Let's say there's a supermarket selling a hundred different products. Before it opens for the day, the staff arrange all the products into their appropriate shelves. This should be a low entropy state, since the products are highly ordered.
After the supermarket opens, a shopper with a trolley goes in. They select some number of products and put them into the trolley. From the shopper's point of view, it also sounds like this is a low-entropy state - under the definition "stuff I want to buy", all the stuff they want to buy is in that trolley and all the stuff they don't want is outside of it. But from the supermarket's point of view, it should be a higher entropy state; if the shopper leaves, they have to take all the stuff out of the trolley and put them back in the appropriate shelves. Who is correct here?
It seems to me that the problem is that "order" can be defined differently, but that would suggest that entropy itself is not well-defined, and that seems implausible.
