I disagree on the randomness aspect. Non-thermodynamically speaking
H(X) = E[i(X)]
In fact your coin toss example is perfectly applicable here too , provided it's a fair coin that can be used in a Bernoulli Trial.
As a side note all measures are human-made because our mind is incapable of thinking without measuring sticks. Think of anything that's based on human studies and you'll find there are scales and levels on which they are measured because that's how our minds work. Take away those systems and it's still random. It's not measuring systems, those are made by us mostly to measure uncertainty and they themselves are uncertain when we get to much smaller or larger levels. It's why Quantum Science today is in a state of flux.
Note: I'm not discussing religion here, but you just brought up all my years of studying Engineering and Maths from nearly 10 years ago. Bah I remember wasting so much time on Theory of Computation and Algorithm Analyses.
Sometimes I can see where the birds are, they flew away years ago, hunted down by a speaking eye, before I can speak my mind much further, the great giant molasses creature appear in front of me and start telling me how lucky I am for being teeth, yes, teeth, just like a canyon in our backyard during our vodka hours!
So be it, maybe I could manage to stay in my place, but sometimes the loneliness is making me sing some Johnny Cash songs, and not in a flight of dancer way, but more like a flying mule.
I cried and I cried, but she kept telling me that when the house is two, I can still swim in my neighbour swimming pool, but I don't want to, do you see how he fill his pool? by asking Marcus, our local treasurer to sing his beloved ballad, The Penguin Alpha.
I laugh at them, maybe this place is just like home, oh wait, I'm home, home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home home.....
I'm so happy I can eat fried rice again.
I love you guys.