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Le Corbusier inscribed those words in the second (1928) edition of his Toward an Architecture. The first sentence is one of the axioms of modernism. A century later, you are running your fingers over it on page 151 of John Goodman’s translation (Getty Research Institute, 2007), where it is shelved under the subtitle “Liners.”

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Liners such as, en route shortly after the launch of Toward an Architecture:

This one was shaped by the modernist aesthetic of Art Deco. Its three sleeked funnels were unequal in height from bow to stern: first tall, then medium, then short (and the short one was a decorative dummy). Viewed from the side, the pattern communicated a knowingly accepted illusion of streamlined speed. Viewed from the bow, the tall funnel allotted the ship’s proportions the way a hat allots a head’s proportions.

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Allotting, the hat inscribed below guides the eye to see a face as a petitesse. Petitesse is a curve and the hat is its generatrix.

Also the hat’s crown rakes back in the illusion of speed while the passive woman within the hat remains still. Also the hat’s ribbon, wrapped halfway up around the domed cylinder of the crown, teaches the senses to imagine ribbon and crown as body parts harmonizing at knowingly accepted cross purposes . . .

An eye made use of an apparatus to create this image of a woman designed and curated. She’s more than a century old now but as good as new. You accept the illusion knowingly. You are a member of its comic audience. Defined by the aesthetic of Euclid, a woman is a machine for wearing a hat.