Email should have an expiry date, specified by the sender. The receiver would then sort by expiry rather than arrival. If a mail is not dealt with by the expiry date it is deleted/archived.
More generally, an email could be given an importance weight that is a sender specified function of time -- the sender's estimate of the expected utility to the receiver of reading the email at any given time. Mail would then be sorted by the utility of reading the mail now as opposed to putting it off until some later date: if a mail will provide just as much benefit in future, it may be safely ignored now. (the math gets a wee bit tricky...)
If you are sending an email which you don't want to ever expire totally, you might give it a high initial weight and a bit of a tail in case the receiver was busy. Mail with a very short initial burst would be functionally equivalent to instant messaging.
An email reader should present mail so as to maximize the expected utility of the user:
- Give priority to mails that must be dealt with quickly (short expiry)
- Order mail by type and subject, to minimize the amount of context switching the user must perform (eg using a 1D Kohonen self organizing map, plus an option to view more email from a particular topic cluster)
- Throw a few lower weighted mails into the mix, so that they are dealt with before they become emergencies. (for example, if there is a lower weighted email on the same topic as a higher weighted email, the user could deal with both while their mind is on the topic)
- Allow the user to specify the utility of not reading their mail right at this instant (ie i'm busy right now, but do notify me of anything super-urgent).
It should do this in a way that leaves the user in charge. It must be very fast, flexible, and understandable -- more a tool that allows the user to control their flow of attention than a straightjacket that forces the user to follow what it thinks is the optimal course.