Some caveats do apply:
In his short paper, Moore expressed some doubt as to whether his prediction would hold for linear, rather than digital, integrated circuits, pointing out that by their nature “such elements require the storage of energy in a volume” and that the volume would necessarily be large.
It does matter when you get down to piles of sand with just one grain, and then technology has to shift and you need to use some new physical property to define the abstraction. Such technology shifts have happened again and again in the maintenance of Moore’s Law over almost fifty years.
The idea does not explain the sociology of how Moore’s Law is implemented or what determines the time constant of a doubling, but it does explain why exponentials are possible in this domain.
COSMIC COMPLEXITY
JOHN C. MATHER
Senior astrophysicist, Observational Cosmology Laboratory, NASA’s Goddard Space Center; coauthor (with John Boslough), The Very First Light
What explains the extraordinary complexity of the observed universe, on all scales from quarks to the accelerating universe? My favorite explanation (which I certainly did not invent) is that the fundamental laws of physics produce natural instability, energy flows, and chaos. Some call the result the Life Force, some note that the Earth is a living system itself (Gaia, a “tough bitch,” according to the late Lynn Margulis), and some conclude that the observed complexity requires a supernatural explanation (of which we have many). But my dad was a statistician (of dairy cows) and he told me about cells and genes and evolution and chance when I was very small. So a scientist must look for the explanation of how nature’s laws and statistics brought us into conscious existence. And how it is that seemingly improbable events are happening all the time.
Well, physicists have countless examples of natural instability, in which energy is released to power change from simplicity to complexity. One of the most common is that cooling water vapor below the freezing point produces snowflakes, no two alike and all complex and beautiful. We see it often, so we’re not amazed. But physicists have observed so many kinds of these changes from one structure to another (we call them phase transitions) that the Nobel Prize in 1992 could be awarded for understanding the mathematics of their common features.
Now for a few examples of how the laws of nature produce the instabilities that lead to our own existence. First, the Big Bang (what an insufficient name!) apparently came from an instability, in which the “false vacuum” eventually decayed into the ordinary vacuum we have today, plus the most fundamental particles we know, the quarks and leptons. So the universe as a whole started with an instability. Then a great expansion and cooling happened, and the loose quarks, finding themselves unstable too, bound themselves together into today’s less elementary particles—protons and neutrons—liberating a little energy and creating complexity. Then the expanding universe cooled some more, and neutrons and protons, no longer kept apart by immense temperatures, found themselves unstable and formed helium nuclei. Then a little more cooling, and atomic nuclei and electrons were no longer kept apart and the universe became transparent. Then a little more cooling, and the next instability began: Gravitation pulled matter together across cosmic distances to form stars and galaxies. This instability is described as a “negative heat capacity,” in which extracting energy from a gravitating system makes it hotter—clearly the second law of thermodynamics does not apply here. (This is the physicists’ version of e. e. cummings’s notion of “the wonder that’s keeping the stars apart.”) Then the next instability is that hydrogen and helium nuclei fuse to release energy and make stars burn for billions of years. And then at the end of the fuel source, stars become unstable and explode and liberate their chemical elements into space. And because of that, on planets like Earth, sustained energy flows support the development of additional instabilities and all kinds of complex patterns. Gravitational instability pulls the densest materials into the core of the Earth, leaving a thin skin of water and air, and makes the interior churn incessantly as heat flows outward. And the heat from the sun, received mostly near the equator and flowing toward the poles, supports the complex atmospheric and oceanic circulations.
And because of all that, the physical Earth is full of natural chemical laboratories, concentrating elements here, mixing them there, raising and lowering temperatures, ceaselessly experimenting with uncountable events where new instabilities can arise. At least one of them was the new experiment called Life. Now that we know there are at least as many planets as there are stars, it’s hard to imagine that nature’s ceaseless experimentation would not be able to produce Life elsewhere—but we don’t know for sure.
And Life went on to cause new instabilities, constantly evolving, with living things in an extraordinary range of environments, changing the global environment, with boom-and-bust cycles, with predators for every kind of prey, with criminals for every possible crime, with governments to prevent them, and instabilities of the governments themselves.
One of the instabilities is that humans demand new weapons and new products of all sorts, leading to serious investments in science and technology. So the natural/human world of competition and combat is structured to lead to advanced weaponry and cell phones. So here we are in 2012, with people writing essays and wondering whether their descendants will be artificial life-forms traveling back into space. And pondering what the origins of those forces of nature are that give rise to everything. The Dutch theoretical physicist Erik Verlinde has argued that gravitation, the one force that has so far resisted our efforts at a quantum description, is not even a fundamental force but is itself a statistical force, like osmosis.
What an amazing turn of events! But after all I’ve just said, I should not be surprised a bit.
