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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

BP550 Experimental Bongard Problems vs. traditional-style Bongard Problems.
BP195
BP200
BP300
BP359
BP538
BP544
BP545
BP548
BP555
BP570
BP793
BP795
BP797
BP801
BP812
BP813
BP844
BP854
BP859
BP862
BP868
BP902
BP911
BP915
BP920
BP939
BP941
BP942
BP953
BP955
BP957
BP959
BP1008
BP1056
BP1073

. . .

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

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

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


Experimental BPs push the boundaries of what makes Bongard Problems Bongard Problems.


Traditional BPs show some simple property of black and white pictures. The OEBP is a place with many wild and absurd Bongard Problems, so it is useful to have an easy way to just find the regular old Bongard Problems.

CROSSREFS

Adjacent-numbered pages:
BP545 BP546 BP547 BP548 BP549  *  BP551 BP552 BP553 BP554 BP555

KEYWORD

subjective, meta (see left/right), links, keyword, left-it

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP646 Bongard Problem with solution relating to concept: imperfection (small) vs. Bongard Problem unrelated to this concept.
BP119
BP130
BP148
BP160
BP168
BP222
BP223
BP224
BP299
BP338
BP548
BP869
BP920
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP641 BP642 BP643 BP644 BP645  *  BP647 BP648 BP649 BP650 BP651

KEYWORD

meta (see left/right), links, metaconcept

CONCEPT This MBP is about BPs that feature concept: "imperfection_small"
Searchable synonyms: "approximately".

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP750 Bongard Problem with solution relating to concept: sameness (equality) of shape vs. Bongard Problem unrelated to this concept.
BP57
BP58
BP125
BP140
BP141
BP142
BP143
BP145
BP195
BP259
BP293
BP303
BP305
BP324
BP338
BP343
BP977
BP986
BP1222
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP745 BP746 BP747 BP748 BP749  *  BP751 BP752 BP753 BP754 BP755

KEYWORD

meta (see left/right), links, metaconcept

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP752 Bongard Problem with solution relating to concept: sameness (equality) vs. Bongard Problem unrelated to this concept.
BP35
BP39
BP56
BP57
BP58
BP61
BP77
BP80
BP91
BP103
BP112
BP124
BP125
BP128
BP137
BP140
BP141
BP142
BP143
BP145
BP169
BP189
BP190
BP195
BP238
BP239
BP244
BP257
BP259
BP281
BP293
BP303
BP305
BP324
BP328

. . .

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

Adjacent-numbered pages:
BP747 BP748 BP749 BP750 BP751  *  BP753 BP754 BP755 BP756 BP757

KEYWORD

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

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP755 Bongard Problem with solution relating to concept: similarity (but not equality) of shape vs. Bongard Problem unrelated to this concept.
BP59
BP60
BP123
BP139
BP145
BP188
BP205
BP248
BP249
BP282
BP338
BP1002
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP750 BP751 BP752 BP753 BP754  *  BP756 BP757 BP758 BP759 BP760

KEYWORD

meta (see left/right), links, metaconcept

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

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

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

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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