Thursday, March 30, 2023

Heat Pump Efficiency

Thermodynamics is a fundamental branch of physics. It gets a bit subtle: I find myself getting tripped up often enough!

The cornerstone of thermodynamics is the Carnot cycle, an ideal process for converting heat to work. It's a model for what steam engines do, for example. The Carnot cycle sets a limit on how efficient an engine can be: it is not possible to convert all the energy from heat to mechanical work.

A heat pump is simply an engine running backwards. An engine has heat flowing from a hot reservoir to a cold reservoir, converting some of that heat to mechanical work. A heat pump uses mechanical work to push heat from a cold reservoir to a hot reservoir. The amount of heat added to the hot reservoir will be the sum of the energy from the work and the heat energy removed from the cold reservoir.

To heat a home, one can use a natural gas furnace, or one can use a heat pump. The heat pump runs off electricity, much of which is generated from an engine running off natural gas. Energy is lost when the natural gas heat energy is converted to electricity, but then energy is gained when the electricity is used to heat the home. Since the heat pump is just an engine running backwards, these losses and gains are in some sense reflections of each other, and might seem to cancel out. But they don't!

The missing detail is that there are three heat reservoirs involved. The engine at the utility power generation plant has energy flowing from a furnace to the environment, converting some of that to electrical energy. The heat pump has energy flowing from the environment to the interior living space, driving that with electrical energy:

The two efficiency factors have inverse forms, but the numbers involved are different, so they don't cancel each other.

Plugging in some roughly plausible numbers, a graph can be generated for maximum effiency of the overall system as a function of the outside temperature. As the outside temperature warms to near the interior living space temperature, the round trip efficiency increases without bound. At cold temperatures, the utility's power generation engine can run more efficiently, but the reduction in effectiveness of the heat pump is more dramatic, so the overall effiency is reduced.

Friday, March 24, 2023

Aperiodic Tiling

I've been seeing reports of an aperiodic tiling. At first, I couldn't imagine how a tiling could be aperiodic. Now the pendulum has swung to the other extreme, where it seems trivial:

The tile is just a 1x2 rectangle. Mostly they are all placed vertically, but there is a line along which horizontal tiles are placed. One could interpret the pattern of absence or presence of a horizontal tile in the sequence of columns as expressing a fraction in base 2. If the fraction is irrational, the pattern will be aperiodic. Hmmm, even if there was just one horizontal tile in the middle, the pattern would be aperiodic!

There must be some trickier definition in play, of what aperiodic means. But anyway, now it doesn't seem so impossible!

Friday, March 17, 2023

Scientific Equipment

Galileo did not invent the telescope. Galileo looked at the night sky with a telescope that someone else built. Scientists do sometimes invent and build the equipment they need, but in general scientists take advantage of existing equipment to enable them to do science. Science is not a free-standing activity; it is an integral part of a much larger world. Science uses its connections with the world, just as the world uses science.

This relationship of mutual use creates a self-reinforcing feedback loop. Scientific discoveries enable new equipment to be constructed, and new equipment enables yet further scientific discoveries. The astounding technological capabilities of our time are the fruit of this system. However, the system is more complex. Our global-scale industry has global-scale impact on the environment. Climate change may be the most immediate concern, but we are seeing many other effects too. It is of course difficult to predict exactly how environmental limits will impace the availability of scientific equipment. But a starting point would be a reflection on the variety of ways that science uses what the world makes available.

Instruments with which to observe and measure natural phenomena are surely at the head of the list. Nowadays we have telescopes in orbit, detecting a wide range of electromagnetic frequencies: not just in orbit around earth, but around other planets too. And we have robots on the surface of Mars, observing at close range. At the tiniest scale we have particle accelerators and electron microscopes. Chromotography, spectroscopy, magnetic resonance imagery... a catalog of today's observation and measurement equipment would fill an encyclopedia.

Another way that science uses what industry provides is the acquisition of raw materials. All kinds of very pure simple and complex substances are available. There is also a rich variety of materials processing equipment by which raw materials can be processed to form both experimental samples and also custom observational devices. Vacuum pumps are a curious sort of equipment, since their function is to remove material rather than to supply it. But vacuum pumps are fundamental to preparing a suitable environment for observations, back to the time of Boyle at the birth of modern science.

Recording experimental observations can rely on little more than paper and pencil, though nowadays all sorts of automated recording devices make continuous accurate measurement and recording possible. A variety of automated analysis can be performed by computers, so the scientist need only attend to a summary report.

