The left hand doesn’t know what the right hand is doing

This originates from the Bible, Matthew 6:3 (King James Version):

But when thou doest alms, let not thy left hand know what thy right hand doeth.

That meaning alluded to the wisdom of not giving oneself credit for providing charity to others – just give and forget about it. That view was reiterated by Henry Thoreau in his Walden; or life in the woods, 1854:

“If you should ever be betrayed into any of these philanthropies, do not let your left hand know what your right hand does, for it is not worth knowing.”

The original meaning of the phrase is now lost. We presently use the phrase to suggest that, in business, one should keep one’s interests independent of each other.