Search: all:new
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| BP568 |
| Solution idea would not be chosen as the simplest solution vs. there is not a simpler solution that always comes along with it. |
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COMMENTS
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Left examples have the keyword "overriddensolution" on the OEBP.
An "overriddensolution" is solution idea for a Bongard Problem that would not be chosen by the solver because there is a simpler solution that always comes with it.
An overridden solution occurs when the Bongard Problem's examples on both sides all share some constraint, and furthermore within this constrained class of examples, the intended rule is equivalent to a simpler rule that can be understood without noticing the constraint. See e.g. BP1146. The solver of the Bongard Problem will get the solution before noticing the constraint.
There is a more extreme class of overridden solution: not only is the solution possible to overlook in favor of something simpler, but even with scrutiny it will likely never be recognized. See e.g. BP570. This happens when intended left and right side rules are not direct negations of one another, but one or both of these rules is not "narrow"-- it can only be communicated in a Bongard Problem by its opposite being on the other side.
TO DO: Should this more extreme version have its own keyword? - Aaron David Fairbanks, Nov 23 2021
The keyword left-narrow (resp. right-narrow) is for Bongard Problems whose left-side (resp. right-side) rule can be recognized alone without examples on the other side.
The keyword notso is for Bongard Problems whose two sides are direct negations of one another. |
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CROSSREFS
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See keyword impossible for solution ideas that cannot even apply to any set of examples, much less be communicated as the best solution.
Adjacent-numbered pages:
BP563 BP564 BP565 BP566 BP567 * BP569 BP570 BP571 BP572 BP573
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EXAMPLE
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BP570 "Shape outlines that aren't triangles vs. black shapes that aren't squares" was created as an example of this. |
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KEYWORD
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meta (see left/right), links, keyword
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WORLD
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bp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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| BP567 |
| Visual Bongard Problems that would sort a blank panel on the left vs. visual Bongard Problems that would sort a blank panel on the right. |
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| BP566 |
| Meta Bongard Problems of the form "[transformation] applied to some examples switch their sorting vs. sorting is invariant under [transformation]" vs. other meta Bongard Problems. |
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COMMENTS
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Left-sorted Bongard Problems have the keyword "invariance" on the OEBP.
Bongard Problems labelled "invariance" are usually (but not always) about transformations that can be undone by other transformations of the same class. (The technical term for this kind of transformation is an "isomorphism".)
When the transformations used in a "invariance" Bongard Problem vary continuously, there could usually be made a corresponding stability Bongard Problem. Stability Bongard Problems are like "invariance" Bongard Problems but for arbitrarily small applications of [transformation] affecting examples' sorting.
Potentially, stability Bongard Problems could be considered "invariance" Bongard Problems. On one hand, they are different, since checking whether arbitrarily small transformations switch an example's sorting is different from checking whether a particular transformation switches an example's sorting; the former is infinitely many conditions. On the other hand, there is actually only finitely much detail in any of the examples, and in practice a stability Bongard Problem generally just amounts to "a small application of [transformation] switches an example's sorting vs. not".
(The keyword gap is another example of a Bongard Problem currently labelled with "invariance" that arguably does not technically fit.)
Also, dependence Bongard Problems could be considered "invariance" Bongard Problems, where the relevant kind of transformation is swapping the example out for any other example that shares the relevant property. |
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CROSSREFS
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"Invariance" Bongard Problems are notso Bongard Problems.
"Invariance" Bongard Problems are often keywords (keyword keyword) on the OEBP.
See keyword problemkiller, which is about transformations making all sorted examples unsortable.
Adjacent-numbered pages:
BP561 BP562 BP563 BP564 BP565 * BP567 BP568 BP569 BP570 BP571
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KEYWORD
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meta (see left/right), links, keyword, metameta
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WORLD
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linksbp [smaller | same | bigger]
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AUTHOR
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Aaron David Fairbanks
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| BP565 |
| Bongard Problems that are hard for humans to solve but easier for computers to solve vs. Bongard Problems that are hard for computers to solve but easier for humans to solve. |
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| BP564 |
| Discrete points intersecting boundary of convex hull vs. connected segment intersecting boundary of convex hull |
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COMMENTS
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If a "string" is wound tightly around the shape, does one of its segments lie directly on the shape?
All examples in this Problem are connected line segments or curves.
We are taking lines here to be infinitely thin, so that if the boundary of the convex hull intersects the endpoint of a line exactly it is understood that they meet at 1 point. |
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CROSSREFS
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Adjacent-numbered pages:
BP559 BP560 BP561 BP562 BP563 * BP565 BP566 BP567 BP568 BP569
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EXAMPLE
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Imagine wrapping a string around the pointed star. This string would take the shape of the boundary of the star's convex hull (a regular pentagon), and would only touch the star at the end of each of its 5 individual tips, therefore the star belongs on the left. |
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KEYWORD
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hard, nice, allsorted, solved, perfect
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AUTHOR
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Leo Crabbe
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| BP563 |
| Bongard Problems such that there is a way of making an infinite list of all relevant possible left-sorted examples vs. Bongard Problems where there is no such way of listing all left-sorted examples. |
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COMMENTS
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Left-sorted Problems have the keyword "left-listable" on the OEBP.
All the possible left examples for the BPs on the left side of this problem could be listed in one infinite sequence. Right examples here are Problems for which no such sequence can exist.
This depends on deciding what images should be considered "the same thing", which is subjective and context-dependent.
All examples in this Bongard Problem have an infinite left side (they do not have the keyword left-finite).
The mathematical term for a set that can be organized into an infinite list is a "countably infinite" set, as opposed to an "uncountably infinite" set.
Another related idea is a "recursively enumerable" a.k.a. "semi-decidable" set, which is a set that a computer program could list the members of.
The keyword "left-listable" is meant to be for the more general idea of a countable set, which does not have to do with computer algorithms.
Note that this is not just BP940 (right-listable) flipped.
It seems in practice, Bongard Problems that are left-listable are usually also right-listable because the whole class of relevant examples is listable. A keyword for just plain "listable" may be more useful. Or instead keywords for left- versus right- semidecidability, in the sense of computing. - Aaron David Fairbanks, Jan 10 2023 |
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REFERENCE
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https://en.wikipedia.org/wiki/Countable_set |
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CROSSREFS
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See left-finite, which distinguishes between a finite left side and infinite left side.
"Left-listable" BPs are typically precise.
Adjacent-numbered pages:
BP558 BP559 BP560 BP561 BP562 * BP564 BP565 BP566 BP567 BP568
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KEYWORD
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math, meta (see left/right), links, keyword
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WORLD
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bp_infinite_left_examples [smaller | same | bigger]
zoom in right (left_uncountable_bp)
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AUTHOR
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Leo Crabbe
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| BP562 |
| There exists a closed trail that hits each vertex exactly once vs. not so. |
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| BP561 |
| Meta Bongard Problems fitting in their own world vs. other meta Bongard Problems. |
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