Right now, I have about a million things I should be doing, but instead I've wasted some perfectly good minutes working out a back-of-envelope estimate for the total pixel resolution of the known universe.
Let me begin by saying right off that I know absolutely nothing about physics or advanced mathematics, and all of my ignorant curiosity is fueled by pop sci books by the likes of Brian Greene and a youth misspent with the Star Trek franchise. So I don't know much, but I do know enough to know that there are probably some very good reasons why everything that follows is total bullshit.
Now that I've gotten that out of the way...
For the last century or so, physicists have largely agreed that there is a unit of spatial measurement below which it is impossible to observe, measure or know anything about the matter that constitutes our universe. Put in other terms, this is the scale at which Newtonian physics fly out the window altogether and quantum weirdness takes over. This unit is called the Planck length. Metaphorically speaking, we can understand the Planck length as similar to a pixel on a television monitor. Looking more closely at a pixel on a screen won't give us any more resolution or information about the object represented on the screen, and the same apparently applies to matter (and energy) itself.
This dynamic also applies to time (which, per Einstein, is equivalent to space). We cannot possibly measure or even conceive of temporal events below the threshold of the Planck time, which is the amount of time it takes a particle traveling at light speed to traverse a Planck length. So there are temporal "pixels" in our universe in addition to spatial ones.
I've been shopping for a new phone, which is probably why the question of relative pixel resolution was bouncing around in my brain. The iPhone 5s has 727,040 total pixels, while the HTC One has 2,138,400, which makes me wonder why I'm sticking with the iPhone, which is another question altogether.
2 million is a lot of pixels for a phone, but how many does the known universe contain? My ridiculously oversimple answer is to measure the volume of the known universe in Planck lengths, and multiply it by the projected age of the universe at heat death, measured in Planck time.
According to Wikipedia (see, students, professors do it too!), the observable universe is a sphere with a diameter of 29 gigaparsecs. If I'm using Wolfram Alpha correctly, this means that the total volume of the universe (as it exists "now," in cosmological time) is equivalent about 9.7 x 10178 Planck lengths. Similarly, the heat death of the universe is expected to kick in at about 10100 years, which amounts to about 5.85 x 10150 Planck time units. If we multiply the total volume by the total time (and, seriously, why wouldn't we?), we get the following tally:
TOTAL PIXELS IN KNOWN UNIVERSE: 5.67 x 10329
Pretty nifty, eh?
Of course, even I can think of a great many good reasons that this is a completely meaningless assertion, but why ruin the fun? If you'd like to ruin or add to the fun, please feel free to comment.
Now, back to our regularly scheduled programming...