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.

How a Steam Locomotive Works


A typical steam locomotive can be dissected into a few major components: a boiler to produce steam; steam engines to rotate driving wheels; a fuel and water supply; a cab and the engineer and fireman housed therein; all carried by a frame supported by a system of wheels.

Most of the information on the web applies to British locomotives, as steam locomotives are still popular across the pond. However, the basic principles hold true for all steam locomotives.
Here are some URL’s of interest: shows an excellent video animation of a steam locomotive in cross-section; the image below is a still from the video:

steam-locomotive-cross-section is the website for the one-third size Romney Hythe and Dymchurch railroad in Kent; explains the basics quite well;, despite being over the top and rather long, goes into a remarkable amount of detail about Union Pacific steam locomotives in general and the “Big Boy” (one of the world’s largest steam locomotives) in particular. In clips of Big Boys in action, smoke and steam are artificially exaggerated for visual effect.

The Boiler

The purpose of the boiler is to create the pressurized steam that powers the engines. It is a cylindrical tank filled with water, lying on its side. At the back is a firebox in which the fuel is burned, while at the front is a chamber called the smokebox. There spent steam from the engines, still under pressure, mixes with the hot gases from the fire and rushes out the smokestack, creating the draft that keeps the fire burning. The hot gas from the fire passes from the firebox to the smokebox through an array of horizontal “firetubes” immersed in the boiler water. The firebox is also immersed in the boiler water, and together with the firetubes, heat the water to create the steam that powers the engines. The steam is typically at a pressure of 200 to 300 pounds per square inch.

The Engines

A locomotive’s job is to rotate its driving wheels or “drivers” so that the friction with the rails creates a force that moves the locomotive forward or backward.

Unlike a car, in which the wheels rotate independently on their axles, trains run on “wheel sets,” pairs of wheels rigidly connected to their axles. In a steam locomotive, two to six (typically three or four) pairs of drivers are linked together on each side by “connecting rods” so they all rotate as a group. The second or third drivers from the front are also connected to the “main rods” powered by the engines, which move back and forth in a cranking motion, causing the whole array of drivers to rotate together.

On each side of each set of drivers is a steam engine. Its job is to move the main rod back and forth. So a locomotive will always have two engines, one on each side, and will have four if it has two sets of drivers, like the Big Boys. That’s why it is properly called a steam locomotive instead of a steam engine, a distinction lost in common parlance.

The engines are obviously the key element of a locomotive and deserves a detailed look.

Each engine consists of a main cylinder within which a piston is alternatively pushed back and forth by the pressurized steam created in the boiler. The piston does its work by pushing and pulling a “crosshead” that runs on one or more lubricated rails called the “crosshead guide.” The main rod is attached to the crosshead with a rotating bearing.

Above the main cylinder is a smaller cylinder housing a valve that has three functions. First, it controls when steam is sent to the pistons, the job done in an automobile engine by the timing mechanism. Second, it controls the amount of steam in each cycle, analogous to an auto engine’s fuel injection system. Third, it controls whether the locomotive goes backward or forward.


The valve is operated through a complex linkage called the “valve gear”. If the locomotive has a brain, it is the valve gear. The linkage is connected to the main driving wheels, and also to a rod controlled by the engineer that adjusts the position of the gear. The dancing, rocking motion of the valve gear is fascinating to watch and adds a delicate grace to the muscular behavior of a locomotive. Judge any attempt at accurate depiction by how the artist draws the valve gear. This web page has an animated depiction of the valve gear, showing how it reverses:

The steam that drives the pistons is collected in a dome at the top of the boiler, then “superheated” in a series of tubes exposed to the hot gases from the fire. Superheating raises the steam temperature above the boiling point of the water, greatly increasing efficiency. At the typical boiler pressure of 200 psi the boiling point is somewhat above 380 degrees F: superheating can raise the temperature another 300 or 400 degrees. The downside is the expense of maintaining the complex tubing required. Superheating became ubiquitous around 1910.

The efficiency of a late-generation steam locomotive – the amount of the energy content of the fuel converted to useful work – was about 6% to 10%. Diesel-electric locomotives are several times as efficient.

Fuel and Water Supply

Some locomotives burned wood, but most burned coal, and in the west, oil. Whatever the fuel, it was was typically carried in the forward section of a water-filled tender towed behind the locomotive. Slow-moving switching locomotives that need to put all their weight on the driving wheels carried their own water and fuel – Thomas the Tank Engine, for example. In early locomotives, the fireman fed wood or coal into the firebox. As locomotives became larger, automatic feed devices were needed, leaving the fireman to tend the fire and adjust the water supply.

