Search: author:Aaron David Fairbanks
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BP1244 |
| Bongard Problem with solution relating to concept: local global vs. Bongard Problem unrelated to this concept. |
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BP1243 |
| Bongard Problems on the OEBP with certain examples that have not yet been proved to fit where they are currently sorted vs. Bongard Problems in which all included examples have been proved to fit where they are. |
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COMMENTS
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Bongard Problems sorted left have the keyword "missingproofs" on the OEBP.
This is an administrative keyword to help us keep track of what Bongard Problems we still need to check for correctness.
The description should indicate which examples are still in need of checking. Once proofs are found, the keyword "missingproofs" can be removed.
The keyword noproofs is similar. The difference is whether we want/expect to find proofs. |
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CROSSREFS
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Bongard Problems tagged "missingproofs" should necessarily be hardsort.
Adjacent-numbered pages:
BP1238 BP1239 BP1240 BP1241 BP1242  *  BP1244 BP1245 BP1246 BP1247 BP1248
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KEYWORD
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meta (see left/right), links, keyword, instruction, time
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AUTHOR
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Aaron David Fairbanks
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BP1242 |
| Meta Bongard Problems of the form "would sort [specific example] left vs. would sort [specific example] right" vs. other meta Bongard Problems. |
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BP1236 |
| Bongard Problem with solution relating to concept: connected component vs. Bongard Problem unrelated to this concept. |
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BP1235 |
| Bongard Problem with solution relating to concept: distingushing between distinct curves that cross vs. Bongard Problem unrelated to this concept. |
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BP1234 |
| Bongard Problem with solution relating to concept: diagonal vs. Bongard Problem unrelated to this concept. |
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BP1231 |
| Bongard Problems where some information is left out from examples and they are only sorted on the side they seem to fit vs. other Bongard Problems. |
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COMMENTS
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Bongard Problems sorted left have the keyword "seemslike" on the OEBP.
In a "seemslike" Bongard Problem, some relevant information is left out by the way objects are displayed. Solutions to "seemslike" BPs sound like "Seems like a ___ based on the information available vs. seems like a ___ based on the information available". The two sides are typically negations of one another (keyword notso).
Since there is information missing, examples can only be sorted assuming they appear in a way that hints psychologically at what they actually are (see help). |
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CROSSREFS
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Although the rule sorting the underlying objects may be precise, the rule sorting the projections of the objects with lost information is fuzzy and subjective.
See also left-couldbe (and right-couldbe), concerning situations in which the information given may be enough to determine when examples fail to satisfy a rule but is never enough to determine when they do satisfy the rule ("could be ___ vs. clearly is not"). In contrast to "seemslike" Bongard Problems, left-couldbe Bongard Problems can be precise; both evidence of fitting right and absence of evidence of fitting right is clear-cut, so no psychologically helpful hints (help) are needed.
Adjacent-numbered pages:
BP1226 BP1227 BP1228 BP1229 BP1230  *  BP1232 BP1233 BP1234 BP1235 BP1236
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KEYWORD
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meta (see left/right), links, keyword
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AUTHOR
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Aaron David Fairbanks
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BP1225 |
| Meta Bongard Problems of the form "solution depends on other information than [property] vs. solution only depends on [property]" vs. other meta Bongard Problems. |
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BP1205 |
| Bongard Problems in which slight deformations (but perhaps across a large area) of examples can switch their sorting vs. Bongard Problems in which examples deformed slightly enough remain sorted the same way. |
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COMMENTS
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Left examples have the keyword "deformunstable" on the OEBP.
Right examples have the keyword "deformstable" on the OEBP.
For the purposes of this Bongard Problem, a "slight deformation" is a way of dragging the details of an image around which is relatively uniform in any local area and moves each point at most an arbitrarily small distance. More precise definitions could be made using mathematics.
In a "deformstable" Bongard Problem, no slight deformation should outright flip an example's sorting. It is allowed for a slight deformation to make an example sorted slightly more ambiguously. |
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CROSSREFS
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See unstable vs. stable for changing content within a small area.
Adjacent-numbered pages:
BP1200 BP1201 BP1202 BP1203 BP1204  *  BP1206 BP1207 BP1208 BP1209 BP1210
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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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BP1204 |
| Meta Bongard Problems of the form "arbitrarily small [transformation] applied to some examples switch their sorting vs. the sorting of each example is invariant under sufficiently small applications of [transformation]" vs. other meta Bongard Problems. |
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COMMENTS
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Left-sorted Bongard Problems have the keyword "stability" on the OEBP.
For any "stability" Bongard Problem there could usually be made a corresponding invariance Bongard Problem ("[transformation] applied to some examples switch their sorting vs. sorting is invariant under [transformation]").
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". |
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CROSSREFS
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Adjacent-numbered pages:
BP1199 BP1200 BP1201 BP1202 BP1203  *  BP1205 BP1206 BP1207 BP1208 BP1209
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KEYWORD
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meta (see left/right), links, keyword
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AUTHOR
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Aaron David Fairbanks
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