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:

Twisted Telemann

My friend J.-S. Truchy pointed me to some interesting microtonal software: tune.js. This software got me thinking in several directions.

The first puzzle for me was: what is a .js file? What programming language is that? Easy enough to do a quick search and discover that it is java script. I have heard of java script! But I have never looked at any! This really underscored for me my situation. I have been writing computer programs since 1970, i.e. for 45 years. My first programs were in IBM 1401 Autocoder. The first programs I ran were in IITRAN (from the Illinois Institute of Technology). From there I got into Fortran, IBM 360 Assembler, etc. In short, I am a dinosaur! I can still read JCL in my sleep, but this was my first look at java script!

The second puzzle was: what exactly does this tune.js program do? I see that I can click on the image of the keyboard and adjust its tuning. But that seems to be merely the tip of the iceberg! Somehow there are many microtonal scales made available by this program, but I can't fathom how to access them!

Rather than getting stuck in my frustration over things I can't figure out how to do, I often like simply to forge ahead with things that I can figure out how to do! With luck I can pick up a little inspiration from the abandoned route whose first handhold proved already beyond my grasp.

So, in this case, what might I do to adapt my current favorite scale, Hanson[11], to a conventional keyboard? To start with, a conventional keyboard really wants 12 notes per octave. Hanson[11] can easily be extended to Hanson[12], so that is easy. What would that look like, just to put that scale on the keys? The only issue is, which note of the Hanson[12] scale to assign to the keyboard C? Here is what I came up with:

The numbers on the keys are based on the equal division of the octave into 53 equal parts, the microtonal system that I have been exploring and in which the Hanson[12] scale works well. The particular numbers are not meaningful: it is the differences between the numbers that matter. So, for example, the lowest C has the number 0 and the lowest D has the number 11. So the frequency ratio between D and C is 2^(11/53). This doesn't correspond very well to any just tuned interval. The truth is, this is a rather warped tuning for a conventional keyboard! But it might be fun, anyway!

The Hanson scales are based on minor thirds. Dividing an octave into 53 equal parts gives a good approximation for a minor third of 14 microsteps. This is to say that 6/5, the frequency ratio of a just tuned minor third, is very close to 2^(14/53). Almost every key on the keyboard has some other key which is 14 microsteps higher and another key which is 14 microsteps lower. Only the E has no key 14 microsteps lower, and only the Eb has no key 14 microsteps higher. These are the notes at the two ends of the stack of minor thirds from which the Hanson[12] scale is constructed.

These minor third relationships can be marked on the keyboard:

Most of the 14 microstep minor thirds appear where they should on a conventional keyboard. For example, C to Eb is a conventional minor third, and with this tuning the notes are indeed 14 microsteps apart. But the fit is not perfect. Some intervals of 3 conventional half-steps are not 14 microsteps apart, e.g. D to F. Instead, it is D to F# that is 14 half-steps. In the above diagram, I used dashed arrows to indicate intervals of 14 microsteps that do not appear 3 conventional half steps apart on the keyboard.

What makes the Hanson scale interesting is that it takes advantage of the tempering of the Kleisma by the underlying microtonal system. Even though the Hanson scale is built out of minor thirds, intervals of a perfect fifth appear. When the octave is divided into 53 equal parts, a perfect fifth is represented as 31 microsteps. It is the very close approximation of 3/2 by 2^(31/53) that makes 53 interesting musically.

The perfect fifths in the Hanson scale appear as follows on the keyboard:

Here again solid arrows are used when the perfect fifth appears in a conventional way, i.e. separated by 7 conventional half steps. Dashed arrows are used when a perfect fifth appears unconventionally.

Given a conventional keyboard, conventional music can easily be played in this unconventional tuning, e.g. a minuet.

Identity

I haven't been following the details of the Rachel Dolezal affair, so I have no useful opinions to offer on the specifics. But the framework of ideas in which the issues unfold is quite fascinating. The Buddhist traditions have explored many of these ideas in a deep and rich way and should be able to contribute constructively to the discussion.

