Normalized energy flows

Some of you readers leave insightful comments. I'd maintain Just Enough Craig even without readers (because I write for me), but those occasional comments of yours fill my sails and make blogging a more rewarding experience.

In my previous post, I wrote that there doesn't exist a word in the English language for obviously connoting (or denoting) the opposite meaning of a conspiracy but offered “opportunity” as a possible best-fit. My greater point in that piece was that push-up understandings of causal relationships within complex systems are generally easier to grasp than push-down ones, and naturally the conspiracy more easier supplants nuanced world views that entail greater systems pushing their influence onto the very components they comprise.

After my piece, reader Filc suggested another antonym for “conspiracy”: “evolution”. Whereas, “opportunity” connotes parts profiting from the emergent behavior of the whole, “evolution” connotes an unplanned series of changes in the parts based on selective pressures of the whole—definitely some push-down causality going on in both cases. “Evolution” a good fit, not just for its standalone semantics, but because the very “intriguing idea to quantify complexity” I said I wished to write about in a future post originates from Eric Chaisson, a scientist in the field of cosmic evolution.

In the freely available paper The Rise of Complexity in Nature, Chaisson describes his idea of a normalized energy flow as a scalar metric for complexity. Before hitting on the complexity part of this, let's spend a little time with the idea of a normalized energy flow.

Simply put, a normalized energy flow is the amount of energy that flows through a system after dividing that energy-flow amount by the mass of that system. Dividing by the mass of the system allows us to compare big systems, such as stars, with small systems, such as bacteria. (Because otherwise big systems' sheer size would allow even the lowest density of energy flows to outweigh even the highest-density energy flows of small systems.) So, for example, our sun puts out a great deal of energy (high energy flow) but is itself really massive; as a result, the sun's normalized energy flow turns out to be rather low: about 2 erg/s/g. (To understand how low this is, consider that an erg is an amount of energy equivalent to one ten-millionth of a joule, and a joule itself is about as much energy as is used by an energy-saving compact fluorescent light bulb during one blink of the eye. (In other words, it takes on the order of 100,000 kg of sun, fusion-powered though it is, to generate enough power to run one energy-saving light bulb.) Thus, our sun is outputting a rather paltry sum of energy after taking into account how big it is. As for our microscopic bacterium, its normalized energy flow is about two orders of magnitude higher than the sun's (~10³ erg/s/g). Humans are yet another order of magnitude higher (~10⁴ erg/s/g). If nothing else, the concept of a normalized energy flow is interesting because it means we humans, powered on burritos and peanut butter sandwiches, have way more energy flowing through us than equal-massed portions of stars, fusion-powered though they are.

Chaisson's point with the idea of normalized energy flow is that it serves to rank rather reliably systems in terms of complexity. Our sun is big and hot, but it isn't terribly complex; it's mainly just a lot of hydrogen fusing into helium. Even the simplest of microorganisms are obviously more complex—more intricate—than stars, and we observe an obvious increase in normalized energy flow to match. Up the scale you go: bacteria, plants, animals, brains. By this measurement, the most complex self-supporting system that we know of—anywhere in the universe—is that of industrialized human society with its nearly $10^{6}$ erg/s/g normalized energy flow. (But then again, perhaps we should seek clarification of the term “self-supporting”!)

At the bottom of the last page of the Chaisson paper I linked to above, there's a logarithmic graph showing normalized energy flows of various systems versus when those systems emerged within the universe. It's an interesting graph, if for no other reason than you don't often see a exponential curve on a logarithmic graph. The graph shows what appears to be an inexorable march by nature to ever greater normalized energy flows and thus ever greater complexity. It's complexity emerging from &ellips; what, exactly? This is not clear. Chaisson is suggesting that the driver behind this upwards march is ever greater normalized energy flows and further suggests that the energy flows themselves are “engendered largely by the expanding cosmos”. Thermodynamically, nature's march towards greater complexity is explained as ever smaller pockets of increasing order created at the expense of ever bigger pockets of increasing disorder elsewhere.

This evolutionary view of the universe with energy flow as a driver for greater complexity is a topic I'd like to write about in a future post.