Cut A... B

Gardner's use of the expressions "Cut A" and "Cut B" in chapter 7 has puzzled many readers. Some relate the term "cut" to the cinematic technique of shifting from one shot to another. And this makes a kind of sense, as Cut A and Cut B begin and end Grendel's reflections on the queen, Wealtheow. This filmic approach seems to be missing something, however, because these reflections begin with Grendel's consideration of the queen in purely mathematical terms.

The queen is "Mathematically, perhaps a torus" (93), defined as "a surface having the shape of a doughnut." A "toroid" is "A surface generated by a closed curve rotating about, but not intersecting or containing, an axis in its own plane" (The American Heritage Dictionary).

I am certainly no mathematician, but I am told that in calculus one can determine the volume of a non-uniform shape (for instance, a drinking glass that begins narrow on the bottom and becomes gradually wider to the top) by imagining that the shape consists of any number of disks (the more disks, the more accurate the measure) piled upon each other within the form (somewhat as in the following crude graphic):

The form's volume would consist of the sum of the volume of each of the imagined disks. Points (or "Cuts") A and B in this illustration represent the extreme limits of the form from the widest (A) to the narrowest (B).

Now, if Gardner (and/or Grendel) has something like this in mind, what do we find? Just before Cut A, Grendel is abstracting the queen into a mathematical form, the torus (but with difficulty, for "how much is queen and how much is queenly radiation"?) Right after Cut A we are given the broad picture of Hrothgar's kingdom, leading up to and beyond his acquisition of the queen, during which time Grendel is profoundly moved by her beauty and nobility. But by Cut B, the opposite extreme, Grendel has brutally attacked and nearly killed the queen.

Another element that seems to support this movement from the broad Cut A to the narrow Cut B is Grendel's movement from the geometrically pure center of the torus to "the ugly hole" he exposes during the assault. Grendel has reduced the queen, from the idealized "beauty," "innocence," and "dignity of a sacrificial virgin" (100) to (in Grendel's obscene view) her most debased physical aspect (109), a hole.

If any reader has further thoughts, corrections, or additions to this subject, please contact me.

Please see the excellent graphics (and very technical explanation) of the torus at the MathWorld site.

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