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to encompass broader questions of systems and systemization. The
decidability part of the programme was also undermined by the
simultaneous work of Gödel and Turing. In order to approach the
question Turing imagined an entirely conceptual machine, which
could be configured to be in a number of different states. He based
this idea on the typewriter, which can be configured to write in
either upper or lower case. The difference was that Turing's machine
could be configured in an infinite number of states. He also imag-
ined his machine having a writing head, like a typewriter key,
which could write and erase marks on an infinite tape. The tape
would contain spaces that were either marked or blank. The writing
head could move up and down the tape in either direction. It could
also read whether the space on the position contained a mark or was
blank. The machine could be configured to undertake a number of
different actions according to what it found. With the appropriate
configuration almost any mathematical problem could be solved,
but certain problems were effectively unsolvable with such mechan-
ical processes. By devising his universal machine Turing proved that
mathematics was not decidable. Turing's virtual machine worked
for him inasmuch as, as a kind of philosophical toy, it enabled
him to conceptualize and solve the problem with which he was
concerned. He also went some way in conceptualizing the modern
computer, by positing a binary machine that could be configured in
any number of different states. 2 Turing was able to use his purely
theoretical ideas about calculating machines during the War when
he developed methods and technologies for decrypting German
U-Boat signals. This work in turn led to some of the first modern
electronic binary digital computers. Turing's Entscheidungsproblem
paper is widely regarded as one of the first conceptualizations of
such machines, and one of the keystones of the development of
digital technology. But it is fascinating as much for the past to
which it alludes, albeit unconsciously, as for the future it antici-
pates. In a sense it contains, in minutiae , many of the elements
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