Science Cathedral

I am spending a few days in Columbia, South Carolina, attending the conference Greening of Religions, sponsored by the Cherry Hill Seminary and the University of South Carolina. One attendee noticed a conflict between two views of science that have come up here. On the one hand, science is responsible for the disenchantment of the world that has opened the door to the environmental crisis that we are facing. On the other hand, scientific theories like ecology and evolution show the kinship of humans with other life on the planet, and the vital importance to human well-being of the well-being of those other forms of life. The observation of this conflict didn't elicit much response at the conference but it is central to my own thinking, my own calling.

In my presentation here, I had a few suggestions for ways to improve our thinking about and practice of science. I suggested that in evaluating the validity of a scientific theory, some kind of middle way is needed. Specifically I would suggest that validity should be something like a function from some parametric space describing a possible context of application of the theory, to some probability of satisfactory application. Roughly speaking, each theory has some large or small range of applicability.

My other suggestion was some kind of democratization of science. Sitting outside at lunch after the session at which I presented, I gave this idea a more concrete form. The way that science students really integrate science is through experiments, by repeating the classic experiments of their field. These repeated experiments are a lot like religious rituals, means to recreate core insights of a tradition. This parallel provides a direction that could work very well.

How about a science cathedral? It could consist of a set of chapels, each chapel dedicated to some classic science experiment. Each experiment could be repeated on a regular schedule, every day perhaps for some simple ones, once a year for complex ones. Each experiment could have a liturgy, starting with a description of the scientific question that initially gave rise to the experiment and some background for the people originally involved. Then as the steps of the experiment are executed, further liturgy would explain what is being done. Perhaps attendees could file by meters or flasks or whatever to observe voltages and colors etc. The ritual performers could wear costumes that reflect the time and place of the origin of the experiment.

Part of the program would also be to invite members of the community to deepen their participation, step by step. The idea is that people can really come to understand how the experiments work, to really share the insight about the world.

Of course some rituals would have to incorporate field work. Traditional religion involves parades and pilgrimages, so the parallel is still holding.

This vision is of course much like a science museum. But science museums tend to be rather dead. Science museums do tend more and more to provide hand-on opportunities. Perhaps a key difference is the focus of the science cathedral on the intent of experiments to induce particular insights. Once I was in a museum where Tibetan Buddhist musical instruments were on display, inside glass cases. Often enough I will play such instruments in ritual practice, e.g. at Kunzang Palchen Ling. It was really sad to see these instruments locked away in a case, away from their intended use. The museum could have provided a hands-on opportunity by leaving the instruments out of the case. But it is still a whole different experience to play a gyaling in a ritual, holding the intent in mind.

The more scientific practice gets isolated in ivory towers, the less it will be understood or trusted by the great number of people without the keys to those towers. It is vital for our future that we cultivate ways to bring scientific insights to the people, not just the technological products enabled by science.

Diversity

What is diversity? It is attributed to a set with many members when the members have characteristics that differ among those members. The most interesting case is where the set is a human community or organization with many human members. Humans have many characteristics, such as: gender, age, size, skin color, neuropsychological pattern, language competencies, religious belief, economic status, organization role, geographical history, ancestral characteristics, etc. Members of a diverse community share at least their membership in that community, while differing in at least some of their other characteristics.

Communities usually have structure beyond a simple boundary between members and non-members. People are generally members of many communities at the same time. People in one community will belong to a variety of other communities. That is part of the diversity of a community.

Communities encourage or discourage various actions of their members. Of course the community is composed of its members; it is the members’ actions which do the encouraging or discouraging. The vector of encouragement combines with the vector of diversity to drive the evolution of the community. This dynamic interplay is what creates our world.

Diversity can be accommodated in various ways; by providing services adapted to the particular needs of community members with their individual characteristics, and also by discouraging member actions that conflict with such accommodation. Of course to discourage is to fail to accommodate, so there are difficult conflicts to resolve. Should a conservative religious organization be permitted to restrict leadership roles to members of a particular gender?

A deeper question is the extent to which diversity should be cultivated, not merely accommodated. There are types of accidental or historical diversity which are not fundamental to the purpose of the community. It is relatively easy for a community to cultivate such diversity. For example, a physics research group might welcome members from many national backgrounds, and make a special effort to cherish that diversity, e.g. by celebrating the holidays of those many nations.

