Adjacent-numbered pages:
BP843 BP844 BP845 BP846 BP847  *  BP849 BP850 BP851 BP852 BP853

creativeexamples, structure, contributepairs, rules

constant_change_seq_increase_right_low_bound_obj [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP841 BP842 BP843 BP844 BP845  *  BP847 BP848 BP849 BP850 BP851

creativeexamples, structure, contributepairs, rules

quantity_change_seq_increase_right [smaller | same | bigger]
zoom in right (constant_change_seq_increase_right)

Aaron David Fairbanks

"Noisy" sequences of change vs. "minimalist" sequences of change.

See BP511 for noise in BPs.

See BP827 for noise in images of BPs.

Adjacent-numbered pages:
BP840 BP841 BP842 BP843 BP844  *  BP846 BP847 BP848 BP849 BP850

creativeexamples, structure, contributepairs, rules

quantity_change_seq_increase_right_noise_allowed [smaller | same | bigger]
zoom in right (quantity_change_seq_increase_right)

Aaron David Fairbanks

Adjacent-numbered pages:
BP838 BP839 BP840 BP841 BP842  *  BP844 BP845 BP846 BP847 BP848

creativeexamples, structure, rules

constant_change_seq_increase_right_lower_bound [smaller | same | bigger]
zoom in left (constant_change_seq_increase_right_low_bound_obj)

Aaron David Fairbanks

Restriction of BP841 to permutations.

Adjacent-numbered pages:
BP837 BP838 BP839 BP840 BP841  *  BP843 BP844 BP845 BP846 BP847

hard, contributepairs, traditional

zoom in left | zoom in right

Aaron David Fairbanks

For example, in a picture on the left of this Bongard Problem, if object A turned 90 degrees clockwise is object B, then there is also an object C which is B turned 90 degrees clockwise.

Positioning is irrelevant.

In all images, any pair of objects ought to be related in a unique (most intuitive) way. Furthermore, one object is not allowed to be related to two distinct objects by the same relationship. Even for images on the right, each analogy of objects A:B::C:_ should have one clear answer, although that object is perhaps missing.

Relationships described by "[undo-able action] applied to ___ is ___" will always form what in mathematics is called a "group". These relationships can be chained one after another to form a total relationship (turn 90 degrees clockwise + turn 90 degrees clockwise = turn 180 degrees), and each relationship has an "inverse" relationship that undoes it and vice versa (turn 90 degrees clockwise + turn 90 degrees counterclockwise = do nothing).

(Moreover actions are by nature associative.)

Sometimes the relationships in a picture wouldn't be consistently read the same way by everybody. For example, if there is a picture showing an L shape next to all vertical and horizontal reflections and 90 degree rotations of it, somebody might read

⅃ L

to be the same relationship as

┗━

┏━.

Meanwhile, someone else might think ⅃ L should be called the same relationship as ┗━ ━┛. There is a conflict between "flipping over the vertical line within the letter 'L'" and "flipping over a vertical line in the background space."

Likewise in any illustration of related objects (as in this Bongard Problem) people might interpret [the transformation that sends A to B] as analogous to [the transformation that sends [transformation x applied to A] to [transformation x applied to B] ].

A "commutative" (also called "abelian") group is a group in which there is no difference between the two in each case. Displayed using pictures like the ones in this Bongard Problem, only commutative groups of relationships can be expected to be read consistently by people.

https://en.wikipedia.org/wiki/Group_(mathematics)

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

See BP842 and BP840 for versions about particular groups.

Adjacent-numbered pages:
BP836 BP837 BP838 BP839 BP840  *  BP842 BP843 BP844 BP845 BP846

nice, rules, miniworlds

zoom in left | zoom in right

Aaron David Fairbanks

Restriction of BP841 to these axis-aligned L-shapes.

Left examples represent subgroups of the dihedral group D4.

Adjacent-numbered pages:
BP835 BP836 BP837 BP838 BP839  *  BP841 BP842 BP843 BP844 BP845

traditional

zoom in left | zoom in right

Aaron David Fairbanks

The original pre-transformed square is the same across all examples, however it is not shown in most examples; what the pre-transformed square looks like must be deduced by the solver.

