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Head movement, while endemic in natural languages, has long been a thorn in the sides of syntacticians as it does not seem to be logically necessary nor does it follow from first principles. I will argue that head movement is not only necessary – it is indispensable. It is an intrinsic part of the language-computational system. Converting two-dimensional “trees” into uni-dimensional linearizations is mathematically difficult and in doing so, losing information is a distinct possibility. If too much information is lost then it would prove difficult for a hearer or a child acquiring the language to infer the original syntactic information from the signal and the system would become unlearnable. Linearization is the strategy of choosing an optimal ordering and head movement is a logical response to an optimization puzzle.

Head movement is an artefact of optimal solutions to linearisation paradoxes