More challenging is the question of the extent to which diversity should be cultivated which touches the purpose of the community. A certain amount of diversity of opinion is essential to the advancement of science, but adherence to totally discredited theories would seem to be good reason for some sort of corrective action. But it is very difficult to know exactly where to draw this line. More than one discredited theory has later triumphed. Another sort of diversity involves frameworks which are more incommensurable than contradictory. For example, an art department may face a decision whether to support both realistic and abstract artists, who may find each other’s aesthetic judgements almost unintelligible.

Communities throughout history have managed diversity in various ways. There are often roles that are rigidly assigned based on a member’s characteristics such as gender or ancestry. Beyond this sort of functional diversity, any accommodation is most often seen as a temporary stage on the way to ultimate uniformity. This general trend has led to the globalization of today. Globalization has proved a mixed blessing and by now seems self-limiting, having exhausted the planetary resources required for its own sustenance. Just as fragmentation of a population creates the opportunity for biological speciation, the collapse of global commerce will make room for the reemergence of cultural diversity.

Did the suppression of diversity by globalization participate in the failure of globalization? If we are to learn from that failure, we need to find new ways to cultivate and cherish diversity!

Markets and Tournaments

Prices are a way of evaluating options. Given two floor mops, if mop A works twice as well as mop B, then an efficient market ought to mark mop A at twice the price of mop B.

We could put prices on sports teams in just this way. For example, gambling pools should, given enough information, be able to put proper odds on each team in a match or a tournament.

But a tournament is more interesting than a match. Suppose we have a tournament with four teams playing, A, B, C, and D. We might be able to predict with reasonable accuracy which team will win in a match between any particular pair. But that doesn't let us assign any kind of price or value to each team. A might always win against B, and B against C, but it might happen that C always wins against A! In a four way single elimination tournament, the final champion team will depend on the way the tournament is arranged: on how the teams are paired up in the first round, etc.

Given a tournament structure, accurate pairwise odds will map cleanly to accurate odds on the eventual champion. But different tournament structure can easily give a different most likely champion. Teams don't have a universal value, but only relative to the tournament structure.

Decision making in general is a matter of evaluating options. Accurate evaluation depends on understanding the context in which the various contemplated actions will unfold. This is just a manifestation of the unity of emptiness and interdependent origination. The value of a thing is not inherent in the thing but rather is a property of how the thing is situated in its environment.

Bicycle Tire Shape

Somehow I am rather fascinated by how bicycle tires work. Probably one reason is that I just enjoy how things that seem very simple before being analyzed, turn out to be rather complicated as they are studied more carefully.

A tire on a bicycle or car etc. must support the vehicle, which involves forces parallel to the radius of the wheel, and also transmit tangential forces from engine torque or braking. To support the vehicle, the tire must push down on the ground with its share of the weight of the vehicle, and also push up on the rim with the same force. If one lifts the vehicle up off the wheels and then gradually lowers it back onto the wheels, the tires will deform from a uniform round shape to a flattened shape.

How much deformation will occur, how deeply will the vehicle sink after the tires first touch the ground until the tires are supporting all the weight? This amount of deformation must satisfy two conditions: the area of the resulting contact patch, times the air pressure inside the tire, must combine to produce sufficient force against the ground to support the vehicles weight. But the deformation must also provide enough net force against the rim to support that same weight, as outlined in Jobst Brandt's article.

At first thought, the deformation looks like a single variable, determined by the height of the rim off the ground. The lower the rim, the more the tire is deformed. But how can a single variable satisfy two conditions, without an impossibly unlikely stroke of luck?

Thinking about this a bit more, it seems that at a given height of the rim off the ground, a range of tire shapes is possible. This range of shapes provides the flexibility for both constraints to be satisfied.

In the following diagram, C is the half width of the tire carcass, i.e. half the distance from bead to bead along the carcass. Where the carcass is not touching the ground it is assumed to have a circular shape. This is still a very simplified picture, because there will be interactions between the neighboring cross-sections of the tire. A very large radius of curvature will permit a large contact patch, increasing the force of the tire against the ground but reducing the lift of the rim. A small radius of curvature will reduce the contact patch, so the force of the tire against the ground is smaller but the lift of the rim is greater. The actual shape should be where the two forces are equal.

