While we can choose which field to order by when searching in advanced mode:
… we cannot choose whether we want to order ascending or descending.
Adding orderdesc modifier would easily make it possible:
order:likes is already descending, right?
So what you want is “the opposite of the normal order that this term means”.
Not sure about this, but… How about order:-views to start at 0 and go up, while order:-latest starts at the oldest?
struggling to think of use cases for orderdesc:likes or orderdesc:views, though I am open to possibly adding order:earliest (its quite rare to need though)
We should find a way to allow for opposite ordering for any ordering type (kind of a universal way of doing it), then easier to remember and use.
You never know what one could come up with 
I’d use orderdesk:likes to identify which type of material is the worst in terms of people likes and not create similar topics, or not include them in the lists.
orderdesc:views might possibly indicate topics that need some more useful information to get more attractions from organic search.
I think there might be more use-cases I can’t think of, why not just make it possible with a single operator.
I want this feature in order to support an “inbox” use case for processing forum traffic: I have a search that I want to sort by least recently posted (so that I can work down the queue of posts awaiting a response), and I can only get most recently posted (afaict).
You might want to consider using the Unanswered filter: /latest?max_posts=1.
However, I did also write a PR to add this sorting option:
Taking suggestions as to what the name in the dropdown menu should be, I don’t really like “Oldest Update”.