Yes, there are attempts to create separate containers on mobile devices to impose that IT mentality; desktop virtualization is one technique that's gone nowhere, and there's the notion of separate personas in BlackBerry OS 10 and in some Android devices. However, I suspect the strict separation of work and personal is a ship that has sailed.
Instead, businesses will adapt to a world where individuals carry their own computing engines -- their smartphones and tablets -- and hook in to networks, monitors, storage, input devices, and so on as needed. Our desks will have peripherals, not PCs. Standardization and security will move down to the information level, not the device level.
That vision is years away, of course. In the meantime, people will still use the PCs they have. But more and more companies will stop replacing them with new PCs and instead issue tablets instead to most workers -- and eventually get out of the device-issuance business altogether, except for those workstation uses.
Steve Jobs' vision is coming true, and Microsoft has made it so much easier to realize it.
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