The Alan Sondheim Mail Archive

modeling, division by zero

when i was very young i lived in a world of division by zero. the result
was infinity with n <> 0, but this was modified. 20/0 = 10/0 of course but
we might write I (for infinity) so that I(20) is distinct from I(10).
generalize: x/0 becomes I(x) and f(x)/0 becomes I(f(x)). what develops is
a sense of process and history; I(f(x)) is dependent on the operations
that lead up to it for any specific I(f(x)); it's as if 2 + 2 = 3 + 1, but
the operations remain different and distinction; 4(2,2) may be considered
distinction from 4(3,1). and this is true, providing the intercession of
an operator is implied; 2 might for example be manageable and 3 not. the
modes become more interesting when other f(x)/0 are involved or when
thinking through (x/0)*(0/y) - the temptation is to produce x/y or even
f(x)/f(y), canceling the 0, and within our mathesis, this may be reason-
able. but again the 0 must be kept visible, historic; we might writer
"(f(x)/f(y)) qua 0/0" or some such; it's evident that indices, both sub-
and super-, quickly develop, become unmanageable. history piles on
history, the mathematics leaves a necessary trace on the result - neces-
sary because (x/0)*(0/y) is strictly I*0, which is up for grabs. the
history imposes exactitude, facticity, where none is; it is a mathematics
of sand-grains, not continua, of course related to infinitesimals, non-
standard analysis, and so forth. but here, and when i was young, i valued
these equations which told stories, stories that not only where inherent,
but integral to their value in both senses of the word.

... i was in revolt, against mathesis, against those equations excluded,
beyond the Pale, for no apparent reason, against the simultaneous weaken-
ing and strengthening of zero, of nothing at all ...

( the shy zero, adding nothing to anything; the murder zero, multiplying
and forgetting; the burgeoning zero, dividing into the production of the
world; the generous zero, taking nothing away )

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