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.

What Would a Sustainable U.S. Be Like?

Ritterhof courtyard, Weingut Fitz-Ritter, Bad Dürkheim, Pfalz (founded 1785), watercolor and ink 1984

Despite our many problems, the U. S. is seen as a model of liberty, justice and prosperity. Many are rightly disturbed by accelerating income and wealth inequality in the U. S. Yet we ignore the profound inequality between our way of life and that of the vast majority of earth’s citizens. At best, we believe that everyone on earth should be able to live as we do.

This belief is self-serving nonsense. Earth’s resources are now being exploited well beyond a sustainable rate, especially its capacity to absorb pollution. As global population continues to grow, each person’s share must get smaller. If we truly believe in justice and equality, we would reduce our consumption of resources to meet a sustainable global average.

What would this mean? China uses roughly the same amount of earth’s resources as the U. S. It is also the same size as the U. S. Until recently, China was using resources at what optimists think might be a sustainable rate for the entire globe, assuming population growth slows rapidly. So using our fair share would be equivalent to adopting a Chinese standard of living.

Here’s the rub: China has more than four times our population. So bringing our consumption down to a sustainable level would amount to adding a billion people to our population without using any more resources than we do now. The share of my town, Norwalk, with a population of about 85,000, would be around 250,000 people. This is a truly ridiculous idea, yet it is the only fair and just solution.

Resolving the un-sustainability crisis requires cooperation, sharing, making do and doing without. That’s what I remember from my childhood during the Great Depression and WWII. It was hard, but it felt right. We could do with a large dose of that old medicine, to help cure us of the delusion that we can continue to live the way we do now.


Music I Must Stop and Listen To

It is common to ask yourself what music you would choose to take with you to a desert island. Instead, I will use this criterion: if I were listening to a broadcast while working on a project, what music would cause me to stop working and listen intently? This by no means is a list of music I revere, it is just those particular pieces that I have to stop and listen to no matter what. I am partial to fugues, luscious orchestral sound, and piano music I used to (attempt to) play.

I can’t imagine why anyone would be interested in this list.

Vivaldi: six violin concertos “La Stavaganza” Opus 4 (almost never played for some reason – I had a recording of it in college that I played incessantly)

Bach: both books of the “Well-Tempered Clavier”; “The Art of Fugue”; the Goldberg Variations; the choral fantasias from the “St. Matthew Passion” that open and close the first part, and the closing fantasia; the two great fugues on Kyrie Eleison and the Crucifixus from the Mass in b minor; and the choral fantasia that opens Cantata 8, “Liebster Gott, wenn werd ich sterben?.” Plus….

Mozart: Barbarina’s lament for a lost pin that begins Act IV of “Le Nozze di Figaro”; the opening Kyrie of the Great Mass in c minor; most of his piano sonatas. Plus….

Beethoven: The first movement of Opus 130 string quartet (top of my list along with Bach’s Well-Tempered Clavier); the first (fugue) and middle (theme and variations) movements of Opus 131 string quartet; piano sonata opus 106 “Hammerklavier”, especially the closing fugue; Diabelli Variations opus 120; many other string quartets and piano sonatas

Schubert: “Winterreise”

Schumann: “Kinderszenen”

Mendelssohn: complete incidental music to “Midsummer’s Night’s Dream” with singing and recitation

Chopin: Preludes; 4th movement, Sonata #2

Verdi: Requiem

Brahms: Requiem; “Variations and Fugue on a Theme by Handel” opus 24; “Liebeslieder Waltzes” Opus 52

Borodin: Polovtsian Dances; “In the Steppes of Central Asia”

Dvorak: “Serenade for Wind Instruments” opus 44; opening movement of “Stabat Mater”.

Mahler: “Kindertotenlieder”

Tchaikovsky: “Romeo and Juliet”

Kodaly: “Hary Janos” (recording out of print, narrated by Peter Ustinov)

Bartok: Opening fugue of “Music for Strings, Percussion and Celesta”; String Quartet #4.

Ravel: “Gaspard de la Nuit”

Stravinsky: “Le Sacre du Printemps”; “Le Chant du Rossignol”; “L’Histoire du Soldat”; “Symphony of Psalms”

Hindemith: “Symphonic Metamorphosis of Themes by Carl Maria von Weber”

Prokofiev: Symphony #5, second movement; “Cinderella” ballet, clock scene; Toccata; “Alexander Nevsky” cantata

Khachaturian: Piano Concerto (second-rate piece I happen to have loved as a youth) played by William Kapell

Britten: “Rejoice in the Lamb”; Serenade for Horn, Tenor and Strings; Four Sea Interludes from “Peter Grimes”

Weill: “September Song”

Gershwin: “Summertime”

Parker: “Klactoveedsedstene”

Beatles: “Fool on a Hill”




Breaking News About Our Ancestry

A New York Times article on Beethoven’s birthday, 2016 (December 16th) alerted me to three studies published in Nature based on extensive and detailed DNA analyses of several hundred living people from all over the globe.

