the error in Ryan's logic

In a gdgt.com article, the author, identified only as Ryan, concludes that doubling the dimensions of the iPad, as measured in pixels (quadrupling the total number of pixels) would not be enough to qualify the new device as having a "retina display" (one with a grain finer than the human retina can discern, such as the Retina Display (an Apple trademark) in the iPhone4 (another Apple trademark)). A cornerstone of his argument appears below...

"Now, the retina display was so named because Apple found that "there's a magic number right around 300 pixels per inch that... is the limit of the human retina to differentiate the pixels."* This assumes holding the device about a foot from your eyes, but I think most people tend hold their phone and their iPad at roughly the same distance (between 15 and 20 inches), it it's probably fair to assume that the iPad retina display should still be somewhere around 300 PPI.

* From Steve's WWDC 2010 keynote; skip to about 36:30 minutes for the retina display introduction."

That's some pretty strange reasoning.

First, I think he's wrong about most people holding phones 15 to 20 inches from their eyes, but even if he's right it's the 12-inch assumption associated with the 300 ppi (pixels-per-inch) figure that matters. If a device is held further away than 12 inches, it requires fewer than 300 ppi to saturate the retina of the human eye, at 24 inches only 150 ppi are needed to achieve the same effect, or 200 ppi at 18 inches.

At 2048 X 1536, a double-dimension iPad display is comfortably above 200 ppi, and even slightly above the 240 ppi that would be needed at 15 inches distance from the eyes, the lower limit of Ryan's own estimate of how far away people hold their iPads, so, assuming the guideline of 300 ppi at 12 inches is accurate, it would definitely qualify as a retina display.

I'm not predicting what Apple will do. The 1024 X 768 display in the first-generation iPad is already very crisp, and they just might decide to stick with it for another year, perhaps lowering prices a bit and concentrating on increasing frame rates in games, or they might increase the screen dimensions by a factor lower than 2. A 1.5 increase would mean 1536 X 1152, still qualifying as a retina display at 20-inches from the eyes, the upper limit of Ryan's range, while increasing the total number of pixels by only 2.25, a factor low enough that they could probably still manage a performance increase by going to a CPU using dual A9 cores paired with any of several GPUs. More importantly, they might be able to put all that together without a price increase that would drive many people to other platforms.

Jumping to a 2048 X 1536 display sounds risky, but if Apple's suppliers can build them fast enough, without significant delays to tweak the production process, at a low enough price, with a low enough failure rate, they just might go for it.