See BP830.

Left examples have the keyword "-narrow" on the OEBP.

"Triangles" will be parsed as the pattern in a huge collection of triangles, so it is a narrow pattern. "Not triangles" can never be parsed as the pattern in a collection of many arbitrary shapes that are not triangles, so it is not narrow.

The key test is whether it would be possible to see the pattern with a million right examples.

Narrowness is very common.

This relates to the intuitive "size" of the collection of examples satisfying a pattern relative to the collection of objects in the whole world. Usually both are (uncountably) infinite, so it is not really possible to make a size comparison between these. In the case either side is finite it is certainly narrow (assuming the pattern and world are possible to perceive, instead of being horribly convoluted).

This also relates to a bias of which examples are implicitly considered to be "typical" examples for a world of examples. If 90% of the shapes usually included in Bongard Problems were triangles, then "not triangles" would be narrow.

Further, this relates to bias of about worlds are most likely to appear in Bongard Problems. If we know the "world" of our Bongard Problem includes only polygons, say, with number of sides less than seven, it becomes possible to see "not triangles" in only examples of hexagons, pentagons, and squares. (We don't even need this restriction on sides because one would expect to see a triangle in a million examples of polygons; see above comment on "typical" examples.)

It may be useful to define another term for whether left examples alone could communicate the pattern given knowledge of what the world is. But for BPs with keyword -narrow on this page, it should be possible to get the pattern from just right examples if the ambient world is everything (BP544).

It is possible for both sides of a problem to be narrow; take for example BP6.

It is furthermore possible for a pattern and its negation to be narrow; take for example BP20.

If a pattern is not narrow and its negation (within the BP's world) is narrow it can be called "wide."

Note that this is not just BP513 flipped.

Left examples have the keyword "-narrow" on the OEBP.

"Triangles" will be parsed as the pattern in a huge collection of triangles, so it is a narrow pattern. "Not triangles" can never be parsed as the pattern in a collection of many arbitrary shapes that are not triangles, so it is not narrow.

The key test is whether it would be possible to see the pattern with a million right examples.

Narrowness is very common.

This relates to the intuitive "size" of the collection of examples satisfying a pattern relative to the collection of objects in the whole world. Usually both are (uncountably) infinite, so it is not really possible to make a size comparison between these. In the case either side is finite it is certainly narrow (assuming the pattern and world are possible to perceive, instead of being horribly convoluted).

This also relates to a bias of which examples are implicitly considered to be "typical" examples for a world of examples. If 90% of the shapes usually included in Bongard Problems were triangles, then "not triangles" would be narrow.

Further, this relates to bias of about worlds are most likely to appear in Bongard Problems. If we know the "world" of our Bongard Problem includes only polygons, say, with number of sides less than seven, it becomes possible to see "not triangles" in only examples of hexagons, pentagons, and squares. (We don't even need this restriction on sides because one would expect to see a triangle in a million examples of polygons; see above comment on "typical" examples.)

It may be useful to define another term for whether left examples alone could communicate the pattern given knowledge of what the world is. But for the examples on this page, it should be possible to get the pattern from just right examples when the ambient world is everything (BP544).

It is possible for both sides of a problem to be narrow; take for example BP6.

It is furthermore possible for a pattern and its negation to be narrow; take for example BP20.

If a pattern is not narrow and its negation (within the BP's world) is narrow it can be called "wide."

Note that this is not just BP513 flipped.

Left examples have the keyword "-narrow" on the OEBP.

"Triangles" will be parsed as the pattern in a huge collection of triangles, so it is a narrow pattern. "Not triangles" can never be parsed as the pattern in a collection of many shapes that are not triangles, so it is not narrow.

The key test is whether it would be possible to see the pattern with a million right examples.

Narrowness is very common.

This relates to the intuitive "size" of the collection of examples satisfying a pattern relative to the collection of objects in the whole world. Usually both are (uncountably) infinite, so it is not really possible to make a size comparison between these. In the case either side is finite it is certainly narrow (assuming the pattern and world are possible to perceive, instead of being horribly convoluted).

This also relates to a bias of which examples are implicitly considered to be "typical" examples for a world of examples. If 90% of the shapes usually included in Bongard Problems were triangles, then "not triangles" would be narrow.