The studies all agreed that there was one population of Africans that migrated out of Africa between 50 and 80 thousand years ago (kya), and that all living peoples except Africans are descended from this small population. In addition, African populations became genetically isolated by 125,000 kya and probably earlier, which implies that language (and very likely art) arose earlier than that.

This is big news, because there has been disagreement both about how many of the populations that emigrated from Africa are ancestral to modern humans, and about when language developed.

There is a small amount of mixing in New Guinea between this founding population and a somewhat earlier population of migrant modern humans, and also between modern humans and both Denisovans and Neanderthals. But the basic news is that almost all our genetic inheritance funneled through a population bottleneck, which corresponds to much earlier findings (the “mitochondrial Eve” hypothesis).

This adds credence to the idea that “click languages” such as that spoken by the Khoi-San people were antecedent to non-click languages, since the Khoi-San split off from our ancestral mainstream around 125 kya. This makes sense simply because clicks are hard to produce and are more likely to have been dropped than added.

What is of particular interest to me is that language developed earlier, maybe much earlier, than many have thought. This makes great sense to me, because I believe that language, music and other arts co-evolved in complex ways over a long period of time, as our ancestors became more able to form symbolic abstractions.

Here is a better write-up than the NYT article:

The Start-Up Drama of a Steam Locomotives

Penichette docked at a mill on the Mayenne River, 2001
Penichette docked at a mill on the Mayenne River, 2001

Starting is a big deal for a steam locomotive.  Unlike the electric motors in diesel-electric locomotives, which deliver maximum power at start-up, steam locomotives are wimpy at startup and gain power with speed. This is the result of a fixed ratio between the pistons and the wheels: the pistons move too slowly at start-up to use the available steam power (you can’t “down shift”). There are four ways to help the locomotive start: increase the coefficient of friction, decrease the weight being towed, maximize the leverage of the rods that crank the wheels, and temporarily increase the number of driving wheels.

To move a train, the locomotive’s drivers must push back against the rails without slipping. The “coefficient of friction” is the percentage of the weight that can be converted into horizontal force before the wheel slips, about 25% for steel wheels on steel rails. One hundred tons on the driving wheels translates into twenty-five tons of pulling force.

So the first step to beef up the starting force is to increase friction by sanding the rails. For this purpose, steam locomotives carry sand in one or two large domes atop the boiler, kept dry by boiler heat. Tubes from the sand domes, each with a valve, curve around the side of the boiler and then around the perimeter of each driver, terminating just above the rail.

Sand pipe
Sand pipe

The second trick, if you are hauling uncomplaining freight, is to reduce the load you are pulling. This is possible because in American trains  lack the “buffers” used in European trains to keep the couplings taut, allowiwng some slack in the couplings between cars. So you set the brakes at the back of the train, and back down until the couplings are compressed together. Then you take off like a bat out of hell, pulling first one car, then two, gathering more and more cars, until the last car, always the unfortunate caboose, became part of the chain only when the train was already moving at 5 or 10 mph.  Serious injury was the fate of  conductors caught unaware, and broken “drawbars” that connect the coupling to the car were common. The sound of a starting freight train was memorable, as the clank of slack couplings coming together ran like a zipper down the train, a kind of rolling thunder.

With a passenger train this approach can’t be used. It was a matter of pride for the engineer not to “spill the soup” when starting. Instead, you stretch out each coupling so all the cars move at once, with no start-up jerk. You are stuck with the whole load.

The third move is back up a bit until the rods that turn the wheels are at the angle at which they exert the most leverage.

The fourth move was available on a few locomotives, including the SP’s 4-8-4’s. These were equipped with “boosters”, a compact steam engine set between the wheels of the trailing truck, that added the weight on that truck to contribute to the tractive force at low speeds. They added almost 25% tractive force while emitting furious sideways snorts of steam, in detailed counterpoint to the much larger main drivers. It made a glorious show for the enjoyment of a track-side teenager.

So the engineer adjusts the position of the wheels, sands the rails, turns on the booster, applies steam very carefully, and hopes for the best.  A youth at track-side hopes for the worst: the drivers lose their grip, and the locomotive rapidly chuffs and clanks in place, like a trained horse.

