The Most Astounding Things Are Possible

"273. Hardy:'That the "finite cannot understand the
infinite" should merely be a theological
and not a mathematical war-cry.'
True, the expression is
inept. But what people are using it to
try and say is: 'We musn't have any juggling!
How comes this leap from the finite
to the infinite?' Nor is the expression all that
nonsensical - only the 'finite' that can't
conceive is not 'man' or 'our understanding'
but the calculus. And *how* this conceives
the infinite is well worth the investigation.
This may be compared to the way a chartered
accountant precisely investigates and clarifies
the conduct of a business undertaking. The aim
is a synoptic comparative account of all
the applications, illustrations, conceptions
of the calculus. The complete survey of
everything that may produce unclarity. And this
survey must extend over a wide domain, for
the roots of our ideas reach a long way.- 'The
finite cannot understand the infinite' means
here: It cannot work *in the way* you,
with characteristic superficiality, are presenting
it.
Thought can as it were, *fly*, it doesn't have
to walk. You do not understand your own
transactions, that is to say you do not have
a synoptic view of them, and you as it were
project your lack of understanding into the
idea of a medium in which the most astounding
things are possible."

from *Zettel*
Ludwig Wittgenstein
edited by G.E.M. Anscombe
and G. H. Von Wright
translated by G.E.M. Anscombe
University of California Press,
1967
{"Wittgenstein left a box of slips
["Zettel"] cut from copies of very
extensive typescripts of his work
from 1929 to 1948, but mostly
belonging to the period
1945-1948..."}

synoptic: [Mod. Lat. *synopticus*;
Gr. *synoptikos*: seeing the whole
together, from *synopsis* a general
view...]

Note to self: read David Berlinksy's
*A Tour of the Calculus*
and *The Advent of the
Algorithm*

"Two ideas lie gleaming on the jeweler's
velvet. The first is the calculus, the second,
the algorithm. The calculus and the rich
body of mathematical analysis to which
it gave rise made modern science
possible; but it has been the
algorithm that made possible the
modern world.
They are utterly different, these ideas.
The calculus serves the imperial
vision of mathematical physics. It is
a vision in which the real elements
of the world are revealed to be its
elementary constituants: particles,
forces, fields, or even a strange fused
combination of space and time.
Written in the language of mathematics,
a single set of fearfully compressed
laws describes their secret nature.
The universe that emerges from this
description is alien, indifferent to human
desires.
The great era of mathematical physics
is now over. The three hundred-year
effort to represent the material world
in mathematical terms has exhausted
itself. The undertaking that it was to
provide is infinitely closer than it was
when Isaac Newton wrote in the late
seventeenth century, but it is still
infinitely far away.
One man ages as another is born, and
if time drives one idea from the field,
it does so by welcoming another.
The algorithm has come to occupy
a central place in the imagination.
It is the second great scientific idea
of the West. There is no third."

*The Advent of the Algorithm*
David Berlinsky
Hacourt, 2000