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Programming as in forming structures of computation is exceedingly beautiful and as intricate as any art, but that's indeed far, far removed from the everyday reality of a programmer.

I'd say the two are as connected as Rembrandt and painting prefab homes' walls are.

Most programmers are in denial about this and think their job is a delicate flower full of undiscovered mathematical gems. Meanwhile all they do is transforming data from and to databases, but refuse to see the general pattern so they'll create the same system over and over and over again in just about any variation possible.