Local Science

The past couple centuries have brought stunning technical transformations in almost every facet of our lives. The fruits we enjoy, e.g. internet access, are provided through complex networks of industrial processes that are based on very significant extraction of raw materials such as fossil fuels and metal ores, while at the same time emitting many waste products from carbon dioxide to solid plastic debris etc. A finite planet cannot support unlimited increases in rates of extraction and pollution. There are surely sustainable rates, at least for some materials, but these sustainable rates are very likely much lower than our present rates. Perhaps we will find much more efficient ways to provide the fruits we enjoy, so the rates of extraction and pollution can be brought down to sustainable levels without impacting our lifestyles. The possibility does seem quite real though, that change, by choice or necessity, will not be limited to factories. Changes in technology have changed our lives in the past, and seem very likely to continue to do so in the future.

A cornerstone of the modern transformation of our world is the feedback loop between science and industry. Advances in our scientific understanding of how the world works enable industrial processes to be designed to exploit that new understanding. In turn, industrial advances provide ever more powerful tools which scientists can use to probe more deeply into phenomena, enabling further scientific advances. But industrial power depends on more than science; it requires access to resources, legal and economic support, etc. If we are indeed entering an age of limits, industry will most likely be producing a significantly reduced range and volume of output. This will impact science.

What will science look like in a post-industrial world? Is there a range of possibilities? Can we somehow steer ourselves toward some happier among the alternatives? These questions are not limited to science, of course. Our entire way of living is going to be different in a post-industrial world. The way we live is both the way that we enact our choices, and a reflection of the outcomes of those choices. The same duality holds in science.

It may be a difficult idea, the notion that we have any choice in how we do science. Scientists observe the world and report on what they see. To the extent that science is such a direct and honest mirror of reality, introducing a notion of choice seems to imply some suggestion of departure from the whole truth and nothing but the truth. But science is an active human process, steered by choices at every step. For example, at the most intimate level, a scientist decides where to focus their attention. At the social level, various institutions decide which scientists and which research projects to support.

One way that people are responding to and respecting resource limits is to return to a more local way of life. This means less reliance on trade across great distances, and cultivation of richer person to person relationships with local community. When we rely less on local community, we rely more on large bureaucratic institutions. These institutions tend to be blind to the rich details of people’s lives and to focus on just a few bottom line statistical summaries. Large institutions also concentrate power, which generally fosters a greater degree of corruption, where the institution begins to promote its own welfare above that of the public it is intended to serve. Such corruption often involves distortion of the measures of the institutions effectiveness, steering institutional action to its own benefit. This kind of institutional blindness surely deserves a significant share of blame in our inability to respond effectively to the various challenges of resource limits. The benefits of resource exploitation tend to be channeled more to those in power, while the costs are channeled to the powerless. Withdrawing support from these institutions can be both a way to reduce the planetary impact of resource exploitation as well as an adaptation to narrowing limits.

Science is in many ways a typical facet of life, having become ever more tied to large bureaucracies. Science needs to change, both to reduce planetary impact and to adapt to limits. But science has a deeper connection to global institutions. A cornerstone principle of modern science is the notion of the uniformity of scientific law. For example, helium atoms in a terrestrial laboratory will behave the same way as helium atoms in a distant star, so we can learn about the behavior of stars through experiments in a laboratory. If observations in one laboratory differ from those in another, there must be some uncontrolled variable to account for the different. Progress in science demands coordination and cross-checking of results from all corners of the world. Modern science by its very nature is an institution with global scale.

Science also provides a model and means for the functioning of global institutions. These global institutions stake their claims to power on coherent policy and uniform rational regulation. Scientific methods are used to coordinate the uniform regulations with the myriad operational details at the street level.

Given the deep connection between science and a global outlook, how might science develop in the approaching age of limits? Will we just continue to practice modern science with the same basic structure but simply with a reduced budget? Or is a new vision of science called for?

The idea of a new vision for science is surely not absurd. Our notion of science has changed over time, so it stands to reason that it can and likely will change again. Indeed, the modern vision of science arose with thinkers like Descartes and Bacon, at the same time that the global institutions of resource exploitation were being established. Our vision of science is a part of our larger world vision. We seem very likely headed for a restructuring of our vision of humanity’s proper role on earth. A new vision for science will almost inevitably arise as a part of this.

We have built up such a solid structure of defenses around our modern vision of science that entertaining alternate visions can be very difficult. A classic tactic is the straw man. If science is not this, it must be that. But that is clearly unsupportable, so science must truly be this after all. But perhaps science is neither this nor that. The alternatives beyond the simple polar extremes are often subtler and more difficult to express or even to conceive with any clarity. But to face our future effectively, perhaps no easy solution will suffice.

