Tuesday, March 24, 2020

What is Essential

Saving lives or saving the economy? That is a truly bizarre dichotomy! More lives could be lost from the collapse of the economy than from the pandemic: that is a perspective that at least focuses on what matters. Merely staying alive, that is a very low bar indeed, but it is certainly a good place to start.

The natural instinct in a crisis like this is to work to reestablish the routine by which we had been living adequately enough. Of course, to ignore a pandemic is not going to make it go away. Wishing doesn't make it so. There is no way to escape this unscarred, but facing the situation and realistically engaging with it, that is the approach that will minimize the damage. We do have to balance lives lost due to supply chain disruptions etc. against lives lost directly from the pandemic. People need food, clothing, shelter, and medicine. There is enough to go around. A modicum of ingenuity can keep people supplied.

The shock of this pandemic reveals in a variety of ways that our routines have not served our needs so very adequately. This virus is the kind of thing that comes around every decade or so. A healthy economy, a healthy society, is one that can handle such challenges effectively and efficiently. So far, the United States appears to be stumbling.

In the short run, we need extraordinary measures to make sure that people are fed and housed. Insuring adequate medical care seems, sadly, out of reach in this crisis. In the longer run, we need to restructure our routines so that the next pandemic doesn't knock us off our feet. Our way of life has been driving us against many ecological limits. Plague, drought, flood, famine: we can expect ever more frequent crises as long as we mistake recovering our routines as essential.

Wednesday, February 26, 2020

Pride and Fall

I was discussing interplanetary colonization with an acquaintance recently. I don’t foresee that in any likely near future, while my interlocutor is convinced it’s a near certainty. Opinions do differ! The discussion did degenerate, sadly, into ad hominem characterizations. I was put into the “genteel-poverty crowd”; I called my acquaintance a “technocrat”. He accepted the label gracefully enough.

Predicting the future involves some kind of model. The simplest common model is an exponential function. For example, the world population might be increasing at 2% per year. With that simple model we can forecast the population at any time in the future. Science is largely a matter of developing, testing, and refining models for various facets of the natural world, by comparing the various models’ predictions against real world experience.

How this whole dialectic interplay between theory and experiment actually proceeds, or should proceed, is a topic of endless discussion among philosophers of science. Scientists have got the orbit of the moon around the earth figured out with remarkable precision. Philosophers of science continue to struggle to come to any basic understanding of how that precise figuring has come about.

Immanuel Kant’s philosophy is a major waypoint in understanding how science progresses. His notion of synthetic a priori judgements accounts for the fact that models cannot be inferred directly from the data of experience. It seems clear by now that our thinking is more adaptable than Kant gave us credit for. But still, it often takes a succession of generations of scientists for a new conception to take root. Our ways of seeing the world are quite deeply rooted.

In my recent discussion on interplanetary colonization, my acquaintance made a remarkable declaration: “Technocrats don’t have preconceptions.” I don’t think this is any kind of unique or even unusual attitude. Most scientists dismiss philosophy of science as being irrelevant. Generally they take for granted a kind of direct insight into the nature of phenomena. The task of science looks, from this perspective, a bit like that of a surveyor mapping out a new territory. Probably even real surveying is a bit trickier than this kind of na├»ve notion would portray it!

Our modern civilization is built on science. Practically every facet of our lives has been explored scientifically. Our lives are, in turn, structured by these scientific models, be they mechanical, chemical, biological, geological, or whatever. It is quite easy to slip into thinking that we have pretty much figured it all out. The stable structures of our lives mesh neatly with the stable structures of our ideas.

It may be just my own preconception, but things do change. The notion of environmental constraints has been talked about at least since Malthus, a couple hundred years ago, but clearly we humans have been very successful in circumventing whatever limits have appeared. How long this run of success will continue… that’s one of the core controversies of our time. What interests me here is not this or that model on which to build a forecast. What interests me is how the shape of the future can appear unquestionable to the cultish wing of the technocratic faith. More precisely, how might this kind of blind faith affect our ability to navigate any turbulence in the coming decades.

There is a curious paradox here. The notions of Malthusian limits, of climate change, of turbulence on the horizon: these are all scientific ideas. Science forecasts change, but science is not really ready for change.

Supposing that we actually do run out of miracles and Malthusian limits do finally get their teeth into us. What’s the impact going to be? Will it just be a matter of maybe replacing our air conditioners with more efficient units? Or are we facing famine and plague and the decimation of the population? These questions have been discussed extensively. A question that gets much less attention, though: what will happen to science? Certainly there are deep visionaries in the scientific community who can foresee the coming turbulence and begin to sketch what a post-collapse laboratory might look like. But a large fraction of the members of the greater scientific-technocratic subculture share my acquaintance’s blind faith, I fear, in the eternal stability of the present system: a steady growth in watts per capita and the rest of it. This kind of blind faith will not help us navigate any sort of coming collapse!

