absorbed / recessed
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absorbed
Mentally very focused on something and unaware of one's surroundings.
Sie saß vertieft in ein Buch am Fenster und bemerkte nicht, wie die Zeit verging.
She sat by the window absorbed in a book and didn't notice how time was passing.
recessed
Lying deeper in a surface or material; having an indentation or recess.
Die Inschrift war tief in den Stein vertieft.
The inscription was deeply recessed into the stone.
'Vertieft' is the past participle of the verb 'vertiefen' (to deepen). It is used as an adjective, and its meanings derive directly from the verb: 'sich in etwas vertiefen' (to become absorbed in something) or 'etwas vertiefen' (to make something deeper).
Er war so in seine Arbeit vertieft, dass er die Zeit vergaß.
He was so absorbed in his work that he forgot the time.
The preposition 'in' helps distinguish the meanings. 'Vertieft in' + accusative describes mental concentration. 'Vertieft in' + dative describes a physical indentation in a material.
Der Forscher war in seine Studien vertieft (Akkusativ).
The researcher was absorbed in his studies (accusative).
When someone is concentrated, they are often 'in ein Buch' (in a book), 'in ein Gespräch' (in a conversation), 'in Gedanken' (in thought), or 'in seine Arbeit' (in their work) 'vertieft' (absorbed).
Die beiden waren in ein langes Gespräch vertieft.
The two of them were absorbed in a long conversation.
focused / concentrated
Vertieft and konzentriert both describe giving something one's full attention. Vertieft more strongly emphasizes being absorbed in an activity and barely noticing one's surroundings, while konzentriert highlights consciously focused attention. When reading out of interest, vertieft is a good fit; for a specific task, konzentriert is more suitable.
Sie war so vertieft in ihr Buch, dass sie die Durchsage nicht hörte.
She was so absorbed in her book that she didn't hear the announcement.
Er arbeitete konzentriert an seiner Aufgabe und ließ sich nicht ablenken.
He worked on his task with concentration and wasn't distracted.
