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BP1139 Bongard Problems where, given any example, there is a way to add details to it (without erasing) such that it is sorted on the other side vs. BPs where this is not the case.
BP35
BP50
BP62
BP72
BP322
BP335
BP388
BP391
BP533
BP935
BP937
BP969
BP977
BP986
BP1016
BP1099
BP1100
BP1101
BP1109
BP1
BP2
BP22
BP23
BP70
BP788
BP892
BP920
BP932
BP933
BP949
BP971
BP972
BP1102
BP1136
?
BP966
(edit; present; nest [left/right]; search; history)
COMMENTS

This classification is specifically concerned with changes to examples that leave them sortable, as there are almost always ways of adding details to a BP's examples that make them unsortable.


Right-sorted BPs in this Bongard Problem are often Bongard Problems where there is always a way of adding to left-sorted examples to make them right-sorted, but not the other way around, or vice versa.


Another version of this Bongard Problem could be made about adding white (erasure of detail) instead of black (addition of detail).

Another version could be made about adding either white or black, but not both.


Where appropriate, you can assume all images will have some room in a lip of white background around the border (ignoring https://en.wikipedia.org/wiki/Sorites_paradox ).


You can't expand the boundary of an image as you add detail to it. If image boundaries could be expanded, then any shape could be shrunken to a point in relation to the surrounding whiteness, which could then be filled in to make any other shape.



How should this treat cases in which just a few examples can't be added to at all (like an all-black box)? E.g. BP966. Should this be sorted right (should the one special case of a black box spoil it) or should it be sorted left (should examples that can't at all be further added be discounted)? Maybe we should only sort BPs in which all examples can be further added to. (See BP1143left.) - Aaron David Fairbanks, Nov 12 2021


Is "addition of detail" context-dependent, or does it just mean any addition of blackness to the image? Say you have a points-and-lines Bongard Problem like BP1100, and you're trying to decide whether to sort it left or right here. You would just want to think about adding more points and lines to the picture. You don't want to get bogged down in thinking about whether black could be added to the image in a weird way so that a point gets turned into a line, or something. - Aaron David Fairbanks, Nov 13 2021

CROSSREFS

See BP1139 for Bongard Problems in which no example can be added to, period.

Adjacent-numbered pages:
BP1134 BP1135 BP1136 BP1137 BP1138  *  BP1140 BP1141 BP1142 BP1143 BP1144

KEYWORD

meta (see left/right), links, sideless

AUTHOR

Leo Crabbe

BP1138 Each attribute is shared by every group or none vs. some attribute is shared by exactly two groups
(edit; present; nest [left/right]; search; history)
COMMENTS

Attributes are shading, shape, and number.

There are always three groups.

This problem is related to the card game Set.

CROSSREFS

Adjacent-numbered pages:
BP1133 BP1134 BP1135 BP1136 BP1137  *  BP1139 BP1140 BP1141 BP1142 BP1143

KEYWORD

nice, precise, allsorted, notso, preciseworld

CONCEPT all (info | search),
number (info | search),
same (info | search),
two (info | search),
three (info | search)

AUTHOR

William B Holland

BP1137 Constructible Polygon vs. Non-constructible Polygon
(edit; present; nest [left/right]; search; history)
REFERENCE

https://en.wikipedia.org/wiki/Straightedge_and_compass_construction


https://en.wikipedia.org/wiki/Constructible_polygon

CROSSREFS

Adjacent-numbered pages:
BP1132 BP1133 BP1134 BP1135 BP1136  *  BP1138 BP1139 BP1140 BP1141 BP1142

KEYWORD

stub, precise, math, hardsort, proofsrequired, preciseworld

AUTHOR

Jago Collins

BP1136 The removal of any one loop disentangles the whole arrangement vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Left-hand examples are called "Brunnian links".

REFERENCE

https://en.wikipedia.org/wiki/Brunnian_link

CROSSREFS

Adjacent-numbered pages:
BP1131 BP1132 BP1133 BP1134 BP1135  *  BP1137 BP1138 BP1139 BP1140 BP1141

KEYWORD

precise, hardsort

CONCEPT knot (info | search)

WORLD

link [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP1135 Each component can be assigned its own layer in the arrangement vs. there is no equivalent way of dividing the arrangement into layers.
(edit; present; nest [left/right]; search; history)
COMMENTS

Put differently, if the examples are imagined to be arrangements of rigid sticks/hoops/etc resting on a flat surface, positive examples include sticks/hoops/etc that could be picked up without disturbing the other objects.