Perhaps, though, I should rather say, contribute deconstructively. So much of the problem here is that we often think we mean something specific but the ranges of possible meaning are so wide and so poorly demarcated that ambiguity and misunderstanding are rife. Mapping out a bit of this terrain would seem to be a useful preliminary.

Rachel Dolezal is reported as saying, "I identify as black." What layers of potential meaning are packed into this?

People seem to carry in their minds, in their perceptions, some kind of tribal classification system. When we see someone or meet someone, we tend to situate them as members of some group or other. This classification system tends to be factored into several dimensions, such as gender, class, ethnicity, and race. This classification system is not entirely conscious. It changes and evolves with our experience in the world. And of course if and as we get to know a person, our initial classification of them will both shift and tend to recede into the background.

We never encounter ourselves in the way we encounter others, but still, we will generally situate ourselves in our own tribal classification system. We may come to realize, as we get to know another person, that they are not very comfortable with the identity that others ascribe to them. And of course we ourselves may struggle with the way we fit into the tribal classification system. We may start to see that other people have their own classification systems that might not always line up so well with our own system. And even when the systems are well aligned, we may come to realize that others situate us in a place where we don't see ourselves properly fitting.

These classification systems are also created and enforced by our social institutions. Having one restroom for men and one restroom for women enforces a binary gender system. There is intense pressure for people to conform to one standard gender or the other. In various times and places there have also been racially segregated restrooms, with even less tolerance for nonconformity.

Nowadays there are various documents on which one is asked to mark boxes that correspond to various classification schemes, including especially gender and race. Sometimes the marks in the boxes are just used to gather statistical data. Other times the marks have consequences specific to the individual, e.g. what kind of job they may be able to get, etc.

Why do we ask people to indicate their own gender and racial identity? The whole history of gender and racial bias is filled with such brutal injustice, and that bias is based on discrimination, i.e. on one person classifying another person, especially a more powerful person classifying a less powerful person. If are working to eliminate that unjust bias, it would seem effective to stamp it out wherever possible. So we can let each person indicate their own identity, rather than imposing it.

I am quite unambiguously a white male, so perhaps I can be a good example to use in exploring what it might mean for me to say, "I am a white male."

When I say that I am a white male, do I intend to subscribe to some racial classification system that divides people into white and non-white, and a gender classification system that divides people into male and non-male? I hereby declare that I do not subscribe to any such systems. I think the whole system of racial classification is one of the stupidest and most pernicious heaps of pseudo-science of our modern age. Gender seems not to be such utter pseudo-science, but I know very well that the closer a person looks into reality, the more complex things get. And anyway biology is just one layer of the puzzle.

When I say that I am a white male, mostly what I am saying is that, in the shared tribal classification system that is most common in the society in which I live, most folks encountering me will quickly and easily sort me into the "white, male" pigeon hole.

Sometimes people get caught up in puzzling about, "Who am I really, essentially, under my skin?" Furthermore, a person might try to answer this question in terms of gender and racial labels. One way to go about this might be: given my deep essential qualities, what social identity would give me the best opportunity to express those qualities? With this approach, the question isn't whether deep down inside am I black or am I white? But perhaps because deep down inside I feel very devoted to the Buddha Dharma, maybe I would have been more able to express that devotion had I been born Asian. That is still a very different thing than saying that deep down inside I am Asian.

But what is the point of classifying oneself in terms of gender and race on e.g. a job application? Is this meant to be a question of my deep inner essence? I rather doubt it. A lot of it has to do with measuring how well an employer is doing at overcoming the gender and racial biases that have plagued our recent past. Probably most applicants know very well how others tend to see them and don't have a problem marking the right box. But that easy answer hides so much that deserves to be examined.

For example, our racial and gender roles have a history, a personal, family, and social history. To understand how a person came to be where they are, it is useful to understand the road they walked to get there. Each person's social context has many facets. A person may well be classified one way in one context, and a different way in some other context. To some extent a person can control, by choice of hairstyle or clothing or language training or cosmetic surgery, how others classify them. To what extent is how others classify a person a matter of that person's choice?

