Author: scott

Each February, I begin the introductory electricity and magnetism course at Princeton University by telling my students that the material we will ultimately cover during the semester provides the basis for modern civilisation.

Who could quibble with such an innocent statement? Without the discoveries of nineteenth-century physicists and their successors, we could hardly imagine today’s world: no electrical power grid, no televisions, no satellites, no iPads.

Physicists are justly proud of the many ways that their achievements have benefited humankind. But building a light bulb or a telephone doesn’t mean that you understand its basic principles Thomas Edison and Alexander Bell certainly didn’t. Unfortunately, many of my colleagues – particularly those who write textbooks – present physics as a towering, seamless basilica, ignoring the gaps in our hodge-podge of skewed models. In fact, what is presented as a shimmering cathedral often more closely resembles a hastily erected shantytown.

For example, one needs only first-semester equations to describe reasonably well the behaviour of a gyroscope; engineers can then go off and build gyrocompasses that guide aircraft or missiles to their destinations. But if you merely ask, “At what, exactly, is the gyroscope pointed?” you are plunged headlong into one of physics’ deepest questions, one that led Einstein to develop his general theory of relativity – and that, even today, has no definitive answer. I know of no undergraduate textbook that acknowledges the question.

Fact or friction
On a more blatant, if less exalted, level, the force of friction makes its appearance in the first days of any first-year course. We declare, as if there can be no doubt, that friction impedes the motion between two bodies, and we invoke sophisticated microscopic models that show how the soles of running shoes bind to a track.

Yet friction produces heat and thus an increase in entropy – which measures the amount of energy that cannot be used to perform work – and it therefore distinguishes past from future. The increase in entropy – the second law of thermodynamics – is the only law of nature that makes this fundamental distinction.

If Newtonian mechanics is at the bottom of everything, then one should be able to derive the second law of thermodynamics from Newtonian physics. But this has never been accomplished satisfactorily: the incompatibility of the second law with the other fundamental laws is perhaps the greatest paradox in all of physics.

Still, we brazenly drop this enigma into the first days of a first-year course without batting an eye. We write down equations that show how friction slows the motion of sliding objects or dampens the vibrations in springs, but, ultimately, the math merely reproduces our observations while disguising our ignorance of what underlies them.

After decades – indeed, centuries – of employing such tricks, physicists have forgotten that they are modelling phenomena, not necessarily uncovering Divine Truth. For instance, we can easily write down the equations for a ball on a swinging spring, but if we stretch the spring enough and swing the ball hard enough, we can’t solve those equations. The motion becomes chaotic, making an exact mathematical solution impossible.

Nowadays, with computers, we can approximate the trajectory as closely as we want. But that is the point: most physicists and students have lost sight of the distinction between the approximate and the exact. We can certainly learn something about chaotic systems without actually solving the equations, but if an old-fashioned mathematician demanded that a student predict where that ball was heading, the student would inevitably fail.

Strictly speaking
Even something as fundamental as Newton’s law of gravity is ultimately an approximation. Textbook authors dutifully write down the famous law without remarking that it results in infinite forces when the two attracting objects get infinitely close together. Never mind that infinite forces are a sure sign that your theory has gone up in smoke: in the current crop of textbooks sitting on my desk, not one mentions the obvious pathology.

Our Princeton text compounds the oversight by declaring that, “strictly speaking” Newton’s law of gravity is valid only for particles. Well, particles are exactly where Newton goes awry – and not just in first-semester physics. The basic equation of electricity is “Coulomb’s law,” which governs the electrical attraction or repulsion between charged particles and looks exactly like Newton’s law of gravity. Now, we always tell students to imagine electrons as point particles, in which case they really do need to worry about those infinite forces.

The problems that arise from modelling particles as vanishingly small points infect all advanced areas of physics. Central to any quantum mechanics course is the concept of electron “spin”, but what exactly is spinning is never made clear. Wolfgang Pauli, one of the concept’s originators, at first rejected the idea, because if the electron has a finite radius, then the surface would be spinning faster than the speed of light. On the other hand, if you view the electron as a point particle, how are you to imagine something without a radius spinning?

To cure the point-particle pathologies, physicists invented modern field theories, with impressive names such as quantum electrodynamics. But these theories turned out to be as riddled with infinities as their grandparents, and elaborate ad hoc schemes were invented to deal with the new problems encountered.
And so, despite headline-grabbing advances such as string theory, it goes to this very day. One can hardly challenge the predictive success of modern physics, but one should remember that one is describing nature, and not always understanding it.

