I would agree with you that it's absurd that the 10x programmer would be 10 times more productive than the average programmer at ALL tasks. But in certain specialized scenarios, it's easy to imagine one programmer being 10x or even infinitely more productive than the average. In other scenarios, the situation could be reversed.
Here is an example anecdote of what it means when people talk about 10x programmer. Here the "hero" of the story was infinitely more productive than everybody on the team.
Henry Ford had ordered a dynamo for one of his plants. The dynamo didn't work, and not even the manufacturers could figure out why. A Ford employee told his boss that von Neumann was "the smartest man in America," so Ford called von Neumann and asked him to come out and take a look at the dynamo.
Von Neumann came, looked at the schematics, walked around the dynamo, then took out a pencil. He marked a line on the outside casing and said, "If you'll go in and cut the coil here, the dynamo will work fine."
They cut the coil, and the dynamo did work fine. Ford then told von Neumann to send him a bill for the work. Von Neumann sent Ford a bill for $5,000. Ford was astounded - $5,000 was a lot in the 1950s - and
asked von Neumann for an itemised account. Here's what he submitted:
Drawing a line with the pencil: $ 1
Knowing where to draw the line with the pencil: $4,999
Ford paid the bill.
Here is an example anecdote of what it means when people talk about 10x programmer. Here the "hero" of the story was infinitely more productive than everybody on the team.
Henry Ford had ordered a dynamo for one of his plants. The dynamo didn't work, and not even the manufacturers could figure out why. A Ford employee told his boss that von Neumann was "the smartest man in America," so Ford called von Neumann and asked him to come out and take a look at the dynamo. Von Neumann came, looked at the schematics, walked around the dynamo, then took out a pencil. He marked a line on the outside casing and said, "If you'll go in and cut the coil here, the dynamo will work fine." They cut the coil, and the dynamo did work fine. Ford then told von Neumann to send him a bill for the work. Von Neumann sent Ford a bill for $5,000. Ford was astounded - $5,000 was a lot in the 1950s - and asked von Neumann for an itemised account. Here's what he submitted: Drawing a line with the pencil: $ 1 Knowing where to draw the line with the pencil: $4,999 Ford paid the bill.