I don't really expect to make any actual dent in these tough social problems. My hope is that maybe I can help connect the rich resources of the living Buddhist traditions to the difficult problems of our time.

The Superpower Trap

At the Dharma Teacher Gathering last week, one day was devoted to "Responding to the World's Needs". A major focus of the presentations was climate change - certainly a crucial issue of our time. At a lunch discussion on our final day we were talking about other needs of the world that deserve our response, and the gun culture of the USA was brought up. I connected this to the role of our military in the world. Upon further reflection, it seems that climate change and military power are deeply intertwined.

At the most basic level, military operations directly consume vast quantities of fossil fuels and other resources. The use of powerful bombs, incendiaries, defoliants, etc. inflict substantial damage to the ecological network along with vast human suffering. The work to reconstruct cities and villages then consumes further resources.

Apart from these direct costs, military power enforces a system of global production and trade driven by remote concentrated centers of power rather than sensitivity to local needs and costs. Regimes are propped up that serve the needs of these remote powers, at great costs to the land and people of the region.

In addition to this, a system of global consumerism is cultivated in order to promote industrial productivity and technological progress, which are the cornerstones of modern military power. The culture of guns and violence seems to work to maintain a population ready to go to war.

Such self-reinforcing destructive patterns do not require any evil genius or conspiracy behind them. It's just the nature of things, like the way thunderstorms arise spontaneously. Understanding these patterns, though, may well lead us to find ways to disentangle ourselves from them!

Gathering Thoughts

This past week I attended a Dharma Teacher Gathering at the Omega Institute in Rhinebeck. That's close enough to home that I could ride my bike to get there and back, which was delightful! I think the last time I was at Omega was in 1990. The place hasn't changed so much over those years... the food is still great!

The gathering included around 240 teachers. It was really an amazing group of people! During the various sessions there were many opportunities for small group conversations and explorations, and of course many more during breaks and meals. I had only met previously a few of the attendees, so the week was just packed with discovery! Most folks were from the USA but also quite a few from Canada and Europe. I think most people came from big cities. The largest contingents seemed to be from the Triratna and Insight Meditation organizations. There were also many teachers from various Zen lineages. Hard to be sure but I think the number of teachers from Tibetan traditions was probably around twenty. But one interesting facet of the group was the way folks participated in multiple traditions. For example, a Zen teacher from Toledo, Ohio told me how he was also teaching Lam Rim, having studied with Gelek Rinpoche. Or a teacher from a Japanese temple in California was also working with Chetsang Rinpoche from the Drikung Kagyu tradition.

With such a short meeting bringing together so many teachers from so many traditions and also covering such a wide range of issues, we could never explore very deeply. But perhaps the point of this kind of meeting is just to start conversations. Certainly doors were opened on important topics!

Our first day was on "Growing as Teachers". I think of myself primarily as someone who practices the Buddha Dharma, or at least I try to keep my practice as a top priority. The teaching I do is a part of my practice, in part a way to practice generosity, but even more a kind of mirror in which to discover my limits and inspire my further efforts to let go of my own rigidity, delusion, etc. So my inclination was to interpret the topic of the day more as "Growing as a Practitioner". Either way, a challenge with such a topic is to establish some kind of reference framework in which growth can be measured or evaluated. The challenge of setting up such a framework came up, too, in several meal-time conversations.

Over the years, I have talked with folks interested in a scientific approach to Buddhism. Can't we measure the processes of the mind and use those measurements to refine our methods of practice to make them more effective, to become better able to liberate ourselves and all beings? How can that not be a worthwhile project and even an urgent project?

But maybe the project is not as straightforward as we'd like it to be. Frameworks of reference have their use, but every such framework casts shadows even as it illuminates. This is the nature of relative or conventional reality. This nature is, indeed, the ultimate reality, the realization of which liberates us. The project of measuring our progress toward liberation is entangled with deep paradox. And of course Buddhist literature is filled with expressions and exploration of that paradox. Frameworks are constructed and deconstructed with amazing alacrity.