CROSSREFS

Adjacent-numbered pages:
BP1130 BP1131 BP1132 BP1133 BP1134  *  BP1136 BP1137 BP1138 BP1139 BP1140

KEYWORD

precise

AUTHOR

Leo Crabbe

BP1134 Bongard Problem with solution relating to concept: impossible vs. Bongard Problem unrelated to this concept.
BP252
BP821
BP868
BP1133
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1129 BP1130 BP1131 BP1132 BP1133  *  BP1135 BP1136 BP1137 BP1138 BP1139

KEYWORD

meta (see left/right), links, metaconcept

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

WORLD

bp [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP1133 Impossible to realize in 3D space vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Each unit is to be imagined as a flat rigid rod/hoop/triangle/etc.

REFERENCE

https://en.wikipedia.org/wiki/Borromean_rings

CROSSREFS

Similar to BP252.

Adjacent-numbered pages:
BP1128 BP1129 BP1130 BP1131 BP1132  *  BP1134 BP1135 BP1136 BP1137 BP1138

KEYWORD

precise

CONCEPT rigidity (info | search),
impossible (info | search)

AUTHOR

Leo Crabbe

BP1132 Circle that passes through points is contained within bounding box vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP1127 BP1128 BP1129 BP1130 BP1131  *  BP1133 BP1134 BP1135 BP1136 BP1137

KEYWORD

precise, allsorted, boundingbox, hardsort, preciseworld, absoluteposition

CONCEPT circle (info | search),
imagined_entity (info | search)

WORLD

three_points [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP1131 One shape can be totally obscured by the other vs. neither shape can be obscured.
(edit; present; nest [left/right]; search; history)
COMMENTS

Rotation of shapes is not required for any left-hand panels, but it should not change any example's sorting if it is considered.

CROSSREFS

Adjacent-numbered pages:
BP1126 BP1127 BP1128 BP1129 BP1130  *  BP1132 BP1133 BP1134 BP1135 BP1136

KEYWORD

nice, precise, allsorted, pixelperfect, unorderedpair

CONCEPT overlap (info | search)

WORLD

2_shapes [smaller | same | bigger]

AUTHOR

Leo Crabbe

BP1130 Start with a rectangle subdivided further into rectangles and shrink the vertical lines into points vs. the shape does not result from this process.
?
(edit; present; nest [left/right]; search; history)
COMMENTS

The description in terms of rectangles was noted by Sridhar Ramesh when he solved this.


All examples in this Bongard Problem feature arced line segments connected at endpoints; these segments do not cross across one another and they are nowhere vertical; they never double back over themselves in the horizontal direction.

Furthermore, in each example, there is a single leftmost point and a single rightmost point, and every segment is part of a path bridging between them. So, there is a topmost total path of segments and bottommost total chain of segments.


Any picture on the left can be turned into a subdivided rectangle by the process of expanding points into vertical lines.


Here is another answer:

"Right examples: some junction point has a single line coming out from either the left or right side."


If there is some junction point with only a single line coming out from a particular side, the point cannot be expanded into a vertical segment with two horizontal segments bookending its top and bottom (as it would be if this were a subdivision of a rectangle).


And this was the original, more convoluted idea of the author:

"Start with a string along the top path. Sweep it down, region-by-region, until it lies along the bottom path. The string may only enter a region when it fully covers that region's top edge and likewise it must exit by fully covering the bottom edge. Only in left images can this process be done so that no segment of the string ever hesitates."

Quite convoluted when spelled out in detail, but not terribly complicated to imagine visually. (See the keyword unwordable.)


The string-sweeping answer is the same as the rectangle answer because a rectangle represents the animation of a string throughout an interval of time. (A horizontal cross-section of the rectangle represents the string, and the vertical position is time.) Distorting the rectangle into a new shape is the same as animating a string sweeping across that new shape.

In particular, shrinking vertical lines of a rectangle into points means just those points of the string stay still as the string sweeps down.

The principle that horizontal lines subdividing the original rectangle become the segments in the final picture corresponds to the idea that the string must enter or exit a single region all at once.

CROSSREFS

BP1129 started as an incorrect solution for this Bongard Problem. Anything fitting right in BP1130 fits right in BP1129.

Adjacent-numbered pages:
BP1125 BP1126 BP1127 BP1128 BP1129  *  BP1131 BP1132 BP1133 BP1134 BP1135

KEYWORD

hard, unwordable, solved

CONCEPT topological_transformation (info | search),
imagined_motion (info | search)

WORLD

[smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

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