A signal lamp on the deck of a ship at night, its beam reaching into the dark
what makes light mean something?
image: ai-generated (gpt-image-2)
A hand giving a thumbs-up against a black background
a symbol is
an agreed,
distinguishable
state.
distinguishable: the receiver can tell it apart from the others.
agreed: both sides gave it the same meaning, beforehand.
image: ai-generated (gpt-image-2.5-flare)

perfect reception, perfect nonsense

every colour arrived correctly, and still the message did not.

the agreement, written down

ALPHABET = { "red": "00", "green": "01", "blue": "10", "yellow": "11", } print(ALPHABET["blue"])
both sides need this table beforehand, which makes it a promise rather than data.

the guessing game, measured

halving finds one card out of 32 in exactly five questions, and not only when you are lucky.

not every answer is worth one bit

you cannot choose which answer you get.

what a question is worth on average

and in general

a fair split is the only way to get a whole bit.

one bit

a light switch holds one bit, and it needs no computer for that.

what a bigger alphabet buys

the file and the symbol rate stay the same, and only the alphabet changes.

two symbols are enough for anything

what a big alphabet does per symbol, two symbols do in a group.

when symbols are not equally likely

rare symbols may cost more, as long as the common ones stay short.

the catch

the size of your alphabet is not a matter of taste but the result of a measurement.
four steps to your alphabet
agree on your alphabet and write it down
measure a profile for every symbol
teach the receiver to recognise every symbol
send 20 random symbols and count the errors
light means nothing
until you agree what it means.
and how much it means, you can count.