Claude Shannon
Can information be measured as a number?
That time, that place
Bell Labs belonged to a telephone company, so its problems were practical: over a line that adds noise, how much can be sent, and how accurately?
At the time this was left to engineers' instinct and experience.
Why this question
The first thing Shannon did was throw something out: he ruled that what a message means has nothing to do with the problem.
A declaration of love and a string of digits are the same to a wire.
What remains? He took the quantity of information to be the amount of surprise. The predictable carries little. That the Sun will rise tomorrow tells you almost nothing. Information is how much uncertainty gets removed.
What was found
With that, information became measurable. The unit is the bit — what it takes to settle one either-or.
Then he proved something startling: even over a noisy channel, error can be made as small as you like.
The method is adding redundancy — not by blunt repetition but cleverly, so that almost perfect transmission is possible through noise. Every channel has a ceiling rate, and below it this is always achievable.
Error stopped being unavoidable and became something you handle.
Where there is noise, error is unavoidable
A proof that every channel has a capacity, below which error can be driven arbitrarily low
Earlier, in his master's thesis, he had shown that Boole's algebra has the same structure as electrical switching circuits. He was twenty-one