login
Hints
(Greetings from The On-Line Encyclopedia of Bongard Problems!)
Search: +ex:BP65
Displaying 1-10 of 13 results found. ( next )     page 1 2
     Sort: id      Format: long      Filter: (all | no meta | meta)      Mode: (words | no words)
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

BP511 Noisy Bongard Problems vs. minimalist Bongard Problems.
BP10
BP25
BP37
BP40
BP42
BP48
BP58
BP60
BP64
BP65
BP66
BP73
BP82
BP98
BP105
BP106
BP109
BP116
BP123
BP127
BP128
BP130
BP131
BP132
BP135
BP136
BP162
BP165
BP174
BP181
BP183
BP192
BP194
BP201
BP202

. . .

BP859
BP962
BP1104
BP1122
BP1156
BP1219
(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted BPs have the keyword "noisy" on the OEBP. Right-sorted examples have the keyword "minimal."


Noisy Bongard Problems include extra details varying between examples that distract from the solution property; more specifically noise is properties independent of the solution property that vary between examples. Minimalist Bongard Problems only vary details absolutely necessary to communicate the solution.


"Noisy" is different than the kind of distraction mentioned at distractingworld, which means the class of examples is distractingly specific, irrelevant to the solution, rather than that there are extra distracting properties changing between examples.


Bongard Problems have varying degrees of noisiness. Only include here BPs that are very noisy or very minimal.

CROSSREFS

See BP827 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

See BP845 for noise in sequences of quantity increase.

Adjacent-numbered pages:
BP506 BP507 BP508 BP509 BP510  *  BP512 BP513 BP514 BP515 BP516

KEYWORD

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis, Aaron David Fairbanks

BP553 Rotation-dependent Bongard Problems vs. rotation-independent visual Bongard Problems.
BP7
BP19
BP36
BP65
BP95
BP106
BP152
BP158
BP199
BP273
BP523
BP551
BP971
BP1014
BP1086
BP1087
BP1213
BP1215
BP1216
BP1218
BP1245
BP16
BP54
BP1122
(edit; present; nest [left/right]; search; history)
COMMENTS

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


If rotating an example about the center can change its sorting the BP is a left example here.


Note that BPs about relative rotation comparisons fit on the right side.

CROSSREFS

See BP872 for the version with pictures of Bongard Problems instead (miniproblems) of links to pages on the OEBP.


Bongard Problems tagged "rotate" are usually handed, since any rotation can be created by two reflections. Not necessarily, however, since the reflected step in between might not be sorted on either side by the Bongard Problem.

Adjacent-numbered pages:
BP548 BP549 BP550 BP551 BP552  *  BP554 BP555 BP556 BP557 BP558

KEYWORD

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

WORLD

visualbp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP610 Bongard Problem with solution relating to concept: convex hull vs. Bongard Problem unrelated to this concept.
BP12
BP65
BP81
BP82
BP83
BP84
BP97
BP138
BP192
BP242
BP268
BP272
BP278
BP280
BP348
BP891
BP1094
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP605 BP606 BP607 BP608 BP609  *  BP611 BP612 BP613 BP614 BP615

KEYWORD

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

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP626 Bongard Problem with solution relating to concept: elongated / compact vs. Bongard Problem unrelated to this concept.
BP11
BP12
BP65
BP168
BP192
BP268
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP621 BP622 BP623 BP624 BP625  *  BP627 BP628 BP629 BP630 BP631

KEYWORD

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

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP645 Bongard Problem with solution relating to concept: horizontal vs. Bongard Problem unrelated to this concept.
BP7
BP13
BP19
BP43
BP65
BP66
BP95
BP116
BP132
BP147
BP192
BP206
BP268
BP270
BP280
BP281
BP1207
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP640 BP641 BP642 BP643 BP644  *  BP646 BP647 BP648 BP649 BP650

KEYWORD

meta (see left/right), links, metaconcept

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP733 Bongard Problem with solution relating to concept: clustering vs. Bongard Problem unrelated to this concept.
BP25
BP26
BP27
BP28
BP29
BP41
BP42
BP48
BP49
BP58
BP61
BP65
BP66
BP81
BP83
BP84
BP89
BP90
BP99
BP128
BP141
BP142
BP143
BP144
BP145
BP147
BP149
BP156
BP166
BP167
BP169
BP186
BP187
BP189
BP190

. . .

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

Adjacent-numbered pages:
BP728 BP729 BP730 BP731 BP732  *  BP734 BP735 BP736 BP737 BP738

KEYWORD

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

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP753 Bongard Problem with solution relating to concept: similarity (but not equality) of feature vs. Bongard Problem unrelated to this concept.
BP65
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP748 BP749 BP750 BP751 BP752  *  BP754 BP755 BP756 BP757 BP758

KEYWORD

meta (see left/right), links, metaconcept

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP757 Bongard Problem with solution relating to concept: similarity (but not equality) vs. Bongard Problem unrelated to this concept.
BP39
BP59
BP60
BP65
BP123
BP139
BP145
BP173
BP188
BP205
BP248
BP249
BP282
BP320
BP338
BP377
BP1002
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP752 BP753 BP754 BP755 BP756  *  BP758 BP759 BP760 BP761 BP762

KEYWORD

meta (see left/right), links, metaconcept

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

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

( next )     page 1 2

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