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In and of itself ppi means little to me once it passes the line of obvious pixelization. There are other things that matter such as contrast, color saturation and accuracy. It also matters how far away the display is. For example, think of those giant jumbotron displays at sports events. When you are 100 years away, they can almost look like a HD TV. When you are 18” away, it looks like a bunch of individual lights.
As for when it is beyond the capability of the average human eye to perceive additional pixel density, there is some disagreement. Most experts (whatever that means) say that the 300-500 PPI range is about the limits of the human eye, while others, such as the blog Christopher cited, claim a much, much higher density is required.
According to this blog:
"If a healthy adult brings any display screen or printed paper or whatever 4 inches (100 mm) from his or her face, the maximum resolution he/she can see at is 2190 ppi/dpi."
That's nearly 10 times sharper than the 239 PPI delivered by the Chromebook Pixel, the sharpest image of any laptop on the market. I tested one for two weeks and it was fantastic. It's hard to believe a picture could be much sharper, or that our eyes can perceive it, but that 2190 figure suggests it's possible.