Imagining Numbers by Barry Mazur

Author:Barry Mazur
Language: eng
Format: epub
ISBN: 9780141931708
Publisher: Penguin Books Ltd
Published: 2009-02-09T16:00:00+00:00

Nabokov then points out a structural problem: “a beetle has no eyelids and therefore cannot close its eyes—a beetle with human eyes.” And to resolve it, he writes:

[Gregor] is half-awake—he realizes his plight without surprise, with a childish acceptance of it, and at the same time he still clings to human memories, human experiences. The metamorphosis is not quite complete as yet.3

This brings home the sense that, despite (or better still, because of) Kafka's clarity, a kind of imagination is called for here that goes beyond architectural visualization.

A movie of Gogol's story “The Nose,” in which a disembodied nose goes “driving about all over town under the guise of a State Councillor,” could quite easily miss the point of the tale. For Gogol in his writing is prodding us, cajoling us, instructing us to engage in precisely the exercise of imagining this unvisualizable image in the full glory of its unvisualizability.4

In her essay “Imagining Flowers,” Elaine Scarry emphasizes how hard it is to imagine a face, in contrast to a flower. She writes: “[T]he daydreamed face expresses the lapse of the imagination from the perceptual ideal.”5 But the problem of recalling the faces of absent friends may be that our imagination of their presence, their own inner life, and their dynamic relationship to us is so vivid that we find it difficult to suppress these imaginings, to focus on the mere static visual image-memory of a face. But there is no such problem with flowers. How much inner life, after all, does a tulip have?

The act of visualization is, to be sure, only one possible act in the repertoire of the imagination. To visualize, we play the image on our already existing internal screen. But the more difficult leaps of the imagination force us to establish larger screens and, perhaps, new theaters of the mind.

For example, the exercise we are engaged in, to imagine imaginary numbers, is not a simple act of visualization. Rather, we will try to do this in two steps:

• first, to comprehend the idea of number as transformation, and

• second, to work at visualizing these transformations.

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