Paradigm shifts are funny things. As Malcolm Gladwell points out in his bestselling The Tipping Point, often there’s an abrupt transition between old worldviews (or behavior patterns) and new ones. Yesterday, nobody even dreamed of phones that take pictures. Today you’re lame if you don’t have a cell phone camera.

I recently noticed that AT&T is promoting its “three-screen” vision — meaning, in essence, that the Internet will reach users in three distinct ways: the TV screen, the PC screen and the mobile device. I like the idea, but I don’t think it goes far enough. For one thing, I don’t think three screens (or any fixed number) will suffice.

The right way to look at Internet use, in my book, is to assume that each individual owns and operates a number of Internet-connected devices: one or more phones with varying bandwidth capabilities and applications (voice, video, e-mail, and so forth); one or more PCs with multiple Internet (Wi-Fi, wireline, Evolution Data Optimized) connections; and one or more TVs (given that most households have more than one TV, though most aren’t Internet-connected yet).

That’s not all. Many users also have multiple network-attached (or -capable) devices, which, while they don’t connect directly to the Internet (yet), may do so in the near future: cameras with USB links, Ethernet-attachable printers and so forth. Cisco senior vice president and general visionary Jayshree Ullal likes to make the point that we should assume that any device that’s capable of an Internet attachment ultimately will get one. I think she’s right. So, instead of assuming a mere three screens, we should be thinking in terms of multiple screens (and Internet applications) per user.

Why does this matter? For a couple of reasons. First, the three-screen view underestimates the per-user consumption of Internet bandwidth. Most of the telcos and equipment providers I speak with assume the old model of Internet connectivity will prevail. That model measures Internet connectivity to each household (or workplace) — not to each user. Big mistake. Users consume far more connectivity (generally from multiple providers) than this model accounts for.

Second, it underestimates the impact of peer-to-peer traffic. Peer-to-peer’s gotten a bad rap because of copyright infringement issues, but even taking those out of the equation, an increasing amount of Internet traffic results not from users accessing sites, but from users communicating with each other in bandwidth-intensive ways: not just voice, but interactive video (including telepresence) and file-sharing.