Other ways of phrasing this:

"Local" vs. "global" properties of collections: to check a collection satisfies a "local" property, it is only necessary to check each individual thing in it satisfies some property.

The rule all collections satisfy is just "every object is a ___" vs. the rule is something more.

Adjacent-numbered pages:
BP1122 BP1123 BP1124 BP1125 BP1126  *  BP1128 BP1129 BP1130 BP1131 BP1132

abstract, creativeexamples, left-unknowable, rules, miniworlds

[smaller | same | bigger]

Aaron David Fairbanks

Left-sorted Bongard Problems have the keyword "left-unknowable" on the OEBP.

Right-sorted Bongard Problems have the keyword "right-unknowable".

Think of searching for needles in endless haystacks. You can be sure a haystack has a needle by finding it, but you can never be sure a haystack does not have a needle.

When a Bongard Problem is "left-unknowable", individual examples cannot be determined for certain to fit left, by any means. The author of the Bongard Problem just chooses some examples that seem to fit left. (See also the noproofs keyword.)

It is very extreme for this to apply to all examples without exception. Often a Bongard Problem is close to being purely left-unknowable, but a few examples spoil it by being obviously disqualified from the right side for some reason.

It is natural for a person to guess the solution to an unknowable Bongard Problem before actually understanding all the knowable examples, taking some of them on faith.

As a prank, take a left- or right- unknowable Bongard Problem and put an example that actually belongs on the unknowable side on the knowable side. The solver will have to take it on faith there is some reason it fits there they are not seeing.

(The property of having this kind of sorting mistake is unknowable for left- or right- unknowable Bongard Problems.)

One interpretation of topology (a subject of mathematics -- see https://en.wikipedia.org/wiki/Topology ) is that a topology describes the observability of various properties. (The topological "neighborhoods" of a point are the subsets one could determine the point to be within using a finite number of measurements.) The analogue of a property that is nowhere directly observable is a "subset with empty interior". Furthermore, the fact that the negation of the property is observable corresponds to the subset being "closed".

Left- or right- unknowable Bongard Problems are generally notso Bongard Problems: an example fits on one side just in case it cannot be observed to fit on the other.

Although the descriptions of left-couldbe and right-couldbe sound similar to "left-unknowable" and "right-unknowable", they are not the same. It is the difference between a clear absence of information and perpetual uncertainty about whether there is more information to be found. For any example sorted on a "could be" side, there is a clear (knowable) absence of information whose presence would justify the example being on the other side.

Sometimes an unknowable BP can be turned into a couldbe BP by explicitly restricting the amount of available information. For example, if there were a hypothetical Bongard Problem with infinitely detailed pictures, using a low resolution for all pictures could simplify the issue of detecting some properties that would be "unknowable". Many fractal-based BPs are this way (e.g. BP1122). See keyword infinitedetail.

Right-unknowable Bongard Problems are generally left-narrow (and left-unknowable Bongard Problems are generally right-narrow).

A Bongard Problem with examples on both sides cannot be tagged both proofsrequired and left- or right- unknowable.

Many Bongard Problems are about finding rules (keyword rules)--in each panel a rule is to be found, and there are no specified limits about what kind of rule it can be or how abstract it can be. (Just like a Bongard Problem.) "There is a rule vs. there isn't" (resp. vice versa) are right- (resp. left-) unknowable. (That is, disregarding cases that obviously do not define a rule because of some trivial disqualifying reason.)

Actually, I think there is something more to be said about this. It is possible to design examples that signal there is no rule to be found. See for example EX9138 in BP1127 and EX6829 in BP829. (Related: keyword help.) Each of these examples communicates a clear rule that "doesn't count". And there is so little information shown that a person can feel confident they've noticed all the relevant details. So, contrary to how they are currently tagged, these Bongard Problems aren't strictly "unknowable"; there are some exceptional knowable cases. But being too strict about the definition of "unknowable" makes it so there aren't any examples of unknowable Bongard Problems, so it's probably better to be a bit loose. - Aaron David Fairbanks, Apr 20 2022

Adjacent-numbered pages:
BP1119 BP1120 BP1121 BP1122 BP1123  *  BP1125 BP1126 BP1127 BP1128 BP1129

The perfect example is BP1163.

Interesting example of a Bongard Problem that is neither left-unknowable nor right unknowable in particular, but for which it is impossible to know whether any example fits on either side: BP1229 (translational symmetry vs. not) made with examples that can be expanded to any larger finite region the solver wants to look at. In this case, examples could only be sorted based on what they seem like (see seemslike), trusting they appear in a way that hints psychologically at what they actually are (see help).

dual, meta (see left/right), links, keyword, side, viceversa

Aaron David Fairbanks