THE GAIA HYPOTHESIS
SCOTT SAMPSON
Dinosaur paleontologist and science communicator; author, Dinosaur Odyssey: Fossil Threads in the Web of Life
For my money, the deepest, most beautiful scientific explanation is the Gaia hypothesis, the idea that Earth’s physical and biological processes are inextricably interwoven to form a self-regulating system. This notion—the 1965 brainchild of chemist James Lovelock, further developed with microbiologist Lynn Margulis—proposes that air (atmosphere), water (hydrosphere), Earth (geosphere), and life (biosphere) interact to form a single evolving system capable of maintaining environmental conditions consistent with life. Lovelock initially put forth the Gaia hypothesis to explain how life on Earth has persisted for almost 4 billion years despite a 30 percent increase in the sun’s intensity over that interval.
But how does Gaia work? Lovelock and Margulis demonstrated that, lacking a conscious command-and-control system, Gaia uses feedback loops to track and adjust key environmental parameters. Take oxygen, a highly reactive by-product of life, generated and continually replenished by photosynthetic algae and plants. The present atmospheric concentration of oxygen is about 21 percent. A few percentage points lower and air-breathing life-forms could not survive; a few percentage points higher and terrestrial ecosystems would become overly combustible, prone to conflagration. According to the Gaia hypothesis, oxygen-producing organisms have used feedback loops to maintain atmospheric oxygen between these narrow limits for hundreds of millions of years.
Similar arguments, backed by an ever-growing body of research, can be made for other atmospheric constituents, as well as for global surface temperature, ocean salinity, and other key environmental metrics. Although the Gaia hypothesis highlights cooperation at the scale of the biosphere, researchers have documented multiple examples showing how cooperation at one level could evolve through competition and natural selection at lower levels. Initially criticized by serious scientists as New Age mumbo-jumbo, Lovelock’s radical notion has increasingly been incorporated into scientific orthodoxy, and key elements are now often taught as “Earth systems science.” One timely lesson resulting at least in part from Gaian research is that food-web comple
xity, including higher species diversity, tends to enhance ecological and climate stability.
So, while Earth may inhabit a Goldilocks zone—neither too close nor too far from the sun—life’s rampant success on this “pale blue dot” cannot be ascribed to luck alone. Life has had a direct hand in ensuring its own persistence.
Science has not yet fully embraced the Gaia hypothesis. And it must be admitted that as an explanation, the idea remains incomplete. The insights cascading from Gaia are unquestionably deep and beautiful, uniting the whole of the biosphere and Earth’s surface processes into a single, emergent, self-regulating system. But this explanation has yet to achieve the third milestone defined in this year’s Edge Question: elegance. The Gaia hypothesis lacks the mathematical precision of Einstein’s e = mc2. No unified theory of Earth and life has been presented to explain why life stabilizes more than it destabilizes.
Evolutionary biologist W. D. Hamilton once compared Lovelock’s insights to those of Copernicus, adding that we still await the Newton who will define the laws of this grand, seemingly improbable relationship. Hamilton himself became deeply engrossed in seeking an answer to this question, developing a computer model that seemed to show how stability and productivity could increase in tandem. Were it not for his untimely death, he might have emerged as that modern-day Newton.
The cultural implications of Gaia also continue to be debated. Arguably the most profound implication of Lovelock’s idea is that Earth considered as a whole has many qualities of an organism. But is Gaia actually alive, akin to a single life-form, or is it more accurate to think of her as a planet-size ecosystem? Lynn Margulis argued strongly (and convincingly, to my mind) for the latter view. Margulis, whose work revolutionized evolutionary biology at the smallest and grandest of scales, died last year. Always the hard-nosed scientist, she once said, “Gaia is a tough bitch—a system that has worked for over 3 billion years without people. This planet’s surface and its atmosphere and environment will continue to evolve long after people and prejudice are gone.”
While not disagreeing with this blunt assessment, I find considerably greater inspiration in Gaian thinking. Indeed, I would go as far as to suggest that this idea can help shift the human perception of nature. In the modernist perspective, the natural world is little more than a collection of virtually infinite resources available for human exploitation. The Gaian lens encourages us to reenvision Earthbound nature as an intertwined, finite whole from which we evolved and in which we remain fully embedded. Here, then, is a deep and beautiful perspective in desperate need of broad dissemination.
THE CONTINUITY EQUATIONS
LAURENCE C. SMITH
Professor of geography, UCLA; author, The World in 2050
These are already familiar to you—at least, in anecdotal form. Almost everyone has heard of the law of conservation of mass (sometimes with the word “matter” in place of “mass”) and probably its partner, conservation of energy, too. These laws tell us that for practical, real-world (that is, non-quantum, non–general relativity) phenomena, matter and energy can never be created or destroyed, only shuffled around. That concept has origins at least as far back as the ancient Greeks, was formally articulated in the 18th century (a major advance for modern chemistry), and today underpins virtually every aspect of the physical, life, and natural sciences. Conservation of mass (or matter) is what finally quashed the alchemists’ quest to transform lead into gold; conservation of energy is what consigns the awesome power of a wizard’s staff to the imaginations of legions of Lord of the Rings fans.
