The On-Line Encyclopedia of Bongard Problems

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BP859

Black pixel vs. white pixel.

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

	COMMENTS	`This is the "smallest" possible valid Bongard Problem on black and white bitmap images (up to switching sides).`
	CROSSREFS	`Adjacent-numbered pages: BP854 BP855 BP856 BP857 BP858 * BP860 BP861 BP862 BP863 BP864`
	KEYWORD	`minimal, blackwhite, perfect, pixelperfect, experimental, funny, unstableworld`
	WORLD	`black_or_white_pixel [smaller \| same \| bigger] zoom in left (black_pixel) \| zoom in right (white_pixel)`
	AUTHOR	`Aaron David Fairbanks`

BP858

Bongard Problems whose examples might be used to teach the rule of the solution vs. other Bongard Problems.

	BP100	BP844	BP862	BP968	BP981	BP1049
	BP1080	BP1083	BP1090	BP1153

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

	COMMENTS	`Left examples have the keyword "teach" on the OEBP.` `Sometimes instead of gauging somebody's ability to guess the pattern, a Bongard Problem might teach the pattern.` `Consider a Bongard Problem whose left examples are images of a specific person's face; after seeing that Problem, one might be able to recognize that person.` `A "teach" Bongard Problem (with a huge number of examples) could be taken as a training set for machine learning.` `"Teach" BPs tend to be convoluted, arbitrary, cultural-knowledge-based (keyword culture), or they illustrate some insight that might be overlooked, perhaps mathematical (keyword math).`
	CROSSREFS	`Adjacent-numbered pages: BP853 BP854 BP855 BP856 BP857 * BP859 BP860 BP861 BP862 BP863`
	KEYWORD	`meta (see left/right), links, keyword`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Aaron David Fairbanks`

BP857

Bongard Problems with solution relating to concept: collision of objects vs. Bongard Problems unrelated to this concept.

BP358

BP856

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

	CROSSREFS	`Adjacent-numbered pages: BP852 BP853 BP854 BP855 BP856 * BP858 BP859 BP860 BP861 BP862`
	KEYWORD	`meta (see left/right), links, metaconcept`
	CONCEPT	`This MBP is about BPs that feature concept: "collision"`
	WORLD	`bp [smaller \| same \| bigger]`
	AUTHOR	`Leo Crabbe`

BP856

Compound shape would hit the dot if rotated vs. not so.

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

	CROSSREFS	`Adjacent-numbered pages: BP851 BP852 BP853 BP854 BP855 * BP857 BP858 BP859 BP860 BP861`
	KEYWORD	`nice, precise, allsorted, left-narrow, preciseworld`
	CONCEPT	`imagined_motion (info \| search),` `collision (info \| search)`
	AUTHOR	`Leo Crabbe`

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`

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