A peek into the quantum world

In https://plus.google.com/117663015413546257905/posts/B16McQB6Vn2, John Baez discusses the amount of information in a gram of water. In Newton's classical world this doesn't make sense. To describe even the position of just one molecule of the water would take an infinite number of decimal places, and hence an infinite number of bits. But when we get into the quantum world things actually get simpler, and Baez can write:

we see a gram of water holds

4.05 × 10^24 bits

of information.  And amazingly, this is something we know quite precisely!  I've rounded off the numbers, but we could actually work it out to more decimal places if we wanted.

[10^24 means a 1 with 24 zeroes following.]

This makes me feel that I understand a bit more about what the quantum mechanical view of reality is [though obviously nobody should take my opinion too seriously]. Any time you have a very large finite system obeying relatively simple rules then it's going to look like some infinite thing which is philosophically more complicated, but likely to be more tractable mathematically. For example, if you plot the distribution of the result of 10^24 coin tosses then it is going to look indistinguishable from a continuous bell shaped curve (a gaussian distribution).

Will this viewpoint help me the next time I try to understand quantum mechanics a bit? We'll see.