
BP515
BP516
BP517
BP518
BP519
BP520
BP521
BP522
BP526
BP534
BP535
BP537
BP539
BP541
BP542
BP544
BP546
BP547
BP549
BP550
BP552
BP553

. . .

BP1
BP2
BP3
BP4
BP5
BP6
BP7
BP8
BP9
BP10
(edit; present; nest [left/right]; search; history)
COMMENTS

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


Meta Bongard Problems are Bongard Problems that sort Bongard Problems. Sometimes abbreviated MBPs.


The first meta Bongard Problem was BP200.


Some meta BP pages sort images of Bongard Problems (keyword miniproblems), while other meta BP pages sort other BP pages (keyword links).

CROSSREFS

BPs that sort meta-BPs are labelled metameta.

Adjacent-numbered pages:
BP532 BP533 BP534 BP535 BP536  *  BP538 BP539 BP540 BP541 BP542

KEYWORD

meta (see left/right), links, keyword, world, left-self, sideless, metameta, left-full, feedback

CONCEPT recursion (info | search)

WORLD

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

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
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

BP967 Keywords on the OEBP that observe properties of Bongard Problems vs. keywords on the OEBP that tag Bongard Problems with instruction for users.
BP501
BP503
BP506
BP507
BP508
BP509
BP510
BP511
BP512
BP513
BP514
BP515
BP516
BP517
BP518
BP519
BP520
BP521
BP522
BP534
BP535
BP537
BP546
BP547
BP549
BP550
BP552
BP553
BP554
BP556
BP563
BP565
BP567
BP568
BP571

. . .

BP504
BP919
BP930
BP947
BP1125
BP1243
(edit; present; nest [left/right]; search; history)
COMMENTS

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

CROSSREFS

See also the keyword presentationmatters.

Adjacent-numbered pages:
BP962 BP963 BP964 BP965 BP966  *  BP968 BP969 BP970 BP971 BP972

KEYWORD

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

WORLD

keyword [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1076 Meta Bongard Problems sorting BP1 left vs. meta Bongard Problems sorting BP1 right.
BP501
BP503
BP508
BP509
BP513
BP515
BP541
BP542
BP544
BP546
BP567
BP573
BP627
BP634
BP798
BP883
BP913
BP947
BP1075
BP504
BP507
BP510
BP522
BP537
BP902
BP963
BP1113
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1071 BP1072 BP1073 BP1074 BP1075  *  BP1077 BP1078 BP1079 BP1080 BP1081

KEYWORD

meta (see left/right), links, metameta

WORLD

linksbp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1126 Meta Bongard Problems in which examples are pages on the OEBP vs. meta Bongard Problems in which examples are pictures of Bongard Problems.
BP501
BP503
BP504
BP506
BP507
BP508
BP509
BP510
BP511
BP512
BP513
BP514
BP515
BP516
BP517
BP518
BP519
BP520
BP521
BP522
BP526
BP534
BP535
BP537
BP539
BP541
BP542
BP544
BP546
BP547
BP549
BP550
BP552
BP553
BP554

. . .

BP200
BP793
BP795
BP796
BP802
BP803
BP827
BP828
BP829
BP830
BP831
BP832
BP833
BP834
BP835
BP836
BP868
BP871
BP872
BP873
BP874
BP875
BP876
BP877
BP878
BP879
BP880
BP881
BP894
BP948
BP952
BP953
BP954
BP955
BP957

. . .

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

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

Bongard Problems sorted right have the keyword "miniproblems" on the OEBP.


The keyword "links" is automatically added to a Bongard Problem on the OEBP if a BP number is added as an example.


Meta Bongard problems that sort Bongard Problems purely based on their solutions (keyword presentationmatters) usually have two versions in the database: one that sorts images of Bongard Problems and one that sorts links to pages on the OEBP. If both versions exist, users should make them cross-reference one another.

CROSSREFS

All the examples of miniature Bongard Problems within any meta Bongard Problem tagged "miniproblems" would fit left on BP1080 (which is a showcase of the various formats for images of Bongard Problems).

Adjacent-numbered pages:
BP1121 BP1122 BP1123 BP1124 BP1125  *  BP1127 BP1128 BP1129 BP1130 BP1131

KEYWORD

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

WORLD

metabp [smaller | same | bigger]

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