To instill courage and confidence in those who might choose to explore less easy alternatives, I would like to point to the tradition of Buddhism. Buddhism is known as the Middle Way, exactly because it cultivates the subtle path that avoids the simple extremes. A new vision for science, appropriate for an age of limits, is not going to be found in any traditional Buddhist text. Surely the development of such a new vision will require every intellectual resource available. But some core Buddhist principles, such as the distinction between relative and ultimate truths, may be found very well suited for building foundations, having already demonstrated their value and robustness over a wide range of human history and geography.

I would like to propose a founding principle for a new vision of science, that a healthy science is one that is not only local in its community relationships but also local in its operational and intellectual goals. The quest for universal laws of nature should be demoted to an auxiliary status. Real knowledge is local knowledge. Abstract general principles certainly have their use and value, but their value is reduced as their generality grows: too much of the rich taste of direct engagement is sacrificed to gain the scope.

A related principle is the notion of tacit knowledge described by Michael Polanyi. Real knowledge is not merely words and numbers in a book, but living practice that is driven by that text and then in turn verifies and regenerates the text. Just like a species alive today is not meaningfully superior to some other species long extinct, the scientific knowledge of today is not meaningfully superior to some other extinct knowledge of the past, nor is it inferior. In five hundred years, it may well be impossible to perform experiments that demonstrate the existence and properties of the Higgs boson. This in itself doesn’t make the science of that future time better or worse. Science needs to be rooted in the human experiences of its place and time.

A Well Regulated Militia

I've been reading Barbara Tuchman's A Distant Mirror, which hasn't put me in any optimistic mood regarding the prospects for creating a society where wholesale violence is absent. All the same, there is clearly great variation across time and space in the frequency and scale of such violence. This variation must have causes and therefore be subject to some degree of control. Surely we can find a way to do better than we presently are!

It seems to me that the root of the problem is our gun culture. There is no way we are going to be able to divide people up into the good people who should be allowed or encouraged to own guns, and the bad people who should be discouraged or forbidden. It's not just that it is difficult to figure out who is good and who is bad; each of us is a complex evolving combination of good and bad elements. But again, this kind of variation opens the door to the possibility of steering the mix. I cannot imagine our gun culture evaporating over any small number of decades. But it is always changing. We can choose the sort of gun culture we want and take action to bring that about.

The constitutional objective of a well regulated militia points us along a viable path of responsible gun ownership. A gun is by design a lethal weapon. Gun owners need to be responsible users of lethal weapons. This clearly implies a level of training that is not trivial or elementary. Components of such a training regime could include:

• psychological tools for managing anger and depression
• dispute resolution
• non-lethal self-defense
• physical conditioning
• laws regarding gun usage
• target shooting
• gun cleaning
• gun storage and transport

Maintaining a permit to own guns could require regular continuing training and regular testing, e.g. a yearly course and a test every five years.

We can transform our gun culture from a national disgrace to a source of national pride. A culture of sober responsibility should spawn vastly fewer senseless mass killings.

Fractal Music

Algorithmic methods for musical composition encompass a vast realm. The general pattern is that a person writes a computer program. When the program is executed, its output is a musical score. Such a program might be designed to generate scores that strongly resemble existing works by a particular composer, for example, or works of some specific musical genre. At the other extreme, the goal might be to create compositions quite unlike any previously existing music, compositions that even test the limits of what might be recognized as music, but preserving enough characteristics of conventional music to avoid violating those limits utterly.

Microtonality represents another vast realm. Microtonality can be used to give fresh expression to conventional musical compositions and structures. Microtonality also opens up musical spaces that push so far beyond conventionality as to degenerate into nonsense.

Algorithmic composition provides a tool for exploring microtonality in a way that avoids simply duplicating conventional tonal structures, while at the same time maintaining enough recognizable patterning so the result sounds at least a bit like music. The approach I have been exploring constructs a score from the very conventional musical intervals of octaves, fifths, and thirds. The rhythmic aspect is also generally built from simple conventional elements, but in the discussion here the rhythmic aspect is left at the most primitive level. What I want to focus on here is how the simple musical intervals are used to form combinations and sequences of pitches.

In the spring of 1977 I visited the University of Pennsylvania and heard a lecture by Richard Voss on the fractal structure of music. At that time he was calling it a 1/f structure, but that is just one example of a fractal. The key idea is that fluctuations in pitch happen over many different time scales, none of which dominate. Around the same time I was studying phase transitions, such as the transition of a material from a liquid to a gas. Some of these transitions are also characterized by fluctuations at many different scales. So the central idea here is to use a simulation of a phase transition to generate fractal fluctuations, but in pitch rather than e.g. material density.