The gradually accelerating tempo of the exhaust blasts has been imitated many times in music. Villa-Lobos’ The Little Train of the Caipira is a delightful piece that vividly captures the sound and motion of a train ride (listen and watch the wonderful graphics at ). Prokofiev intentionally or unintentionally captures the essence of a starting locomotive in the second movement of his great 5th Symphony. You can hear it at : the start-up begins at 5:06, but I encourage you to listen to the whole movement – it is a thrilling performance (learn more about this remarkable youth orchestra at the Wikipedia entry for “El Sistema”). Train enthusiast Arthur Honegger’s 1923 composition Pacific 2-3-1  is best heard at I also found a wonderful 10-minute 1949 film that captures the excitement of the steam locomotive, using Honegger’s score. The clearest video on YouTube is at  (it is the better for being without sound).

Why I Went to Architecture School

I drew a lot when I was a kid, mostly sequences depicting incredible explosions, or cars each with more exaggerated features than the last. I didn’t have good drawing materials, just bond paper and pencils, so the drawings had no depth – they were outlets for my distressed imagination rather than productions for display.

Then I got into model railroading, and spent all my spare time designing the layout, putting the layout together in our tiny cellar, or making rolling stock, but I never finished the layout – I dreamed its completion, just as I dreamed my own completion, my own empowerment. I was never finished.

My uncle Bud, one of father’s half-brothers, was a contractor, and he designed and built suburban houses in Southern California were we lived at the time. I watched his and others’ houses go up, utterly fascinated by the wood framing. I remember climbing onto the roof of one of his houses under construction and sticking a meat thermometer under the black shingles – it read 180 degrees, a datum that I found useful many years later.

I took mechanical drawing in high school and loved it. I loved the wonderful ruling pens, I loved the precision, and I loved the geometry. We drew other views of objects for which some views were given – a great aid to spatial visualization (which may be learned and not innate – why don’t they teach mechanical drawing today?)

My brother Bob and brother-in law John ran a blueprint company for a couple of years and I helped out, trimming blueprints. In those days, the early 50’s, blueprints were really blue. A roll of heavy paper coated with light-sensitive dye was kept in the dark under the machine. You pulled the paper across a table and up through a series of rollers. Once the machine was started, you laid the tracing paper original drawings one after the other onto the moving paper, being careful to align them correctly and avoid wrinkles or folds.

In their trip through the machine’s rollers, the blueprint paper and drawings first moved under a brilliant light source, which exposed the paper except where the pencil or ink links on the tracing paper blocked the light. The paper then ran up vertically, and you had to grab the originals as they peeled off the blueprint paper (while simultaneously feeding in the new originals – it required some skill). Up and over, the paper then ran through a bath of developing fluid that activated the dye, turning the exposed paper a beautiful Prussian blue.

The wet paper traveled over some burners that dried it (and shrunk the image – hence the dictum “never measure a blueprint”). All this paper was under tension, and if it got off track, it would wrinkle up dramatically, and you had to cut the paper and re-feed it. Finally, the trimmer used long scissors to trim the final prints as they came out of the machine. I searched the web and could find only one image of blueprint machine, from a patent application. This one has many more rollers than the ones I worked with, and doesn’t have a table to trim the prints.

Blueprint machine diagram from patent application
Blueprint machine diagram from patent application

The new “diazo” process was just coming into favor. Diazo paper was coated with a yellowish dye that was actuated by intense ammonia fumes. In this process the paper didn’t shrink, plus you got a black on white image (actually more purple on yellowish-white). Not long after this, the diazo process replaced blueprinting, but the old name stuck. The diazo machine was trade-named “Ozalid”, which is diazo backward with an added “L”. The ammonia came in big 10-gallon glass bottles. Once my brother-in-law dropped a full bottle and we all had to run out of the shop before we burned our lungs. Both diazo and blueprints faded when exposed to light for any period of time.

When I trimmed blueprints and diazos in the blueprint shop, I got to look at the plans for new houses that we were printing. I would take cast-off prints of them home to study, and then draw up my own floor plans. All these houses were one-story ranch houses without basements, with hipped roofs, one where the roof planes slope in all directions, like a tent. You can design a hipped roof over any plan, no matter what its shape, so you never had to think about anything but the plan layout. That’s where the idea of architects “drawing up the plan” came from. Few people were sophisticated enough to ask an architect to “draw up the spaces.”

