(1) Total entropy:
The total amount of disorder in the system (which is always increasing if the system is closed– 2nd law)

(2) Rate of entropy:
The rate at which order is being transformed into disorder. This is basically a derivative of (1) and time.

I’m thinking about these two measures in relation to the “flower” in my previous post. When the blossom is at its apex of beauty/symmetry/complexity (the moment just before it first begins to whither), its rate of entropy (2) is at its highest level. At that moment, the flower has the most “order” available to be transformed into “disorder,” and its rate of entropy (2) is highest. As it begins to whither, less and less order is available to be transformed into disorder, so its rate of entropy (2) decreases.

But all the while the system’s total entropy (1) is increasing, however high or low the rate of entropy (2).

So, with that said….

@rafefurst: You write: “As entropy increases, symmetry also increases.”

I’m wondering which entropy you’re talking about here. If you’re talking about total entropy (1), then in a sense you’re claiming that symmetry is always increasing (because total entropy is always increasing), which clearly isn’t the case, is it?

If you’re talking about the rate of entropy (2), then I would agree, but would flip around the statement:

As symmetry increases, the rate of entropy increases.
(think of the blossom above)

[Then again, maybe symmetry is always increasing... if you see the end state (after entropy is finished) as perfectly symmetrical, which it may very well be. For example, if the universe doesn't contract and continues to expand and eventually all subatomic particles have broken down to their constituent parts (quarks and leptons and whatever) and all these particles are spread across the universe in perfect equidistance from each other.... at that moment entropy is complete, but we also have a completely symmetrical physical state, no?]

Re biodiversity: could you think of an ecosystem as a larger version of the flower above? As the ecosystem grows and diversifies by way of speciation, its symmetries become ever more complex and and its future ever more unpredictable. At some point, it reaches a kind of apex or peak where it has the most available order (complex symmetries) to transform into disorder. From that point on, it goes into decline as total entropy continues to increase while the rate of entropy slows down with each ratchet down in diversity and complexity.

Yes, entropy is sometimes viewed as the rate of degradation of energy to less useful forms, but this definition is unsatisfying because it doesn’t specify what “useful” means. The forms of energy that are useful to us are precisely those that come in predictable, harnessable forms, like light or electricity. Heat is not so useful because it is literally the random motions of individual particles.

So yes, your statement “as more energy is degraded by the system, the system’s complexity and diversity increase while its predictability decreases” is correct, though “complexity” is a slippery word.

Your second question is worthy of a blog post of its own, but I will give a short answer that the relationship between entropy and beauty is not so simple. Compete randomness (think white noise on a TV screen) is not much more interesting than compete predictability (e.g. an unchanging blue screen). True beauty requires a sophisticated mixture of order and disorder.

As entropy increases, symmetry also increases. Beauty is a bit more complicated because some people feel symmetry is beautiful and others prefer asymmetry. Still others find symmetry ‘fearful’ :-)

I have gone out on a limb and claimed that asymmetry is the root of all value, and similarly it is the root of complexity (even though we still don’t quite know how best to define complexity itself).

Symmetry breaking is talked about as an important concept in physics for explaining the specific and seemingly arbitrary (but not random) configuration of matter and energy in the universe, given that the supposed “universal laws” seem to be all about symmetry. Can’t say I understand it at more than a superficial level.

Aesthetically, I am a fan of both symmetry and asymmetry…

If so, are you claiming that a system’s unpredictability is a function of its energy flow? That is, as more energy is degraded by the system, the system’s complexity and diversity increase while its predictability decreases.

A related question:
Is there a connection between increased entropy and increased symmetry/beauty. For example, it seems that the more entropy a flower has, the more symmetry and beauty it has. At the moment when it’s “falling apart” the most, it is also displaying the most beauty, no?

By extension, is predictability inversely correlated with symmetry/beauty?