The Problem with Opinion Pieces

The federal government just shut down, and Trump is going to unceasingly trumpet, pardon the pun, that the Democrats shut down the government just to satisfy a small minority of illegal immigrants. I was furious that the Democrats would do such a stupid thing, alienating the white voters they need to regain power.

So despite my firm belief that political pundits are right only by chance, I dashed off an essay bemoaning the Democrats’ elevation of principle over reality. Then I remembered that if enough Hispanics and blacks voted, they would tip the balance in favor of Democrats. So maybe this strategy was a good one after all.

By considering alternative viewpoints, my certainty that the Democrats had made a terrible error dissolved into skepticism about whether I could predict which strategy might work, or in general that I had more insight into the unpredictable future than the next self-proclaimed pundit.

It is impossible to predict events on a fine scale, as civilization is far too complicated to model in any detail. However, I do believe that if you back far enough away it is possible to create accurate (if approximate) models of selected aspects of complex systems. The one about which I hammer away is the ample scientific evidence that civilization in general and the U.S. way of life in particular are both unsustainable, that some sort of major correction will occur in the near future, and that no one is making plans for dealing with this over-riding issue.

So you are spared another liberal rant.

“The Evolution of Beauty” by Richard O. Prum

Still life, watercolor, 9 x 12.

Another must-read! Either I am not discriminating enough, I don’t read enough, or terrific books are more common (I unsurprisingly favor the latter interpretation).

I first heard about Richard Prum when he gave the talk at one of the annual Darwin’s Day Dinners* in Norwalk, CT, where we lived until late 2017. He gave a terrific presentation, but it didn’t quite register with me how revolutionary his ideas were. I had read Darwin’s second major book on Evolution, “The Descent of Man, and Selection in Relation to Sex,” and had internalized the notion of sexual selection in a dim way, so Prum’s  featuring it was not surprising. Prum calls it “Darwin’s really dangerous idea,” a reference to Daniel Dennett’s book “Darwin’s Dangerous Idea,” about natural selection.

Alfred Russel Wallace famously came up with the idea of natural selection independently and sent Darwin a letter outlining his theory. This galvanized Darwin to finish his book, which he had been reluctant to publish. Wallace was younger than Darwin, and had not spent the years of intense thought and field research that gave Darwin’s theory such depth and explanatory power. Far from feeling resentful that natural selection had become “Darwin’s theory,” he was an enthusiastic promoter of Darwin. But he was also deeply religious, unlike the agnostic, growing on atheistic, Darwin.

When “Descent of Man” was published in 1871, 12 years after “Origin,” it was brutally attacked for a variety of reasons described by Prum. It was just too much for a Victorian readership. Wallace was scandalized, feeling that Darwin had betrayed his own theory and feeling that the book undermined his religious beliefs. Wallace subsequently did such a thorough job of trashing the idea of sexual selection based on aesthetic choice that it was basically ignored for 140 years.

Instead, there grew the notion, embedded in nearly all research to the present and parroted in every book on evolution I have read, that traits were either adaptive (fit to the animal’s environment), neutral, or the secondary result of adaptive traits. In my extensive thinking about the origins of art, I have gone along with the herd, searching for some reason why art would be adaptive. That’s why this book was so revealing to me, because it opened the door to other ways art might have evolved. I hope to parse the implications in the near future.

I had not registered the extent to which adaptationism had permeated the field of evolutionary studies until I read Prum’s book. I happened to reread the section on art in Steven Pinker’s book “How the Mind Works” and it was now clear to me why he had famously dismissed art as a form of sensory “cheesecake:” he couldn’t envision how pleasure could be the basis for the evolution of art. Prum bars no holds in his scorn of stubborn adaptationists like Pinker and Richard Dawkins. He also convincingly debunks many notions that have made it into the popular press, such as the idea that men have evolved to prefer hourglass figures, symmetrical features, and features that are an averaged composite, all of which have been thoroughly disproved. He particularly attacks the tired notion that fancy plumage is an indication of fitness, another attempt by adaptationists to explain beauty in nature.

