'non-hierarchically' originates from English, formed by the prefix 'non-' (from Latin 'non' meaning 'not'), combined with 'hierarchical' (from Greek 'hierarkhia' meaning 'rule of priests' via Latin/French), and the adverbial suffix '-ly' (from Old English '-lic'/'-ly').

'hierarchy' comes from Greek 'hierarkhia' → Latin/Old French forms → Middle English 'hierarchie' → modern English 'hierarchy' and adjective 'hierarchical'; the negative prefix 'non-' was attached in Modern English to form 'non-hierarchical', and adding '-ly' produced 'non-hierarchically'.

Originally 'hierarchy' referred to 'rule (archia) of priests (hier-)', but its sense broadened to mean any graded order or ranked system; 'non-hierarchical' and 'non-hierarchically' therefore came to mean 'not arranged in ranked levels' in modern usage.