Left examples have the keyword "math" on the OEBP.

Although everything is arguably related to math, these BP solutions include content that people don't inherently understand without learning at least some mathematics.

Left examples do not technically have "culturally-dependent" content (keyword culture), but knowledge and previous learning plays a role in how easy they are to solve.

Adjacent-numbered pages:
BP566 BP567 BP568 BP569 BP570  *  BP572 BP573 BP574 BP575 BP576

fuzzy, meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks

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.

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

BP570 "Shape outlines that aren't triangles vs. black shapes that aren't squares" was created as an example of this.

meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks

Left-sorted BPs have the keyword "left-null" on the OEBP.

Right-sorted BPs have the keyword "right-null" on the OEBP.

See BP796 for the version with pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

See BP1160 for the version about an all-black panel instead of all-white.

Adjacent-numbered pages:
BP562 BP563 BP564 BP565 BP566  *  BP568 BP569 BP570 BP571 BP572

meta (see left/right), links, keyword, side, wellfounded, testexample

visualbp [smaller | same | bigger]

Aaron David Fairbanks

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.

"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

meta (see left/right), links, keyword, metameta

linksbp [smaller | same | bigger]

Aaron David Fairbanks

Left examples have the keyword "antihuman" on the OEBP.

Right examples have the keyword "anticomputer" on the OEBP.

Easy abstract Bongard Problems are typically anticomputer Bongard Problems.

See keyword help for Bongard Problems that can be made easier for humans to solve by the selection of helpful examples.

Adjacent-numbered pages:
BP560 BP561 BP562 BP563 BP564  *  BP566 BP567 BP568 BP569 BP570

spectrum, anticomputer, meta (see left/right), links, keyword, right-self, viceversa

bp [smaller | same | bigger]

Leo Crabbe

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

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

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

math, meta (see left/right), links, keyword

bp_infinite_left_examples [smaller | same | bigger]
zoom in right (left_uncountable_bp)

Leo Crabbe

This prompts thinking about left-self and right-self keywords.

Adjacent-numbered pages:
BP556 BP557 BP558 BP559 BP560  *  BP562 BP563 BP564 BP565 BP566

meta (see left/right), links, left-self, sideless, metameta

linksbp [smaller | same | bigger]
zoom in left (bp_in_own_world)

Aaron David Fairbanks

Left-sorted examples have the keyword "blackwhite" on the OEBP.

Right-sorted examples have the keyword "blackwhiteinvariant" on the OEBP.

All examples are visual Bongard Problems that allow black to touch the bounding box (keyword bordercontent).

Adjacent-numbered pages:
BP551 BP552 BP553 BP554 BP555  *  BP557 BP558 BP559 BP560 BP561

meta (see left/right), links, keyword, invariance, wellfounded

visualbp [smaller | same | bigger]

Leo Crabbe

Left examples have the keyword "size" on the OEBP.

If applying a scaling to the whole of any example can change its sorting the BP fits on the left side here. (For BPs with bounding boxes means scaling an object appearing in a box within the bounding box.)

Note that BPs about relative size comparisons of multiple objects fit on the right side.

Adjacent-numbered pages:
BP549 BP550 BP551 BP552 BP553  *  BP555 BP556 BP557 BP558 BP559

meta (see left/right), links, keyword, invariance, wellfounded

visualbp [smaller | same | bigger]

Aaron David Fairbanks

Left examples have the keyword "rotate" on the OEBP.

If rotating an example about the center can change its sorting the BP is a left example here.

Note that BPs about relative rotation comparisons fit on the right side.

See BP872 for the version with pictures of Bongard Problems instead (miniproblems) of links to pages on the OEBP.

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:
BP548 BP549 BP550 BP551 BP552  *  BP554 BP555 BP556 BP557 BP558

notso, meta (see left/right), links, keyword, invariance, wellfounded

visualbp [smaller | same | bigger]

Aaron David Fairbanks