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BP954 |
| Solution could appear in a Bongard Problem that has itself as a panel vs. not so. |
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COMMENTS
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Loosely speaking, examples on the left are "Bongard Problems that can be self-similar". However, Bongard Problems with images of themselves deeply nested in boxes or rotated/flipped are not here considered "self-similar"; the Bongard Problem must use itself, as-is (allowing downward scaling and allowing infinite detail, ignoring pixelation--see keyword infinitedetail), as a panel.
Bongard Problems fitting left evidently come in three categories: 1) the Bongard Problem could only appear on its own left side, 2) the Bongard Problem could appear on its own right side, or 3) the Bongard Problem could appear on its own left or the right side. See BP987.
Meta Bongard Problems appearing in BP793 that are presentationinvariant necessarily fit left here.
All examples here are in the conventional format, i.e. white background, black vertical dividing line, and examples in boxes on either side. (A more general version of this Bongard Problem might allow many formats of Bongard Problems, sorting an image left if a self-similar version is possible having the same solution and format. This more general version would no longer be tagged presentationinvariant, since sorting would not only depend on solution, but also format.)
It would hint at the solution (keyword help) to only include images of Bongard Problems that, as it stands, are already clearly categorized on one side by themselves. (That is, images of Bongard Problems that belong on one of the two sides of BP793.) It is tricky to come up with images that are categorized by themselves as it stands but that could NOT be recursively included within themselves. EX7967, EX7999, EX7995, and EX6574 are some examples. |
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CROSSREFS
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See BP987 which narrows down the left-hand side of this BP further based on whether or not the BP could contain itself as a panel on both sides.
Adjacent-numbered pages:
BP949 BP950 BP951 BP952 BP953  *  BP955 BP956 BP957 BP958 BP959
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KEYWORD
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hard, abstract, challenge, meta (see left/right), miniproblems, infinitedetail, presentationinvariant, visualimagination
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CONCEPT
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fractal (info | search), recursion (info | search), self-reference (info | search)
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AUTHOR
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Leo Crabbe
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BP955 |
| Images of Bongard Problems that sort an image of their left side on their left and an image of their right side on their left vs. images of Bongard Problems that sort an image of their left side on their right and an image of their right side on their right. |
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CROSSREFS
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See also BP957 for the other two evident possibilities.
Adjacent-numbered pages:
BP950 BP951 BP952 BP953 BP954  *  BP956 BP957 BP958 BP959 BP960
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KEYWORD
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abstract, dual, handed, leftright, solved, meta (see left/right), miniproblems, creativeexamples, assumesfamiliarity, structure, experimental
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CONCEPT
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self-reference (info | search)
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WORLD
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oblong_boxes_bpimage_sorts_both_sides_skewed [smaller | same | bigger] zoom in left (oblong_boxes_bpimage_sorts_both_sides_left) | zoom in right (oblong_boxes_bpimage_sorts_both_sides_right)
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AUTHOR
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Leo Crabbe
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BP957 |
| Images of Bongard Problems that sort an image of their left side on their left and an image of their right side on their right vs. images of Bongard Problems that sort an image of their left side on their right and an image of their right side on their left. |
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BP958 |
| Visual Bongard Problems about examples being read with infinite detail vs. other visual Bongard Problems. |
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COMMENTS
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Left examples have the keyword "infinitedetail" on the OEBP.
Image files on the OEBP do not really have infinite detail. For a panel to be intuitively read as having infinite detail, there usually needs to be some apparent self-similarity, or perhaps a sequence of objects following an easy to read pattern getting smaller and smaller with increasing pixelation.
Usually in "infinitedetail" Bongard Problems, not only is it a puzzle to figure out the solution, but it is another puzzle to find self-similarities and understand the intended infinite detail in each example. |
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CROSSREFS
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BPs tagged with the keyword "infinitedetail" usually feature pixelated images that give the closest approximation of the intended infinite structure up to pixelation. This means they should be tagged with the keyword perfect, but should not be tagged with the keyword pixelperfect.
Just because a Bongard Problem has "infinitedetail" does not necessarily make it infodense. Some fractal images might be encoded by a small amount of information (just the information about which places within itself it includes smaller copies of itself) and may be recognized quickly.
Adjacent-numbered pages:
BP953 BP954 BP955 BP956 BP957  *  BP959 BP960 BP961 BP962 BP963
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KEYWORD
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notso, meta (see left/right), links, keyword, wellfounded
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WORLD
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visualbp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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BP959 |
| This image of this Bongard Problem vs. empty image. |
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CROSSREFS
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See BP953, BP902.
Adjacent-numbered pages:
BP954 BP955 BP956 BP957 BP958  *  BP960 BP961 BP962 BP963 BP964
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KEYWORD
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meta (see left/right), miniproblems, left-finite, right-finite, left-full, right-full, right-null, perfect, infinitedetail, finished, experimental, funny
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CONCEPT
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fractal (info | search), recursion (info | search), self-reference (info | search)
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WORLD
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zoom in left | zoom in right (blank_image)
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AUTHOR
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Aaron David Fairbanks, Leo Crabbe
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BP960 |
| Bongard Problems that require the solver to create their own new picture in the process of solving vs. other Bongard Problems. |
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COMMENTS
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Left-sorted Bongard Problems have the keyword "visualimagination" on the OEBP.
