Learn Arabic (Modern Standard): الخوارزمية بمثابة عقل الحاسوب. - The algorithm serves as the brain of the computer.

The word بِمَثابَةِ is always followed by a noun in the genitive case (majrur). Here, it forces عقل (brain) to take a kasra ending (عقلِ). Think of it as triggering an Idafa (genitive construct) with the noun right after it.

Is بِمَثابَةِ عقلِ الحاسوبِ considered one long Idafa (genitive chain)?

Yes! The preposition بِـ makes مَثابَةِ genitive. Then مَثابَةِ acts as the first part of an Idafa, making عقلِ genitive. Finally, عقلِ is the first part of another Idafa with الحاسوبِ, making it genitive too. The whole phrase translates literally as 'in the position of the brain of the computer.'

Where is the verb for 'serves as' in the Arabic sentence?

There is no verb! This is a nominal sentence (a verbless equational sentence). The subject is الخوارزمية (the algorithm), and the predicate is the phrase starting with بِمَثابَةِ. While بِمَثابَةِ translates smoothly to 'serves as' or 'acts as' in English, grammatically in Arabic it simply means 'in the position of'.

The word for algorithm, الخوارزمية, looks like it is derived from a proper noun. Is it?

Yes, it is derived from the name of the famous 9th-century Persian mathematician Al-Khwarizmi. By adding the suffix ـيّة, which is commonly used to make abstract nouns or feminine adjectives, it becomes the specific term for 'algorithm'.