What does the ringing of the bell mean?

Have you ever heard of the old saying "For whom the bell tolls"? This famous statement was coined by John Donne, a famous Renaissance poet. The bell is s symbol, of not only our mortally, but it also represents our connectedness, so Donne says.

When the bell is rung by Lady Macbeth, it is a signal telling Macbeth that the chamberlains are in a drunken stupor, but it also is summoning King Duncan to his grave. However, the irony here is astonishing, if we consider Donne's philosophy that the bell represents our connectedness, for Macbeth is about to sever that connectedness.