Quote from : The Disappearing Spoon: And Other True Tales of Madness, Love, and the History of the World from the Periodic Table of the Elements Book

Today alpha equals 1/137.0359 or so. Regardless, its value makes the periodic table possible. It allows atoms to exist and also allows them to react with sufficient vigor to form compounds, since electrons neither roam too freely from their nuclei nor cling too closely. This just-right balance has led many scientists to conclude that the universe couldn’t have hit upon its fine structure constant by accident.