The meat of Prum’s book are his wonderful descriptions of the behavior of tropical birds – he is a master ornithologist who has spent much time studying birds in tropical forests around the world (deafness has reduced his field work). Of particular interest is his discussion of the details of sexual anatomy and mating behavior in ducks (which have penises, unlike 95% of birds). Later in the book he applies his insights to human beauty, and particularly to how sexual selection is the likely source for the exaggerated sexual ornaments and behavior in humans. This is worth reading regardless of your interest in the details of evolution.

Throughout he relates his findings to female empowerment by means of sexual selection. He is careful to distinguish female power through choice from female domination, which is nowhere found. Prum makes the depressing conjecture that prior to the evolution of agricultural civilization women had “domesticated” men and established a substantial amount of female control through choice, only to have this  control almost completely undermined by the evolution of paternalistic hierarchies.

Prum is always careful to distinguish solid fact and observation from speculation, and to note that many of his fruitful ideas need to be verified by further research.

This is a beautifully written book full of visual delight and descriptions of nature at her most lavishly creative. Most of all, it dramatically expands the horizons of evolution. Along with “evo-devo” and horizontal gene transfer among prokaryotes, sexual selection reduces the need to burden natural selection with carrying the entire load of explaining how and why organisms are as they are.

  • The celebration in Norwalk is among a very short list of celebrations of Darwin’s birthday, and it is truly wonderful, bringing together intellectually curious people who might not otherwise meet each other. There is a science quiz that is quite sophisticated, with various tables of 10 competing. Ours never won, but we placed a couple of years.  I hope some day that such celebrations become commonplace.  See the Wikipedia entry on “Darwin Day.”

More About “Scale”

Watercolor from life, 2016 (9 x 12)

In my last post on “Scale” by Geoffrey West I didn’t discuss in any detail the results of applying power laws to cities, and entirely avoided the last chapter, which applies scale laws to the issue of growth. I want to address these issues in this essay. The bottom line: we have a limited time to make fundamental changes.

In his approach to cities he quotes the urbanist Lewis Mumford: “The chief function of the city is to convert power info form, energy into culture, dead matter into the living symbols of art, biological reproduction into social creativity.” By analogy with biological systems, West applies the concept of metabolism to cities. But he distinguishes the “physical metabolism,” consisting of electricity, gas, oil, water, materials, products, artifacts and so on, from the “social metabolism” consisting of wealth, information, ideas and social capital.  By analyzing masses of data from many cities, he and his colleagues found that the social metabolism roughly follows a power law with an exponent of 1.15, while the exponent for physical metabolism is roughly 0.85.

What this means is that the larger the city, the more efficient is its infrastructure, by about 15% compared with what would be expected if all cities were equally efficient. By contrast, the social metabolism on average grows at a rate of about 15% greater than expected as cities get bigger. This means that the vitality and creativity of a city (as well as stress and crime) grow faster than expected as cities grow larger. In other words, after providing regular maintenance, the city’s physical metabolism provides a substantial residual of energy for growth. Quoting the author (p. 374) “The bigger the city, the faster it grows – a classic signal of open-ended exponential growth. A mathematical analysis indeed confirms  that growth driven by superlinear scaling  is actually faster than exponential: in fact it’s superexponential.” He goes on to discuss how specific cities differ from the average (for example, Corvallis Oregon greatly exceeds the number of patents expected for a city of its size while New York lags well behind expectation).

In the last chapter, he picks up the thread of superexponential growth. The scaling laws for various characteristics of animals (such as metabolism) all had sublinear exponents, meaning that they grew slower at various rates than would be expected if they increased proportionally with size). But cities are growing faster than expected. Analyzed mathematically, such growth leads to a finite time singularity. While exponential growth goes to infinity, but at some infinite time, superexponential growth goes to infinity at a specific time. Analysis by his colleagues estimate that in a growth as usual scenario the cut-off date is around 2045 – 2050.