Tony Rothman lectures in physics at Princeton University. His most recent book, with Fukagawa Hidetoshi, is Sacred Mathematics: Japanese Temple Geometry

(c) Project Syndicate, 2011

The basic material things society and the economy need are energy, raw materials and a healthy environment. People talk as though we can only use energy and materials in one way: we take fossil fuels from the ground, use them up and when they are gone our world will end. Likewise; we mine metals and other essential substances and, when they are used up, we will be finished.
But the universe is awash with energy. Our sun releases twenty trillion times as much energy per year as our economy uses. Raw materials, meanwhile, are just the hundred or so chemical elements that everything is made of. Anything we need can be assembled from these.
Fossil fuels have become too problematic, but there are other sources of energy. Most obvious is the heat and light from the sun. Energy from the sun reaching the Earth each year is ten thousand times what the world economy consumes.   
There is also the tidal energy and the geothermal heat leaking slowly from the Earth’s core. Finally, there is nuclear energy, which can be obtained by fission – the splitting of elements such as uranium or fusion of elements such as hydrogen. Geothermal and nuclear are not truly renewable, but could last for millennia.

Practical energy sources 
The question is: would it be practical, with current or reasonably expected knowledge, to get all the energy we need from such sources? To analyse this, we must introduce a very large unit of energy – the ‘exajoule’. One exajoule is equal to five times the energy of the biggest nuclear weapon ever detonated. The world economy uses roughly five hundred exajoules every year.

Tidal power resources are quite limited, being practical at only a few locations. They are estimated at five exajoules per year, around one percent of current needs. Tidal power is, however, completely predictable – being linked to the cycles of the sun and moon. Geothermal power is most abundant where there are volcanoes, but drilling means it can be harnessed anywhere. Fifteen hundred exajoules of geothermal energy flow out of the Earth each year, but it would only be practical to extract a small portion of this – equal to a few percent of the current energy demand.

Bioenergy is limited too. Turning crops into fuels competes with food production and drives up prices, threatening the world’s poor. But we can grow algae in lakes or greenhouses, producing from them oils very like diesel. We can grow fuel crops on marginal land. Engineers estimate that using biological waste that is already produced could sustainably yield fifty exajoules a year, ten percent of current energy needs. 

Turning the turbines
Wind power is very promising. Offshore wind alone represents a vast resource. There are three hundred and sixty million square kilometres of ocean, but perhaps just one percent of this is shallow and breezy enough for turbines. Assuming we could put fifteen turbines of five-megawatt capacity on each square kilometre, operating at an average twenty-five percent of that capacity, we get an average output of nearly twenty megawatts per square kilometre. With the available area, this scales up to two thousand exajoules per annum globally – four times current energy needs.

Nuclear fission is a mixed picture. Known resources of uranium-235, which can be used directly in reactors once refined, contain a total of two thousand exajoules of recoverable energy, only four years of current total energy use. However, resources of uranium-238, which must be converted in breeder reactors before use, are equivalent to over two hundred thousand exajoules of energy, or half a millennium of current needs.

Nuclear fusion would be better. Relevant forms of hydrogen are sufficiently abundant to meet current energy needs for thousands of years. Only mildly radioactive waste is produced. However, progress with fusion has only inched forward over recent decades and will take decades more to reach fruition. 

Harnessing the sun
The most promising energy resource is solar. Covering one percent of all land area (itself one third of the Earth’s surface) in solar collectors that operate at twenty percent efficiency would yield over three thousand exajoules per year – seven times current energy usage. This could be done using solar photovoltaic panels, solar thermal facilities or other methods. Over one percent of land use today is urban – making the scale of construction needed for solar power seem feasible. In short, we have enough energy to support an economy at least ten times bigger than today’s.  If we increase efficiency so that one unit of energy produces twice as many units of GDP, the space for growth doubles. Poor nations can thus aspire to Western living standards.

Energy is one aspect of sustainability. When it comes to the others – raw materials and the environment – a key phrase is ‘closed cycles’. Living things have used the same finite pool of a few essential elements (carbon, oxygen, hydrogen, etc) for billions of years, re-using them in an unending process of life, death, decay and re-birth. There is no reason the industrial economy cannot do the same, endlessly re-using a finite pool of essential materials.

The key question is what ‘rate of flux’ can be supported in a closed cycle. If the world has fifty billion tons of some material, and the world economy needs to process five billion tons of it every year, is this feasible? At some point, there will be a limit where the percentage of a given resource that is processed in a year cannot be increased. Closed cycles in water, topsoil and fertiliser minerals could all face such limits not far above current levels of use. But agricultural and water scientists have found efficient ways we could get much more sustenance from current fluxes of these, so we should be able to comfortably feed and water the 10bn or so that world population is forecast to plateau at.

