In John C. Baez "What is Entropy?" (A 122 page PDF best suited for reading on airplanes without wifi and in flight entertainment), he states:

> It’s easy to wax poetic about entropy, but what is it? I claim it’s the amount of information we don’t know about a situation, which in principle we could learn.

The entropy of a random integer being 1 makes intrinsic sense to me, given I didn't spend years in theoretical math classes