West goes on to show that periodic innovations have “reset the clock,” effectively postponing the date certain for the system to stagnate and collapse. For example, Malthus’ expectation of imminent starvation was made obsolete by improvements in agriculture, although we may have finally run out of options for improvement (or even maintaining the status quo). However, to keep the wolf from the door, these innovations must occur at closer and closer intervals. At some point the interval between needed innovations become impractically small and the system stagnates and collapses, just somewhat later than without the innovations. Looking at how long it has taken us to make solar and wind energy practical (around 40 years), I personally think we are past the time when we can create technological innovations fast enough to stave off the singularity, for the reason that we have picked the low-hanging fruit, and important innovations may  now take longer than before.

Here I want to fall back on quotes from the book, which express the issues much better than I could summarize then:

P. 424 We live our lives on the metaphorical accelerating socioeconomic treadmill. A major innovation that might have taken hundreds of years to evolve a thousand or more years ago may now take only thirty years. Soon it will have to take twenty-five, then twenty, then seventeen, and so on, and like Sisyphus we are destined to go on doing it, if we insist on continually growing and expanding. The resulting sequence of singularities, each of which threatens stagnation and collapse, will continue to pile up, leading to what mathematicians call an essential singularity – a sort of mother of all singularities.

The great John von Neumann…made the following remarkably prescient observation more than seventy years ago: “The ever accelerating progress of technology and changes in the mode of human life…gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.”

P.425 The increasingly rapid rate of change induces serious stress on all facets of urban life. This is surely not sustainable, and, if nothing changes, we are heading for a major crash and a potential collapse of the entire socioeconomic fabric. The challenges are clear: Can we return to an analog of a more “ecological” phase from which we evolved and be satisfied with some version of sublinear scaling and its attendant natural limiting, or no-growth, stable configuration? Is this even possible?

West acknowledges that many other factors will influence the outcome: he has concentrated on things he can measure, like any good scientist, and discovered unexpected regularities that lead to useful predictions. Climate change, pollution, extinction, pandemics, political and religious turmoil, superstition, corruption,  and so on will obviously have a huge role to play in the outcome, and only the first four can be measured to any useful extent. But taking his results as a sound analysis of one aspect of the problem – availability of energy and resources – it is sobering to realize that even this very restricted slice of a hugely complex system yields a familiar result: we must totally revise our expectations or watch civilization collapse around us. I am not optimistic that we can pull this off, and I believe West’s view is not far from mine.


“Scale” is a fascinating new book (2017) by a physicist using his mathematical and analytic skills to explore the world of biology. The author, theoretical physicist Geoffrey West, is a distinguished  professor at the Santa Fe Institute, famous for studies of complexity. The central theme of the book is the discovery by West and others that underlying many biological systems are surprising regularities known as “scaling laws” or “power laws.” This means that many features of an organism can be predicted simply by knowing the size of the organism.

After describing how these laws were discovered and why they arise in organisms, he extends them to studies of cities and companies. Admittedly more speculative and less precise, the application to cities and companies of power laws reveal surprising regularities. For example, you can roughly predict the number of gas stations in a city simply by knowing its size and the country it is in.

West points out that in physics it is often useful to model a system at the “zeroth order” of approximation, one step below a first order. By ignoring relatively minor variations, you can discover hidden patterns that are obscured by focusing on the details. The general pattern visible at the coarse resolution suggests predictions that can be tested experimentally. Also, developing an explanation of why the general pattern occurs often suggests testable explanations of why the exceptions do not follow the general pattern.

This is the approach he used when examining biological and social systems, which are orders of magnitude more complex than the “simple” phenomena studied by physicists. It was a surprise to almost everyone that simple power law behavior emerged out of such complex systems.

While the book has some editing lapses, it is accessible to the general reader and is full of fascinating and highly topical information. He clearly explains fractals and how they relate to power laws. His discussion of exponential growth is highly pertinent to what I consider the central problem we face: systems based on exponential growth cannot survive in a finite environment (see my heading “Troubling Stuff”). This  book is a must-read.

Some of West’s explanations of the simple math behind the scaling laws puzzled me, so I had to probe deeper to really understand the concepts. The following rather lengthy discussion supplements the discussions in the book.