It is possible for both sides of a problem to be narrow; take for example BP6.

It is furthermore possible for a pattern and its negation to be narrow; take for example BP20.

If a pattern is not narrow and its negation (within the BP's world) is narrow it can be called "wide."

Note that this is not just BP513 flipped.

Left examples have the keyword "-narrow" on the OEBP.

"Triangles" will be parsed as the pattern in a huge collection of triangles, so it is a narrow pattern. "Not triangles" can never be parsed as the pattern in a collection of many shapes that are not triangles, so it is not narrow.

The key test is whether it would be possible to see the pattern with a million right examples.

Narrowness is very common.

This relates to the intuitive "size" of the collection of examples satisfying a pattern relative to the collection of objects in the whole world. Usually both are (uncountably) infinite, so it is not really possible to make a size comparison between these. In the case either side is finite it is certainly narrow (assuming the solution and world are possible to perceive, instead of being horribly convoluted).

This also relates to a bias of which examples are implicitly considered to be "typical" examples for a world of examples. If 90% of the shapes usually included in Bongard Problems were triangles, then "not triangles" would be narrow.

It is possible for both sides of a problem to be narrow; take for example BP6.

It is furthermore possible for a pattern and its negation to be narrow; take for example BP20.

If a pattern is not narrow and its negation (within the BP's world) is narrow it can be called "wide."

Note that this is not just BP513 flipped.

Left examples have the keyword "-narrow" on the OEBP.

"Triangles" will be parsed as the pattern in a huge collection of triangles, so it is a narrow pattern. "Not triangles" can never be parsed as the pattern in a collection of many shapes that are not triangles, so it is not narrow.

The key test is whether it would be possible to see the pattern with a million right examples.

Narrowness is very common.

This relates to the intuitive "size" of the collection of examples satisfying a pattern relative to the collection of objects in the whole world. Usually both are (uncountably) infinite, so it is not really possible to make a size comparison between these. In the case either side is finite it is certainly narrow.

This also relates to a bias of which examples are implicitly considered to be "typical" examples for a world of examples. If 90% of the shapes usually included in Bongard Problems were triangles, then "not triangles" would be narrow.

It is possible for both sides of a problem to be narrow; take for example BP6.

It is furthermore possible for a pattern and its negation to be narrow; take for example BP20.

If a pattern is not narrow and its negation (within the BP's world) is narrow it can be called "wide."

Note that this is not just BP513 flipped.

"Triangles" will be parsed as the pattern in a huge collection of triangles, so it is a narrow pattern. "Not triangles" can never be parsed as the pattern in a collection of many shapes that are not triangles, so it is not narrow.

The key test is whether it would be possible to see the pattern with a million right examples.

Narrowness is very common.

This relates to the intuitive "size" of the collection of examples satisfying a pattern relative to the collection of objects in the whole world. Usually both are (uncountably) infinite, so it is not really possible to make a size comparison between these. In the case either side is finite it is certainly narrow.

This also relates to a bias of which examples are implicitly considered to be "typical" examples for a world of examples. If 90% of the shapes usually included in Bongard Problems were triangles, then "not triangles" would be narrow.

It is possible for both sides of a problem to be narrow; take for example BP6.

It is furthermore possible for a pattern and its negation to be narrow; take for example BP20.

Left examples have the keyword "-narrow" on the OEBP.

Note that this is not just BP513 flipped.

Bongard Problems whose positive examples alone communicate the pattern.

Usually means left examples are the norm.

Note that this is not the negation of BP513.

Aaron David Fairbanks

Usually means left examples are the norm.

Left examples have the keyword "-narrow" on the OEBP.

Note that this is not just BP513 flipped.

Usually means left examples are the norm.

Left examples have the keyword "-ex" on the OEBP.

Note that this is not just BP513 flipped.

Bongard Problems whose negative examples alone communicate the pattern vs. other Bongard Problems.

Usually means left examples are the norm.

Left examples have the keyword "-ex" on the OEBP.

Note that this is not the negation of BP513.

Usually means left examples are the norm.

This is the keyword "-ex" on the OEBP.

Note that this is not the negation of BP513.

Bongard Problems whose negative examples alone communicate the pattern.

Usually means left examples are the norm.

Note that this is not the negation of BP513.

This is the keyword "-ex" on the OEBP.