For years now HD has been a magic word, and for just as long I've found humor in its use, when not shaking my head at the naievete involved. Everybody knows that you have two options with HD, 720 or 1080. Clearly 1080 is the better option, because it's a bigger number... right? Well, yes and no. These numbers represent the vertical resolution or number of rows of pixels from top to bottom of the screen. Of course vertical resolution is only half the picture, for whatever reason the horizontal resolution is implicit: 720 has a full resolution of 1280x720, 1080 has 1920x1080. In terms of resolution, yes, 1080 is better, but this is a really restricted and possibly misleading analysis. In terms of actual clarity, a vastly more important measure is PPI (pixels per inch). Imagine for instance that the big man on the block has a 60" 1080 HD lcd screen, in his own little world he is really special for having such a ginormous TV with such crystal clarity. But in reality, his neighbor's 20" 1080 HD lcd screen looks much clearer, and the reason is simple: both TVs have the exact same number of pixels, which means that to fill the extra space the 60" has pixels that are 3 times as big (with 9 times the area), making them much easier to distinguish from the same distance, making the contrasting areas of the image look blocky and jagged. To further illustrate, imagine another neighbor has a sad little 5" 1080 HD lcd screen--in truth, he is the one to envy! The clarity of such a screen would be astounding, with 440.6 pixels per inch it could draw letters and numbers 1/100th of an inch tall, just about twice the width (diameter) of an average human hair. On the other hand, Mr. big man only has 36.7 ppi, the smallest letter his TV could draw would be 1/7th of an inch tall, close to the width (diameter) of a pencil eraser!
The reason I say HD isn't HD is that as a computer user, I'm accustomed to HHD (higher than high-def)--you probably are too, you just weren't aware of it. Suppose we ignore all this (very relevant) pixel density stuff and focus solely on resolution; the average computer monitor has been capable of resolution better than 720 for a long time. 1280x1024 is the most common computer resolution, and it has 142% the resolution of 720. It is only 63% of 1080, but 1280x1024 is rapidly going out the window--in fact, you can now get a new 22" lcd computer monitor with greater than 1080 HD resolution for $200. The discovery of this recently surprised me, that seems like a great bargain. I'm a big fan of 30" 2560x1600 monitors, but unfortunately they are tremendously expensive, so in my idle pondering and interest in value metrics I ended up deriving the very simple math to get the numbers above and a few more that relate to 30" monitors. In short, a 2048x1152 screen has only 57.6% the resolution of a 30", but can be bought for 15-20% of the price. Likewise, if you really want to match the 30" experience, a 24" 2048x1152 monitor will have the same PPI... but any smaller size with the same resolution will also have a smoother image (or higher definition) than the 30". With this perspective it's no longer a great bargain, but an amazing deal.