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BP504 BP pages on the OEBP in need of more examples vs. BP pages with a list of examples that should not be altered.
BP860
BP865
BP928
BP969
BP970
BP988
BP989
BP993
BP994
BP1001
BP1082
BP1085
BP1091
BP1098
BP1137
BP1206
BP1207
BP1208
BP1209
BP1210
BP1211
BP1213
BP1214
BP1215
BP1216
BP1217
BP1218
BP1220
BP1221
BP1222
BP1223
BP1224
BP1226
BP1227
BP1228

. . .

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
BP32
BP33
BP34
BP35
BP36

. . .

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

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

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


Users are not able to add or remove examples from Problems tagged "finished." (This is unusual; most Bongard Problems on the OEBP can be expanded indefinitely by users.)


A "finished" Bongard Problem will always admit the alternative, convoluted solution "is [left example 1] OR is [left example 2] OR . . . OR is [last left example] vs. is [right example 1] OR is [right example 2] OR . . . OR is [last right example]".

CROSSREFS

Bongard's original Problems are tagged "finished."

Adjacent-numbered pages:
BP499 BP500 BP501 BP502 BP503  *  BP505 BP506 BP507 BP508 BP509

KEYWORD

meta (see left/right), links, keyword, oebp, presentationmatters, left-finite, right-finite, instruction

WORLD

bppage [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
(edit; present; nest [left/right]; search; history; show unpublished changes)
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

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

BP522 Invalid Bongard Problems vs. valid Bongard Problems.
BP237
BP301
BP538
BP545
BP812
BP882
BP902
BP939
BP941
BP942
BP1056
BP1141
BP1174
BP1263
BP1
BP522
(edit; present; nest [left/right]; search; history)
COMMENTS

Bongard Problems that break the rules or spirit of Bongard Problems but are interesting enough to keep in the database.

CROSSREFS

See BP829 and BP968 (flipped) for versions with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

Adjacent-numbered pages:
BP517 BP518 BP519 BP520 BP521  *  BP523 BP524 BP525 BP526 BP527

KEYWORD

meta (see left/right), links, keyword, right-self, 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
?
BP1080
(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

BP902 This Bongard Problem vs. anything else.
BP902
BP1

becious

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

Although this Bongard Problem is self-referential, it's only because of the specific phrasing of the solution. "BP902 vs. anything else" would also work. The number 902 could have been chosen coincidentally.

CROSSREFS

See BP953, BP959.

Adjacent-numbered pages:
BP897 BP898 BP899 BP900 BP901  *  BP903 BP904 BP905 BP906 BP907

KEYWORD

notso, meta (see left/right), links, left-self, left-narrow, left-finite, left-full, right-null, right-it, invalid, experimental, funny

CONCEPT self-reference (info | search),
specificity (info | search)

WORLD

everything [smaller | same]
zoom in left (bp902)

AUTHOR

Leo Crabbe

BP963 Bongard Problems in which small changes to examples can switch their sorting vs. Bongard Problems in which examples changed slightly enough remain sorted the same way.
BP1
BP4
BP15
BP72
BP211
BP324
BP325
BP335
BP344
BP348
BP367
BP368
BP523
BP816
BP860
BP861
BP920
BP935
BP937
BP2
BP9
BP11
BP14
BP34
BP62
(edit; present; nest [left/right]; search; history; show unpublished changes)
COMMENTS

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

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


For the purposes of this Bongard Problem, "small change" means adding to or removing from an arbitrarily small portion of the image. Other kinds of small change could be explored, such as making changes in multiple small places, translating, rotating, scaling, or deforming the whole image slightly (see also keywords deformunstable vs. deformstable), or even context-dependent small changes (e.g., changing the shadings slightly in BP196, or making small 3d changes to the represented 3d objects in BP333), but they are not considered here.


In a "stable" Bongard Problem, no small change should outright flip an example's sorting. It is allowed for a small change to make an example sorted slightly more ambiguously.


Small changes that make an example no longer even fit in with the format of a Bongard Problem are not considered. (Otherwise, far fewer Bongard Problems would be called "stable".)


For whether small changes make an example no longer fit in with the Bongard Problem, see unstableworld vs. stableworld.


If a Bongard Problem is shown with imperfect hand drawings (keyword ignoreimperfections), it is fine to apply the keyword "unstable" ignoring this. For instance, a hand-drawn version of BP344 would still be tagged "unstable", even though it would show examples wrong by small amounts.

(Note: a BP would only be tagged "ignoreimperfections" in the first place if the underlying idea were such that several small changes could make an example switch sides, no longer fit in with the format of the Bongard Problem, or otherwise be ambiguously sorted.)

CROSSREFS

Stable Bongard Problems are generally perfect and pixelperfect.

Gap (technically) implies stable. (However, in practice it has seemed unnatural to tag BPs "stable" when ALL small changes render certain examples unsortable, as is sometimes the case in "gap" BPs.)


Unstable Bongard Problems are often precise.

Stable Bongard Problems tend to either be fuzzy or otherwise either have a gap or be not allsorted.


See BP1144, which is about all small changes making all examples unsortable rather than some small change making some example switch sides.


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

Adjacent-numbered pages:
BP958 BP959 BP960 BP961 BP962  *  BP964 BP965 BP966 BP967 BP968

EXAMPLE

BP1 is unstable because it's possible to change nothing slightly by adding a pixel to end up with something.

KEYWORD

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

AUTHOR

Aaron David Fairbanks

BP1113 Bongard Problems relating to the OEBP vs. Bongard Problems unrelated to the OEBP.
BP503
BP504
BP518
BP542
BP546
BP919
BP930
BP943
BP967
BP1113
BP1121
BP1125
BP1150
BP1174
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

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


Most Bongard Problems relating to the OEBP are meta.

CROSSREFS

Adjacent-numbered pages:
BP1108 BP1109 BP1110 BP1111 BP1112  *  BP1114 BP1115 BP1116 BP1117 BP1118

KEYWORD

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

AUTHOR

Leo Crabbe

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