There are many technical hurdles to be overcome, and economics will decide exactly which technologies are adopted. But there are no physical limits to maintaining our way of life.

In June, I participated in a meeting sponsored by the Clinton Global Initiative, the giant philanthropy, which focused on creating more jobs in the US – presumably a goal shared by most countries. Our little group – made up of philanthropists, a few entrepreneurs, venture capitalists, and ‘angel’ investors – concentrated on start-up companies, the source of so much commercial energy and of so many jobs.

We spent a lot of time considering which short-term measures (specifically excluding government regulations and policy) could make a difference. We came to the conclusion that what start-ups need most is greater access to mentors. Yes, they need money, contacts, customers, and knowledge, but often the best way to get almost all of these is through help and advice from proven, experienced mentors.

There were lots of good ideas; large companies could second redundant managers, technicians, and professionals to act as mentors for local start-ups. Professional associations could team up with incubators. Entrepreneurs could organise and join Meetup groups to share experiences, and they could invite potential mentors to speak to their groups sessions. (I’m on the board of Meetup.)

Differing motives
But, in the end, even though the investors were there to help, it was clear that there is a fundamental mismatch in the real world. Venture capitalists try to pick winners and help them; philanthropists try to help more people become winners. Venture capitalists want to fund the next Facebook, while philanthropists want to use Facebook to support good causes.

Looking for winners, venture capitalists use what signals they can to weed people out. When I get emails from would-be entrepreneurs, I can dismiss them easily if they spell my name wrong – or, indeed, if they spell anything wrong. If they can’t be bothered to get the details right, why should I waste my time with them?

If they have an unclear marketing plan or lack relevant experience in their target market, I can save myself time and move on to the next opportunity. Other VCs focus almost exclusively on Stanford and Harvard graduates, not because they believe that only people from those elite campuses and institutions can succeed, but because they already have too many opportunities and want to limit their “search costs.”

A philanthropist has a different approach. How much does it really matter if an entrepreneur can’t spell, as long as she can hire a copywriter who can? If there is no marketing plan, perhaps the philanthropist can help the founder develop one, or suggest a particular approach to follow or an expert to hire. If the entrepreneur is focused on a small but needy market, the venture capitalist will suggest shifting focus, whereas the philanthropist will help him figure out how to serve that market effectively.

Of course, these two approaches are not fundamentally incompatible – and a good economy needs both. But it does help to understand the dynamics underlying each approach, and to make trade-offs explicitly rather than blindly. Venture capitalists would argue, correctly, that companies such as Google and eBay make life more efficient and convenient for everyone. And philanthropists would reply, correctly, that in order to prosper, large companies need a healthy economy and a fair income distribution, not just a few winners. Each side needs the other – and needs to keep the other side in check.

Refocusing wealth
Both groups often make the mistake of short-term thinking: venture capitalists behave too much like stock traders, and philanthropists often give money to strangers instead of donating time (as a mentor!) to make a charity more effective. Venture capitalists trying to build world-scale companies don’t focus much on the environment around them, but angel investors, even finance-oriented angels, tend to invest in a particular community and understand that the health of their business ultimately depends on the health of the schools and the economy around them. Venture capitalists who fancy themselves global thinkers should likewise think long-term about the health of the world around them.

No one expects venture capitalists to divert their resources to village schools, but perhaps they could focus a little more on training new employees rather than poaching them from the competition at inflated salaries. They could also encourage their employees to donate their time to a local entrepreneurs’ club. This is already happening more than one might think, and it has more impact (on customers and employees as well as on recipients) than donating money to a charity.

An efficient market works best at allocating resources even for mentoring services, but it works on more than just money. Potential mentors may be motivated not by money or even generosity, but by pride: they want to be recognised for the wisdom that they can share. Like entrepreneurs, they may want to solve problems and have an impact (but without doing so full-time). They may want a chance to try things again through someone else. Some of them may even be venture capitalists in their day jobs.

As for the entrepreneurs and the people they hire to launch their start-ups, people need jobs, but they also create start-ups to solve a problem that bothers them or to pursue an opportunity that inspires them. They may want freedom from a corporation, or freedom to do things in a way that they could not in their old job.
In fact, the primary way a “market” approach can lead to bad outcomes, when venture capitalists destroy competition and actually harm the market, is through predatory behaviour or the more common practice of buying competitors they cannot beat. To be sure, an economy without a few big winners won’t have enough disruption, economies of scale, and inspirational examples to be as dynamic as the US once was. Ultimately, however, an economy in which there are only a few big winners won’t have enough customers to support them.

Esther Dyson is CEO of EDventure Holdings and an active investor in a variety of start-ups around the world. Her interests include information technology, healthcare and space travel

(c) Project Syndicate, 2011