Our modern age is characterized by large scale bureaucratic institutions. Probably religious institutions have the longest track record for such bureaucracies. How can all the rules and procedures serves to enhance the effectiveness of the institution, instead of serving to rigidify and corrupt? What resources does Buddhism have to help tackle this problem generally as well as for the institutions that embody the Buddhist tradition itself?

Our second day was was focused on the issue of diversity. This issue was framed primarily in terms of the polarity between white and, uh, PoC, People of Color. (This whole business of ethnic, national, racial, etc. identity - and labels! - it really is problematic. No doubt there is value in identity at a relative level. But all the politics! Violent battles over labels! Wow!) In one presentation one question was resolved, something that has puzzled me for years. Why are white people called "Caucasian"? What is the link between white people and the Caucasian region, between the Black and Caspian seas? White people seem to come from Northern Europe, which is not so close to the Caucasus.

Apparently, back in the eighteenth Century when the first anthropological theories about race were being formulated, a very large old skull was unearthed in the Caucasus. Such a large skull must have come from a superior human. Since white people are superior, that skull must have been from a white person, and so white people must have come from the Caucasian region. Whether or not the white-Caucasian link really started with this bit of history, without a doubt commonly held ideas very often start from such odd accidents and then somehow snowball and stick.

The strange paradox here is that the polarity between white and PoC is really a product of white supremacy thinking. It is certainly a polarity that needs to be confronted. We have to take our ideas seriously in order to examine them thoroughly so we can see their limits or their utter delusiveness. But in Buddhist institutions, the connections between race and power are particularly diverse. The notion of race and the white-PoC polarity, these are products of European and Euro-American thinking. Buddhism developed quite independently of any of that. Of course, most every society has some way of dividing up people into groups that tend to track along family lines, and power tracks within group boundaries. These boundaries get scrambled across history: Buddhism can provide many examples of this kind of scrambling, as well as method for understanding the scrambling.

Certainly in the USA today, the white-PoC polarity still has great weight. Addressing the suffering that creates is both a challenge and an opportunity for Buddhism here today. I do wonder if stepping back and seeing the broader picture might not be useful in meeting that challenge. Then again, my typical pattern is stepping back and avoiding intimate engagement, so perhaps I am just avoiding a real confrontation with my own white privilege!

Our third day was devoted to "Responding to the World's Needs". There was some discussion about the spread of Mindfulness cultivation beyond Buddhism, but at least for me the topic of high impact was climate change. We heard some very frightening figures on carbon dioxide and methane emissions. On the other hand, we were encouraged to be confident that a solution could be found if the appropriate will could be summoned to the task.

I had volunteered to lead a breakout discussion on how Buddhism might address this challenge. Putting together an outline for the discussion did give me a good opportunity to think through many aspects of the topic beforehand. I was hoping to hear and learn from other participants, but there were so many other fascinating breakout sessions... oh, well!

I do think, though, that Buddhism has a tremendous amount to offer here, a middle way between the extremes of a solution and an apocalypse. Just as reflection on the inevitability of death can serve to inspire a deep sense of responsibility, contemplating the profound disruptions the world will undergo as the encounters with resource limits accelerate can help us see how our actions now are of crucial import for future generations.

With so much left to explore, I hope such gatherings of teachers can continue to dig deeper and keep our various institutions vital, to benefit both their own memberships and all sentient beings!

Technology and Distraction

His Holiness Karmapa taught recently in Kingston, NY. He answered a few questions at the end of the afternoon. One question dealt with the relationship between science and meditation:

Q. Can neuroscience open a new door for meditation?

A. The benefit of neuroscience for meditators, by which I mean not only Buddhists but everyone interested in meditation, is that neuroscience can actually map and reveal, visually, changes in the brain caused by meditation, which naturally increases our confidence in the practice of meditation. When we meditate, we don’t directly see evidence of a result, which used to not be a problem, but now in the 21st Century we’re all in such a hurry and so lacking time that we have neither the patience nor the time that Jetsun Milarepa did. So it’s easy for us to become discouraged or disheartened by a lack of evidence of improvement. Because neuroscience can literally show the results of meditation practice, it increases one’s confidence. Nevertheless we are just beginning to study this. Neuroscientists are really just beginning the active experimental study of meditators. As the technology develops further and is constantly updated, evidence of the results of meditation, more specific results and so forth, will no doubt increase.

