Money: from physical to bitcoin

We started trading using physical objects, like gold. If I gave a coin to someone I no longer had the coin. This does not work in the digital realm: If I give a file to some-one I can still keep the file. 

So digital cash required centralisation, in the form of banks that act as trust-worthy middleman. 

Bitcoin works without a central authority to verify the integrity of the transactions. The authority is replaced by an algorithm running on the devices of all bitcoin players.