2:01 am: After spending
four and
forty hours in deep and dirty
contemplation of
n-dimensional topology, I became
thoroughly convinced that I could successfully turn my insides, out, within the
postitudinal bounds of
regular homotopy.
2:02 am: Unable to immediately
envision a simple
affine eversion, I was forced to result to a more
practical, or "
brute force"
methodology... By crossing my arms and pushing up into my
armpits, I thought, perhaps, I would be able to undergo the necessary
bodily transfigurations. Slowly I became aware that I was an impervious
manifold, pitifully incapable of
self-intersection, which
disturbed me
deeply.
2:44 am: Realizing that any
polynomial or
parametric expansion of my
figure would likely be of sufficiently
high degree to render my
visual intuition ineffectual, I decide to
compute my
degree from
experimental data and develop a rough
path model of the
transformations necessary, using my weighty library of
theorems and
corollaries in
differential geometry. Despite the
inelegance of this
approach, I continued to feel
confident that the final transformation will be
smooth.
2:59 am: Casting
marble to the
wind, I
reluctantly embarked on this venture into the rough
loci that is
coordinate geometry. I began by
plotting points on my
skin, using a
black magic marker. My lack of a
mirror inhibited exact spacing, but I intended to use a leveling
bell curve to
average and
normalize the
data, which I developed, while plotting, with my free hand. Although
the shrieking statistician inside my skin protested both
vocally and
violently, I continued to pursue my original
processes; if I proved to be at all
periodic, a good
Fourier Transform simplification would vastly increase my ease in
translating and
rotating in normal
3-space. Note: In afterthought, this would have been useless, seeing as I didn’t even have the
O(n log n) required to complete the
mixed-radix Cooley-Tukey FFT algorithm.
3:43 am: I began to run into
additional difficulties when I found the marks on my
extremities were smudging against the
carpet while I
spotted my
stomach; thinking this would be a
recurrent issue, I sought to
develop a
statistical model to
compensate for the smudging; however, I soon realized that I could just suspend myself bodily from the
ceiling fixture, and engage the
mathematicians’
prerogative,
dismissing the existent smudging as
unavoidable '
experimental error'.
Unfortunately, I also fell and fully pricked my hand on
a rusty doornail, thus
invalidating my original
assumption that I was a
surface of
Genus 1.
To be continued: How I was forced to conclude that I was most definitely insoluble by a general case.