login
Hints
(Greetings from The On-Line Encyclopedia of Bongard Problems!)
Search: +ex:BP2
Displaying 1-10 of 12 results found. ( next )     page 1 2
     Sort: id      Format: long      Filter: (all | no meta | meta)      Mode: (words | no words)
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

. . .

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

BP541 Bongard Problems vs. anything else.
BP1
BP2
BP3
BP4
BP541
BP1073

blllmam

cat

nongard

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

This refers to all Bongard Problem solution ideas. No need to be a particularly well-made or well-defined Bongard Problem.

CROSSREFS

Adjacent-numbered pages:
BP536 BP537 BP538 BP539 BP540  *  BP542 BP543 BP544 BP545 BP546

KEYWORD

notso, meta (see left/right), links, world, left-self, right-null, left-it, feedback

WORLD

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

AUTHOR

Aaron David Fairbanks

BP542 BP Pages on the OEBP vs. anything else.
BP1
BP2
BP3
BP542
BP1073
BP0

nolab

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

Adjacent-numbered pages:
BP537 BP538 BP539 BP540 BP541  *  BP543 BP544 BP545 BP546 BP547

KEYWORD

notso, meta (see left/right), links, oebp, world, left-self, right-null, left-it, feedback

WORLD

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

AUTHOR

Aaron David Fairbanks

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

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

BP798 Bongard Problems by Bongard vs. other Bongard Problems.
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

. . .

BP101
BP102
BP103
BP104
BP105
BP106
BP107
BP108
BP109
BP110
BP111
BP112
BP113
BP114
BP115
BP116
BP117
BP118
BP119
BP120
BP121
BP122
BP123
BP124
BP125
BP126
BP127
BP128
BP129
BP130
BP131
BP132
BP133
BP134
BP135

. . .

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

Alternatively, BP pages on the OEBP with number less than or equal to 100 vs. other BP pages.


Bongard's original Problems have the keyword "bongard" on the OEBP.

CROSSREFS

Adjacent-numbered pages:
BP793 BP794 BP795 BP796 BP797  *  BP799 BP800 BP801 BP802 BP803

KEYWORD

meta (see left/right), links, keyword

WORLD

bppage [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP964 Bongard Problems such that making repeated small changes can switch an example's sorting vs. Bongard Problems in which the two sides are so different that it is impossible to cross the gap by making successive small changes to examples while staying within the class of examples sorted by the Bongard Problem (there is no middle-ground between the sides; there is no obvious choice of shared ambient context both sides are part of).
BP2
BP4
BP8
BP9
BP3
BP16
BP23
BP363
BP962
BP1219
(edit; present; nest [left/right]; search; history)
COMMENTS

Right-sorted BPs have the keyword "gap" on the OEBP.


A Bongard Problem with a gap showcases two completely separate classes of objects.


For example, the Bongard Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there is a space of partially filled black-and-white images between them, or any number of other ambient contexts.


Bongard Problems about comparing quantities on a spectrum should not usually be considered "gap" BPs. (Discrete spectra perhaps.) A spectrum establishes a shared context, with examples on both sides of the BP landing somewhere on it. (However, if it is reasonable to imagine getting the solution without noticing a spectrum in between, it could be a gap, since the ambient context is unclear.)


Bongard Problems with gaps may seem particularly arbitrary when the two classes of objects are particularly unrelated.

CROSSREFS

If a Bongard Problem has a "gap" it is likely precise: it will likely be clear on which side any potential example fits.


"Gap" implies stable. (This technically includes cases in which ALL small changes make certain examples no longer fit in with the Bongard Problem, as is sometimes the case in "gap" BPs. See also BP1144.)


See also preciseworld. "Gap" Bongard Problems would be tagged "preciseworld" when the two classes of objects are each clear; it is then apparent that there is no larger shared context and that no other types of objects besides the two types would be sorted by the Bongard Problem.


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

Adjacent-numbered pages:
BP959 BP960 BP961 BP962 BP963  *  BP965 BP966 BP967 BP968 BP969

KEYWORD

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

AUTHOR

Aaron David Fairbanks

BP1140 Bongard Problems where there is a way of adding details to some example (without erasing) that would sort it on the other side vs. Bongard Problems where there is no way of adding details to examples that would sort them on the other side.
BP1
BP2
BP3
BP4
BP6
BP14
BP15
BP335
BP5
BP8
BP10
BP11
BP12
BP13
BP16
(edit; present; nest [left/right]; search; history)
COMMENTS

This classification is specifically concerned with changes to examples that leave them sortable, as there are almost always ways of adding details to a BP's examples that make them unsortable.


Another version of this Bongard Problem could be made about adding white (erasure of detail) instead of black (addition of detail).

Another version could be made about adding either white or black, but not both.

CROSSREFS

Closely related to gap Problems and stable Problems.

Bongard Problems tagged finishedexamples will fit right.

Adjacent-numbered pages:
BP1135 BP1136 BP1137 BP1138 BP1139  *  BP1141 BP1142 BP1143 BP1144 BP1145

KEYWORD

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

AUTHOR

Leo Crabbe

( next )     page 1 2

Welcome | Solve | Browse | Lookup | Recent | Links | Register | Contact
Contribute | Keywords | Concepts | Worlds | Ambiguities | Transformations | Invalid Problems | Style Guide | Goals | Glossary