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Difference between Not know how the other half lives and Not know what the other hand is doing

not know how the other half livesnot know how other, especially poorer people live:

  • People with steady jobs, decent income, and money in the bank often don’t know how the other half lives.

not know what the other hand is doing —(used in allusion to the saying “one hand does not know what the other hand is doing”) said of a state of utter disorganization and confusion within an organization, etc.:

  • There are lots of subcommittees that don’t know what the other hand is doing.