When one is enquiring if someone else is doing something, there are different ways to go about asking this question. One can ask them if they are busy or, alternatively, one can ask them if they are occupied. If you choose the latter option, you are speaking Nathanish. Let us discuss the implications of asking a question in this way and discuss why occupied instead of busy is the proper Nathanish choice.
When one is comparing busy to occupied, let us first note the obvious. Busy is a two-syllable word with only four letters, while occupied is three syllables long and double the length. Already here we can see a bias in favor of occupied as it is clearly the longer option. Ceteris peribus, when choosing between two words as to the more Nathanish option, the longer and less obvious choice should be selected. This need not be the selection in every case where a choice is to be made, but when it comes to the most important word of an otherwise straightforward message, the more complex and larger option is the more desirable choice to make.
Aside from considerations of length and complexity, it is also worthwhile to consider the semantic domain of the two words. While busy and occupied can both be used to describe someone who is unavailable for conversation, they are not strictly synonyms of each other and in fact have somewhat different semantic domains that are worth exploring. Busy relates to the domain of what one is doing, and evokes questions of business and the domain of activity. While this is sometimes appropriate, it is quite often not activity but rather the absence of (productive) activity that marks someone’s inattention. On the other hand, occupied rather looks at the question not of activity but as one of space that is filled by one thing or another. Is that space filled by attentiveness to communication, or is it filled with eating and drinking, playing games, working, sleeping, or something else? The choice of a semantic domain that is focused on space rather than activity is the far more Nathanish option.
This is especially true given the context of the sort of things that can be occupied. One’s belly, for example, can be occupied by a tasty and filling meal. A restroom can be occupied by someone on a plane or in another public location, thus preventing that spot from being filled by someone else. People occupy jobs and positions, thus filling them and making them unavailable for others. And, perhaps most Nathanish of all, during wartime a given territory can be under the possession of one’s enemies, in the manner we speak of occupied Europe or Southeast Asia during World War II history, and any semantic domain that leads people to think of the confluence of geography, military history, and food is going to be a highly Nathanish option.
Let us therefore summarize, in that busy and occupied both serve the purpose of querying someone about what they are about. Asking if someone is busy, however, assumes that someone is in fact doing something when they in fact may not be doing anything and may not even be conscious. Regardless of whether or not someone is actually busy, though, if someone is not focused on communicating you, their attention is being filled another way, be it by unconsciousness or some other activity, and framing a question in an abstract way that focuses on space and territory and using analogical reasoning to discuss that which is often hard for people to visualize is a proper and judicious way to speak in a Nathanish fashion, not only in such a question as this but in many other areas as well.