So that’s why I went to architecture school at Berkeley: to learn how to draw up the plans for houses. Nothing more enlightened than that. My folks somehow managed to pay for college, which was affordable in 1953. The $1,200 cost per year for tuition, room and board was partly offset by $200 scholarships, available to anyone who had a B average. I had a scholarship every semester, one I remember getting because I was from Nebraska. In later years when I had my own apartment and car, my annual outlay including plane fare to and from home for Christmas and summer vacation, was around $2,500.

My first job as an architectural drafter (draftsman in those days) was 65 cents an hour, so $2,500 was not chump change, especially for my not so rich parents. It’s an interesting exercise to compare the 65 cent hourly wage and $1,200 annual cost with contemporary numbers. Let’s say a beginning drafter in an architectural office makes $15 an hour ($31,000 a year). The cost of a year in college varies, but I read on the web that Berkeley is in the $30,000 range. So that’s a year’s pay. A year’s pay at 65 cents an hour is $1,352. If my numbers are correct, today’s college tuition compared with earning power hasn’t changed that much, at least at Berkeley. It has become much more selective, however. In the 50’s, you got in if you had a good grade-point average and were a California resident.

Needless to say, architectural education does not consist solely of “drawing up the plan.” But that is another story.

I'm still drawing up plans for houses, typically in traditional styles
I’m still drawing up plans for houses, typically in traditional styles

MBL Lectures

Ritterhof courtyard, Weingut Fitz-Ritter, Bad Dürkheim, Pfalz (founded 1785), watercolor and ink 1984
Ritterhof courtyard, Weingut Fitz-Ritter, Bad Dürkheim, Pfalz (founded 1785), watercolor and ink 1984

We summer in Woods Hole (when our house is not rented, which is most of the summer) and occasionally can go to one of the Friday night public science lectures at the Marine Biological Laboratory, the world-famous research facility in Woods Hole. It is a magnificent privilege to hear and see world-class scientists give beautiful slide lectures on fascinating, cutting-edge science.

On occasion, when the lecture is particularly clear and my brain is fresh, I can go home and write down the gist of the lecture. So since I haven’t posted anything for almost a month, I dug up one of these writeups.


The lecturer, a famous Chinese neuroscientist Mu-Ming Poo, around 70, spoke on neural plasticity.

He started with a much-cited quote by the famous neuroscientist Donald Hebb, to the effect that neurons that fire together wire together, forming more or less permanent circuits – i.e. memories. This is a qualitative statement; Poo and his colleagues sought to explore it quantitatively.

He asked how close together in time the two firings had to be in order to create a memory. He found that the window generally was 40 milliseconds wide, with exceptions in certain animals. He also asked whether the sequence mattered (i.e. what happened if the second neuron fired before the first one), and he found that when the sequence was reversed, exactly the opposite effect occurred: the two neurons became less likely to fire together than previously.

Background: neurons collect inputs from “dendrites”, sum them in complicated ways, and if the incoming stimulus is sufficient, they fire. The electrical signal runs rapidly down the cell’s axon (at about 45 mph), which is the long “wire” that carries the electrical charge from the cell to the other cells to which it is connected, when the cell fires. During development, each neuron seeks out and finds the neurons in the part of the brain to which it “should” be connected. Retinal cells connect via intermediate links to cells in the visual cortex, which in humans is located at the back of the brain (“cortex” is the thin grey-colored coating of neurons on the outer surface of the convoluted brain). Back to the lecture.

To understand why the 40 millisecond window is adaptive, imagine a row of adjacent retinal cells. Each retinal cell connects with a large number of cortical cells in the visual cortex that are adjacent to one another. Call the retinal cells “A” and the cortical cells “B.” This means that each B cell receives inputs from a lot of A cells. So the image created by one A cell is spread out and blurred in the visual cortex.

The goal is to create a sharply focused “map” on the visual cortex that matches the image falling on the retina. To accomplish this, the brain needs to prune away connections between A cells and distant B cells, and strengthen connections between A cells and B cells that are close together.

Imagine a moving spot falling on the retina and hitting one A cell. The A cell will fire and cause all the B cells to which it is connected to fire. Since the B cells fire together within the 40 millisecond window, with the A cell firing first, the connections are strengthened. Now the spot moves to the next A cell (it is moving fast). Again the A cell sets off all the B cells to which it is connected. But some of these will already have fired during the previous 40 millisecond window mentioned above. In those cases, the B cell has fired before the A cell, which weakens the connection. Over many occurrences, this process sharpens the map in the visual cortex.

