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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
(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

BP608 Bongard Problem with solution relating to concept: conjunction (logical) vs. Bongard Problem unrelated to this concept.
BP26
BP28
BP140
BP141
BP142
BP143
BP144
BP145
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP603 BP604 BP605 BP606 BP607  *  BP609 BP610 BP611 BP612 BP613

KEYWORD

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

CONCEPT This MBP is about BPs that feature concept: "and"
Searchable synonyms: "conjunction logical".

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP672 Bongard Problem with solution relating to concept: number (countable quantity of feature or object) vs. Bongard Problem unrelated to this concept.
BP6
BP10
BP23
BP27
BP28
BP29
BP53
BP85
BP86
BP87
BP88
BP89
BP90
BP91
BP96
BP98
BP107
BP110
BP114
BP122
BP126
BP127
BP141
BP143
BP144
BP145
BP151
BP156
BP159
BP160
BP164
BP166
BP167
BP169
BP181

. . .

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

Adjacent-numbered pages:
BP667 BP668 BP669 BP670 BP671  *  BP673 BP674 BP675 BP676 BP677

KEYWORD

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

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP676 Bongard Problem with solution relating to concept: outlined / filled vs. Bongard Problem unrelated to this concept.
BP3
BP25
BP26
BP27
BP28
BP41
BP45
BP48
BP56
BP58
BP79
BP90
BP93
BP94
BP128
BP157
BP180
BP189
BP190
BP211
BP244
BP261
BP282
BP283
BP284
BP288
BP301
BP337
BP341
BP1223
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP671 BP672 BP673 BP674 BP675  *  BP677 BP678 BP679 BP680 BP681

KEYWORD

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

CONCEPT This MBP is about BPs that feature concept: "outlined_filled"
Searchable synonyms: "color", "filled".

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

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

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

BP983 Bongard Problem with solution relating to concept: comparison of multiple quantities (within one example) vs. Bongard Problem unrelated to this concept.
BP7
BP27
BP28
BP29
BP36
BP37
BP38
BP53
BP969
BP970
BP1208
BP1214
BP1217
(edit; present; nest [left/right]; search; history)
COMMENTS

"More," "fewer," "greater than," "less than."

See BP752 and BP749 for equality.

CROSSREFS

Adjacent-numbered pages:
BP978 BP979 BP980 BP981 BP982  *  BP984 BP985 BP986 BP987 BP988

KEYWORD

meta (see left/right), links, metaconcept

CONCEPT This MBP is about BPs that feature concept: "quantity_comparison"
Searchable synonyms: "more", "less", "greater", "lesser", "greater than", "less than", "fewer".

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP1152 Solution involves discrete quantity vs. solution involves continuous quantity.
BP28
BP29
BP53
BP1044
BP1046
BP2
BP36
BP37
BP38
BP62
BP67
BP79
BP173
BP176
BP196
BP211
BP338
(edit; present; nest [left/right]; search; history)
COMMENTS

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

Bongard Problems sorted right have the keyword "continuous".

CROSSREFS

All examples are spectrum Bongard Problems.


See BP873 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

Adjacent-numbered pages:
BP1147 BP1148 BP1149 BP1150 BP1151  *  BP1153 BP1154 BP1155 BP1156 BP1157

KEYWORD

meta (see left/right), links, keyword

AUTHOR

Aaron David Fairbanks

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

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