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Otherwise, the non-standard order can be understood incorrectly. While the distinction between agents and patients is the most important that depends on word order in English, there are also other order-dependent distinctions, e.g. between beneficiary and patient, when the beneficiary is not marked by a preposition, or between a noun and its attribute, e.g. "police dog" is not the same as "dog police" and unless there is a detailed context you cannot know what is meant when the word order is wrong.
English is one of the languages with the most rigid word order. There are languages, especially among older languages, where almost any word order can be used without causing ambiguities, because all the possible roles of the words are marked by prepositions, postpositions or affixes (or sometimes by accentuation shifts).
> Left to Right English - read can, who? Anyone with [which] impressed am I.
and the causation is wrong; instead of the ability being impressive, it's the impressive character than allows reading in the opposite order.
So, you're right, and now I'll wait for the dog police to come pick me up.