In the second example of neural plasticity, he explored how mature neurons in a frog’s brain form short term memory by training a string of neurons to fire in sequence. Remarkably, there are instruments that can probe individual neurons in a living animal brain, as well as a brain in a petri dish (in vitro – glass – as opposed to in vivo – life). First the investigators associated neurons in the retina with the corresponding neurons in the visual cortex. Then they passed a moving spot over the retinal cells and noted that the cortical cells lit up one after the other.

After doing this many times, training the cells, they then stimulated just the first retinal cell, which caused the string of cells in the visual cortex to fire one after the other. The neurons had learned that the spot moves on this particular track  (this is short term memory, lasting only about 10 minutes). When they stimulated the last cell in the sequence, nothing happened. They then stimulated the cortical cells directly, and the same thing happened, showing that it was the cortical neurons that learned and not the retinal cells.

In a third demonstration, they found that cells in a zebra-fish could remember the timing between sequential stimuli. This became evident because if they stimulated the cells five times or more, the cells fired one more time after the stimulus was removed at exactly the same interval as the initial sequence. This occurred at intervals up to about 10 seconds. The larger the number of sequential stimuli the more firings occurred after the stimuli stopped, but only up to 3 repetitions. He showed a movie in which the stimuli caused the tail of the fish to twitch to the side (an escape behavior), and sure enough, after the stimuli ceased, the tail twitched twice at exactly the same interval as the stimuli.

Finally, it was believed that only humans and some apes could recognize themselves in a mirror and that monkeys could not. He experimented with Rhesus monkeys. If you paint a spot on the monkey’s face (or even shine a light at the spot so he doesn’t feel anything) he ignores it when looking in the mirror, showing that he is not aware that the image is of himself.

So Poo did a clever thing: he applied the spot in a way that irritated the same location on the monkey’s face, which caused the monkey to reach up and touch the spot. By doing this many times, he trained the monkey to associate the two spots and thereby become aware that the image in the mirror was himself. Once they learned this (2 out of 3 could do so) they took advantage of their new skill by examining parts of themselves that they couldn’t see (their bottoms). It was hilarious to see the contortions they went into in order to inspect their nether regions.

Ritterhof courtyard, contemporary photo
Ritterhof courtyard, contemporary photo

More is Less

Our son David inherited his grandmother’s 1969 white Pontiac convertible with red vinyl upholstery. It was sexy, but it was a beast, a gas-guzzler and perfect example of the dangerous designs Ralph Nader successfully fought against during the same era. Just to list a few of its more egregious features, it had a rigid frame, lap belts, bench seats, tiny rear view mirrors, manual windows and door locks, carburetor, spongy suspension and a big V-8 motor that drank a half-pint of fuel every mile. Its heating, air conditioning and ventilation system hardly functioned and the radio was a joke. The bumpers could not withstand a 5 mph collision. It did have power steering and power brakes – drum brakes. It was huge.

In 2015, when we sold the Pontiac, I still owned a 1992 Camry station wagon I had bought used many years before. In the 23 years between 1969 and 1992, all major mechanical, safety and comfort issues had been addressed. It had a transverse V-6 engine with fuel injection driving the front wheels that delivered 25 mpg on the highway (its in-city mileage is not that great because of the big engine, but still was more than twice that of the Pontiac). It had a driver’s side air bag, over the shoulder seat belts, individual adjustable front seats, electric windows and door locks, rear window wipers, big motor-adjusted mirrors, cruise control, an impact-absorbing frame, highly effective rust protection, ABS disk brakes, impact-resistant bumpers, a modern suspension system, and an excellent radio with tape and CD players. It was quiet, comfortable, capacious, compact and reliable. In short, it was a fully modern car.

In the twenty-three years between 1992 and 2015, what important features have been added? More air bags, endless electronics and other small refinements, some very nice but of minimal importance and at a substantial increase in maintenance. All aspects have been refined, but there have been no innovations that increase safety, durability or efficiency remotely comparable to the dramatic changes that took place between 1969 and 1992. In addition, the progress made in compacting the car between 1969 and 1992 has been reversed. We are now used to tall huge vehicles instead of the low and wide huge vehicles we loved in the 60’s.

This is an example of one way in which “progress” is a misnomer: adding expensive, high-maintenance incremental changes to mature products. An important factor in the escalation of medical care in advanced societies is expending large sums to add a small increment of time at the end of life. I am very glad I have a titanium knee and a piece of cow in my heart, because otherwise I would not be nearly as active as I am, and might well have expired. But these surgeries cost tens of thousands of dollars, and it is simply impossible to extend such benefits to billions of people; we can’t even do so for a large fraction of our own citizens.

And can anyone argue that the difference between iPhones six and seven is remotely comparable to the difference between a flip phone and an iPhone? Or between no cell phone and a cell phone?

