The fingers are the digits and are therefore used for counting. Thus did digits become numbers and when information is stored in numbers it becomes digital.
The Old English names for the fingers are much more fun than those which have been more recently fangled.
The index finger was once the towcher, or toucher, because it was used for touching things. We non-tactile moderns no longer use this finger for touching things and instead only point at, or indicate them. Hence index finger.
Though you may, dear reader, run your inky index finger down the index of a book, that's not where the name comes from. Like a co-owned onion, they merely share a root.
The index of a book indicates where a passage may be found (and the index expurgatorius indicates where the good, dirty stuff is). From this idea of indicating come all the other dull and dreary stock market and scientific indices.
The dully-named middle finger was, to our forbears the fool's finger, but not, alas, because it was covered in ink. Instead we got the name from the Romans who called it the digitus infamis (infamous), obscenus (obscene), and impudicus (rude). Nobody is sure why the Romans bore such a grudge against the middle finger, but it seems that it was they who invented the habit of sticking it up at those they did not like.
As Martial so delicately put it:
Rideto multum qui te, Sextille, cinaedum
dixerit et digitum porrigito medium
Which translates extraordinarily loosely as:
If you are called a poof don't pause or linger
But laugh and show the chap your middle finger.
What do leeches have to do with love? A leech is an old metonym for a doctor, and doctors are interested in the heart. Because it was believed that there was a nerve that ran from the fourth finger to the heart, doctors thought that they could influence the one through the other. Lovers believe that by putting a ring around the fourth finger they had, so to speak, lassoed the loved one's heart. And that's how the leech finger became the ring finger.
And the little finger? It was called the ear-finger. Why? Because it's just the right size for digging wax from your shell-like.
The Inky Fool consults the future