The continuity equations take these laws an important step further, by providing explicit mathematical formulations that track the storage and/or transfers of mass (mass continuity) and energy (energy continuity) from one compartment or state to another. As such, they are not really a single pair of equations but are instead written into a variety of forms, ranging from the very simple to the very complex, in order to best represent the physical phenomenon they are supposed to describe. The most elegant forms, adored by mathematicians and physicists, have exquisite detail and are therefore the most complex. A classic example is the set of Navier-Stokes equations—sometimes called the Saint-Venant equations—used to understand the movements and accelerations of fluids. The beauty of Navier-Stokes lies in their explicit partitioning and tracking of mass, energy, and momentum through space and time. However, in practice, such detail also makes these equations difficult to solve, requiring either hefty computing power or simplifying assumptions to be made to the equations themselves.
But the power of the continuity equations is not limited to complex forms comprehensible solely to mathematicians and physicists. A forest manager, for example, might use a simple, so-called mass-balance form of a mass-continuity equation to study her forest by adding up the number, size, and density of trees, determining the rate at which seedlings establish themselves, and then subtracting the trees’ mortality rate and number of truckloads of timber removed, so as to learn whether its total wood content (biomass) is increasing, decreasing, or stable. Automotive engineers routinely apply simple energy-balance equations when, for example, designing a hybrid electric car to recapture kinetic energy from its braking system. None of the energy is truly created or destroyed, just recaptured—in this case, from a combustion engine, which got it from breaking apart ancient chemical bonds, which got it from photosynthetic reactions, which got it from the sun. Any remaining energy not recaptured from the brakes is not really lost, of course, but instead transferred to the atmosphere as low-grade heat.
The cardinal assumption behind these laws and equations is that mass and energy are conserved within a closed system. In principle, the hybrid electric car satisfies energy continuity only if its consumption is tracked from start (the sun) to finish (dissipation of heat into the atmosphere). This is a cumbersome calculation, so the process is usually treated as an open system. The metals used in the car’s manufacture satisfy mass continuity only if tracked from their source (ores) to landfill. This tracking is more feasible, and such cradle-to-grave resource accounting—a high priority for many environmentalists—is thus more compatible with natural laws than our current economic model, which tends to treat such resource flows as open systems.
Like the car, our planet is, from a practical standpoint, an open system with respect to energy and a closed system with respect to mass. (Although Earth is still being bombarded by meteorites, that input is now small enough to be ignored.) The former is what makes life possible: Without the sun’s steady infusion of fresh, external energy, life as we know it would quickly end. An external source is required because although energy cannot be destroyed, it constantly degrades into weaker, less useful forms, in accordance with the second law of thermodynamics. (Consider the hybrid-electric car’s brake pads—their dissipated heat is not of much use to anyone.) The openness of this system is two-way, because Earth also streams thermal infrared energy back out to space. Its radiation is invisible to us, but to satellites with “vision” in this range of the electromagnetic spectrum the Earth is a brightly glowing orb, much like the sun.
Interestingly, this closed/open dichotomy is yet another reason that the physics of climate change are unassailable. By burning fossil fuels, we shuffle carbon (mass) out of the subsurface—where it has virtually no interaction with the planet’s energy balance—to the atmosphere, where it does. It is well understood that carbon in the atmosphere alters the planet’s energy balance; the physics of this has been known since 1893, thanks to the Swedish chemist Svante Arrhenius. Without carbon-based and other greenhouse gases, our planet would be a moribund, ice-covered rock. Greenhouse gases prevent this by selectively altering the Earth’s energy balance in the troposphere, the lowest few miles of the atmosphere, where the vast majority of its gases reside—thus raising the amount of thermal infrared radiation that Earth emits. Because some of this energy streams back down to Earth as well as out to space, the lower troposphere warms to achieve energy bala
nce. Continuity of energy commands this.
Our planet’s carbon atoms, however, are stuck here with us forever—continuity of mass commands that, too. The question is, What choices will we make about how extensively and rapidly to shuffle them out of the ground? The physics of natural resources, climate change, and other problems can often be reduced to simple, elegant equations—if only we had tools masterful enough to dictate their solution.
PASCAL’S WAGER
TIM O’REILLY
Founder and CEO of O’Reilly Media
In 1661 or 1662, in his Pensées, philosopher and mathematician Blaise Pascal articulated what would come to be known as Pascal’s Wager, the question of whether or not to believe in God in the face of the failure of reason and science to provide a definitive answer:
You must wager. It is not optional. You are embarked. Which will you choose then? . . . You have two things to lose, the true and the good; and two things to stake, your reason and your will, your knowledge and your happiness; and your nature has two things to shun, error and misery. Your reason is no more shocked in choosing one rather than the other, since you must of necessity choose. This is one point settled. But your happiness? Let us weigh the gain and the loss in wagering that God is. Let us estimate these two chances. If you gain, you gain all; if you lose, you lose nothing. Wager, then, without hesitation that He is.
While this proposition of Pascal’s is clothed in obscure religious language and on a religious topic, it is a significant and early expression of decision theory. And stripped of its particulars, it provides a simple and effective way to reason about contemporary problems like climate change.
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