It took me 10 years to understand entropy

The typical measure of entropy (Shannon or Gibbs, and let's spare details for later and after you've read up on the theory of large deviations) is

- sum (p log(p))

which is not that different than the formula for the mean

sum (p 1/n)

the critical difference is the normalization constant is based on the probability of the state rather than assuming a uniform probability over all states.

So, in effect, the entropy is a measure of the mean. It is a measure adopted to the case where "mean" is ill-defined because the number of modes and/or the variation around those modes is not handled well by simpler metrics.

I had the pain, and pleasure, of taking and then (assistant) teaching thermodynamics at MIT.

One of the tidbits that always stuck with me was that astronomers have estimated that observable universe’s total entropy:

When you compare that value to the maximum possible entropy, i.e. the heat death of the universe, and then to the ridiculously low entropy state of the beginning of the universe, we are currently halfway along in that ‘timeline’.

It always brought to mind a grandfather clock; the clock stops when the weight hits the floor, and we are halfway there…

First, entropy is a macroscopic property, it makes no sense to talk about the entropy of a single particle. Second, entropy is not a fundamental property, it depends on what the observer cares about. Take the common example of a gas in the corner of a box, in that case we care about the density distribution in the box, a macroscopic property. To make this more concrete, one way to quantify the density distribution could be to tessellate the box with cubes of some size, find the ones with the lowest and highest density, and use the difference between those two densities as a measure of density variation.

Once we have decided that all we care about is the density variation in the box, we can go through all possible microscopic states and group them together by their density variation. Finally a low entropy macroscopic state is simply a macroscopic state - a certain density variation - for which there are only a few microscopic states that have the corresponding density variation. On the other hand a high entropy macroscopic state is a macroscopic state for which there are many microscopic states that have the corresponding density variation. You can also call the microscopic states low or high entropy but only with reference to the macroscopic property you use to group them, in themselves microscopic states are not low or high entropy.

If you observe a low entropy macroscopic state, then you know a lot about the microscopic state, after all there are only very few. If you observe a high entropy macroscopic state, then you know a lot less about the microscopic state, there are much more possibilities even though they are microscopically indistinguishable. And if there are no limiting constraints on how the microscopic states can evolve, if the evolution is essentially a random walk through all possible microscopic states, then the entropy of the system will increase with high probability as it is much more probable to randomly walk into one of the many microscopic states associated with a high entropy macroscopic state than to walk into one of the few microscopic states associated with a low entropy macroscopic state.

not to brag but it took only 2 months to forget anything about it

Well that's not quite what it is, first of all, and second of all I don't like the practice of calling something a catastrophe when its just predicted by a theory, but didn't happen. I mean, bad theories always predict something horrible should be happening. What's next, do flat earthers get to have an "ocean water catastrophe" because their theory implies all the water drains away? Or a "super luminal" catastrophe because their theory requires infinite unending linear acceleration of the earth (and moon and sun)? I mean, it really is a catastrophe I guess...for the theorist.