So how can a computer program simulate a phase transition? I first read about this in 1975 when I was reading Introduction to Phase Transitions and Critical Phenomena by H. Eugene Stanley. The book included some wonderful pictures of two dimension systems at the critical point and their fractal fluctuations, though again the term fractal was not used then. Ever since reading about this, I have been fascinated by how long range order can abruptly emerge out of short range interactions. What is also fascinating is that these phenomena also exhibit universality, which is to say the coarse level behavior is only weakly dependent on the low level details. In other words, a very simple computer program can simulate some very complex behavior!

The foundation of such a simulation is a multidimensional array or network of some type. When simulating a physical system, the array corresponds to space, so typically one would use a three dimensional array. The value contained in each element the array corresponds to the physical state of the material in the spatial region represented by that element. For composing a musical score, each element of the array corresponds to a particular time interval and voice within the composition. The value contained in the element will then be the pitch to be played by that voice at that time.

The multidimensionality of a musical score is not immediately obvious. But on second thought, the musical structure of theme and variation is almost universal. Music consists of phrases that are varied and repeated. The pitch to be played during one statement of a phrase is very closely related to the pitch to be played at a later statement of the phrase in the same position within the phrase.

Given such an array of elements, each of which consists of a pitch value, how should a computer algorithm simulate a phase transition with its fractal fluctuations? The core idea is to repeatedly pick a single array element, reassign its pitch value, then pick a different array element, reassign that pitch value, doing this again and again so that every array element gets many different values over the course of the program’s execution. Each array element has a small set of neighboring elements in the array. When assigning a new pitch value for a particular array element, the pitch values of the neighboring elements are examined. The pitch value is chosen so that it has some good harmonic relationship with the pitches of those neighboring array elements. Each time an array element is assigned a fresh pitch value, that new value can differ from the old value for two reasons: the pitch values for the neighboring array elements may have changed in the intervening time, so a different pitch value is needed to maintain a good harmonic relationship with the new neighboring pitches; and a weighted randomization method is used, where more closely related pitches are preferentially selected, but sometimes a pitch is assigned that is not the best possible.

Harmonic distances are given fixed numerical values which correspond to the energy contributions of microscopic interactions in a physical system. Just as the total energy of a macroscopic physical system, such as a cup of water, consists of the sum of all the microscopic energies from the interactions of the water molecules in the cup, the total energy of a musical score can be computed by adding up all the individual contributions from the harmonic relationships between pitches assigned to neighboring array elements.

The degree of bias toward close harmonic relationships is governed by a top level control variable that corresponds to the temperature of a physical system. When the temperature is high, there is little preference for selecting pitches with close harmonic relationships. As the temperature is lowered, the degree of preference is gradually increased. What is quite remarkable about the behavior of such a simulation is that an abrupt drop in the total system energy arises, despite the gradual increase in preference for individual lower energy relationships.

This abrupt drop in energy corresponds to a phase transition and the emergence of long range order. Musically, a tonal center spontaneously arises! As the temperature drops, the score changes from highly disordered to highly ordered. With luck, a sweet spot will emerge where there is enough disorder to make the composition interesting, but enough order so it still makes some sense. This transition from disorder to order can be illustrated by four scores.

The first score, prw691, was built at a temperature of 6.91. From the above energy graph, this is clearly below the transition point. To my ear, this music is too disorderly to make much sense of. But a histogram of pitch class occurrences shows that a tonal center is already becoming clear:

Of the 53 pitch classes in the microtonal system in use here, many do not occur at all, and just few are dominating.

The next score, prw542, is from temperature 5.42. The pitch class histogram now shows a clear tonal center:

I must confess, the tonal center being around the pitch class 0 makes me suspect that there is a bug somewhere in my code. A very slight consistent bias to any particular pitch class will strongly bias the emergence of the tonal center to land on the preferred pitch class. I am still trying to find out how my code is creating a bias. The fact that a clear phase transition emerges does seem to indicate, though, that this bias is not too strong. In any case, despite the tonal center's clear presence in the pitch class histogram, this score still sounds overly disordered to my ear.

The next score, prw392, sounds close to the sweet spot. Perhaps a slightly higher temperature than 3.92 would be a bit better. Still, this score sounds interesting to me, despite the highly dominant tonal center shown in the pitch class histogram:

The final score, prw246, from temperature 2.46, does sound too orderly to be interesting enough. The total number of array elements in this structure is 8748. Of these, prw246 has assigned 8221 to pitch class 0: