The left hand doesn't know what the right hand is doing (or the other way round, 'the right hand doesn't know what the left hand is doing') is a common expression -- it is often used critically about government departments or large organisations to indicate a lack of co-ordination between different departments, a situation where there are conflicting or contradictory objectives being pursued by different departments, or a complete unawareness on the part of managers of what is going on. The speaker on the Thought for the Day segment in this morning's Today programme on Radio 4 (listen here for a few more days - scroll to 00:46), drew attention to the biblical origin of this phrase. Martin Wroe was referring to the current 'ice bucket challenge' craze among celebrities, and the desire by celebrities to have their charitable activities recorded for all to see.
The phrase comes originally from Matthew 6:3 in the Bible: 'But when thou doest alms, let not thy left hand know what thy right hand doeth'. Here, we are being advised to be discreet when we give to charity.