You are familiar with Cartesian graphs, where one variable is plotted against another on a rectangular grid. Such graphs are ubiquitous, for example the Dow-Jones Average on the vertical Y-axis plotted against time on the horizontal X-axis, a plot that appears in weekday newspapers.

The value of the Dow is not determined by the date. That is, as time goes on, its value does not increase according to some formula or function in the technical, mathematical sense. If the value of the Dow were a mathematical function of time, a lot of people would be out of business!

By contrast, the distance of the moon from the earth is a mathematical function of time. Careful observation coupled with theory has led to a series of equations that define the distance to the moon. Solving the equations for each interval of time produces a curve that can be plotted on a graph. In this case observation has defined the function, which is then plotted on the graph:

Things get more interesting when you go backward from the plot to the function. To take an example from the book, if you plot the average weight of each species of mammal against its average metabolism, does any kind of formula pop out of the data, or do the data points “scatter” randomly all over the graph?

Don’t try this at home! To plot the entire range of mammals from the smallest (Etruscan pygmy shrew) to the largest (blue whale), you need to choose a scale to plot the weight of the mammals on the X-axis. To distinguish the Etruscan shrew (about 2 grams) from a common shrew (about 8 grams), a good scale would be one millimeter per gram. But if you tried to plot the blue whale (165,000 kilograms) on that same graph, the paper would be about 100 miles long. This kind of graph is called a “linear” plot.

In addition, the data points will be scattered around some kind of curve that might not be easily seen. While you might be able to figure out some function whose curve would be close to that of the plotted values, the significance of the function would be far from obvious. We need some kind of graph that suggests relationships more diredctly.

If instead of plotting the actual values you plot the logarithms of the values, you solve both problems at once. Quoting Wikipedia, the logarithm of a number is the exponent to which another fixed number, the “base” must be raised to produce that number.  Commonly used bases are 2, e (2.71828… ), and 10. So for example, in base 10 (the one we use in counting), the exponent of 10 that produces 100 is 2, so 2 is the logarithm of 100 in base 10. Of course a logarithm that is a simple integer is a special case; the logarithm of 3 in base 10 is 0.477121255…. A graph with both the X and Y axis scaled in logarithms is called a “log-log plot.”

You may have seen a logarithmic plot showing the sizes of things from the smallest possible to the largest possible in a line on a single sheet of paper, marked off in powers of 10. The powers of 10 in such a plot range from the Planck length (1.6 x 10 to the -35th power) to the diameter of the universe (8.8 x 10 to the 26th power), thus ranging over almost 62 powers of ten. Logarithms allow us to see relationships that would otherwise escape notice (but see my post at The Wonderful, and Wonderfully Misleading, Powers of Ten , which delves into the downside of logarithmic plots).

Producing useful graphs is hardly the only neat thing about logarithms. To multiply two numbers, you simply add their logarithms to produce the logarithm of the product. Until the advent of electronic calculators, every scientist and engineer consulted tables of logarithms and used slide rules, which are based on logarithms. I still have a couple of slide rules.

A surprising and extremely useful feature of log-log plots is that it converts simple curves into straight lines. This happens when you plot functions where one variable is some power of the other variable. For example, here is a linear plot of the functions Y=X¹ (blue), Y=X² ( red), and Y=X³ (green):

Linear plots of Y = X to the powers 1, 2 and 3.

If you plot the same functions on a plot where the each axis is marked off in logarithms (a log-log plot), the curves magically become straight lines:

Log-log plots of Y = X to the powers 1, 2 and 3.

This happens for any power of x. The only thing that changes when you change the exponent of x is the tilt of the line (its “slope”). Note that x¹ is just x, so the plot of that function is the line where X = Y, which is the same line on both graphs.

The slope of the line is the y value divided by the x value; so the slope of x=y is 1/1 = 1; the slope of y=x² is 2; and the slope of y= x³ is three. Similarly, the slope of y= x to the 1/2 power is .5 and y= x to the 1/3 power is .333…

Log-log plot of Y = X to powers 1, 1/2 and 1/3.

