Antedating of "Outside the Box" (UNCLASSIFIED)

victor steinbok aardvark66 at GMAIL.COM
Tue May 4 00:21:29 UTC 2010

I agree with everything that Garson wrote. The three-line solution is
exactly what he described--slightly tilting the lines to cover the
three dots of each row or column and yet keeping them non-parallel. I
can't cite the specific Gardner piece on this, as my original source
was a Russian translation and these were all arranged somewhat
differently from the US collections (and no SciAm references of
original publication). And I would have no recollection of the
specific location in any case.

Newt may be crazy, but his mention of "thinking outside the dots"
exactly complements the 1887 mention of "think[ing] outside the
lines", but, I suspect, neither has anything to do with thinking
outside the box--I would expect the antecedent for both of them to be
"connecting the dots", merged with "toeing the line". I've done a
partial search of "outside the box" from the 1950s and 1960s, but I am
a long way of completing the task or getting any conclusive evidence
in any particular direction. But my initial response was based on
these searches.

When I have more, I'll post on it again. Right now, I am behind on
about 10 different things... (four of which I've promised to post
weeks ago).


PS: the topology to make a single line to pass through all nine is
simple. Take the entire cluster and wrap it around a cylinder. Then
follow with the slightly slanted line that hits all three dots in the
lowest row, then winds around--could be several twists, depending on
the ratio of diameter and distance between the "dots" and the slant of
the line--to the second and third row eventually. Doing the same thing
with all nine as geometric points is quite another matter--I can
certainly do two lines on a Moebius strip, but not one. Of course,
then there is the question of what it means to "pass through" a point,
since there is only one side, but you can hit the point from two
different directions.

On Mon, May 3, 2010 at 7:40 PM, Garson O'Toole
<adsgarsonotoole at> wrote:
> William Safire discusses the nine dots puzzle in 1995 and quotes Newt
> Gingrich using the phrase "thinking outside the dots."
> ON LANGUAGE; Grotesquerie in a Box by William Safire
> Published: May 21, 1995
> Finding exact and near-exact matches is important. Sometimes it is
> also useful to look for antecedents and phrases that are thematically
> and semantically related. Here are a few possibilities, e.g.:
> beyond the box
> break outside the box
> go outside the box
> think outside the lines
> think outside the limits
> color outside the lines
> There are matches for some of these phrases with Google Books dates
> before 1971, but many are limited to snippet view and a hassle to
> verify. Here is an old-fashioned antecedent in full view:
> Cite: 1887 October, The Annual Register of World Events, Page 168,
> Longmans, Green.
> ... the Liberal party became a one-man party, which scarcely ventured
> to think outside the lines prescribed by its dictator.
> Victor Steinbok wrote:
>> To make matters even more interesting, as far as the puzzle is
>> concerned, Gardner had proposed a solution that uses only three
>> lines--provided we are dealing with "physical dots" or circles, not
>> geometric points. I'll leave it to your outside the box thinking to
>> figure that one out.
> Right. If the dots have non-zero radius then the first line goes
> through the first row, the second line goes through the second row and
> the third line goes through the third row. I am sure that for some
> topologies of the universe one can go through all nine dots with one
> line. That would involve going way outside the box but staying within
> the universe.
> Garson

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