2 A number
4 is called normal if
9
any sequence of digits, zero, one,
up to nine,
4 in any order, appears
3 just as often
7 in that number's decimal expansion, as
in
2 a random
3 sequence of digits.
8 Such a number cannot continue repeating ad
infinitum
3 and so must
0 be irrational.
6 Among the irrational numbers (of which
8 there are so many more than there are
5 of rationals --- though there are
4 infinitely many of each)
1 few
5 are known to be normal.
3 This simple-to-describe property
2 proves elusive.
7 A slight preference for sevens over
nines,
4 enough to wreck it.
8 It is not known whether pi is normal.
5 And yet we don't think
4 a superstar like pi,
7 in demand for every kind of formula,
8 from elementary school geometry, to the
abstract heights
0 of number theory,
2 disdaining neither
6 to appear in engineers' practical
calculations
8 nor in statisticians' attempts to
quantify the random---
8 we don't think such a number would
niggle
9 about its decimal expansion, preferring
some sequences over others.
2 Such considerations
6 are, we feel, beneath its notice.
1 Surely,
6 although its decimal expansion famously
begins
5 three point one four one,
8 somewhere else in that infinite sequence
of digits
7 we could find three one four two
2 as well.
4 And both those sequences
4 not just once, but
2 infinitely often,
9
neither more nor less often, in the
long run,
7 than a seemingly "unlikely"
sequence such as
0 one two three four
5 or five five five five.
4 In "Mechanophilia," the poets
8
match the number of words in each
line
2 to the
1 successive
3 digits of pi
0
(where zero indicates a
"free" line, whose length is at the poet's whim).
8 If we accept the conjectural normalcy of
pi,
5 the sequence of line lengths
4 of my poem, though
7 I confess it, counted afterwards, not
predetermined,
2
nonetheless appears
4 somewhere in pi's expansion.
1 Why
8 am I writing this poem? It is admittedly
4 not much like "Mechanophilia,"
5 a poem distinguished by the
3 scintillation of its
0 vocabulary
8 and the way the two poets delicately tug
7 the poem's fabric in slightly divergent
directions.
9 But "Mechanophilia" already
acknowledges the unfinishedness of its endeavour.
6 Extended to infinity wouldn't that poem
4 contain all possible words
3 including even these?
Hugh Thomas lives in Tiohtià:ke/Montréal/Montreal, where he teaches mathematics at UQAM. His most recent chapbook, Jangle Straw, was published last year by Turret House Press.