Another form of spurious progress is the loss of functionality in the service of reducing costs. Not only is ours a throw-away economy, but the products often break down after only a few hours or even minutes of use. In countless cases, new products are less reliable, less durable and less functional than those they replace.

We purchased a cheap set of wooden lawn furniture made with some kind of tropical hardwood (Americans import 95% of the tropical hardwoods, a large fraction of which are harvested unsustainably). To reduce the assembly cost of the chairs, the slats that formed the seats were designed with joints that were guaranteed to fail if a robust adult sat on them. Edward O. Wilson once commented that cutting tropical rain forest for profit was like burning a Renaissance painting in order to cook dinner. Our tropical chairs made a nice fire one chilly evening.

To keep the economic growth engine running, governments, corporations and consumers (previously known as citizens) need to buy more stuff. Some of the new stuff is indeed useful, notably electronic devices. Even in that case, functional innovations are becoming marginal, and sometimes (as in the case of Microsoft operating systems) run in reverse.

There are exceptions. One is scientific instruments, where innovation and refinement allow us to uncover entirely new layers of natural phenomena, genome sequencing and deep space imaging being only two examples. Another is technology that has enhanced the arts.

It’s too bad all this extra stuff isn’t making us happier: even though  at the moment Americans are the safest people who have ever lived on earth, we don’t feel safe. And the religion of growth is making us much less safe in the long run.

As I argue in other essays, the survival of human civilization requires moving from the economy we have to one where growth is parceled out in ways that are productive, equitable and sustainable.

This will require a fundamental shift from an emphasis on competition to one of cooperation, sharing, redistribution and making hard choices to shed amenities we can’t support. No one has yet figured out how to make these hard choices in a way that will be acceptable to a free people in a liberal economy.

My wife and I, my daughter and her family, and almost everyone I know continue to consume like mad, just like everyone else who can afford it and way too many who can’t (our son is admirably abstemious). We don’t know what else to do, and I suspect you are in the same boat.

It is time to put the sapiens back in Homo sapiens, but it will require us to work together, give up many luxuries, and base our actions on science. This is not exactly a recipe for getting elected to public office.

The Genetics of Steam Locomotives

My experience with and understanding of 20th Century steam locomotives is very limited relative to a locomotive historian, but probably encyclopedic for the average person, especially since no one born after 1960 has seen an operating steam locomotive on a main-line railroad in the U.S. or Canada.

This essay is mostly about wheels, so we need some nomenclature. Per a 2016 Scientific American article, there are three types of wheel: the sort used in a motor vehicle, where each wheel rotates independently on an axle; a wheel set, in which two wheels are rigidly connected to an axle; and a caster, in which the wheel’s axle is offset from a pivoting vertical axis.

Typical railroad car wheel set
Typical railroad car wheel set

Trains run on wheel sets. A frame holding one or more wheel sets and pivoting around a vertical axis is called a “truck” in the U.S. and a “bogie” in the UK. Most railroad cars have two trucks or bogies with two and occasionally three wheel sets each. In Europe, where curves were sharp, cars tended to be shorter than elsewhere, and could be mounted on two wheel sets supported by frames that were rigidly attached to the “wagons”, that is, with no bogies, just a box on four wheels.

Model of a typical British goods wagon
Model of a typical British goods wagon

Locomotives are classified by their wheel arrangement. In Europe, they count the axles, while we count the wheels – so Honneger’s “Pacific 2-3-1” is a 4-6-2 in the U.S. Each wheel arrangement had a name, the Pacific type being perhaps the most common. The numbering system assumes that the locomotive has the usual three or four groups of wheels, and so always has three or four numbers. If any group is missing, the system inserts a zero. For example, you can have a 4-6-2, an 0-6-2, a 4-6-0, an 0-6-0 or a 4-6-6-2.

Pilot Wheels

The front set of wheels supports the front end of the locomotive, and guides it around turns. The rear set supports the rear portion. The center one or two sets are the driving wheels that are powered by the pistons.

The portion of the locomotive’s weight that is carried by the drivers is the result of some complex tradeoffs. The primary tradeoff is between power and steering. “Switch engines” that shunted cars around in freight yards and dock sides had only driving wheels, and often carried their water and fuel without a tender. This maximized its tractive force, but the downside was that it could only operate at very slow speeds. Why is this?