Wednesday, January 8, 2020

Schismatic Tuning

I am fascinated by musical tuning, from the conventional 12 equal steps per octave to all sorts of wild possibilities. Sometimes when I am out playing on the fringes, I learn something that can bring me back into much more conventional possibilities. So here is a way to tune a conventional keyboard. I'll call it "schismatic tuning" but I don't doubt that it has been explored again and again in the past.

Musical tuning is essentially a branch of mathematics, especially the way I approach it. Often in mathematics and science the focus is on novelty, on fresh discoveries, where fresh means not previously encountered by the human mind. This focus is unnecessary in math and science, is somewhat distracting or misleading, and will likely serve us much less well in the future. Since the time of Kepler and Galileo, math and science have expanded in a stunning fashion. Predicting the future is a fools game, but it seems unlikely that environmental constraints will permit continuous growth in extracting resources and dumping wastes. The modern trend of constant growth seems destined to end sooner rather than later. Math and science will be of great value in any post-growth society. To keep them alive, though, the focus will need to shift away from novelty.

So here is a historical preface to the schismatic tuning I have (re)discovered: Emilio de’ Cavalieri’s mysterious enharmonic passage - a modern rendition of a renaissance recovery of an ancient Greek tuning! Paul Erlich has written a thorough discussion of tuning A Middle Path Between Just Intonation and the Equal Temperaments - I have barely scratched the surface of this paper! I imagine that schismatic tuning is described in there somewhere! I would just like to share my (re)discovery here of this one small facet of the vast universe of tuning. I offer it as an invitation to explore further!

A quick review of fundamentals. A musical interval is the relationship between two pitches, which can be analyzed as the ratio between their frequencies. If pitches are an octave apart, their frequencies are in a 2:1 ratio; a fifth apart, a 3:2 ratio; a major third apart, a 5:4 ratio. These ratios are ideal. Just Intonation is a tuning that uses these ideal ratios. But for a variety of practical reasons, it is often useful to adjust, or temper, these ratios. There is no perfect solution to the puzzle of temperament. Modern keyboard tuning adjusts the fifth to 2^(7/12) ~= 1.4983 and the major third to 2^(4/12) ~= 1.26. The human ear can detect reasonably well the difference between this tempered major third and the ideal of 1.25.

Schismatic tuning is actually a family of tunings. I will present one version, based on dividing an octave into 53 equal steps, rather than the conventional 12. With 53 steps available, a fifth is tempered to ~1.499941 (31 microsteps) and a major third to ~1.248984 (17 microsteps). The fifth is improved, but the conventional tuning was already very good; the main improvement is in the major third.

How can such an improved tuning be adapted to a conventional keyboard? Here is my proposed schismatic tuning:

The top row names the keys on the keyboard. The second row gives the number of microsteps from the low C to the particular key of that column. The bottom row re-expresses that pitch in terms of cents. The conventional tuning would result in pitches of 0, 100, 200, 300, etc. cents. So this last row makes clear the difference in pitch between the schismatic tuning and conventional tuning, e.g. D is 3.774 cents sharper.

Some points to observe:

  • Almost all of the fifths are 31 microsteps, i.e. very accurate. From D to A is only 30 microsteps, though.
  • Four of the major thirds are the ideal 17 steps: C to E, F to A, G to B, and D to F#. The others are sharp by a microstep, i.e. closer to a pythagorean major third, 81:64.
  • The sizes of the chromatic intervals in this tuning are not all the same: 4, 5, 4, 4, 5, 4, 5, 4, 5, 5, 4, 5.
  • The syntonic comma is not tempered. E.g. moving by fifths up from C to E, one must cross the "wolf" fifth from D to A. This is a distinctly unconventional tuning.

One can certainly play in any key signature with this tuning - none of the intervals is too far off. But certainly a piece of music will sound different when the key signature is changed. This tuning does allow though a simple dynamic shift as outlined in my post Dynamically Tuned Piano. With perhaps a push of a foot pedal, A can be sharpened by a syntonic comma:

or a different pedal could instead flatten the D by a syntonic comma:

These shifts will move the wolf fifth up or down a fifth, and also rotate which major thirds are pythagorean, etc.

