Problems with a "gap" in which it is always clear whether an example should fit in the Problem or not are "exact" (left-BP508).

Problems with a "gap" in which it is always clear when an example fits in the Problem or not are "exact" (left-BP508).

"Gap" implies "exact" (left-BP508).

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals can seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap. Many gaps could even be understood as discrete 0-to-1 spectra. Generally, in these cases, if it is reasonable to imagine understanding the Problem's solution without parsing a spectrum, consider it a gap, since that means the ambient context is unclear.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals can seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap. Many gaps could even be understood as a discrete 0-to-1 spectra. Generally, in these cases, if it is reasonable to imagine understanding the Problem's solution without parsing a spectrum, consider it a gap, since that means the ambient context is unclear.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals can seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap. Many gaps could even be understood as a discrete 0-to-1 spectra. Generally, i these cases, if it is reasonable to imagine understanding the Problem's solution without parsing a spectrum, consider it a gap, since that means the ambient context is unclear.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals can seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap. Many gaps could even be understood as a discrete 0-to-1 spectra. Generally, i these cases, if it is possible to understand the Problem's solution without parsing a spectrum, consider it a gap, since that means the ambient context is unclear.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals can seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap at all. Most situations with a gap could even be understood as a discrete 0-to-1 spectrum. In most of these cases, if it is possible to understand the Problem's solution without parsing a spectrum, consider it a gap, since that means the ambient context is unclear.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals can seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap at all. Most situations with a gap could even be understood as a discrete 0-to-1 spectrum.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals can seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap at all. Most situations with a gap might be understood as a discrete 0-to-1 spectrum.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals can seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap at all. Furthermore, most situations with a gap might be understood as a discrete 0-to-1 spectrum.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

Whether there is a "gap" becomes vague in cases of discrete spectra. For example, with BP6, "triangle vs. quadrilateral," triangles and quadrilaterals seem like separate cases with no middle ground, but they are also neighbors on the spectrum of polygons with respect side number, and from that perspective there is no gap at all. Furthermore, most situations with a gap might be understood as a discrete 0-to-1 spectrum.

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases.

Contrast "whole" (left-BP509).

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

A Problem with a gap showcases two completely separate classes of objects. Problems with gaps may sometimes feel arbitrary, like non-sequiturs, because the two classes of objects are so unrelated.

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases that may as well be completely unrelated.

Contrast "whole" (left-BP509).

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

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them, or any number of other ambient contexts. The Problem is about two separate cases that may as well be completely unrelated.

Contrast "whole" (left-BP509).

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

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black-and-white bitmap images between them.

Contrast "whole" (left-BP509).

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

For example, the Problem "white vs. black" (BP962) has a gap; there is no obvious choice of shared context between the two sides. One could imagine there is a spectrum of grays between them, or that there are pixel-by-pixel slightly changed black and white bitmap images between them.

Contrast "whole" (left-BP509).

Bongard Problems in which the two sides are so different that it is impossible to cross the gap by making successive small changes to examples (there is no intuitive "middle-ground" between the sides and there is no obvious choice of shared ambient "world" both sides are in) vs. other Bongard Problems.

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

Contrast "whole" (left-BP509).

Bongard Problems in which the two sides are so different that it is impossible to cross the gap by making successive small changes to examples (there is no intuitive "middle-ground" between the sides and there is no obvious ambient "world" both sides are in) vs. other Bongard Problems.

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

See BP509.

Aaron David Fairbanks