Model of a B&O dockside locomotive
Model of a B&O dockside locomotive

There are two reasons. First, on a turn the heavy locomotive “wants” to continue in a straight line. Without a properly designed front set of wheels (called the “pilot wheels”) the locomotive will lurch around corners and start oscillating from side to side, causing it to derail and damage the tracks. But it doesn’t even need a curve to start oscillating (”hunting”): minor imperfections or simple random motion can set up the oscillations. You need wheels up front that guide the locomotive back to its center position as soon as it tries to rotate sideways, and that help pull the front end to the side when negotiating a curve. Switch engines waddle down the tracks.

By mid-19th Century, the standard locomotive was the ten-wheeler, with six driving wheels, four pilot wheels and no trailing wheels. It struck a good balance of weight between the pilot wheels and the drivers.

Baltimore and Ohio 1907 Ten-Wheeler
Baltimore and Ohio 1907 Ten-Wheeler


The middle number or pair of numbers refers to the driving wheels, or “drivers.” These are the big wheels driven by the pistons that provide the traction to pull a train of cars. They carry as much of the locomotive’s weight as possible, because the pull of a locomotive is about one-fourth the weight on the drivers. The weight on each pair of drivers is in turn limited by the weight-bearing capacity of the rails and roadbed.

You can’t indefinitely add driving wheels, because the locomotive has to negotiate curves, especially at track switches. Three ways were used to extend the wheelbase: make the flanges of the inner wheels a little narrower than the rail gauge; allow the front and rear drivers to move a small amount from side to side (typically held in the center by springs); and/or eliminate the flanges on the middle drivers. The practical limit of the wheelbase is typically about 25 feet. But there were exceptions, like the Union Pacific 9000 class 4-12-2. It worked in the prairies, where the turning radii were large, but not on the mountain routes.

Union Pacific 4-12-2
Union Pacific 4-12-2

To extend the wheelbase, you could use several smaller wheels or fewer larger ones. Locomotives with five or six drivers on each side were made, but they were rare: four on each side became standard in the latter days of steam power, each typically six feet in diameter. The largest locomotives, such as the 4-8-8-2 cab-forward articulateds on the SP the so impressed me as a child, have two complete sets of driving wheels, one of which pivots relative to the other (hence the term “articulated”), thereby doubling the wheelbase.

With more drivers, the weight of the rods connecting the wheels to the piston and to each other limits the maximum speed of the locomotive. That is why the fastest trains used locomotives with only four drivers. The 4-4-2 “Atlantic” locomotives used by the New York, New Haven and Hartford between New York and Boston, was scheduled to reach speeds exceeding 100 mph. It made the trip in about the same time as today’s Amtrak trains. Other locomotives could go this fast, but were not operated at maximum speed.

New York, New Haven and Hartford 4-4-2 "Atlantic" type
New York, New Haven and Hartford 4-4-2 “Atlantic” type

Trailing Wheels

Early locomotives had a narrow firebox that fit between the drivers, so it didn’t need trailing wheels. An older freight locomotive might have four pairs of small drivers and a pair of pilot wheels, creating a 2-8-0 wheel configuration called a Consolidation, like the little engine that hauled my mother and me from Aberdeen to Council Bluffs that stormy night I described in an earlier essay. The Ten-Wheeler (shown earlier) had four pilot wheels and six larger drivers for higher speeds, and like the Consolidation, no trailing wheels.

The power of a steam locomotive also depends on how much heat can be produced in the firebox, which in turn depends on the area of the fire in the firebox. Increasing the area of the firebox made it too wide to fit between the drivers, requiring a trailing truck to carry its weight (see the 4-4-2 Atlantic, above).

Here is another tradeoff, this time between traction and power. The more weight carried by the trailing truck, the less weight on the drivers. The first trailing trucks had two wheels, with four becoming standard in later locomotives. On most locomotives, the firebox was set entirely behind the drivers, but on articulated locomotives, the firebox typically extended over the rear-most drivers – a result of the longer boiler and commensurately larger firebox.

Southern Pacific cab-forward 4-8-8-2
Southern Pacific cab-forward 4-8-8-2

To pull trains over the Sierras, a route with many tunnels and snowsheds, a crew would have to wear gas masks to avoid being asphyxiated by the locomotive’s smoke. This problem was eliminated by turning the locomotive around. The distinctive 4-8-8-2 cab-forward design was possible because they burned oil (which could be piped to the front). The 4-wheeled truck under the firebox now became the pilot truck.

Understanding the basics of wheel classification can tell you a lot about the age, purpose and power of a steam locomotive.

Symbolism – Part One

Lago de Garda, 1968
Lago de Garda, 1968

The subject of symbolism has intrigued me for 60 years. I am not talking about symbols like the Christian cross or a national flag, but about the symbolism of language and mathematics, and how this applies to art.