Tuesday, November 5, 2019

Rotta Model for Bicycle Tires

I recently discovered Andrew Dressel who recently wrote a PhD dissertation Measuring and Modeling the Mechanical Properties of Bicycle Tires. There's a lot in there, of course, but amongst all that I found a description of the Rotta model for tires. This is much the same as what I have been exploring. I polished up my math and wrote a bit of new software to generate some new tables for recommended inflation pressures base on Frank Berto's rule of 15% squish.

The Rotta model is quite simple:

The tire is flat where it contacts the ground, and has a circular cross section where it is not in contact. Each cross section of the tire is treated independently.

Here are tables from which inflation pressure can be computed. The rows correspond to tire widths, in mm. The columns represent rim width, as a ratio to tire width. E.g. the column with 2 at the top is for tire width twice the inner rim width, e.g. a 50 mm wide tire on a 25 mm wide rim.

The tables give the area in square inches of the contact patch. To compute the inflation pressure, divide the load on the wheel by the area of the contact patch. E.g. a 50 mm tire on a 25-559 ETRTO rim will have a 2.06 sq in contact patch when it is squished down 15% of its width. For that contact patch to support a 100 pound load, the inflation pressure should be 100 / 2.06 = 48.5 PSI.

For 622 BSD:

For 559 BSD:

For 406 BSD:

These tables are calculated purely from theory, i.e. no parameters are used to fit them to any experimental data. Do not follow them blindly! They're food for thought & perhaps provide a useful starting point for exploration.

And a 305 BSD table:

Friday, September 13, 2019

A Simple Fix

Chris Hedges recently wrote about some top CEOs who proclaim the positive value of capitalism. These terms and ideas get packaged and promoted so heavily that it becomes very difficult to see how they actually work. I'd like to take them apart a little bit and suggest a simple change that could have profound effects.

Our large scale society functions by way of complex organizations. Our welfare, indeed our survival, depends on the smooth functioning of these organizations. These organizations can only maintain themselves by earning profits, i.e. by selling finished products for prices high enough to pay for raw materials, maintain factories, pay workers and managers, etc. Investors who contribute start-up and expansion up-front costs need to earn a reasonable return on their investment, or they'll find something better to do with their money.

The distortion at the foundation of many of our problems today is that investors hold the ultimate decision-making power of corporations. Corporations are created and structured by means of the law. The law gives investors this power. A change in the law would change the way corporations are organized.

The classic straw-man for corporate governance is government control of corporations. But there are many other alternatives. Much of our problem today is that corporate power is too centralized. Government control would increase centralization. What we need is to distribute power.

Corporate governance needs to be widened. The Board of Directors of a corporation, the embodiment of regular decision-making, should include representatives from the workers and the managers, from suppliers and customers, from the local community, from folks living downstream and downwind, as well as from investors. Investors should not, in most cases, have a majority vote. Investors deserve a fair return on their investments, but this should be balanced with the legitimate concerns of the other stakeholders of the business.

It would be a catastrophic error to blame all our ills on big businesses and therefore to work to destroy those businesses. The fabric of our society consists of the goods and services flowing through these businesses. A small adjustment to the steering mechanism would have a profound effect on the path of evolution of this fabric. This is a simple and practical step that could fix the worst excesses of our current system.

Friday, August 16, 2019

Beyond Wonk Perfection

Some years back, the Washington Post's Wonkblog published an example of how precincts might be partitioned into districts unfairly versus fairly.

I would like to propose an improved partition, better than the "perfect" example of the Wonkblog:

In the Wonkblog's perfect partition, each district is entirely red or entirely blue. This makes the representation very rigid. Shifts in voter sentiment will not be reflected in shifts in representation, until the shifts are massive. In the partition I propose, some districts have slim majorities and others have large majorities. This approach is less rigid.

Sunday, June 30, 2019

Partitioning the Vote

My earlier notion for preventing gerrymandering was not very effective. Looking at the data for the Michigan 2018 election, the Democrats had a majority of the vote but a minority of the districts. My proposed rule would have done nothing to prevent that.

Exactly what a good rule might be, I don't know. It's a difficult problem! But the basic criterion that seems logical is that the fraction of districts won by each party should be roughly proportional to the fraction of votes for that party. A general shift in voter preference should be reflected with a proportional shift in election results, in the fraction of districts won by a party. This would be achieved by having district boundaries drawn so that the fractions of votes for each party across the districts varies across a reasonably wide spectrum.

The challenge with this approach is that the notion of "a general shift" is too vague to be of much use. Still, a simple model can get the idea across.

Here is an idealized situation, a state with ten districts. When the vote is split equally, the range of district results could be:

With a general drift to 60% of the vote for one of the parties, the number of districts won could change proportionally:

A further shift, to 70%, would continue to be reflected in the proportion of districts won: