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Free
Imaginative Variation
Dan Lukiv
What change or changes
to a circle make it into something else? In other
words, when is a circle not a circle (Circle,
2003)? When is an ellipse not an ellipse (Ellipse,
1999)? A hyperbola not a hyperbola (Hyperbola,
1999)? A line not a line (Kline, 1967)? An elliptic
(or hyperbolic) paraboloid not an elliptic (or
hyperbolic) paraboloid (Paraboloid, 2005)? Is
a chair still a chair if it has only three legs
instead of the usual four? Polt (n.d.) discusses
the form of "a triangle [that] makes it
be a triangle, rather than any other sort of
thing--its triangleness" (para. 3; see,
also, Boeree, n.d.a, n.d.b). Polt speaks about
free imaginative variation in terms of a technique,
a way to "imaginatively subtract one feature,
then another, discovering in the process which
features are essential and which are not [i.e.,
which are incidental]" (para. 6). Some know
about this technique through their studies of
Husserl, the mathematician and phenomenologist
(see, e.g., van Manen, 1990).
Mathematicians describe the essential features
of circles, ellipses, hyperbolas, lines, elliptic
and hyperbolic paraboloids, and other geometric
figures in their one, two, or three dimensional
domains. Mathematicians even describe the essential
features of figments of their imaginations, such
as n-dimensional hyper-spheres defined by formulas
of the form x12 + x22 +
x32 + ... + xn2 =
r2. I invite the reader to begin listing
the essential features of a chair. Phenomenologists
describe essential features that define phenomenon
(van Manen, 1990). In the arena called hermeneutic
phenomenology, as a research methodology, researchers
often use free imaginative variation to help
them determine essential versus incidental themes
(1990).
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