However there is one problem, which is that generally where there are great meditators, there is no technology, and where there is technology, there are no great meditators. In the past, for example in Tibet, there were lots of great meditators because there was no technology so therefore there were no distractions. There was nothing to do other than meditate, so they meditated very well. On the other hand, now, when we have all of this technology that would enable neuroscience to examine great meditators, we’re all too distracted and entertained by the technology to be great meditators.

Pilgrimage

How about a bicycling pilgrimage of the Buddhist temples of the Catskills and the Mid-Hudson Valley?

• Kunzang Palchen Ling, Red Hook
• Kagyu Thubten Choling, Wappingers Falls
• Chuang Yen Monastery, Carmel
• Tsechen Kunchab Ling, Walden
• Dharma Drum Retreat Center, Pine Bush
• Blue Cliff Monastery, Pine Bush
• Dharmakaya Center, Cochecton
• Dai Bosatsu Zendo, Livingston Manor
• Padma Samye Ling, Sidney Center
• Palyul Retreat Center, McDonough
• Zen Mountain Monastery, Mount Tremper
• Karma Triyana Dharmachakra, Woodstock
• Retreat Mahayana Temple, Leeds
• Won Dharma Center, Claverack

It'd probably end up being about 400 miles, with plenty of hills. Perhaps ten days would be a reasonable schedule, leaving a bit of time to spend at each temple. The next challenge is to find places to stay. There are a few New York State campgrounds not too far:

• Taconic State Park, Copake Falls
• Fahnestock State Park, Carmel
• Mongaup Pond Campground, Livingston Manor
• Little Pond Campground, Andes
• Oquaga Creek State Park, Bainbridge
• Kenneth Wilson Campground, Mt. Tremper

Here is a nice map of New York campgrounds: Allstays

At Zen Mountain Monastery:

At Kunzang Palchen Ling:

At Karma Triyana Dharmachakra:

Initial route ideas:

• Berentsen to Beaverkill
• Beaverkill to Oquaga Creek
• Oquaga Creek to Little Pond
• Little Pond to Kenneth Wilson

The Dress

I have been having far too much fun with the wonderful color illusion of the dress that has been making the internet rounds lately!

I copied the main colors of the stripes from the photograph, and tried to create two different contexts, one where the colors are easy to interpret as blue and black:

another where it is easy to interpret them as white and gold:

It's a nice illustration of interdependence!

Maybe it is too shocking to believe, but...

Hanson-11

I love exploring the relationships between mathematics and music. My exploration tends to be more hands-on research than library research. So I am surely rediscovering many old ideas, and I almost never learn the proper terminology. But I do have a lot of fun!

Lately I have been exploring a pitch class set that is sometimes called Hanson[11]. Others have certainly explored this, e.g. http://dkeenan.com/Music/ChainOfMinor3rds.htm and http://xenharmonic.wikispaces.com/Kleismic+family which even include some music composed in this system. I must confess that the folks that work in this area have developed an enormous collection of terms and ideas, very little of which I understand. I am going to explain here some of the ideas that have led me to this approach.

Most any musical pitch system is based on a collection of intervals, i.e. frequency ratios. The most fundamental intervals are simple rational numbers. E.g. an octave is the ratio 2:1 and a perfect fifth is a ratio of 3:2. There is a simple algebra of intervals: if pitches P and Q are separated by an interval X, and then Q and R are separated by an interval Y, then the interval from P to R will be X*Y, the multiplicative product of X and Y.

One can certainly make very good music by starting with a single pitch and a small collection of primitive rational intervals. The various combinations of these intervals will generate an infinite collection of more complex intervals. This system is known as Just Intonation.