BP1260 is about applying the same transformation to different objects.

Adjacent-numbered pages:
BP834 BP835 BP836 BP837 BP838  *  BP840 BP841 BP842 BP843 BP844

easy, abstract, arbitrary, anticomputer, traditional, rules

Aaron David Fairbanks

Left-sorted Bongard Problems have the keyword "consistentsymbols" on the OEBP.

A most extreme "consistentsymbols" Bongard Problem is BP121: the solution is about codes consistently symbolizing objects. However, "consistentsymbols" Bongard Problems may have solution unrelated to the symbolism; the symbolism may just be implicit, e.g. always meaning dots as numbers, always meaning stacked dots as fractions, repeatedly using the same simple drawings as shorthand to represent platonic solids. Most BPs have some symbolism in this sense; a Bongard Problem should only be labelled "consistentsymbols" if there is a relatively high amount of varied symbolism, particularly if it is visual symbolism not all people would naturally understand.

A Bongard Problem featuring a real language would be another extreme example of "consistentsymbols".

A Bongard Problem with many varied images meant to be interpreted in unique ways is not necessarily "consistentsymbols," since there is no specific-to-this-Bongard-Problem vocabulary of symbols that must be known to understand it. (Even so, some might say that how people intuitively interpret images is a vocabulary on its own.)

Sometimes, the symbolism isn't an important part of the Bongard Problem, and it just helps make the Bongard Problem easier to read (see the help keyword). For example, a Bongard Problem may include many clumps of dots, and the solution of the Problem may have to do with counting the number of dots in each clump; the Bongard Problem might build up a symbolic context by always arranging each number of dots in a consistent way (e.g. how they conventionally appear on dice faces).

"Consistentsymbols" is related to the keyword structure, a format that all examples fit that the solver needs to know how to read. In "consistentsymbols" Bongard Problems, not all examples need to fit a rigid format; instead there may be various smaller structures of meaning that only appear in some examples.

"Consistentsymbols" is related to assumesfamiliarity, BPs that require the solver to take certain assumptions about what the examples are for the solution to seem simple. A "consistentsymbols" Bongard Problem may have a very convoluted solution that involves explaining the meaning of each appearing object; however, the solution can become simple given correct interpretations of all objects. This effect works best when each object must be interpreted the same way across all boxes in order for the simple solution to fit. The comments sections of "consistentsymbols" BP pages on the OEBP ought to explain the symbolism used.

Adjacent-numbered pages:
BP833 BP834 BP835 BP836 BP837  *  BP839 BP840 BP841 BP842 BP843

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

visualbp [smaller | same | bigger]

Aaron David Fairbanks

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

Some Bongard Problems are "collective" in a more extreme way than others. Perhaps there are absolutely no individual examples that anyone would confidently sort on either side, and the solver can only be expected to get a vague gist by seeing them all together. Or perhaps in practice most people agree about where most examples should fit, even though a stretch of an argument could conceivably be made for each one fitting on the other side.

In some collective Bongard Problems, each example admits a number of possible interpretations, and the correct choice of interpretation is only clear once the solution is known. The group of examples together improve the solver's confidence about having understood each individual one right. This is common in rules Bongard Problems), where each example communicates its own rule.

Collective Bongard Problems are borderline invalid Bongard Problems (see https://www.oebp.org/invalid.php ). There is no one rule dividing the sides; the solution is not a method to determine whether an arbitrary example fits left or right. It is a less strict kind of Bongard Problem.

Collective implies fuzzy.

Collective Bongard Problems are often abstract".

Subjective Bongard Problems are often collective.

In some Bongard Problems, each example has a corresponding slightly different twin example on the other side (keyword contributepairs), and it is necessary to see both examples together in order to be able to sort either of them. This is related to "collective" but not quite the same. It becomes unambiguous where an example fits once its twin is seen.

Adjacent-numbered pages:
BP832 BP833 BP834 BP835 BP836  *  BP838 BP839 BP840 BP841 BP842

meta (see left/right), links, keyword

bp [smaller | same | bigger]

Aaron David Fairbanks