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BP855 Object below ambiguously sorted (not clearly left or right) by Bongard Problem image above vs. object below clearly sorted by Bongard Problem image above.
(edit; present; nest [left/right]; search; history)
COMMENTS

Represented are Bongard Problems and an extra object to sort, a.k.a. the Bongard's Dozen format.

A variety of kinds of ambiguities showcased as left examples.

CROSSREFS

Adjacent-numbered pages:
BP850 BP851 BP852 BP853 BP854  *  BP856 BP857 BP858 BP859 BP860

KEYWORD

nice, creativeexamples, structure, rules

WORLD

bdimage_shapes_extra_below [smaller | same | bigger]
zoom in right (bdimage_shapes_extra_below_clear_sort)

AUTHOR

Aaron David Fairbanks

BP854 Nothing vs. nothing.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP849 BP850 BP851 BP852 BP853  *  BP855 BP856 BP857 BP858 BP859

KEYWORD

left-finite, right-finite, left-full, right-full, finished, experimental, funny

WORLD

nothing [same | bigger]
zoom in left (nothing) | zoom in right (nothing)

AUTHOR

Aaron David Fairbanks

BP853 Prime knot vs. composite knot.
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP848 BP849 BP850 BP851 BP852  *  BP854 BP855 BP856 BP857 BP858

KEYWORD

math, hardsort

CONCEPT knot (info | search)

WORLD

knot [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP852 Object shown below is the "limit" of the sequence above (end result after "infinite time") versus not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

The conceptual limit of the sequence may not be the limit of the points in the image. For example in a sequence of halvings the limit value is never reached, so the bottom would never change color and thus its limit would not would not either.


Sequences progress from left to right (and there is not usually a way to intuitively extend the sequence in the other direction).

CROSSREFS

Adjacent-numbered pages:
BP847 BP848 BP849 BP850 BP851  *  BP853 BP854 BP855 BP856 BP857

KEYWORD

notso, creativeexamples, perfect, infinitedetail, assumesfamiliarity, structure, contributepairs, rules

AUTHOR

Aaron David Fairbanks

BP851 Figure with points (small white circles) can be smoothly deformed within the 2D plane without passing through itself so that all points touch to make the other figure vs. not so (movement out of the plane required).
(edit; present; nest [left/right]; search; history)
CROSSREFS

All examples here fit left in BP369, a version where the figure is allowed to pass through itself while being deformed.

Adjacent-numbered pages:
BP846 BP847 BP848 BP849 BP850  *  BP852 BP853 BP854 BP855 BP856

KEYWORD

math, traditional

CONCEPT topological_transformation (info | search)

WORLD

figure_made_of_curves_and_quotient_by_hollow_dots [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP850 Shape can be maneuvered around the corner vs. not so.
(edit; present; nest [left/right]; search; history)
REFERENCE

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

CROSSREFS

Adjacent-numbered pages:
BP845 BP846 BP847 BP848 BP849  *  BP851 BP852 BP853 BP854 BP855

KEYWORD

nice, precise, physics, creativeexamples, proofsrequired, left-narrow, right-narrow, dithering

CONCEPT rotation_required (info | search),
imagined_motion (info | search),
physically_fitting (info | search)

AUTHOR

Leo Crabbe

BP849 Loop is time-symmetrical (loop is like ABCBABCBA... instead of like ABCABCABC...) up to rotation of object vs. not so (neither up to rotation nor reflection).
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP844 BP845 BP846 BP847 BP848  *  BP850 BP851 BP852 BP853 BP854

KEYWORD

hard, convoluted, solved, rules

WORLD

constant_change_seq_loop_right [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP848 Lower bound object shown vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP843 BP844 BP845 BP846 BP847  *  BP849 BP850 BP851 BP852 BP853

KEYWORD

creativeexamples, structure, contributepairs, rules

WORLD

constant_change_seq_increase_right_low_bound_obj [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP847 Evokes the idea of symmetry vs. not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

Or, perhaps more concretely, "Depiction of object with some symmetry (invariance under transformation) vs. depiction of object with no simple symmetries."

CROSSREFS

Adjacent-numbered pages:
BP842 BP843 BP844 BP845 BP846  *  BP848 BP849 BP850 BP851 BP852

KEYWORD

nice, fuzzy, abstract, math, concept, collective, dithering

CONCEPT symmetry (info | search)

AUTHOR

Leo Crabbe

BP846 A quantity increases by fixed constant amount each step vs. not so.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP841 BP842 BP843 BP844 BP845  *  BP847 BP848 BP849 BP850 BP851

KEYWORD

creativeexamples, structure, contributepairs, rules

WORLD

quantity_change_seq_increase_right [smaller | same | bigger]
zoom in right (constant_change_seq_increase_right)

AUTHOR

Aaron David Fairbanks

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