Turing machines are easier to understand than lambda calculus, but lambda calculus is more elegant.
By
Omnifarious
on March 04, 2007
The most widely used programming languages are imperative which hearkens back to the punch symbols into an infinite paper tape model of the Turing machine. But functional programming languages (which have their roots in lambda calculus) are still important and used by many, and it's claimed they are more elegant and 'pure'.
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When it comes to actually writing code, Lambda Calculus is superior IMO. Turing machine tape is too much like assembly language -- you get bogged down in details faster.