I was strongly influenced by two books by the aesthetician Suzanne K. Langer, “Feeling and Form” and “Philosophy in a New Key,” both of which were published around the time I was in college. She had an unusually practical mind, and at the same time had a deep understanding of all the (fine) arts, not just easel painting, so often the sole focus of aestheticians.

Langer developed her aesthetic theory out of earlier work on symbolic logic, a field developed by the great logicians of the late 19th and early 20th Centuries and one very fresh and vital at the time she wrote. She was strongly influenced by Alfred North Whitehead, who along with Bertrand Russell prepared much of the foundation for symbolic logic. Both symbolic logic and mathematics are precise formalizations of discursive language (the language of statements), and language is universally acknowledged to be the quintessential example of symbolism (Langer’s lucid writing made her little book ”Symbolic Logic” close to a page-turner).

Symbols point to things: naming is of their essence. When Langer extended to art the language-based concept of symbolic representation, she naturally looked for something concrete that the art symbol could represent. Her solution was to postulate that the art symbol pointed to the form of the life of feeling, something she saw as complex patterns of rising and falling tensions, so complex as to be forever impossible to depict using ordinary language. Only the art symbol could present the life of feeling in a way that made it understandable.

I believe that Langer is correct that a work of art symbolizes patterns of feelings that occur in the lives of people, but I believe she made a mistake when she characterized these patterns as forms. I am an architect, and the word immediately conjures up an image of the forms into which concrete is poured. Forms are rigid, while the patterns of felt experience are fluid and difficult to pin down.

By her insistence that a work of art symbolized some kind of form, Langer created a problem for herself: how do you decipher the work of art to reveal the symbolized form? Langer invoked intuition, a famously vague term, and argued that the work of art must be intuitively seen as a whole, all at once (of course in music, dance, drama and literature the work unfolds over time, but we can still imagine the work as a whole after it is completely presented or read).

The form to which the symbol refers is the meaning of the work of art; in her later work, Langer substituted “import” and especially “significant form” for “meaning,” but the sense was the same: the art symbol referred to some kind of pattern representing the ebb and flow of feelings. (To confuse matters, the expression “significant form” was used by art critic Clive Bell in a famous 1913 article “Art and Significant Form” at Langer strongly disagreed with Bell’s ideas, as do I, but the confusion of terms did not help her argument.)

The problem of how to decipher the underlying form to which the symbol refers was clarified for me through an article I found on the web by chance. It was written by Berel Lang, who I find is a philosopher at Wesleyan University, and is entitled “Langer’s Arabesque and the Collapse of the Symbol” (see In this essay, Lang argues that it is not possible to distinguish the art symbol from what Langer argued that it represents, the form of the life of feeling. She notes that this problem was raised in a review of Langer’s seminal book “Philosophy in a New Key” by philosopher Ernest Nagel, and that Langer took his criticism seriously and tried to resolve the problem in her later writings, in Lang’s view without success.

Summarizing Lang’s critique, a work of art is not a symbol because instead of referring to an objective content, a meaning, the work is itself the content. There is no symbolism because it is impossible to abstract the symbolic form from the details of the work. Here Langer herself makes this point:

But a work of art does not point us to a meaning beyond its own presence.  What is expressed cannot be grasped apart from the sensuous or poetic form that expresses it. In a work of art we have the direct presentation of a feeling, not a sign that points to it.” (Principles of Art, pp.133-34)

Put another way, the patterns that one detects in a work of art are far too complex to be perceived as a single form, no matter how elaborate. Think about how you take in a work of art: at each viewing or hearing, it always takes time, and all art lovers comment that you can come back to a familiar painting or piece of music hundreds of times and never cease to discover something new. How, if we perceive the whole work as a single form (a gestalt, as Langer would put it), can we continue to reconstruct it as we experience it over time? Would we not each time find a new overall form?

If all the intricate details of a work are cast into the form, it must be a very flexible form indeed to accommodate the reinterpretations by each perceiver, not to mention the dramatic reinterpretations that take place as cultural norms change over the decades – so flexible as to lose its character as a form. And Nagel’s and Lang’s telling criticism also applies, that the form is so intricately trapped in the actuality of the work of art that you cannot separate the work from its import. The work, as the quote from Langer above suggests, is the import.

The solution to this dilemma, I maintain, is that the pattern and flow of human feeling cannot be symbolized as a form, a conceptual object, something that is remembered in the same way that we remember objective things. Instead, the art symbol needs to be thought of as a process rather than an objective thing, as a verb instead of a noun. What this means is not obvious, but I will try to make my idea clear in subsequent essays in this series.