Every indexed document

we will ask it to try every possible index for

it will tell us if the program finds an answer. If I am trying to

I will have solved Fermat’s Last Theorem! Do you see why?

which can run any program you throw at it.

the computer reads the number and interprets it as a series

drills and saws – to fashion objects. Each machine does

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