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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°."


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

BP512 Abstract Bongard Problems vs. concrete visual Bongard Problems.
BP218
BP331
BP360
BP373
BP378
BP379
BP393
BP512
BP543
BP792
BP793
BP795
BP796
BP797
BP801
BP812
BP813
BP824
BP833
BP839
BP847
BP865
BP869
BP871
BP879
BP880
BP881
BP882
BP894
BP917
BP954
BP955
BP957
BP978
BP987

. . .

BP1
BP322
BP334
BP946
BP1123
(edit; present; nest [left/right]; search; history)
COMMENTS

BPs sorted left are tagged with the keyword "abstract" on the OEBP. The solution is not an easily-checked or concretely-defined geometrical or numerical property in pictures.

CROSSREFS

Adjacent-numbered pages:
BP507 BP508 BP509 BP510 BP511  *  BP513 BP514 BP515 BP516 BP517

KEYWORD

abstract, meta (see left/right), links, keyword, left-self, sideless

WORLD

bp [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP520 Bongard Problems whose sorting of examples depends on subjective opinion vs. not so.
BP237
BP501
BP503
BP506
BP550
BP801
BP812
BP864
BP865
BP869
BP882
BP894
BP939
BP1000
(edit; present; nest [left/right]; search; history)
COMMENTS

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


Subjective Bongard Problems are fuzzy.

CROSSREFS

Adjacent-numbered pages:
BP515 BP516 BP517 BP518 BP519  *  BP521 BP522 BP523 BP524 BP525

KEYWORD

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

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

BP760 Bongard Problem with solution relating to concept: symmetry (invariance under transformation) vs. Bongard Problem unrelated to this concept.
BP50
BP152
BP172
BP265
BP269
BP342
BP811
BP836
BP847
BP869
BP986
BP1206
BP1207
BP1210
BP1213
BP1215
BP1228
BP1229
BP1230
BP1246
BP1264
(edit; present; nest [left/right]; search; history)
CROSSREFS

See BP836 for the version with pictures of Bongard Problems instead of links to pages on the OEBP.

Adjacent-numbered pages:
BP755 BP756 BP757 BP758 BP759  *  BP761 BP762 BP763 BP764 BP765

KEYWORD

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

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Harry E. Foundalis

BP814 Bongard Problems with solution "object features concept: ___" vs. other BP pages.
BP373
BP543
BP797
BP847
BP869
BP1002
(edit; present; nest [left/right]; search; history)
COMMENTS

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

Each concept has a corresponding metaconcept page, which describes that concept and catalogues Bongard Problems featuring that concept.

CROSSREFS

Adjacent-numbered pages:
BP809 BP810 BP811 BP812 BP813  *  BP815 BP816 BP817 BP818 BP819

KEYWORD

meta (see left/right), links, keyword

WORLD

bppage [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP913 Bongard Problems in which fine subtleties of images may be considered with respect to the solution (no slightly wrong hand-drawings!) vs. other visual Bongard Problems.
BP1
BP160
BP199
BP210
BP211
BP213
BP216
BP217
BP223
BP312
BP321
BP324
BP325
BP335
BP341
BP344
BP348
BP367
BP368
BP386
BP523
BP529
BP530
BP531
BP532
BP533
BP551
BP557
BP559
BP564
BP816
BP852
BP859
BP860
BP861

. . .

BP5
BP6
BP72
BP91
BP136
BP148
?
BP119
(edit; present; nest [left/right]; search; history)
COMMENTS

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

Right examples have the keyword "ignoreimperfections".


Consider the difference in style between BP344 and BP24.


Hand-drawn figures in BPs are typically imperfect. A "circles vs. squares" BP may only show what are approximately circles and approximately squares. A pedant might append to the solutions of all Bongard Problems the caveat "...when figures are interpreted as the most obvious shapes they approximate."

This is the meaning of the label "ignoreimperfections". On the other hand, the label "perfect" means even the pedant would drop this caveat; either all the images are precise, or precision doesn't matter (see also keyword stable).


Even in BPs tagged "perfect", the tiny rough edges caused by image pixelation are not expected to matter. If the OEBP would indeed prefer users only upload pixel-perfect examples, a BP can be tagged with the stricter keyword pixelperfect.

E.g., for BPs having to do with smooth curves and lines, "perfect" only requires images offer the best possible approximation of those intended shapes given the resolution.


Most Bongard Problems involving small details at all would be tagged "perfect". However, this is not always so; sometimes the small details are intended to be noticed, but certain imperfections are still intended to be overlooked.


BP119 ("small correction results in circle vs. not") is an interesting example: imperfections matter with respect to the outline being closed, but imperfections do not matter with respect to circular-ness.


If a Bongard Problem on the OEBP is tagged "ignoreimperfections" -- i.e., it has imperfect hand drawings -- then other keywords are generally applied relative to the intended idea, a corrected version sans imperfect hand drawings. (For example, this is how the keywords precise and stable are applied. Alternative versions of these keywords, which factor in imperfect hand drawings, could be made instead, but that would be less useful.)




It may be better to change the definition of "perfect" so it only applies to Bongard Problems such that small changes can potentially switch an example's side / remove it from the Bongard Problem. That would cut down on the number of Bongard Problems to label "perfect". There isn't currently a single keyword for "small changes can potentially switch an example's side / remove it from the Bongard Problem", but this is basically captured by unstable or unstableworld. There is also deformunstable which uses a different notion of "small change". - Aaron David Fairbanks, Jun 16 2023

CROSSREFS

See BP508 for discussion of this topic in relation to Bongard Problems tagged precise.


Stable Bongard Problems are generally "perfect".

Pixelperfect implies "perfect".


The keywords proofsrequired and noproofs (BP1125) have a similar relationship: "noproofs" indicates a lenience for a certain kind of imperfection.

Adjacent-numbered pages:
BP908 BP909 BP910 BP911 BP912  *  BP914 BP915 BP916 BP917 BP918

EXAMPLE

Many Bongard Problems involving properties of curves (e.g. BP62) really are about those wiggly, imperfect curves; they qualify as "perfect" problems. On the other hand, Bongard Problems involving polygons, (e.g. BP5) often show only approximately-straight lines; they are not "perfect" problems.

KEYWORD

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

WORLD

visualbp [smaller | same | bigger]
zoom in left (perfect_bp)

AUTHOR

Aaron David Fairbanks

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