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BP2 Big vs. small.
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COMMENTS

The meaning of "big" left intentionally vague. There are various specific ways to define size, such as diameter, minimum distance between points on edge, and size of smallest bounding circle.

All examples in this Bongard Problem are single simple shapes, either outlines or solid black.

All examples on the same side are approximately the same size.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 214.

CROSSREFS

Adjacent-numbered pages:
BP1  *  BP3 BP4 BP5 BP6 BP7

KEYWORD

easy, nice, fuzzy, spectrum, size, stable, finished, traditional, continuous, bongard

CONCEPT size (info | search)

WORLD

outline_or_fill_shape [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

BP974 "Bounding-box-dependent" Bongard Problems vs. Bongard Problems in which the bounding box can be extended arbitrarily in any direction (in white space) without switching the sorting of any examples.
BP8
BP157
BP209
BP210
BP243
BP257
BP312
BP321
BP525
BP818
BP942
BP966
BP971
BP972
BP1008
BP1014
BP1089
BP1093
BP1104
BP1122
BP1132
BP1156
BP1245
?
BP2
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COMMENTS

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.

CROSSREFS

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

KEYWORD

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

AUTHOR

Aaron David Fairbanks

BP507 Bongard Problems about comparison of quantity vs. other Bongard Problems.
BP2
BP11
BP12
BP28
BP29
BP34
BP36
BP37
BP38
BP53
BP62
BP65
BP67
BP79
BP173
BP176
BP196
BP211
BP292
BP338
BP501
BP565
BP869
BP882
BP915
BP971
BP972
BP978
BP1044
BP1046
BP1208
BP1
?
BP6
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COMMENTS

Bongard Problems sorted left have the keyword "spectrum" on the OEBP.


In a "spectrum" Bongard Problem, there is an evident way to assign each object a value (e.g. "size" or "number of holes"). Then, to determine whether an object fits left or right in the Bongard Problem, its value is compared with a fixed threshold value.


Spectra can be continuous or discrete.


A "spectrum" Bongard Problem is usually arbitrary, since there could be made many different versions of it with different choices of threshold value. However, sometimes a certain choice of threshold is particularly natural. For example, the threshold of 90 degrees in "acute vs. obtuse angles" does not come across as arbitrary. And in BP2, the spectrum of values ("size") is vague, so much that the fuzzy threshold, of about half the size of the bounding box, does not seem arbitrary.


A spectrum Bongard Problem may or may not have the following properties:

1) The values assigned to objects are precise.

2) The threshold value between the two sides is precise.

3) The threshold value is itself sorted on one of the two sides.

Each of the latter two typically only makes sense when the condition before it is true.


If a spectrum Bongard Problem obeys 1) and 2), then it will usually be precise.

For example:

"Angles less than 90° vs. angles greater than 90°" is "precise".


If a spectrum Bongard Problem obeys 1), 2), and 3), then it will usually be allsorted.

For example:

"Angles less than or equal to 90° vs. angles greater than 90°" is "allsorted".


Discrete spectra usually satisfy 1) but do not satisfy 2). In a discrete spectrum Bongard Problem, there isn't one unambiguous threshold value. Consider "2 or fewer holes vs. 3 or more holes". (Is the threshold 2? 3? 2.5?)


In an especially extreme kind of spectrum Bongard Problem, one side represents just a single value, just the threshold value. For example, "right angles vs. obtuse angles." In certain cases like this the threshold is an extreme value at the very boundary of the spectrum of possible values. For example, consider "no holes vs. one or more holes." Cases like this might not even be understood as two sides of a spectrum, but rather the absence versus presence of a property. (See the keyword notso.)


Even more extreme, in some Bongard Problems, each of the sides is a single value on a spectrum. For example, BP6 is "3 sides vs. 4 sides". We have not been labeling Bongard Problems like this with the keyword "spectrum".


After all, any Bongard Problem can be re-interpreted as a spectrum Bongard Problem, where the spectrum ranges from the extreme fitting left to the extreme of fitting right.

REFERENCE

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

CROSSREFS

See BP874 for the version sorting pictures of Bongard Problems (miniproblems) instead of links to pages on the OEBP.

Adjacent-numbered pages:
BP502 BP503 BP504 BP505 BP506  *  BP508 BP509 BP510 BP511 BP512

KEYWORD

notso, meta (see left/right), links, keyword, sideless

WORLD

bp [smaller | same | bigger]
zoom in left (spectrum_bp)

AUTHOR

Aaron David Fairbanks

BP14 All big individual figures vs. all small individual figures.
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COMMENTS

All examples in this Problem show one or more connected figures made up of lines.

Some big shapes and some small shapes would be ambiguous.

REFERENCE

M. M. Bongard, Pattern Recognition, Spartan Books, 1970, p. 218.

CROSSREFS

See BP2 for the same idea using one shape.

Adjacent-numbered pages:
BP9 BP10 BP11 BP12 BP13  *  BP15 BP16 BP17 BP18 BP19

KEYWORD

fuzzy, size, stable, finished, traditional, bongard

CONCEPT all (info | search),
length_line_or_curve (info | search),
size (info | search)

WORLD

curves_drawing [smaller | same | bigger]

AUTHOR

Mikhail M. Bongard

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