Tuesday, December 26, 2017


Sophomore year at Princeton was definitely mind expanding for me! Two physics classes are on my mind right now: electromagnetic theory, taught by Stewart Smith, and Thermodynamics, taught by Steve Schnatterly. I learned about the dynamics of vibrating strings in Smith’s class, which got me into musical tuning, one of my lifelong obsessions. In Schnatterly’s class I learned about phase transitions, another lifelong obsession. I’ve been using software to explore these realms in theoretical ways ever since. I've been looking into a new little wrinkle in the phase transitions realm that I would like to share here.

The basic idea is to make an image that is striped, but where the stripe pattern is not consistent across the entire image. The width of the stripes won’t change, but their direction can change and also they can be offset. The image will be broken into an array of cells, and a stripe pattern assigned to each cell. Randomly assigning stripe direction and offset to each cell produces this kind of image:

This random assignment is not very interesting though. The real fun is in introducing correlations between the directions and offsets of neighboring cells. To do this, I use a cost function. The total cost for the whole image is the sum of a cost for each neighboring pair of cells. If neighboring cells have the same direction and offset, the cost for that pair is zero. The more their direction and offset differ, the more that pair contributes to the total cost.

There are some interesting details in how direction and offset can vary. The set of possible stripe patterns of a cell has a topology that characterizes when one stripe pattern, given by a direction and offset, is close to another stripe pattern. For example, when the direction of a stripe pattern is rotated by 180 degrees, it returns to the original stripe pattern. So the direction of the stripe pattern forms a circle, topologically.

Similarly, the offsets of the stripe pattern form a circle topologically. If the stripes are offset far enough, they just end up back where they started.

Given a circular topology of directions and a circular topology of offsets, the obvious way they would combine would be in a torus topology. But that is not what happens here. As the direction is rotated through 180 degrees, offsets in one direction are transformed to offsets in the opposite direction. The topology of the set of directions and offsets of the stripe patterns for a cell actually has the topology of a Klein bottle!

With this understanding of the choices available for a cell, the cost function can be used to drive a simulated annealing algorithm. This algorithm is driven by a temperature parameter. High temperatures give high costs which imply loose correlations between neighboring cells. Low temperatures give low costs and tighter correlations between neighboring cells. Systems such as these generally exhibit phase transitions, where local correlations extend to global correlations. The image above was generated at a temperature just above the phase transition. At a slightly lower temperature, very much higher correlation is observable:

At a lower temperature yet, the system is nearing uniformity.

Generally the fluctuations near the phase transition have a fractal character, so that is where the most interesting patterns appear.

With these elements in place, we can then toy with the various parameters, e.g. the number of cells and the number of stripes per cell.

Here is a plot of the heat capacity which has a sharp peak indicative of a phase transition:

Tuesday, December 19, 2017


Self and other, us and them, winning and losing, growth and decay: life is struggle. And yet, as one looks closely at the pattern and how the parts fit together, the struggle appears more like a dance. A dance alternates between posture and movement. We can understand a situation in one way, and then look at it from a different perspective. Each phase illuminates the other, with boundless transformative potential.

The basic game in Buddhism consists of a very large number of players called sentient beings, each of whom has a score called karma. It gets tricky though: while most of the time we can track a sentient being because it is attached to a physical body, those physical bodies are subject to gross impermanence, a.k.a. birth and death. How does the associated sentient being come to have whatever karma they do at the time they become associated with a newly born body? What happens to the karma of a sentient being when their body dies?

There is a similar problem in particle physics. There the players are elementary particles such as electrons and quarks. Each particle has a score which includes components such as position and momentum. Curiously, elementary particles are also subject to gross impermanence. What happens to the momentum of a particle when the particle ceases to exist? In physics, particles decay into other particles. Two particles might collide and both cease to exist as a result of the collision, but in their place new particles will appear. These newly appearing particles will carry the scores of the particles that have ceased to exist. In physics, quantities such as momentum are conserved. Momentum can be transferred from one particle to another but it cannot be created or destroyed. These conservation principles are the cornerstones of modern physics. The details of what kinds of particles there are and how they are created and destroyed, these details are constantly being reworked and refined through advances in theory and experiment. But a principle like the conservation of momentum is accepted more or less as an axiom. Of course every principle in science is subject to revision based on evidence. But conservation of momentum is so fundamental that some rather fanciful interpretations of the data will be allowed in order to maintain the conservation principle.

