On Tuesday morning, newly anointed Apple chief executive Tim Cook took to the stage in Cupertino at the company’s One Infinite Loop campus and introduced the next version of the wildly popular iPhone. And it wasn’t what people were expecting.

The device itself, dubbed the iPhone 4S, looks nearly identical to the previous version of the phone, the iPhone 4. It’s got a faster processor, a better camera and an improved antenna design, but by all appearances, it’s business as usual.

To many Apple fanatics, seeing a rehash of the iPhone 4 design appear after nearly 16 months of waiting for a new device from the company was a disappointment. To Apple, however, this was not just par for the course — it was a carefully executed example of how the company is marching to its own, steady beat.

In the years since the launch of the original iPhone, Apple has taken a two-pronged approach to how it handles consumers: on the one hand, informing them that seemingly impressive specifications and loud promises of performance don’t necessarily make for a better product; while on the other, quietly reminding everyone that the company’s devices are in a class of their own.

On Tuesday, that message was more pronounced than ever. While Apple’s public relations team didn’t skip a beat in telling the reporters that they were currently in the process of crushing Google’s Android platform in all the ways that matter, the goal was to show where they think real innovation happens.

The launch wasn’t really about the phone at all. It was about the software inside and possibly the kick-start of the next big revolution in how we interact with our gadgets.

That software is called Siri, but Apple would like for you to think of it as your “intelligent assistant.” And what Siri does is nothing short of amazing.

Siri can listen to your “natural language” (that is, words spoken as you would to another human, not a computer) questions or requests and respond like a digital secretary. It’s not just that Siri listens, either. The software is capable of understanding the context of what you’re talking about, so if you ask it to set an alarm on your phone, it will ask you for what time. And again, you don’t. Have. To. Talk. Really. Slowly.

If you ask Siri to schedule an appointment, it will not only check to see if it conflicts with any of your other meetings but will help you juggle the time slot until you have your day’s events mapped out. Siri will find movie theaters close to you or tell you how to get home from your current location. It can identify family members, spouses and co-workers you’re always talking to, and it knows when people’s birthdays, anniversaries or other big events are coming up.

Here’s an example of a chat I had with Siri:

Me: “Schedule an appointment with Jack for 3:30 p.m.”

Siri: “Okay, here’s your meeting. Note that you already have a meeting that overlaps with this. Should I schedule it anyway?”

Me: “Change the time.”

Siri: “Okay, Joshua, what’s the new time and date for this meeting?”

After I learned that my new time overlapped again, I asked Siri to cancel the meeting, and it asked me if I wanted it removed from my calendar. All this happened in the span of a minute or so, and all of it felt strangely normal.

More interestingly, Siri is plugged into Yelp and Wolfram Alpha (a search engine dedicated to finding facts instead of Web pages). If you ask Siri how much $45 is in British pounds, it can tell you the answer. Or how many cups are in a gallon (16, for the measurement challenged). But again, the best part of this is that you don’t have to tone down or over compensate for computer hearing. Siri listens like a person, and often responds that way, too.

As we’ve seen with the iPad, and frankly the entire focus of Apple over the past few years, the company wants the desktop computer to disappear and something else to take its place. Siri looks like it’s going to be a big part of that disappearing act.

But not everything with this technology is perfect. It uses a network connection to get answers, so you won’t be able to use Siri on a train. It’s still in beta, meaning there are bugs to be found. Only the newest iPhone will be able to take advantage of the software, so you’ll need to purchase a new device to experience all this innovation.

And there’s still that lingering feeling among some in the tech community — even with all this futuristic thinking about software — that Apple somehow missed a beat this week by not launching a completely new phone after such a long wait.

Will that affect sales of the iPhone 4S when the device becomes available Oct. 14?

Maybe Siri knows. Let’s ask her.

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