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BP999 |
| The collection of collections obeys the same rule as the individual collections vs. it does not. |
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COMMENTS
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Rhetorical question: Where would the collection of left examples of this Bongard Problem be sorted by this Bongard Problem? (The question is whether these examples considered together satisfy the pattern that all the parts do, namely that the whole satisfies the pattern that all the parts do.)
See BP793 and BP1004 for similar paradoxes. |
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CROSSREFS
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See BP1005 for the version about only numerical properties; examples in that BP would be sorted the same way here that they are there.
See BP1003 for a similar idea. Rather than the collection of collections imitating the individual collections, BP1003 is about the total combined collection imitating the individual collections. A picture showing (for example) an odd number of even-numbered groups would be sorted differently by these two BPs.
Also see BP1004, which is likewise about the whole satisfying the same rule as its parts, but there the parts don't themselves have to be collections; there the parts are just plain individual objects. The panels in BP999 (this BP) should be sorted the same way in BP1004.
See BP1002, which is about only visual self-similarity instead of more general conceptual "self-similarity".
Adjacent-numbered pages:
BP994 BP995 BP996 BP997 BP998  *  BP1000 BP1001 BP1002 BP1003 BP1004
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KEYWORD
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nice, abstract, creativeexamples, left-narrow, rules, miniworlds
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CONCEPT
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recursion (info | search), self-reference (info | search)
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WORLD
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[smaller | same | bigger] zoom in left | zoom in right
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AUTHOR
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Aaron David Fairbanks
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BP998 |
| X "X _" vs. all are "X _"; X Y. |
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COMMENTS
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Right:
All are "all but one are ___"; all but one are black.
All are "every other is ___"; every other is solid polygons.
All are "gradually becoming ___"; gradually becoming thickly outlined.
Left:
All but one are "all but one are ___".
Every other is "every other is ___".
Gradually becoming "gradually becoming ___".
Here is another way of putting it:
Call it "meta" when the whole imitates its parts, and call it "doubly-meta" when the whole imitates its parts with respect to the way it imitates its parts. Left are doubly-meta, while right are just meta.
Here is a more belabored way of putting it:
Call something like "is star-shaped" a "rule". An object can satisfy a rule.
Call something like "all but one are ___" a "rule-parametrized rule". A collection of objects can satisfy a rule-parametrized rule with respect to a particular rule.
On the right: every collection fits the same rule-parametrized rule (with respect to various rules); furthermore the collection of collections fits that same rule-parametrized rule (with respect to some unrelated rule that collections can satisfy).
On the left: The collection of collections fits a rule-parametrized rule with respect to the rule of fitting that rule-parametrized rule (with respect to various rules).
Previously, an unintended solution to this BP was "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because the rule-parametrized rule (see explanation above) usually has to do with not all objects in the collection fitting the rule. (See BP568, which is about BP ideas that are always overridden by a simpler solution.) The example EX10108 "all five are 'all five are ___'" was added, foiling the alternative solution. |
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CROSSREFS
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The right side of this Problem is a subset of BP999left.
Adjacent-numbered pages:
BP993 BP994 BP995 BP996 BP997  *  BP999 BP1000 BP1001 BP1002 BP1003
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EXAMPLE
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"Odd one out with respect to what property is the odd one out" would not fit left: even though this example does seem doubly-meta, it is not doubly-meta in the right way. There is no odd one out with respect to the property of having an odd one out.
Similarly, consider "gradual transition with respect to what the gradual transition is between", etc. Instead of having the form "X 'X __' ", this is more like "X [the __ appearing in 'X __']". Examples like these two could make for a different Bongard Problem. |
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KEYWORD
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hard, unwordable, challenge, overriddensolution, infodense, contributepairs, funny, rules, miniworlds
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CONCEPT
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self-reference (info | search)
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WORLD
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zoom in right
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AUTHOR
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Aaron David Fairbanks
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BP997 |
| There exists a loop that passes through every white square once without passing through the black square vs. there exists no such loop. |
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BP996 |
| Net corresponds to a convex solid vs. net corresponds to a concave solid. |
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BP995 |
| Animated visual Bongard Problems vs. static visual Bongard Problems. |
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BP994 |
| Net corresponds to a solid that can tessellate 3D space vs. net does not correspond to a solid that can tessellate 3D space. |
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COMMENTS
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More specifically these solids are polyhedra, and are often called "space-filling".
There is ambiguity here regarding some nets that can be folded to make multiple different solids. For example EX8175 could correspond to a cuboid with a pyramid-like protrusion at each end, a protrusion at one end and an indent at the other, or 2 indents. Only the second of these options can tessellate 3D space. For clarity's sake examples like this are not sorted on either side. |
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CROSSREFS
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Adjacent-numbered pages:
BP989 BP990 BP991 BP992 BP993  *  BP995 BP996 BP997 BP998 BP999
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KEYWORD
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stub, precise, 3d, perfect, preciseworld
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CONCEPT
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3d_net (info | search), 3d_solid (info | search)
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WORLD
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polyhedron_net [smaller | same | bigger]
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AUTHOR
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Leo Crabbe
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BP993 |
| Net corresponds do a unique solid vs. net can be folded into multiple different solids. |
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BP992 |
| Concave shapes with concave cavities vs. convex cavities |
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COMMENTS
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All examples in this Problem are solid concave black shapes. In this Problem, the "cavities" of a concave shape are defined to be the convex hull of the shape minus the shape itself. For example, if you take a bite out of the edge of a piece of paper, the piece of paper in your mouth is the cavity of the bitten piece of paper. The idea may be indefinitely extended, considering whether the cavities of the cavities are concave or convex, and so on. |
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CROSSREFS
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Adjacent-numbered pages:
BP987 BP988 BP989 BP990 BP991  *  BP993 BP994 BP995 BP996 BP997
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KEYWORD
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nice, precise, perfect, traditional
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CONCEPT
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recursion_number (info | search), recursion (info | search)
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WORLD
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concave_fill_shape [smaller | same | bigger]
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AUTHOR
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Jago Collins
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