In 2011 Samsung unveiled a smartphone so big it looked as if it must have been a joke, a mistake or a turn toward conceptual art.

With a screen measuring 5.3 inches diagonally, the device, the Galaxy Note, was met with instant and slightly unhinged criticism.

A writer for the Boy Genius Report, an industry blog, called the Note "the most useless phone I’ve ever used," adding, "You will look stupid talking on it, people will laugh at you, and you’ll be unhappy if you buy it."

The critics were wrong.

Samsung went on to sell millions of the huge Note; and its successors, the even larger Note 2 and Note 3, became some of the best-selling smartphones of the past few years. The Note also spawned dozens of copycats, making for an entire new category: phablets, or smartphones almost big enough to be considered tablets.

Today, just about every smartphone manufacturer — including, at long last, Apple — makes a phone as big as the Note, and plus-size phones are threatening to overrun both the smartphone and tablet business.

So the Note has become a watershed device; along with the original iPhone and iPad, Samsung’s phone is one of the most important and influential digital inventions of the past decade.

Now there’s a new Note, and it is better than ever.

The Galaxy Note 4, which went on sale Oct. 17, is superior to just about every other phablet on the market. Its only real competition is Apple’s iPhone 6 Plus, which has a more intuitive interface. But the Note 4 has at least a half-dozen clever features that should prompt even the most die-hard Apple fan to begin salivating.

Among them: The Note 4 has a sharper, larger display; the ability to charge its battery to half-full in just 30 minutes; and a series of on-screen features that make it easier to use in one hand.

Also, like previous versions, the Note 4 has a stylus, which Apple fans have long argued was proof of its inferiority. They’re wrong; despite Steve Jobs’ objections, the stylus is a handy tool for manipulating such a big phone, and after using the Note, I often found myself missing it when I went back to the iPhone.

With the Note, Samsung is aiming for something transformative, a device that is more than just a big phone: The Note 4 feels like an ambitious effort to reach for the future of computing, in which our phones are more useful and powerful than PCs, and in which we barely bother with any other kinds of computers.

Granted, the Note 4 is far from perfect; in true Samsung fashion, a lot of gimmickry can be found in it, and several features seem half-baked. The heart-rate monitor is pointless, and the fingerprint scanner isn’t nearly as good as Apple’s. But if you can overlook the rough edges, you’re left with a truly useful machine.

Any assessment of the Note 4 must begin with its stunning display.

Even though the Note 4 is just about the same size, overall, as the iPhone 6 Plus — it’s about 5 millimeters shorter than Apple’s device, but 1 millimeter wider and thicker — Samsung has packed a slightly larger display into the Note than Apple does into its giant phone. Even though the screen is only about 6 percent larger than the iPhone’s, it’s a noticeable pleasure, like an extra inch of legroom in coach.

And the Note’s display is not just bigger; it is also better. DisplayMate, a company that performs technical tests on digital displays, recently called the Note 4’s screen "the best performing smartphone display that we have ever tested."

Although DisplayMate also found the iPhone 6 Plus’ display to be very impressive, it gave the Note 4 the edge because of a couple of technical advances, including what Raymond Soneira, DisplayMate’s president, called "significantly better color accuracy."

To my eyes, the Note 4’s screen did look better than Apple’s — sharper, more vivid and just generally delicious, the kind of screen you don’t mind staring at.

The Note 4 runs Android, Google’s mobile operating system, but like most Samsung phones, it has been dolled up by TouchWiz, the company’s horrendous homegrown user interface.

For the most part, TouchWiz isn’t pretty; it is a mess of garish colors and unintuitive gestures, and until you get accustomed to its quirks, it will seem to add unnecessary steps to just about every common task.

The surprise, then, is that for the Note 4 Samsung has built several useful features into TouchWiz that collectively recognize an important truth about phablets: We use them in different modes.

Sometimes, we use them as phones, or quick-hit devices to use on the go, when we need to scan email or look up directions. Other times, we use them in deeper ways, to go through morning mail, plan a day in a calendar, take notes while on a phone call or watch a show.

Samsung has smartly built its interface to facilitate either of these ways of using a phablet. Apple’s big iPhone, by contrast, does not appreciate these two modes; you use the iPhone 6 Plus pretty much as you would any other phone.

For use as a smartphone, Samsung has come up with a few tricks that make the phone easier to use in one hand.

The best of these is the side-key panel, a pop-up menu of useful icons that sits on the left or right side of the screen, right under your thumb.

Need to go to the home screen, the previous screen or see all of your open apps? On the iPhone those commands require stretching your thumb down to the Home button or all the way across the screen. On the Note 4, with the side-key panel, they’re all available with just a tap under your thumb.

Samsung has spent most of its effort improving the phablet’s second mode, its capacity for deep, two-handed tasks. Previous Note versions allowed you to place multiple apps on the screen at the same time. The Note 4 expands this feature, letting you place apps in small pop-up windows of any size you wish, pretty much like on a desktop PC.

The stylus, too, contributes to deeper productivity. It lets you select text and click on links with more precision than your finger can muster, and it can turn every screen into a notepad for your scribbles.

I admit I had to go through a lot of trial-and-error to figure out where the stylus and multiple windows would be useful, and at first blush, they both feel like pointless gimmickry. Eventually I did find some interesting uses. Managing my calendar and email at the same time, on the same screen, was far easier than popping back and forth between the two.

Samsung’s labyrinthine interface does not make the Note 4’s utility obvious, and even if it did, there would be a learning curve to grasping its unusual powers.

That’s why Apple’s phablet is far easier to use. But if you’re patient, and you want a glimpse of the phone of tomorrow, you should take a look at the Note 4.

© 2014 The New York Times Company