Now the import of all this is that when you plot various properties of a system (mammals, cities and companies are the ones discussed in the book) and compare them on log-log plots, they track remarkably close to a straight line. For organisms, the slopes of these lines are often multiples of 1/4th: 3/4, 1/2, 1/4, 1/8th. For cities, the values .85 and 1.15 come up frequently.

This is what is meant by “power laws.” The major theme of the book is why these systems exhibit these power law behaviors. West uses other terms to describe power laws: scaling laws, allometric data, self-similarity, fractal. They all refer to the cases where two sets of data, when plotted on a log-log graph, fall roughly on a straight line. The scale of the power law is the slope of the line, which is also the power of X.


Exponential functions are quite different from the power functions we have been discussing (where the Y value equals some power of X). In an exponential function, Y is equal to a constant raised to the power X. At small values, the two kinds of functions yield similar values, but exponentials suddenly take off, as shown in this plot:

Parabola (Y – x squared) in red; exponential function (Y – constant raised to the power X) in blue

Again, you can convert an exponential function into a straight line, but this time you use a “log-lin” plot, where the X axis is linear and the Y axis is logarithmic. The slope of the line is the growth rate. Compound interest is the most familiar example of an exponential function.  West discusses the implications of exponential growth (as do I in my posts under the category “Troubling Stuff.”)


In discussing the application of power laws to cities and corporations, West discusses Zipf’s Law. Over a surprising range of texts, the words in English follow Zipf’s Law closely. It states that the second most common word occurs about one-half as often as the most common (the), the third one-third as often, the fourth one-fourth as often, etc. This also applies to cities: the second largest (Los Angeles) is about one-half as large as New York, the third largest (Houston) about one-third as large, the fourth (Chicago) about one-fourth as large etc. Many phenomena roughly follow Zipf’s Law.

The function that describes this kind of behavior is a power function, but of the form Y = 1/X, where the power of X is negative. This curve is a hyperbola. I show a linear plot above and a log-log plot below:

Y = 1/X, a hyperbola
Log-log plot of a hyperbola

In these two plots I have shown all four sectors of the function (positive and negative X and Y). All the earlier graphs just show the upper right sector, where X and Y are both positive. In the book, you only see the lower right sector of the graph just above, where X is positive and Y is negative. The slope of the line is negative, as is the power of X.

All the above will become much clearer as you read the book, which I dearly hope you will.

Who Needs Function?


Despite being retired, I maintain my Massachusetts architect’s license. $125 a year allows me to add RA to my name and seems a small price for the privilege of officially calling myself an architect. There is a catch, familiar to most professionals: I must acquire 12 “Continuing Education Units” or CEU’s to maintain my license.

For many years I was privileged to teach a summer seminar at Harvard with my friend and colleague Bill Rose, in which architects in need of CEU’s paid dearly to spend 3 days listening to us lecture and enjoying the pleasures of Cambridge. Those days are long gone: today all one needs to do is read an article on the Architectural Record website, pass a 10-question quiz and bingo, you get a PDF certificate for 1 CEU. You can refer to the article during the test, and if you don’t pass they show you which questions you missed so you can try again. This year I forgot to renew until the last possible day, so had to speed-read 12 boring articles to log my CEU’s in time. This took about 6 hours.

Architectural Record and Architect (the journal of the American Institute of Architects) are the only American architectural magazines left standing (discounting Architectural Digest, a vanity magazine focused on interiors). When I was in school and apprenticing there were four. The best of them, Architectural Forum, dropped away in 1974, then Progressive Architecture disappeared in 1995 (the AIA magazine picked up its awards program).

I subscribe to Architectural Record mainly to marvel at the preposterous, expensive, impractical, solipsistic, irrelevant and/or environmentally disastrous monstrosities that pass for avant-garde architecture, along with occasional handsome and well-thought-out works. But one article in the August 2017 issue struck me so forcibly I must share it.

