Multi-Scale Times

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The parable of the giant leaf:
It takes about 100 watts to power a person's metabolism.
Earth's average insolation is about 250 watts per square meter.
As a result, photosynthesis at 2.5% efficiency
would power us entirely if we each carried around
a giant leaf more than 15 feet in diameter.
We might be carrying this leaf today,
were it not a focus of the most abiding agreement
in the natural history of metazoan inventions. To wit:
"I'll plant myself and hold our leaves, while in turn
you eat my fruit and spread the seeds." Can you name a
multi-celled organism who has NOT benefited from such a deal?
As a tale about sustainability, of course, there may be
a few of us not keeping our side of the bargain...


An ability to comprehend processes taking place on many different scales is important for understanding time and the natural history of invention, as well as for understanding space and nanoscale science. For example, this ability may help us put our (short-term and long-term) future in context with our (short-term and long-term) past. The figure below combines Eric Chaisson's upbeat depiction of time's arrow in Complexity 9 (2004, p14-21), with Peter Ward and Don Brownlee's sobering depiction of earth's clock in Life and death of planet earth (2002, Owl Books, NY) based on geological and astrophysical observations. For readers accessing this page from the bottom of a deep gravitational well, or a spaceship traveling near lightspeed with respect to our galaxy's center of mass, we'll use "Milky Way far-time clocks" to define the relative timing of events.

The numbers on the arrow at left are in billions of years, and hence don't show what's going on in any detail from our perspective. Cosmologists often focus on what's happening at the very beginning of the arrow. Things apparently did happen pretty fast. Economists, of course, focus in much closer to the present (the horizontal bar on the arrow), with historians and paleontologists focussing somewhere in between. Although there are an infinite number of points along the arrow to zoom in on, on this page (and on our time-wiki page here) we initially take a closer look at times surrounding the present.

Billion-year clocks and calendars

By zooming in on the multi-billion year scale twice, to what might be called the age of metazoans, and of mammals within that, the arrow-expansion above lets us taste the effects of changing scale. Each of the new boxes expand a tiny patch of time from the box to its left. There is a lot of new detail. For example, note (from the middle box) that both our fossil fuels, and our metazoan species diversity, were built up during the half-billion years of earth history leading up to the present. Even though microbes did a lot of inventing too (e.g. our first replicable-codes and molecular motors), zooming in elsewhere on the earth's time scale reveals much less activity. For example, when else have we seen the development not once, but multiple times, of wings, legs, webs, eyes, air-breathing apparatus, mechanisms to inherit function as well as structure (including object-oriented programming), and long-range communication tools (including backbones)? In fact, we've yet to find evidence for a period of energetic innovation like this anywhere else.

The time scales on these "billion-year clocks" are still quite long compared to times that individual humans experience. Zooming in even further yields the "million-year calendar" series below...

Million-year calendars

A lot of interesting discovery went on in the time periods explored by these more detailed expansions of scale, which might for example anthropocentrically be called the ages of primates, controlled-fire, and human-community. These times were likely central, for example, to the development of human languages, and concepts of self. The time-increments are still long compared to the length of recorded history, let alone in comparison to one lifetime. Nonetheless, these times are "a blink of a blink of a blink" compared to the half-billion year age of plants and animals, which I'd like to think has not run out of surprises yet.

Further zooming yields the "thousand-year calendar" series below...

Thousand-year calendars

Have you noticed yet how changes in climate and modes of communication often correlate with fundamental developments of other sorts? These trends continue with this final set of telescoping boxes, which cartoonify what might be called the ages of food-production, circumnavigation, and planet-think. Also note from the middle box that, following the invention of combustion engines, we are burning through our half-billion year's reservoir of fossil fuels in well under a millionth of the time it took to build it up. Let's summarize future concerns like this, working out from the last box: In the next few decades we face the possibility of some global warming, caused by the rapid burning of this sequestered carbon. Also within a century the most easily-available energy and reduced carbon from those reservoirs will be gone.


