reversal / inversion
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reversal
The act of putting something in the opposite direction, order, or position; the state of being reversed.
Die Umkehrung der Fahrtrichtung in dieser Einbahnstraße führte zu großem Chaos.
The reversal of the driving direction on this one-way street led to major chaos.
reversal
A complete change of a situation or state into its exact opposite.
Wir erlebten eine völlige Umkehrung der Machtverhältnisse im Unternehmen.
We experienced a complete reversal of the balance of power in the company.
inverse / inversion
In logic or mathematics, the formation of a new proposition or operation by swapping elements.
Die Subtraktion kann als Umkehrung der Addition betrachtet werden.
Subtraction can be regarded as the inverse of addition.
'Die Umkehrung' (the reversal/inversion) is the noun corresponding to the separable verb 'umkehren' (to turn around/reverse). The ending '-ung' forms nouns from verbs that describe an action or its result. Someone who reverses something carries out an 'Umkehrung' (reversal).
Wegen des Staus mussten die Autofahrer umkehren.
Because of the traffic jam, the drivers had to turn around.
The noun 'Umkehrung' (reversal/inversion) is very often used with a genitive object to specify what is being reversed. Examples are 'die Umkehrung der Tatsachen' (the reversal of the facts) or 'die Umkehrung eines Prinzips' (the reversal of a principle).
Seine Aussage war eine reine Umkehrung der Wahrheit.
His statement was a pure reversal of the truth.
To emphasize that a change is complete, 'Umkehrung' (reversal) is often combined with adjectives such as 'völlige' (complete), 'komplette' (complete), or 'radikale' (radical).
Nach der Wahl gab es eine völlige Umkehrung der politischen Strategie.
After the election, there was a complete reversal of political strategy.
This meaning of 'Umkehrung' (inversion/inverse) is typical of specialized language such as mathematics, logic, or music theory. For example, people speak of the 'Umkehrung einer Funktion' (inverse of a function) or the 'Umkehrung eines Akkords' (inversion of a chord).
In der Musik ist die Umkehrung eines Intervalls eine grundlegende Technik.
In music, the inversion of an interval is a basic technique.
perversion
Umkehrung neutrally describes a complete change into the opposite. Perversion, by contrast, describes such a change as a negative distortion or falsification of a thing or principle. Umkehrung is therefore appropriate for a simple reversal of circumstances, while Perversion is appropriate for a development that distorts something.
Der überraschende Sieg führte zu einer vollständigen Umkehrung der bisherigen Machtverhältnisse.
The surprise victory led to a complete reversal of the previous balance of power.
Die Unterdrückung im Namen der Freiheit ist eine Perversion dieses Prinzips.
Oppression in the name of freedom is a perversion of this principle.
