Adjacent-numbered pages:
BP979 BP980 BP981 BP982 BP983  *  BP985 BP986 BP987 BP988 BP989

meta (see left/right), links, metaconcept

bp [smaller | same | bigger]

Aaron David Fairbanks

"More," "fewer," "greater than," "less than."

See BP752 and BP749 for equality.

Adjacent-numbered pages:
BP978 BP979 BP980 BP981 BP982  *  BP984 BP985 BP986 BP987 BP988

meta (see left/right), links, metaconcept

bp [smaller | same | bigger]

Aaron David Fairbanks

Adjacent-numbered pages:
BP977 BP978 BP979 BP980 BP981  *  BP983 BP984 BP985 BP986 BP987

meta (see left/right), links, metaconcept

bp [smaller | same | bigger]

Aaron David Fairbanks

On the left, each row and column could be labeled by a certain object or concept; on the right this is not so.

More specifically: on the left, each row and each column is associated with a certain object or concept; there is a rule for combining rows and columns to give images; it would be possible without changing the rule to extend with new rows/columns or delete/reorder any existing columns. On the right, this is not so; the rule might be about how the images must relate to their neighbors, for example.

All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey.

Left examples are a generalized version of the analogy grids seen in BP361. Any analogy a : b :: c : d shown in a 2x2 grid will fit on the left here.

To word the solution with mathematical jargon, "defines a (simply described) map from the Cartesian product of two sets vs. not so." Another equivalent solution is "columns (alternatively, rows) illustrate a consistent set of one-input operations." It is always possible to imagine the columns as inputs and the rows as operations and vice versa.

There is a trivial way in which any example can be interpreted so that it fits on the left side: imagine each row is assigned the list of all the squares in that row and each column is assigned its number, counting from the left. But each grid has a clear rule that is simpler than this.

BP1258 is a similar idea: "any square removed could be reconstructed vs. not." Examples included left here usually fit left there, but some do not e.g. EX9998.

See BP979 for use of similar structures but with one square removed from the grid.

Adjacent-numbered pages:
BP976 BP977 BP978 BP979 BP980  *  BP982 BP983 BP984 BP985 BP986

nice, convoluted, unwordable, notso, teach, structure, rules, grid, miniworlds

grid_of_images_with_rule [smaller | same | bigger]
zoom in left (grid_of_analogies)

Aaron David Fairbanks

All examples show grids of squares with an image in each square, such that there is some "rule" the images within the grid obey. The "rule" can be about how the images relate to their neighbors, it can involve the position of the images in the grid, and it can involve properties of the grid considered as a whole. One square from somewhere along the edge of the grid is removed.

Intentionally left out of this Problem (shown above sorted ambiguously) are cases in which the rule is not possible to deduce without seeing more squares. Due to this choice to omit those kinds of examples from the right, another acceptable solution is "it is possible to deduce the contents of the missing square once the underlying rule is understood vs. not so."

https://en.wikipedia.org/wiki/Raven%27s_Progressive_Matrices

BP1258 is very similar: whether ALL squares can be deduced from the rest.

Adjacent-numbered pages:
BP974 BP975 BP976 BP977 BP978  *  BP980 BP981 BP982 BP983 BP984

nice, notso, structure, rules, miniworlds

grid_of_images_with_rule_one_on_edge_missing [smaller | same | bigger]

Aaron David Fairbanks

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

Consider the amount of data a person has to consciously unpack in each example in the process of determining how it should be sorted. In BP3, it is only necessary to notice the color of the shape. In BP871, however, it is important to read various qualities of every tiny shape shown.

Images of Bongard Problems that are "infodense" typically need to include a large number of examples in order to communicate the solution clearly without admitting unintended solutions. With so much data packed in each example, it becomes more likely that some of the random patterns in the data will happen to distinguish between the two sides in an unintended way. A similar issue appears in convoluted Bongard Problems.

Contrast "infodense" Problems to hardsort Bongard Problems, in which examples are difficult to sort, but perhaps that difficulty does not stem from reading a high amount of information; perhaps there is a small amount of information extracted from the examples, but it is hard to determine whether or not that information fits a rule.

Adjacent-numbered pages:
BP973 BP974 BP975 BP976 BP977  *  BP979 BP980 BP981 BP982 BP983

abstract, spectrum, meta (see left/right), links, keyword

Aaron David Fairbanks

An "object" is everything within some black boundary.

See BP1071 for a version with only squares and with infinite nesting allowed.

Adjacent-numbered pages:
BP972 BP973 BP974 BP975 BP976  *  BP978 BP979 BP980 BP981 BP982

nice, precise, allsorted, creativeexamples, traditional

Aaron David Fairbanks

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

Slightly different: sliding the content in a box around without letting it cross the bounding box and without changing the size of the bounding box. (See keyword absoluteposition.)

Expanding the boxes of BP2 ("big vs. small") makes the contents smaller in comparison to the box, but not smaller in an absolute sense. Hence the situation is ambiguous.

If a Bongard Problem has the keyword absoluteposition, then it likely has the keyword boundingbox.

If a Bongard Problem has the keyword boundingbox and does not have the keyword bordercontent, then it likely has the keyword absoluteposition.

Adjacent-numbered pages:
BP969 BP970 BP971 BP972 BP973  *  BP975 BP976 BP977 BP978 BP979

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

Aaron David Fairbanks

A similar, but different, solution is "center of mass is above the horizontal vs. center of mass is below the horizontal."

See BP971 for the version with examples rotated a quarter-turn.

Adjacent-numbered pages:
BP967 BP968 BP969 BP970 BP971  *  BP973 BP974 BP975 BP976 BP977

precise, spectrum, dual, handed, updown, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent

Aaron David Fairbanks

A similar, but different, solution is "center of mass is on the left half vs. center of mass is on the right half."

See BP972 for the version with examples rotated a quarter-turn.

Adjacent-numbered pages:
BP966 BP967 BP968 BP969 BP970  *  BP972 BP973 BP974 BP975 BP976

nice, precise, spectrum, dual, handed, leftright, rotate, boundingbox, blackwhite, traditional, viceversa, absoluteposition, bordercontent

Aaron David Fairbanks