A recent article by William F. Ruddiman, in the March 2005 Sci Am 292 pages 46-54, discusses evidence that our activity may also exacerbate the transition we face hundreds of years from now, when the current inter-glacial period ends and "Ice Age 2C" makes a belated return. Regardless, at that point it might not hurt to be ready for another 80,000 year stretch of serious glaciation, like that from development of our partnership with man's best friend (followed by many three-dog nights) to the emergence of food production in the fertile crescent (at the onset of the current interglacial).

Assuming we make it through that next glaciation, we'll be looking at a sun that's warming up, and a planet that is slowly taking carbon out of the cycle that keeps life going on earth. Hence when this current ice age ends, it may be one of the last that our planet experiences. I'm tempted to call this a "back burner" problem, at least unless nature at some point decides to tell us that the present ice age ended early. A more current issue is our prospect for designing nanostructures able to positively impact new star systems, distributable by a combination of radiation pressure and galactic mixing (time scale around 0.1 billion years). Terrestrial studies of presolar grains show that the process works in reverse, although outward distribution efficiencies remain to be examined. Results of such work will only manifest themselves long after those who do it are gone, but hopefully while the age of plants and animals on earth is still underway.

According to Ward and Brownlee, we can also look forward to another super continent in a few hundred million years, after which the depletion of CO2 available for plants may well send Earth back into the 2nd "age of microbes". That's still a few billion years before runaway H2O greenhouse processes send our oceans into space, and leave us with mostly hot rock to hang out on while the sun works its way into a highly luminescent red giant phase before moving into possible short-lived (e.g. 25,000 year) planetary nebula and long-lived white dwarf phases.

The bottom line is that as a planet and/or as a species we face some non-trivial short-term and long-term challenges in the days ahead. Much has been happening fast, but it's not clear that our ability to work together over the long haul has been getting better. For example the world wide web, allowing almost anyone anywhere on the planet to make an idea (like this) available to everyone else within seconds, has not been around for very long. Will instant electronic communications last for a long time, or will it only be available for a brief moment when compared to the billion year age of plants and animals?

More specifically does Chaisson's observation that complexity develops as free-energy burns suggest that, when fossil fuels are gone, our complexity will be cut back as well? Is the free energy rate per human already on its way down from a 1979 peak near 2.2 kW even though hotspots in per capita consumption remain? Perhaps the rekindled battle for hegemony of intra-memepool (cultural) perspectives over outward-looking (multi-cultural empirical) perspectives is an early sign of this natural trend toward decreased complexity.

If these things are on point, can we at least for a while turn this decline around by giving everyone a chance to bargain for that 22-foot leaf, plus a 55-foot diameter solar-cell operating at 10% efficiency? The surface area needed to meet our free energy needs, in the US, is on order that of the road system already in place! What other valuable things (like history itself) may be around for a fleet instant on the cosmic clock? Monitoring correlations we'd like available to our descendants is another skill we may want to explore in this context.

Since some of the long term challenges involve reliable action over long times (e.g. like efforts at improving climate in the Sahara, or modifying earth's orbit), the answer might reside in our ability to address challenges (hence visualizing and reliably nurturing processes) that are unfolding over several time-scales at once. The idea that one generation in a thousand could squander the dedication of earlier generations, by letting its short-term rants drown out the sound of its long-term responsibilities, is a sobering thought indeed. A closer look at the million-year clock, as well as today's news, may show that this sort of thing is not without precedent.

Reflections on the road at night, about...

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This site is the result of helpful inputs by many, including the authors cited above. It is hosted by the Department of Physics and Astronomy, and the Center for NanoScience (formerly Molecular Electronics), at the University of Missouri - StLouis. The person responsible for mistakes is P. Fraundorf. MindQuilts site page requests are on their way up (we think) to about a million per year. Requests for a "stat-counter linked subset of pages" since 4/7/2005: .