The most scattered, confused, or slightly crazy in behavior; the superlative form of dotty.
From 'dotty' (British slang meaning scatterbrained or eccentric), which comes from 'dot'—the idea being that a scattered mind is like dots rather than a connected line. The -iest suffix makes it superlative.
Dotty entered English slang in the early 1900s, possibly influenced by the idea of a dotted or speckled mind, and became especially popular in British English to describe absent-minded elderly people—notice how we use spatial metaphors like 'scattered' to describe mental confusion?
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