Science is a communal enterprise. Scientists compare results, critique each other's methods, exchange tools and materials, hire each other's students, etc. The worldwide transportation and communication networks make these exchanges possible. Scientists travel, too, to observe phenomena that occur at special locations, such as biological species in their native habitat, or geological phenomena in place.

Another sort of equipment that science needs is social. At the most basic level, there need to be scientists, people with the capability and freedom to pursue scientific research. The various physical equipment necessary must not only exist but be made available for use by scientists. For the self-amplifying feedback loop of scientific advancement to work, industry must be confident in the validity of scientific results so that the know-how produced by science will be applied to produce the next generation of more capable scientific equipment.

The reader is invited to augment this list. But a further exercise is to consider what impact environmental limits might have on any of these sorts of equipment. There could be other potential feedback loops that get excited as we enter some new regime of system behavior. It is not impossible that environmental limits push industry into less efficient processes, which accelerate the impact of those limits.

It seems clear enough that science has a large share of responsibility for creating our modern world, with all its miraculous technological capabilities. That is another facet of the self-amplifying feedback loop: powerful people understand how science has enhanced their power, and so they promote scientific research. We certainly seems to be at very real risk of entering a new regime, where our miraculous technological capabilities are seen instead as driving us ever more violently against environmental limits. Just has science earned support by taking credit, science may well lose support by taking blame.

Science is not a free-standing activity, but is embedded in a multi-faceted world. This relationship has been at the heart of modern industrial civilization, which is about 200 years old. We seem to be headed for a major shift. If science is to survive the shift in good health, the scientific community will need to find ways to adapt to the new patterns.

Friday, March 10, 2023


Our actions have consequences. When we're being careful, we choose our actions so they'll have the best possible consquences. Most commonly what this means is that we try to change the world so it satisfies our desires more. But our actions don't just change the world, they change our selves. We often divide our activities into two phases, e.g. rehearsal and performance. The purpose of rehearsal is to refine our capabilities. Performance is when apply those capabilities to create an aesthetic experience for an audience, for example. But this division is just a rough cut. All of our actions change who we are at the same time that they change the world.

This division of experience into self and world is problematic. An athlete might consider their own body to be a component of the world. One's actual self might be perhaps the rational component of mind, something constant underlying even one's shifting mental capabilities. One of the essential insights of the Buddhist tradition is that the search for this constant underlying component of the self is futile. And yet this framework of thinking, e.g. "I will do this," seems practically unavoidable. If we want to use a conceptual framework of self and world, how can we think about this without getting distracted by illusions?

Organizational behavior is a doorway to a different perspective. It is not just individual human beings who act. All kinds of organizations act: political, military, industrial, academic, religious, etc. At a planetary scale, all of humanity acts. A basic principle of systems theory is that analysis starts with a clear definition of the system to be analyzed: what is part of the system, and what is not. A complementary axiom is in easy reach: the self is what is not in the system. The key point here is that the division of experience into self and world is like establishing a coordinate system or a frame of reference. It has no ontological foundation but is a practical step to allow conceptual elaboration for solving specific problems.

In organizational situations, it is commonly understood that actions both change the world and also change the self, i.e. change the organization engaged in the action. Teams develop cohesion by working together.

That what we are is a dynamic pattern that is constantly being shaped by our actions and experiences, that an important factor in choosing our actions is how those choices will reshape who we are... this perspective seems easier to achieve when we feel safe and secure. When things are good, we are happy to train ourselves to make them even better. When things are difficult, our entire focuse is on fixing problems with the world so we have no desire or opportunity to train ourselves. People do train themselves to be able to respond to difficult situations, though mostly that is to make themselves more capable of making whatever necessary changes to the world. But sometimes people do understand that shaping the world to meet their desires is not going to go very far, and they need to shape their own expectations. Aging gracefully can include such adjustments. What an older person can do is not the same as what a younger person can do. There is a lot less frustration in playing the hand you've been dealt.

At the planetary scale, the growing human population and the growing levels of consumption are driving us up against ecological limits, mostly prominently due to climate change but many other problems are accelerating too, such as aquifer depletion and ocean desertification. The reflex response is to demand that the world change in order to let us preserve our way of life. But of course our way of life is always changing and will continue to change as a consequence of our actions. However one chooses to partition the situation, it is always a dance between self and world. Our habits change, our understandings change, our values change. This dynamism is both a challenge and an opportunity. If our response to our discomfort is to become ever more stubborn and insensitive, we can certainly ramp up the level of mutual frustration to a catastrophic breaking point. But if we can respond to discomfort with care and flexibility, then we can discover tender joys in the most suprising places.