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BP376 A "chess piece" that moves as shown may reach every square vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP371 BP372 BP373 BP374 BP375  *  BP377 BP378 BP379 BP380 BP381

KEYWORD

precise, allsorted, notso, left-finite, right-finite, traditional, fixedgrid, preciseworld

CONCEPT all (info | search),
chess-like (info | search),
imagined_motion (info | search),
motion (info | search)

AUTHOR

Aaron David Fairbanks

BP381 Adding the top two waves yields the bottom wave vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

This problem is about wave interference.

CROSSREFS

Adjacent-numbered pages:
BP376 BP377 BP378 BP379 BP380  *  BP382 BP383 BP384 BP385 BP386

KEYWORD

nice, notso, math, orderedtriplet, traditional

CONCEPT addition (info | search),
wave (info | search),
2_inputs_1_output (info | search)

AUTHOR

Aaron David Fairbanks

BP385 Nets of cubes vs. not nets of cubes.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP380 BP381 BP382 BP383 BP384  *  BP386 BP387 BP388 BP389 BP390

KEYWORD

nice, notso, left-finite, traditional

CONCEPT 3d_net (info | search)

WORLD

square_outlines_sharing_edges [smaller | same | bigger]
zoom in left (cube_net)

AUTHOR

Jago Collins

BP390 Each graph vertex is uniquely defined by its connections (the graph does not admit nontrivial automorphisms) vs. the graph admits nontrivial automorphisms.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP385 BP386 BP387 BP388 BP389  *  BP391 BP392 BP393 BP394 BP395

KEYWORD

precise, allsorted, notso, traditional, preciseworld

CONCEPT graph (info | search),
self-reference (info | search),
topological_transformation (info | search),
imagined_shape (info | search),
imagined_entity (info | search)

WORLD

connected_graph [smaller | same | bigger]

AUTHOR

Jago Collins

BP506 Bongard Problems whose solutions are hard to put into words vs. Bongard Problems whose solutions are easy to put into words.
BP524
BP956
BP964
BP998
BP1130
BP1142
BP1148
BP1149
BP1155
BP1157
BP1161
BP1181
BP1242
BP1246
BP1247
BP1248
BP1250
BP1251
BP2
(edit; present; nest [left/right]; search; history)
COMMENTS

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


"Unwordable" does not just mean convoluted, that is, involving a long description. "Unwordable" also does not just mean hard. Unwordable Bongard Problems are instead those Bongard Problems whose solutions tend to occur to people nonverbally before verbally. The typical "unwordable" Bongard Problem solution is not too difficult to see, and may be easy to describe vaguely, but hard to pin down in language.


The solution title given on the OEBP for "unwordable" pages is often something vague and evocative, further elaborated on in the comments. For example, the title for BP524 is "Same objects are shown lined up in both 'universes' vs. the two 'universes' are not aligned." If someone said this, it would be clear they had seen the answer, even though this is not a clear description.



Bongard Problems have been sorted here based on how hard they are to put into words in English. (See keyword culture.) It may be interesting to consider whether or not the same choices would be made with respect to other languages.

CROSSREFS

Adjacent-numbered pages:
BP501 BP502 BP503 BP504 BP505  *  BP507 BP508 BP509 BP510 BP511

KEYWORD

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

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

BP515 Bongard Problems with a finite number of possible left examples vs. not.
BP1
BP244
BP376
BP385
BP504
BP538
BP795
BP854
BP868
BP902
BP920
BP934
BP959
BP962
BP1056
BP1097
BP1156
BP1219
BP1220
BP1223
BP1197
?
BP1146
(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted BPs have the keyword "left-finite" in the OEBP.


How to distinguish between different examples depends on the Bongard Problem. For example, in BPs about little black dots, examples may be considered the same when they have the same number of dots in all the same positions.


Note that this is not just BP516 (right-finite) flipped.

CROSSREFS

"Left-finite" implies left-narrow.

See left-listable, which is about an infinite left side that can be organized into a neverending list versus infinite left side that cannot be organized into a neverending list.


"Left-finite" BPs are typically precise.


See BP1032 for a version that sorts images of Bongard Problems (miniproblems) instead of links, and which only sorts images of Bongard Problems about numbers.

Adjacent-numbered pages:
BP510 BP511 BP512 BP513 BP514  *  BP516 BP517 BP518 BP519 BP520

KEYWORD

notso, dual, meta (see left/right), links, keyword, side

WORLD

bp [smaller | same | bigger]
zoom in right (bp_infinite_left_examples)

AUTHOR

Aaron David Fairbanks

BP516 Bongard Problems with a finite number of possible right examples vs. not.
BP244
BP376
BP503
BP504
BP544
BP795
BP854
BP934
BP959
BP962
BP1056
BP1097
BP1219
BP1223
(edit; present; nest [left/right]; search; history)
COMMENTS

Left-sorted BPs have the keyword "right-finite" in the OEBP.


BPs are sorted based on how BP515 (left-finite) would sort them were they flipped; see that page for a description.

CROSSREFS

"Right-finite" implies right-narrow.

See right-listable, which is about an infinite right side that can be organized into a neverending list versus infinite right side that cannot be organized into a neverending list.


"Right-finite" BPs are typically precise.


See BP1041 for a version that sorts images of Bongard Problems (miniproblems) instead of links, and which only sorts images of Bongard Problems about numbers.

Adjacent-numbered pages:
BP511 BP512 BP513 BP514 BP515  *  BP517 BP518 BP519 BP520 BP521

KEYWORD

notso, dual, meta (see left/right), links, keyword, side

WORLD

bp [smaller | same | bigger]
zoom in right (bp_infinite_right_examples )

AUTHOR

Aaron David Fairbanks

BP538 Shown is a box of this Bongard Problem (BP538) vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP533 BP534 BP535 BP536 BP537  *  BP539 BP540 BP541 BP542 BP543

KEYWORD

less, notso, left-finite, finished, invalid, experimental, funny

CONCEPT recursion (info | search),
self-reference (info | search)

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

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