Search: all:new
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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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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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BP561 |
| Meta Bongard Problems fitting in their own world vs. other meta Bongard Problems. |
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BP556 |
| Visual Bongard Problems such that if black and white are switched some examples switch sides vs. visual Bongard Problems that would always sort two switched versions the same way. |
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BP554 |
| Size-dependent Bongard Problems vs. size-independent visual Bongard Problems. |
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BP553 |
| Rotation-dependent Bongard Problems vs. rotation-independent visual Bongard Problems. |
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BP552 |
| Orientation-dependent Bongard Problems vs. orientation-independent visual Bongard Problems. |
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COMMENTS
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Left examples have the keyword "handed" on the OEBP.
If mirroring any example along the any axis can change its sorting the BP is "handed."
Note that BPs about comparing orientation between multiple things in one example fit on the right side. |
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CROSSREFS
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See BP871 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.
The keyword leftright is specifically about flipping over the vertical axis, while the keyword updown is specifically about flipping over the horizontal axis.
Bongard Problems tagged rotate are usually "handed", since any rotation can be created by two reflections. Not necessarily, however, since the reflected step in between might not be sorted on either side by the Bongard Problem.
Adjacent-numbered pages:
BP547 BP548 BP549 BP550 BP551  *  BP553 BP554 BP555 BP556 BP557
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KEYWORD
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meta (see left/right), links, keyword, invariance, wellfounded
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WORLD
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visualbp [smaller | same | bigger] zoom in left (handed_visualbp)
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AUTHOR
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Aaron David Fairbanks
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BP550 |
| Experimental Bongard Problems vs. traditional-style Bongard Problems. |
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COMMENTS
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Left examples have the keyword "experimental" on the OEBP.
Right examples have the keyword "traditional" on the OEBP.
Experimental BPs push the boundaries of what makes Bongard Problems Bongard Problems.
Traditional BPs show some simple property of black and white pictures. The OEBP is a place with many wild and absurd Bongard Problems, so it is useful to have an easy way to just find the regular old Bongard Problems. |
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CROSSREFS
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Adjacent-numbered pages:
BP545 BP546 BP547 BP548 BP549  *  BP551 BP552 BP553 BP554 BP555
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KEYWORD
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subjective, meta (see left/right), links, keyword, left-it
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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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