A replacement for email probably won't look very much like email. It'll inherit the good and drop the bad.
Speech ---> messenger ---> letters ---> telegraph ---> telephone ---> fax ---> email ---> ???
What's good about email? You can send it at any time. It's standardized and supported everywhere. UTF-8/UTF-16. Cheap/free. Extremely fast. Extremely easy.
What's bad about email? Spam. Conversations get broken (reply instead of reply-to-all). Prioritization must be done manually, and differs between the sender and receiver. Lack of privacy (PGP is a bandaid on a severed limb). Reading and interpretation takes time. Fonts, colors, and graphics can too easily be used terribly (e.g. the "view" is broken in MVC). Micro-managing messages and contact lists. Search (http://theoatmeal.com/pl/brain/memory). Conveying context and emotions is difficult. I'm sure you can can list more.
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I've been thinking about the prioritization issue, using a sort of expensive cipher, but for humans.
In the morning, Kate in accounting gets a call from their supplier for car engines. They demand $6.7M payment on an invoice 90 days overdue, and won't make the engine delivery tomorrow unless they get the cash wired to them by 5pm tonight. Kate knows they need those engines to put in cars coming off the assembly line tomorrow, so Kate sends an urgent message to Susan, the CEO. They have the cash, all Kate needs is Susan's approval to wire it.
Susan gets the message in her inbox marked "urgent", but doesn't read it. She has 1,000 other unread messages, 200 "urgent". Susan gets through 800 messages before leaving, but never gets to Kate's.
The next day Susan finally reads Kate's message and FREAKS OUT! She calls up the car engine supplier about the late payment. "Sorry, no engines today! Next time make sure you pay us on time!" Car assembly halts, productivity bottoms, and they start burning money from idle workers and sales lost to late car deliveries.
In a small company, Kate would just walk into Susan's office and remind her. In a large company, with a CEO who's "SO BUSY", or another human who's "SO BUSY", important messages like that can be read too late. Here, Kate knew it was really important, and marked it "urgent", but because too many other people cried wolf too, Susan never got the message.
So, how can you prioritize a message, relative to all other messages someone else has queued?
Imagine an economically-consuming task. We'll use time, but money could work too. When you press "Send", a button pops up. The more times you click on it continuously, the higher priority your message will be relative to others who clicked it fewer times. Your message isn't sent until you stop clicking for 5 seconds.
So, if you click your button for 10 minutes in a row, which is a total waste of your time, your message will appear higher on someone's message-queue than someone who clicked it for 9 minutes in a row.
Furthermore, when the receiver gets the message, and see's that you're a drama queen over-reacting on something that's really low-priority, she can down-vote you. Next time, 10-minutes of button clicking will only count for 5 minutes. The sender gets notified that they cried "wolf! wolf!" and can alter their behavior accordingly.
Clicking of a button doesn't have to be the actual task. It shouldn't be able to be automated (button-clicking can), and it should be boring (playing Tetris would be disastrous, yielding every message as URGENT).
Cash works too. If you cold-send an email to Bill Gates, he's probably not going to read it. What if you risked $100 sending the message? Bill has 48 hours to read/reply to it, otherwise the $100 goes back to you. If he does read/reply in 48 hours, he can keep the $100 (don't bug me again!), or return the $100 (let's keep chatting...).