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BP107 Three simple lines vs. three complex lines.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP102 BP103 BP104 BP105 BP106  *  BP108 BP109 BP110 BP111 BP112

KEYWORD

number, traditional

CONCEPT number (info | search),
curve_texture (info | search),
texture (info | search)

AUTHOR

Douglas R. Hofstadter

BP106 Negative slope vs. positive slope.
(edit; present; nest [left/right]; search; history)
COMMENTS

All examples feature a white circle and a black circle. The answer refers to the slope of the line connecting the two circles.

The coloring of the circles is irrelevant.

CROSSREFS

Adjacent-numbered pages:
BP101 BP102 BP103 BP104 BP105  *  BP107 BP108 BP109 BP110 BP111

KEYWORD

nice, noisy, dual, handed, rotate, orderedpair, traditional

CONCEPT positive_negative_slope (info | search),
line_slope (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search)

AUTHOR

Douglas R. Hofstadter

BP105 Ends of line point to the same direction vs. ends of line do not point to the same direction.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP100 BP101 BP102 BP103 BP104  *  BP106 BP107 BP108 BP109 BP110

KEYWORD

noisy, traditional

CONCEPT slope_at_endpoint (info | search),
tracing_line_or_curve (info | search)

AUTHOR

Douglas R. Hofstadter

BP104 One circle passes through the center of the other circle vs. no circle passes through the center of the other circle.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP99 BP100 BP101 BP102 BP103  *  BP105 BP106 BP107 BP108 BP109

KEYWORD

precise, unorderedpair, traditional

CONCEPT on_line_or_curve (info | search),
center_of_circle (info | search),
center (info | search),
imagined_point (info | search),
imagined_entity (info | search)

AUTHOR

Douglas R. Hofstadter

BP103 Isosceles triangle vs. scalene triangle.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP98 BP99 BP100 BP101 BP102  *  BP104 BP105 BP106 BP107 BP108

KEYWORD

precise, allsorted, stretch, orderedpair, traditional, preciseworld

CONCEPT line_or_curve_endpoint (info | search),
length_line_or_curve (info | search),
imagined_line_or_curve (info | search),
imagined_entity (info | search),
same_feature (info | search),
same (info | search),
isosceles_triangle (info | search),
triangle (info | search)

AUTHOR

Douglas R. Hofstadter

BP102 Internal arrows point outward vs. internal arrows point inward.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP97 BP98 BP99 BP100 BP101  *  BP103 BP104 BP105 BP106 BP107

KEYWORD

traditional

CONCEPT arrow (info | search),
between (info | search),
tracing_lines_or_curves_meet (info | search),
tracing_line_or_curve (info | search),
imagined_point (info | search),
imagined_entity (info | search)

AUTHOR

Douglas R. Hofstadter

BP101 Parallel dents vs. perpendicular dents.
(edit; present; nest [left/right]; search; history)
CROSSREFS

Adjacent-numbered pages:
BP96 BP97 BP98 BP99 BP100  *  BP102 BP103 BP104 BP105 BP106

KEYWORD

traditional

CONCEPT indentation (info | search),
imagined_shape (info | search),
imagined_entity (info | search),
parallel (info | search),
perpendicular (info | search)

AUTHOR

Douglas R. Hofstadter

BP100 The letter A vs. the letter Б.
(edit; present; nest [left/right]; search; history)
COMMENTS

This is the final problem in Bongard's original collection. It is the only member of the collection that makes reference to human culture. This can be interpreted symbolically as foreshadowing that computers will be able to perform the various tasks that humans can do.


Another idea introduced by this Bongard Problem is that a Bongard Problem can teach its solution to the solver. (See keyword teach.) A large pool of examples can be used for training, as is common in machine learning.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 247.

CROSSREFS

Adjacent-numbered pages:
BP95 BP96 BP97 BP98 BP99  *  BP101 BP102 BP103 BP104 BP105

KEYWORD

easy, nice, teach, arbitrary, anticomputer, culture, finished, bongard

CONCEPT specific_shape (info | search),
specificity (info | search)

AUTHOR

Mikhail M. Bongard

BP99 Outlines made by triangles and circles intersect vs. outlines made by triangles and circles do not intersect.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.

CROSSREFS

Adjacent-numbered pages:
BP94 BP95 BP96 BP97 BP98  *  BP100 BP101 BP102 BP103 BP104

KEYWORD

finished, traditional, bongard

CONCEPT collinear (info | search),
x-crossing (info | search),
cluster (info | search)

AUTHOR

Mikhail M. Bongard

BP98 Triangles vs. quadrangles.
(edit; present; nest [left/right]; search; history)
REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 246.

CROSSREFS

Adjacent-numbered pages:
BP93 BP94 BP95 BP96 BP97  *  BP99 BP100 BP101 BP102 BP103

KEYWORD

easy, nice, noisy, number, finished, traditional, bongard

CONCEPT number (info | search)

AUTHOR

Mikhail M. Bongard

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