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Is this because these early computers were more often used to keep tabs and sort things (put things in order) rather than merely compute things?

(I'm aware that in order to perform those tasks the processing unit will also have to perform arithmetic operations)

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No, "ordinateur" was a marketing term created for IBM that meant to evoke godliness, from the somewhat archaic phrase, "Dieu qui met de l'ordre dans le monde", God who sets the world in order.

https://www.lemonde.fr/planete/article/2005/04/15/16-avril-1...

Spain calqued the word into ordenador while most of Latin America calqued computadora from the USA.

Orden in Spanish means both command (mandate, instruction) and order (as from sort).

So it means both order and order.

https://en.wiktionary.org/wiki/order

1. (countable) Arrangement, disposition, or sequence.

[…]

5. (countable) A command.

[…]

Exactly the same as the Portuguese word ordem.

ordem e progresso = sorting and soup? https://www.progresso.com

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