The challenge with just intonation is that different combinations of intervals can result in complex intervals that are very close together. The standard tuning for a guitar illustrates this quirk. The intervals between successive pairs of strings on a guitar are a fourth from E to A, a fourth from A to D, a fourth from D to G, a major third from G to B, and a fourth again from B to E. From the first E to the last E should be two octaves. In just intonation a fourth is the ratio 4:3 and a major third is the interval 5:4. So the complex interval which is the product of the simple intervals between the strings is 320:81. But two octaves would be 4:1 = 320:80. The small interval between these two intervals is 81:80, known as the syntonic comma.

There are many such small intervals that arise in just intonation. In fact, the infinite collection of complex intervals will fill the entire pitch space densely. In notating music, in building musical instruments, and in performance, managing such an infinitely dense collection of pitches is practically impossible. Still, the underlying music concept can adhere to just intonation, while the notation and the instrument can simply collect pitches into clusters and use a single pitch to stand for the cluster. Analysis might still reveal the underlying intention. Perhaps our ears even interpret the sound relationships as the appropriate just intervals, at least when the musical sense is clear.

But Easley Blackwood's book The Structure of Recognizable Diatonic Tunings shows that the mainstream European tradition from Bach to Mahler does not work this way. A particular note to be played at a particular time in a piece of music will stand related to several other notes, e.g. other notes played at the same time, or immediately before or after, or in corresponding positions in musical phrases played not too far away in time. One set of relationships might imply one just intonation interpretation of a note, while another set of relationships implies a different interpretation. And this sort of ambiguity is pervasive in the European tradition. A lot of what is happening with the music is a kind of playing with ambiguities, with musical puns.

From this perspective, what makes a tuning useful or interesting is the set of ambiguities that it provides! Because different tuning systems work with different ambiguities, music won't in general translate from one system to another. It's like trying to translate puns between languages. But of course each language can support a wonderful collection of entertaining and insightful puns. So different tuning systems should support music, though different music.

My fascination for quite a while has been the microtonal tuning system that divides an octave into 53 equal parts. More recently I have been looking at ways to pick a subset of the 53 pitch classes with which to make music. In the conventional tuning system that divides an octave into 12 equal parts, music typically works with just 7 of the 12 pitch classes at a time, though there might be accidentals or key changes too in a piece of music. One way to think about these 7 pitch classes is as a contiguous region of the circle of fifths. I.e. the seven notes C D E F G A B can be arranged as F C G D A E B. While the primary structure of this set is governed by this sequence of intervals of a perfect fifth, there are other relationships among these, e.g. C to E is a major third. This ambiguity, is C E four perfect fifths or a major third, is again the blurring of the small interval of a syntonic comma.

What I am working with now is a set of 11 pitch classes out of the total palette of 53. This set is generated by 10 intervals of a minor third. When an octave is divided into 53 microsteps, a minor third is 14 microsteps. We can start this set of 11 pitch classes from any of the 53 pitch classes, just as a major scale can start from any of the 12 pitch classes of conventional tuning. Here is a diagram of one set:

In this diagram, each pitch class has six neighbors. The intervals between the neighbors are perfect fifths (31 microsteps), perfect fourths (22 microsteps), major thirds (17 microsteps), major sixths (36 microsteps), minor thirds (14 microsteps), and minor sixths (39 microsteps). The first important observation to make about this subset of 11 pitch classes is that, while the subset is generated by a sequence of minor thirds, the subset also includes pairs of pitch classes separated by fifths. This property is due to one of the ambiguities that arise when dividing an octave into 53 equal parts. The small gap between a fourth and 6 minor thirds is known as a klesma. The blurring or tempering of the kleisma in this system corresponds to the tempering of the syntonic comma in the convention 12 pitch class system.

Another nice feature of this set of 11 pitch classes is that when the pitches are arranged in order, e.g. 0 8 11 19 22 25 33 36 39 47 50 53, there are just two sizes of intervals that occur, 3 microsteps and 8 microsteps. This is analogous to the half step and whole step of a conventional major scale.

Here is what this pitch class set sounds like:

http://soundclick.com/share.cfm?id=13004205

http://soundclick.com/share.cfm?id=13004263

http://soundclick.com/share.cfm?id=13043974