Many things might be called "creating a picture". For example, drawing a path in a maze. However, use this keyword to indicate a Bongard Problem requires the solver to create something totally new "on a separate piece of paper" (whether mentally or physically), beyond just annotating the existing picture. |
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CROSSREFS
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A "visualimagination" BP will likely be hardsort.
"Visualimagination" BPs are abstract.
"Visualimagination" BPs are are often about deciding whether some potential thing exists. (See BP634 for Bongard Problems featuring the concept ofexistence.) One can demonstrate it exists by constructing it.
Adjacent-numbered pages:
BP955 BP956 BP957 BP958 BP959  *  BP961 BP962 BP963 BP964 BP965
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KEYWORD
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notso, meta (see left/right), links, keyword
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AUTHOR
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Aaron David Fairbanks
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BP963 |
| Bongard Problems in which small changes to examples can switch their sorting vs. Bongard Problems in which examples changed slightly enough remain sorted the same way. |
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COMMENTS
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Left examples have the keyword "unstable" on the OEBP.
Right examples have the keyword "stable" on the OEBP.
For the purposes of this Bongard Problem, "small change" means adding to or removing from an arbitrarily small portion of the image. Other kinds of small change could be explored, such as making changes in multiple small places, translating, rotating, scaling, or deforming the whole image slightly (see also keywords deformunstable vs. deformstable), or even context-dependent small changes (e.g., changing the shadings slightly in BP196, or making small 3d changes to the represented 3d objects in BP333), but they are not considered here.
In a "stable" Bongard Problem, no small change should outright flip an example's sorting. It is allowed for a small change to make an example sorted slightly more ambiguously.
Small changes that make an example no longer even fit in with the format of a Bongard Problem are not considered. (Otherwise, far fewer Bongard Problems would be called "stable".)
For whether small changes make an example no longer fit in with the Bongard Problem, see unstableworld vs. stableworld.
If a Bongard Problem is shown with imperfect hand drawings (keyword ignoreimperfections), it is fine to apply the keyword "unstable" ignoring this. For instance, a hand-drawn version of BP344 would still be tagged "unstable", even though it would show examples wrong by small amounts.
(Note: a BP would only be tagged "ignoreimperfections" in the first place if the underlying idea were such that several small changes could make an example switch sides, no longer fit in with the format of the Bongard Problem, or otherwise be ambiguously sorted.) |
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CROSSREFS
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Stable Bongard Problems are generally perfect and pixelperfect.
Gap (technically) implies stable. (However, in practice it has seemed unnatural to tag BPs "stable" when ALL small changes render certain examples unsortable, as is sometimes the case in "gap" BPs.)
Unstable Bongard Problems are often precise.
Stable Bongard Problems tend to either be fuzzy or otherwise either have a gap or be not allsorted.
See BP1144, which is about all small changes making all examples unsortable rather than some small change making some example switch sides.
See BP1140, which is about any (perhaps large) additions of detail instead of small changes.
Adjacent-numbered pages:
BP958 BP959 BP960 BP961 BP962  *  BP964 BP965 BP966 BP967 BP968
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EXAMPLE
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BP1 is unstable because it's possible to change nothing slightly by adding a pixel to end up with something. |
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KEYWORD
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meta (see left/right), links, keyword, stability
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AUTHOR
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Aaron David Fairbanks
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BP964 |
| Bongard Problems such that making repeated small changes can switch an example's sorting vs. Bongard Problems in which the two sides are so different that it is impossible to cross the gap by making successive small changes to examples while staying within the class of examples sorted by the Bongard Problem (there is no middle-ground between the sides; there is no obvious choice of shared ambient context both sides are part of). |
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COMMENTS
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Right-sorted BPs have the keyword "gap" on the OEBP.
A Bongard Problem with a gap showcases two completely separate classes of objects.
For example, the Bongard Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there is a space of partially filled black-and-white images between them, or any number of other ambient contexts.
Bongard Problems about comparing quantities on a spectrum should not usually be considered "gap" BPs. (Discrete spectra perhaps.) A spectrum establishes a shared context, with examples on both sides of the BP landing somewhere on it. (However, if it is reasonable to imagine getting the solution without noticing a spectrum in between, it could be a gap, since the ambient context is unclear.)
Bongard Problems with gaps may seem particularly arbitrary when the two classes of objects are particularly unrelated. |
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CROSSREFS
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If a Bongard Problem has a "gap" it is likely precise: it will likely be clear on which side any potential example fits.
"Gap" implies stable. (This technically includes cases in which ALL small changes make certain examples no longer fit in with the Bongard Problem, as is sometimes the case in "gap" BPs. See also BP1144.)
See also preciseworld. "Gap" Bongard Problems would be tagged "preciseworld" when the two classes of objects are each clear; it is then apparent that there is no larger shared context and that no other types of objects besides the two types would be sorted by the Bongard Problem.
See BP1140, which is about any (perhaps large) additions instead of repeated small changes.
Adjacent-numbered pages:
BP959 BP960 BP961 BP962 BP963  *  BP965 BP966 BP967 BP968 BP969
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KEYWORD
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unwordable, meta (see left/right), links, keyword, sideless, invariance
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AUTHOR
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Aaron David Fairbanks
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