Berkeley stated that the calculus involved a logical fallacy
and described derivatives thus: "They are neither finite quantities,
and described derivatives thus: "They are neither finite quantities,
nor quantities infinitely small, nor yet nothing.
May we not call them ghosts of departed quantities?"
Below you will find Adam Dickinson's poem which takes as its title Berkeley's questioning phrase. Dickinson teaches at Brock University in Ontario where he specializes in poetics. Although without formal training in mathematics, he says that he has always been interested in it -- particularly in overlaps between mathematical and metaphorical thinking. I found "The Ghosts of Departed Quantities" in The Shape of Content, Creative Writing in Mathematics (edited by Chandler Davis, Marjorie Senechal, Jan Zwicky, A K Peters, 2008)--and the poem first appeared in Problematical Recreations (Littlefishcartpess, 2008).
The Ghosts of Departed Quantities by Adam Dickinson
Speak of small,
so small
that we differ from it
by as little as one wish.
But this implies motion,
sidling up to hope.
Are we any closer?
Cantor's family moved from Judaism
to Protestantism,
from Russia to Germany.
To prove that two set of objects are the same size,
Cantor relieved us of counting.
Simply put your hands together,
no need to add the fingers.
Relation before number;
body to faith,
A set of misunderstandings,
a list of languages you never learned,
the number of intentions two people have in common.
all the days that have come before today.
He put the infinite in a bag
and shook;
everything came out larger.
What separates us is innumerable,
but like applause,
other words for the same thing,
all our differences fit.
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