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BP570 Shape outlines that aren't triangles vs. black shapes that aren't squares.
(edit; present; nest [left/right]; search; history)
COMMENTS

An example of an overriddensolution.

CROSSREFS

Adjacent-numbered pages:
BP565 BP566 BP567 BP568 BP569  *  BP571 BP572 BP573 BP574 BP575

KEYWORD

less, example, overriddensolution, experimental, funny, neither

WORLD

outline_or_fill_shape [smaller | same | bigger]

AUTHOR

Aaron David Fairbanks

BP953 Image of this Bongard Problem vs. empty image.
(edit; present; nest [left/right]; search; history)
COMMENTS

"Image of Bongard Problem with solution X vs. empty image" where X is the phrase in quotes.

CROSSREFS

See BP959, BP902.

Adjacent-numbered pages:
BP948 BP949 BP950 BP951 BP952  *  BP954 BP955 BP956 BP957 BP958

KEYWORD

nice, precise, meta (see left/right), miniproblems, overriddensolution, right-full, right-null, perfect, infinitedetail, experimental, funny

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search)

WORLD

zoom in left (bp953_image) | zoom in right (blank_image)

AUTHOR

Leo Crabbe

BP998 X "X Y" vs. all are "X Y"; X Z.
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(edit; present; nest [left/right]; search; history)
COMMENTS

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 fit a rule.

Call something like "all but one are ___" a "rule-parametrized rule". A collection of objects, with respect to a particular rule, can fit a rule-parametrized rule.

A drawing on the right shows many collections. 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 rule collections can fit).

Likewise a drawing on the left shows a collection of collections, with some noticeable recurring rule-parametrized rule. The collection of collections must fit that rule-parametrized rule with respect to the rule of fitting that rule-parametrized rule (with respect to various rule).


An unintended solution to this BP is "not all groups share some noticeable property vs. all do." It is hard to come up with examples foiling this alternative solution because (what was above called) the rule-parametrized rule 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.)


Some examples would fit left under a certain interpretation: EX8220 "all are 'all are ___' " and EX8222 "palindrome with respect to being a palindrome with respect to ___" (every shown collection is a palindrome with respect to some property, and all things in a list being the same is a palindrome). But those rules are not necessarily the most obvious ways of interpreting these pictures, so they have been marked as ambiguous. Either of these placed on the left would prevent the intended solution being overridden (see the previous paragraph).


Here is a list of left example ideas that would be impossible to make:

- Exhaustive list of all exhaustive lists of all ____.

CROSSREFS

The right side of this Problem is a subset of BP999left.

Adjacent-numbered pages:
BP993 BP994 BP995 BP996 BP997  *  BP999 BP1000 BP1001 BP1002 BP1003

EXAMPLE

"Odd one out with respect to what property is the odd one out" would not fit left in this Problem: 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.

KEYWORD

hard, unwordable, challenge, overriddensolution, infodense, contributepairs, funny, rules, miniworlds

CONCEPT self-reference (info | search)

WORLD

zoom in right

AUTHOR

Aaron David Fairbanks

BP1141 Object inside of bounding box vs. object outside of bounding box.
(edit; present; nest [left/right]; search; history)
COMMENTS

This Problem is not to be taken seriously.

CROSSREFS

Adjacent-numbered pages:
BP1136 BP1137 BP1138 BP1139 BP1140  *  BP1142 BP1143 BP1144 BP1145 BP1146

KEYWORD

example, overriddensolution, right-full, right-null, invalid, experimental, funny

AUTHOR

Leo Crabbe

BP1146 Same number of dots in top row as in leftmost column vs not so.
(edit; present; nest [left/right]; search; history)
COMMENTS

This is a difficult-to-read attempt at making a Bongard Problem about perfect numbers. Grouping columns together to make rectangular arrays, each maximal (most dots possible) rectangular array of a particular height in any given example has the same number of dots in it (a perfect number, in left-sorted cases), and the dot-width of each array represents a particular divisor of that number.


It is not currently known whether there are a finite amount of examples that would be sorted left.


Every example in this Bongard Problem corresponds to a distinct natural number. There is not a way of representing the number 1 using the rules of construction for examples in this problem (if the problem were simply "Perfect number of dots vs. other number of dots", the example with 1 dot would be sorted right).

REFERENCE

https://en.wikipedia.org/wiki/Perfect_number

CROSSREFS

Adjacent-numbered pages:
BP1141 BP1142 BP1143 BP1144 BP1145  *  BP1147 BP1148 BP1149 BP1150 BP1151

KEYWORD

overriddensolution, left-listable

AUTHOR

Leo Crabbe

BP1242 Tiled by pair of fractals including itself such that both tile the other vs. tiled by pair of fractals including itself such that the other tiles itself.
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(edit; present; nest [left/right]; search; history)
COMMENTS

Proofs still needed that all the examples on the left hand side cannot fit on the right hand side as well, and that EX9881 cannot fit on the left hand side as well.

CROSSREFS

The left hand side implies the left hand side of BP1116.

The right hand side does not imply the right hand side of BP1116. (EX9881 is meant to be a counterexample.)

Adjacent-numbered pages:
BP1237 BP1238 BP1239 BP1240 BP1241  *  BP1243 BP1244 BP1245 BP1246 BP1247

KEYWORD

unwordable, overriddensolution, perfect, infinitedetail, both, missingproofs

CONCEPT fractal (info | search),
recursion (info | search),
self-reference (info | search),
tiling (info | search)

AUTHOR

Aaron David Fairbanks

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