The understanding of beta decay is an example of such fanciful interpretation. Atomic nuclei are composed mainly of protons and neutrons, two types of particles. The simplest atomic nucleus is that of hydrogen, which consists of a solitary proton. This solitary proton is quite stable. Left to itself it will not manifest any sort of gross impermanence but will continue its existence indefinitely. Solitary neutrons, on the other hand, are quite unstable. They can be ejected from a complex nucleus through radioactive decay or through collisions, but they do not last very long outside a nucleus. What one observes is that the neutron decays into a proton and an electron. However, if the momenta of these new particles are added up, the sum will not be equal to the momentum of the neutron that disappeared. The great physicist Enrico Fermi posited a rather fanciful interpretation in order to preserve the principle of the conservation of momentum: there must be a third, invisible, particle also created alongside the proton and the electron. This third particle carries the missing momentum. Further physical principles showed that this third particle could only have tiny mass and would have no electrical charge, so Fermi called it a neutrino: like a very small neutron. These tiny particles were actually detected some years after Fermi’s prediction, one of the great successes of modern physics.

Karma is about as fundamental to Buddhism as momentum is to physics. Cultivate virtue and avoid evil: why? In order to improve one’s situation in the future. If the karma accumulated through one’s actions does not actually lead to future consequences, if karma can come or go independent of one’s actions, then the argument for cultivating virtue falls apart. For the most part it is not too difficult to see how karma might be accumulated and stored in association with a physical body. For example, it is not easy to see how memories are accumulated in a physical body, but it is clear that somehow they are. Karma is much like a habit, which is a kind of memory. The challenge comes when a body manifests gross impermanence, i.e. birth and/or death. We do not generally observe any kind of subtle body which could carry the karma to a newly born body or from a newly deceased body. But the situation is quite similar to beta decay in particle physics. We can maintain the principle of karma by hypothesizing the existence of such subtle bodies. And when expert observers use advanced methods that can actually detect such subtle bodies, we can have confidence in the accuracy of their reports.

The analogy with particle physics, where sentient beings are like particles and karma is like momentum, can be explored in other ways. Emmy Noether proved a mathematical theorem that provides some of the deepest structure in modern physics. She showed that conservation principles are associated with symmetries. For example, conservation of linear momentum is associated with the translational symmetry of space. The interchange symmetry of sentient beings seems like a natural reflection of the conservation principle of karma. After all, a modern paraphrase of the law of karma is: what goes around, comes around. What we do to others, we ultimately do to ourselves.

There is another perspective on the world, another way of seeing the world as a game, another system of accounting: economics. The players are economic agents such as individuals and corporations. Their scores are their property, which can be reduced to the single dimension of monetary value. The analogy between money and karma can shine a little light on the nature of money. Money, like karma, is relational. Karma is a pattern that relates sentient beings. Money is a pattern that relates economic agents. Henry Ford manifested this insight when he understood that the workers in his factories were also his customers. Naively he would maximize his wealth by raising the prices of the cars he was selling, and lowering the wages of the workers who made those cars. But in fact that naïve formula misses the fact that money lives by flowing in a network. Stationary money is dead money.

Particle physics can provide some further insights to challenge our understanding in Buddhism and economics. The wild thing about particles is that they don’t exactly exist or not exist at any particular time. This is very much in line with the argument of the Buddhist sage Nagarjuna, who showed that atoms cannot exist. One of the fascinating manifestations of this kind of quasi existence of particles is associated with the physics of crystals. Particles such as holes and phonons exist in crystals but not in empty space. Particles exist as collective behaviors of other particles. Particles become a way of understanding a system rather than parts whose existence is prior to the system.

This kind of shifting perspective can be seen in another game, in biology. At one level, biology is about organisms and their interactions. At another level, it is about species. Species can compete with other species much like organisms can compete with other organisms. At yet another level, biology is about genes. The evolution of a species can be viewed as a competition among the genes in the gene pool of the species.

This shifting perspective creates some of the great challenges of our time. Climate change is a consequence we all experience of actions we all perform. Individual persons can act, municipalities can act, corporations can act, nations can act, international organizations can act: these are not separate actions, but different perspectives on actions. The fact that we can see a situation as actions by, and consequences for, different sorts of beings, depending on the perspective we choose to take: this does not imply that these actions and consequences are not real. On the contrary, it is just this resilient play, this presentation of fresh appearance to every perspective, that makes the system real, that makes the world real. There is always more to learn.

