As you get ready to leave the office on Friday night, you close the Excel spreadsheet that you have open on your Windows 8 PC, knowing that it’s stored in the cloud with Office 365. You slip your Surface tablet into your bag, then pop in your headphones and pull up a track from Xbox Music on your Nokia Lumia phone, as you use Bing to find a place to grab a beer. While you’re sipping on your Guinness, you email your friends from your Outlook account to see if they’re still up to play a round of the new Halo game for the Xbox One on Xbox Live, which is powered by Windows Azure, after which you plan to fall asleep watching a movie you rented from Xbox Video.

This is Microsoft’s platonic ideal of the world. Right now, very few people live in it. But it’s the one that its freshly anointed C.E.O., Satya Nadella, wants to create for everyone, and which he is perhaps uniquely qualified to build. A twenty-two-year veteran of Microsoft, Nadella was most recently in charge of Microsoft’s successful cloud and enterprise group. In his first letter to Microsoft employees, Nadella rhapsodized about how, in the future, “computing will become even more ubiquitous and intelligence will become ambient” in a “software-powered world.” Software, he added, in a mock interview that was broadcast on the Web this afternoon, is going to mediate everything. In particular, it will be the kind of software that connects many devices to massive server farms, to vast troves of data, and to each other. It’s the kind of software, in other words, that Nadella has been in charge of building for years.

The Microsoft that Nadella is inheriting is different from the one that Steve Ballmer took over in 2000. Back then, Microsoft was perhaps the most powerful and influential technology company in the world. It wasn’t merely that its operating system, Windows, powered the vast majority of personal computers on the planet, or that office drones slaved away almost exclusively using its productivity software, Office, or that its monopoly on Web browsers, with Internet Explorer, shaped how people experienced the Web. It was that Microsoft dominated how most people thought about high technology in their lives. Apple hadn’t launched the iPod; Google had only just figured out how to make money; Mark Zuckerberg had not dropped out of college; and BusinessWeek wondered if Amazon would even make it. Under Ballmer, Microsoft’s powers—though, to be sure, not its revenue—diminished. The aughts saw the Web renaissance, and the rise of search, social networking, and mobile computing. Ballmer, in response, struggled to remold the software company into one that would sell devices and the services that powered them. He, in other words, arrived at the same conclusion as his counterparts at Apple and Google: Microsoft needed to control and sell all of the atoms and all of the bits, and they all needed to work together seamlessly. In Ballmer’s final years, Microsoft scrambled to reimagine Windows so that it could fit on any screen, build mobile devices that people would adore, and continue to fend off threats in both the office and the living room. Nadella gave little indication today that he would drastically deviate from the course that Ballmer charted when he radically reorganized Microsoft and bought Nokia’s phone business last year. His ascension to C.E.O. suggests a confidence that he, as a technologist with deep expertise in the cloud, can execute that strategy and innovate in a way that Ballmer, as a businessman and steward, could not.

The peculiar reality of a technology company that operates at the size and scale of Microsoft—and Google, and Apple—isn’t merely that it must continue to grow its sales and user base but that it must also continually expand its spheres of influence; its technology must touch and mediate everything. Every part of our lives or our businesses that’s left untouched is a space that another company can invade. Apple used music; Google used search; Facebook used your friends. The sprawling web of interconnected products that has resulted now thoroughly dominates our experience of consumer technology: if you own a Google Chromebook, your life will be much easier if you use Android and Chromecast and Google Drive, and much more painful if you try to use Windows Phone, Apple TV, and Dropbox. As I noted in October, “what people are choosing is less an iPhone 5s over a Moto X than an entire digital ecosystem that surrounds and permeates their life, and which will affect every other piece of technology that they buy.” People are deciding, in other words, how they want to live through technology.

Over the past couple of years—under Ballmer, no less—Microsoft has begun to articulate a fairly credible vision of its current ideal world for users. It has failed, however, to flesh out that vision enough to convince people to abandon their perfectly comfortable, increasingly Apple- or Google-centric existences on their phones and in the cloud. This makes Nadella’s challenge all the more profound: he cannot merely finish constructing the world for which he’s been handed the blueprints; instead, he must begin to imagine a wholly new one.

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Photograph by Kim Kulish/Corbis.