Every indexed document

and subsequently many early computers used tapes

every 14 th character subtracted 15 and every

many of them doing exactly this. You might think that

and Churchill believed Turing’s work shortened the war

the Allies would have needed a much larger

with a second army in Scotland poised to

the British were soon able to read almost every coded

so Turing returned to England to take up

but one of the most influential mathematical works of

Enigma got off to a difficult start. The

waiting to hear whether the German army will

in 1989 Roger Penrose picked up the baton and put

all of logic falls apart as well. Whenever we allow inconsistency

except for the numbers 5 and 6. You may use them to count

which don’t greatly affect the day-today

then working at the University of Vienna

you are saying that 3 doesn’t really ‘mean’

refining them into three distinct questions: Is

London staged its first marathon. The field of

the second digit from the second number add one