Friday, December 15, 2017


I saw a film last night, Happening: A Clean Energy Revolution, written and directed by Jamie Redford. It was a pleasant enough film. Redford admits that he doesn’t know much about the subject; the film was about his beginning to learn about it a bit. I spent a few years working in the field, developing software to help manage the grid as more PV panels are introduced, which create large net load fluctuations that utilities need to respond to. The film didn’t address the puzzles that my path brought me to! But probably for many people it would be a good introduction to some of what is going on.

The major dramatic confrontation of the film was how the Nevada Public Utility Commission cut the rate that home PV owners would be paid for energy fed back into the grid. Obviously this makes installing PV systems less attractive. For those who had already installed systems, their electric bills would be increasing substantially. The damage was quite real.

The film then showed how a year later the Nevada legislature passed bills that reversed the PUC decision. The people had rallied and defeated the big bad corporation. The way the movie portrayed things, the people were in favor of new clean technology, while the corporation was holding on to their old ways that made them big profits.

I was disappointed to see the situation pictured this way. I don’t know about the specifics in Nevada, but I would like to sketch out some general parameters, to propose a more fruitful perspective, one that opens opportunities for greater progress.

At the foundation, there seems to be a widespread notion that being driven by profits is at the core of the capitalist system that is destroying our world. I’m not an economist or political philosopher by any stretch. But I suspect that a lot of these highly trained folks go off into specialized concepts and leave the basics rather unattended. Getting the basics backwards creates real obstacles! I would like to try to tidy up a bit to help us move more effectively in a positive direction.

Profit, meaning that some enterprise provides more benefit than it costs, is not a goal peculiar to capitalism. I would say that profit is the foundation of life. Every organism expends resources in order to gain access to further resources. If the newly acquired resources are not of greater value to the organism than the resources expended to acquire them, the organism is running at a loss. Such losses lead to death. Life requires profit.

What precisely distinguishes capitalism? I expect there are many conflicting definitions. I think a useful criterion would be: ownership by investors. By ownership I mean decision-making authority. Every enterprise is given coherency by some decision making process. There are all sorts of people involved in an enterprise, such as customers, workers, managers, suppliers, neighbors, and investors. In a capitalist system it is the investors who have the final authority in how the enterprise is to be run.

One curious feature of the situation in Nevada regarding net metering for residential PV systems is that the Public Utility Commission is, at least theoretically, not representing the investors in the utility. Generally a PUC is appointed by the government and represents the public interest. Electric power utilities in general are heavily regulated by a variety of government agencies and other non-investor bodies. Electric power is not a very capitalist industry! Of course there are powerful investors with enormous influence and decision making authority, so there is a large capitalist component.

Political power doesn’t really flow through textbook channels. Large investors can certainly cast their votes at shareholder meetings, the classical capitalist channel. But there are many other channels of influence. I don’t doubt that the Nevada PUC is pressured in a variety of ways by big money interests, certainly including utility investors. This kind of corruption, where centers of concentrated power can steer decisions to funnel even more wealth and consequent power back to those same centers, is hardly a distortion particular to capitalism. Still, a capitalist system will manifest such steering in its particular way.

Why did the Nevada PUC resist the growth in residential PV systems? No doubt it was to preserve the utility’s profits. But that answer barely scratches the surface. The folks with residential PV systems wanted to stay connected to the grid. If there is no profit in maintaining the grid, the grid will die. So if folks want to stay connected, it’s in their own interest to help insure the profitability of the utility.

The whole electric power system is enormously complex. Some of this complexity is technological and some of it is social. Technologically, the power system can be divided coarsely into generation, transmission, and distribution. The social structure is governed by regulations which vary from region to region. In general, the electric power system was de-monopolized some decades ago. The ownership of generating plants is typically different than the ownership of transmission and distribution systems. Transmission networks usually cross many state lines. Electric power consumed in one state is very often generated in a different state.

The decision of the PUC very likely was intended to protect corporate profits, but the profits of which corporations? If the clean energy revolution is to succeed, what enterprises need to maintain profitability? How can we structure the power system, socially and technologically, to make clean energy profitable? What structures should we avoid that will put the health of the system at risk?

