The complete question was:
If you were to look at the universe as an organism, was the early universe a simpler organism than the present-day organism? Is the total complexity of the universe growing, shrinking or staying the same? And how do you measure that?
Physicist: Absolutely. The total complexity of the universe is increasing, due to the inevitable march of entropy (or information), which is exactly the measure of complexity. A more intuitive way to talk about complexity and entropy is: can you predict what you’ll see next? If you look at part of a checker board, you can probably guess what the whole thing looks like, so the board is predictable and has low entropy. In the early universe matter was distributed pretty uniformly, almost all of it was hydrogen, almost everything was the same temperature, and there were no complex chemicals of any kind (going back far enough everything was ionized). So if you’d seen one part of the universe, you’ve pretty much seen all of it.
Nowadays the universe is full of a wide variety of different elements with very complicated ways to combine together, matter shows up hot, cold, as plasma, as proteins, in stars, and clouds, and not at all. The amount of data it would take to accurately describe the universe as it is now utterly dwarfs the amount that it would take to describe the early universe. On an atom-by-atom basis, in the early universe you could grab an atom at random and feel fairly confident that: it’s hydrogen, it’s ionized, it’s about “yay” far away from the other nearby hydrogen, etc. Today you’d probably be right if you guessed “hydrogen” (about 3/4 of the universe’s mass is still hydrogen), but you’d have a really hard time predicting anything beyond that.
Oddly enough, life is surprisingly uncomplex compared to say, dirt or sea water. If you look at a single cell in your body, you’ve already got a pretty good idea of what you’ll see everywhere else in your body. Admittedly, we are more complex than single celled life, but most of that is a symptom of being physically bigger.