"BONGARD HELL."

This the flipped version of BP793 but using only images of Bongard Problems with solution "__ half more black/less white than other half versus vice versa," that all use rotated, reflected, and inverted versions of the same examples.

See BP971 (left vs. right more black) and BP972 (top vs. bottom more black).

Adjacent-numbered pages:
BP790 BP791 BP792 BP793 BP794  *  BP796 BP797 BP798 BP799 BP800

hard, nice, abstract, dual, handed, leftright, meta (see left/right), miniproblems, presentationmatters, left-finite, right-finite, assumesfamiliarity, structure, experimental, funny

bongard_hell [smaller | same | bigger]
zoom in left | zoom in right

Aaron David Fairbanks

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

This BP is not wellfounded, but its right side is. A paradoxical BP would be "Meta Bongard Problems that can contain an infinite chain of Bongard Problems containing Bongard Problems on the right side vs. this can never happen": where does it sort itself?

left-self or right-self implies not wellfounded.

Wellfounded implies not feedback.

Adjacent-numbered pages:
BP789 BP790 BP791 BP792 BP793  *  BP795 BP796 BP797 BP798 BP799

meta (see left/right), links, keyword, left-self, metameta, left-it, feedback

linksbp [smaller | same | bigger]

Aaron David Fairbanks

Rhetorical question: Where does this Bongard Problem sort an image of itself?

See BP999 and BP1004 for similar paradoxes.

Bongard Problems fitting left here evidently come in three categories: 1) would sort all Bongard Problems with the same solution left, 2) would sort all Bongard Problems with the same solution right, or 3) would sort some Bongard Problems with the same solution left and some right. See BP927.

See BP517 for the version with links to pages on the OEBP instead of images of Bongard Problems (miniproblems).

See BP954, which is about Bongard Problems not only sorting themselves, but moreover fractally appearing in themselves as panels.

Adjacent-numbered pages:
BP788 BP789 BP790 BP791 BP792  *  BP794 BP795 BP796 BP797 BP798

hard, nice, abstract, dual, handed, leftright, solved, meta (see left/right), miniproblems, creativeexamples, presentationmatters, assumesfamiliarity, structure, experimental

boxes_bpimage_sorts_self [smaller | same | bigger]
zoom in left (boxes_bpimage_sorts_self_left) | zoom in right (boxes_bpimage_sorts_self_right)

Aaron David Fairbanks

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

Examples of "structures": Bongard Problem, Bongard Problem with extra unsorted panel ("Bongard's Dozen"), 4-panel analogy grid, sequence of objects with a quantity changing by a constant amount.

If the solver hasn't become familiar with the featured structure, the Bongard Problem's solution may seem convoluted or inelegant. (See keyword assumesfamiliarity.) Once the solver gets used to seeing a particular structure it becomes easier to read that structure and solve Bongard Problems featuring it.

A Bongard Problem can non-verbally teach someone how a particular structure works, showing valid examples of that structure versus non-examples. E.g., BP968 for the structure of Bongard Problems and BP981 for the structure of analogy grids.

Adjacent-numbered pages:
BP784 BP785 BP786 BP787 BP788  *  BP790 BP791 BP792 BP793 BP794

meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks

Right examples have the keyword "number" on the OEBP. The solution must only depend on counting the number of something: no comparison between numbers of different things.

When a "number" Bongard Problem sorts numbers unambiguously (keyword precise), the left side and the right side define disjoint sets of numbers. When a "number" Bongard Problem sorts all numbers (keyword allsorted), the subsets are complements of one another.

Many but not all right examples require nontrivial mathematical knowledge to solve (keyword math).

BP200 is a version of this with sides flipped, sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP, and with emphasis on feature-based solutions as an alternative to number-based solutions.

Adjacent-numbered pages:
BP570 BP571 BP572 BP573 BP574  *  BP576 BP577 BP578 BP579 BP580

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

bp [smaller | same | bigger]

Aaron David Fairbanks

Left-sorted BPs have the keyword "right-full" on the OEBP.

BPs are sorted based on how BP573 (left-full) would sort them were they flipped; see that page for a description.

For non-meta BPs, right-full implies right-finite (at least until the OEBP implements a feature that allows algorithmic generation of infinite examples).

Adjacent-numbered pages:
BP569 BP570 BP571 BP572 BP573  *  BP575 BP576 BP577 BP578 BP579

meta (see left/right), links, keyword

bppage [smaller | same | bigger]

Aaron David Fairbanks

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

For meta-BPs about solution ideas, left-full only means the BP page hopes to include all fitting BP pages on the OEBP (as opposed to all possible Bongard Problems).

As with applying the keywords left-finite and right-finite, deciding what should count as "different" examples depends on the Bongard Problem.

Note this is not just BP574 (right-full) flipped.

TODO: Maybe this should be changed into two keywords: one for non-meta-BPs and one for meta-BPs. - Aaron David Fairbanks, Feb 11 2021

For non-meta BPs, left-full implies left-finite (at least until the OEBP implements a feature that allows algorithmic generation of infinite examples).

Adjacent-numbered pages:
BP568 BP569 BP570 BP571 BP572  *  BP574 BP575 BP576 BP577 BP578

meta (see left/right), links, keyword

bppage [smaller | same | bigger]

Aaron David Fairbanks

Left examples have the keyword "physics" on the OEBP. These are visual Bongard Problems that are most easily recognized by people as depicting some physics-related phenomenon. Usually, since physics is described by mathematics, this means there is also a (perhaps complicated) solution that can be described in terms of pure geometry.

See also keyword math.

Adjacent-numbered pages:
BP567 BP568 BP569 BP570 BP571  *  BP573 BP574 BP575 BP576 BP577

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

visualbp [smaller | same | bigger]

Aaron David Fairbanks

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