There are certainly large investments in fossil fuel generation – in coal mines, natural gas wells, in railroads and pipelines, and in generating plants that burn fossil fuels. The investors in these facilities want to continue to receive a good return on their investment. Folks that work in these facilities, the municipalities that receive tax revenues from their operations, etc. – it’s not just the investors who want to see these enterprises continuing to operate and continuing to be profitable. For the clean energy revolution to succeed, these are the people whose projects need to be derailed. To whatever extent there can be established alternate ways for these various groups to survive and even thrive despite this disappointment – the less these folks fight against clean energy, the more the revolution can grow.

It’s hard to say exactly what the clean energy system of the future should look like. Redford’s movie provided admiring portraits of large scale facilities such as wind farms and solar thermal generating plants. It’s hard to foresee a practical future where each home and family manages energy usage independently, off any grid, i.e. where the grid is gone. Of course the grid is barely a century old, i.e. humanity survived through almost all its history without the electric grid. So it is entirely conceivable that the grid could just disappear as quickly as it appeared. Still, in trying to plan out a practical path for a clean energy revolution, it seems most practical to incorporate a grid, where generation and consumption can be more loosely coupled.

Building and maintaining a grid, the transmission and distribution networks, together with large scale generation and large scale storage facilities, is a considerable expense. The consumers of electric power who use the grid will have to provide the funds, one way or another, to keep the grid running. Nowadays the main way that consumers pay for their use of the grid is by paying for their total energy use each month, or, equivalently, for their average power use. But this becomes a problem as more and more consumers are also generators of power. Distributed generation adds new sources of fluctuation of power flow in the grid. Distributed generation makes maintaining the grid more difficult and more expensive, while reducing revenue.

Our modern era has created such huge networks that people often lose track of where things come from. We earn money by working at a job and then spend that money paying bills. By keeping up with our bill payments, we maintain the privilege to acquire the various things we need and want. It’s actually our work that fulfills our needs and wants. But there are so many abstract layers between that the connection is hard to recognize. There is a lot of work required to maintain the electric power grid. The idea that there is a greedy corporation that charges us for electric power and that the smart game is to arrange things to avoid paying that corporation: that idea has lost sight of the fact that we rely on systems that take a lot of work to maintain.

There are many challenges we face in bringing about a clean energy revolution. One fundamental shift that we need to navigate is how we pay for the maintenance of the electric power grid. A consumer that uses zero net power but that sometimes pushes energy into the grid and at other times draws energy from the grid, that consumer is deriving benefit from the grid. If the grid is to survive, the users of the grid need to pay to maintain it. Net energy consumption is not going to work anymore as a way to allocate costs across consumers. The clean energy revolution requires us to find a new way to charge consumers for their use of the grid.

This perspective turns upside-down the picture presented by Redford’s movie. Again, I don’t know the specific details driving the decisions of the Nevada PUC. But it is quite reasonable to guess that the PUC understood that net metering is not a method of cost allocation that is going to enable the survival of the grid. Net metering is not going to move the clean energy revolution forward in the long run.

It’s hard to say what sort of cost allocation system can work well in the new clean energy world. For example, maintenance of the grid could simply be funded through government tax revenue. But this approach tends to insulate consumers from the costs their actions incur. Such a lack of feedback tends to foster inefficiency. Another approach is to use smart meters. The typical consumer’s power meter today just accumulates the total power used. Alternative meters could track various statistics of the fluctuations in power consumption and generation. Part of a consumer’s bill could be proportional e.g. to their 90th percentile peak power consumption. After all, the grid operations need to maintain readiness to supply such peak power usage, so it is reasonable to bill customers for such access to power.

After the showing of the movie yesterday in Salt Lake City, there was a short period of discussion with Jamie Redford who was present in the room. I had the opportunity to ask him, “What about smart meters?” He said he hadn’t heard too much about them but had heard about some resistance from consumers who worried about electromagnetic radiation – generally these meters can be read from the street by way of microwave communications. Redford noted that most of us regularly use cell phones that emit very much the same sort of microwave signals, so the resistance to smart meters seemed a bit misplaced.

If the clean energy revolution requires smart meters rather than net metering, it might just be that the consumers are more of a drag on progress than the Public Utilities Commission!

Redford’s film was a reasonable introduction to the clean energy revolution. I hope I have argued effectively here that we need to take the discussion a few layers deeper if we are really going to fulfill the promise of clean energy!