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"Simplicity, simplicity, simplicity! I say, let your affairs
be as two or three, and not a hundred or a thousand;
instead of a million count half a dozen,
and keep your accounts on your thumb-nail."
— Henry David Thoreau, Walden
This quotation is the epigraph to Section 1.1 of
Alexandre V. Borovik's Mathematics Under the Microscope:
Notes on Cognitive Aspects of Mathematical Practice
(American Mathematical Society, Jan. 15, 2010, 317 pages).
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From Peter J. Cameron's review notes for
his new course in group theory—
From Log24 on June 24—
Geometry Simplified
(an affine space with subsquares as points
and sets of subsquares as hyperplanes)
(a projective space with, as points, sets
of line segments that separate subsquares)
Exercise—
Show that the above geometry is a model
for the algebra discussed by Cameron.