It is the Visitor Center for Park Groot Vijversburg in the small town of Tytsjerk, The Netherlands, about 100 miles from Amsterdam. It was designed by Junya Ishigami and Associates with Studio Maks; I know nothing about either architect. Their brief was to design a visitor’s center in association with a locally treasured landmark, a handsome 19th Century villa. The center was to have a tearoom, shop, information desk and toilets.

Instead, it is a Y-shaped glass-enclosed walkway with a flat roof, winding through the park from the villa to, as far as I can discern from the article, nowhere in particular. It was influenced by and somewhat resembles the SANAA structure at Grace Farms in New Canaan Connecticut, which I recently visited. However, unlike the open SANAA structure, it is completely enclosed, the roof supported by glazed walls on both sides, something of a technical feat. Both are curving walkways that purportedly blend into the landscape (a favorite conceit of architects who plant structures in the middle of nice parks). Being fully enclosed, it had to be mechanically heated, ventilated and air conditioned.

The punch line, quoted from the article:

” ‘We asked for a functional building, and the pavilion is not functional,’ admits the park manager Audrey Sielstra in a matter-of-fact way. ‘If you look at it in practical terms, the building is problematic [!]. Yet a practical building requires walls for each separate program, and that would clash with the landscape [Grace Farms has subterranean bathrooms and mechanical spaces and fully glazed above-ground enclosures]. What Kums and Ishigami designed is an artwork. In order to use this artwork as a building, people need to be creative, and that, I think, is very beautiful,'”


Almost ready

View of Grand Canyon, May 2017, from Mather Point – pencil, actual size

The process of preparing the house (and ourselves) for sale is traumatic in the extreme for most people, and especially for my wife and myself. But we are almost there, and the house will be on the market next week if all goes as planned.

This has been a huge distraction and I have not had the energy to post anything. I have lots to say about current events, and would like to do a review of a great (but rather technical) book “The Vital Question” by biochemist Nick Lane and the more accessible “I Contain Multitudes” by Ed Yong. Both are well-written and up-to-date, and both describe startling discoveries that drastically revise one’s view of life. The books are complementary, the first dealing with the origins of all life and of complex life, the latter the meaning and extent of the symbiotic relationships among animals, plants and microbes.

So I look forward to more posting, once the last-minute crunch is over with and our house is finally in the unlivable state necessary to attract buyers.


Hurricane Katrina: How a “Free Enterprise” Economy Budgets

In sorting my papers, I ran across an article I had saved from the April 30, 2002 NY Times entitled “Nothing’s Easy for New Orleans Flood Control.” It described in detail what would happen if a major hurricane hit New Orleans. One quote:

“Perhaps the surest protection is building up the coastal marshes that lie between New Orleans and the sea and that have been eroding at high rates. But restoration will require time, a huge effort, and prohibitive sums of money, perhaps $14 billion according to a study…”

Here are a couple of quotes from Wikipedia entry on Hurricane Katrina, which occurred three and half years later:

“All of the major studies concluded that the USACE [U.S. Army Corps of Engineers], the designers and builders of the levee system as mandated by the Flood Control Act of 1965, is responsible. This is mainly due to a decision to use shorter steel sheet pilings in an effort to save money.”

“Overall, at least 1,245 people died in the hurricane and subsequent floods, making it the deadliest United States hurricane since the 1928 Okeechobee hurricane. Total property damage was estimated at $108 billion.

Free enterprise is anything but!

More Depressing News

I wish I could find something to cheer about, but this article in today’s Times is so terrifying that I have to pass it on. It is unfortunately a must-read.


The 60’s Cough

Listen to recordings of live performances by pianist Sviatoslav Richter from the 1950’s and 1960’s and you will hear frequent coughs in the audience. I only heard Richter once, in Newark in 1960, but I vividly recall the coughing. He played Prokofieff’s 7th sonata, brilliantly and powerfully.

Today, it is rare to hear anyone cough in an audience. I wonder what was going on then. Was it bad manners, or bad air pollution, or radioactive fallout, or less effective medical care, or leaded gasoline, or something else, or some combination? I have no data on the dates when coughing was common in audiences.

Today’s cough is the cell phone.