Trackside water tanks and coaling stations were common sights in the landscape:

Typical water tank and coaling station. Hopper cars on an elevated trestle (seen at the back of the photo) emptied coal onto a conveyor belt that moved it to the top of the coal bin.
Typical water tank and coaling station. Hopper cars on an elevated trestle (seen at the back of the photo) emptied coal onto a conveyor belt that moved it to the top of the coal bin.

The Cab, Frame and Wheels

The cab is a weather-protected space in which the engineer and fireman stand or sit. In nearly all locomotives, it was at the rear end of the locomotive, between the tender and the firebox. One exception was the “Camelback” locomotives on the Reading Railroad that had a wide firebox for the slow-burning anthracite coal it used, which pushed the engineer’s cab in front of the firebox to allow visibility ahead. Another was the “cab-forward” locomotives used by the Southern Pacific, which I describe in “The Genetics of Steam Locomotives”. In that essay I also cover the frame, suspension and wheel arrangements.

No-Growth Economy

Looking for enlightenment on the subject, and hoping to find some good news, I Googled “no-growth economy” and found this article at the top of the list:

It lays out a convincing case that civilization as we have constituted it cannot exist without growth. As far as I know, most mainstream economists would agree with him.

At the end, he references another 2014 article he wrote that lays out how to grow and not fry ourselves:

Its credibility is marred by his comment that he is not considering “speculative technology” like cold fusion, which has long since been round-filed as a bad piece of research. He also features carbon capture, which is highly speculative. This indicates to me that he is behind the curve regarding technological possibilities.

If you have some time (ha!) and want to see what no-growth theory looks like, you might read

I am impressed with its detachment from reality, especially with these prescriptions:

  • The first institution is to correct inequality by putting minimum and maximum limits on incomes, maximum limits on wealth, and then redistribute accordingly.
  • The second institution is to stabilise the population by issuing transferable reproduction licenses to all fertile women at a level corresponding with the general replacement fertility in society.
  • The third institution is to stabilise the level of capital by issuing and selling depletion quotas that put quantitative restrictions on the flow of resources in the economy. Quotas effectively minimise the throughput of resources necessary to maintain any given level of capital (as opposed to taxes, that merely alter the prevailing price structure).

These policies aren’t consistent with a democratic, liberty-based social structure, to dramatically understate the issue. However, the prescriptions are the sorts of measures that would be needed to control growth. So I deduce that solving the problem of growth means giving up many of our liberties. I am highly skeptical that this can happen without a crisis.

Stop Being Terrified

It turns out, unsurprisingly, that most of my ideas have been expressed much more succinctly by someone else. Here is an excellent article pleading for calm and reason in response to bomb-throwers. Our obsession with perfect safety is making us miserable.

Reason is needed, but emotion guides our actions, as predicted by the psychologists and amply demonstrated by events.

History in Lifetimes

Outbuilding at Cardney-Dunkeld, 1968
Outbuilding at Cardney-Dunkeld, 1968

Born in 1935, I began to be vaguely aware of the wider world in 1941, at age 6, when we declared war on Japan. So 75 years of sentience have passed for me as I write in 2016.

It is hard for me to realize that had I been born just one lifetime earlier, in 1855, the Civil War would have replaced WWII, and I now would be living in the depths of the Great Depression. Further, my life expectancy at birth would have been 43 years instead of 65 years. Another lifetime earlier, and from then all the way back, it would have been in the 30’s.

So it seemed useful to look back in time in 75-year steps – my long lifetime – beginning in 2015 to keep the numbers simple. As I go back in time, there is less detail. Partly this is a matter of perspective, but mainly it is that events with crucial implications for the future are occurring much more rapidly. A decade today is equivalent to a century a few hundred years ago, millennia before that, and hundreds of millennia as humans evolved from earlier species.

The timeline begins at the present, and steps back for 10 lifetimes. After that, the steps become progressively longer. Prior to the point at which the human lineage splits off from that leading to chimps, the steps become snapshots of key evolutionary events.

YBP means “years before the present”. I will omit “CE” for common era dates (formerly AD), and stick with “BC” instead of “BCE” (before the common era).

My Lifetime: 1940-2015

Human population more than triples

Humans and their livestock and pets now account for 98 percent of the world’s vertebrate biomass (mammals, marsupials, reptiles, amphibians, fish, birds). 10,000 years ago, they accounted for one-tenth of one percent.

Global warming is confirmed and accelerates

Sixth Extinction is confirmed and accelerates

Communism, Nazism, WWII, Chinese Revolution, Cold War, numerous regional wars

Invention, use and proliferation of nuclear weapons – humans gain the capacity to exterminate all complex life on earth through “nuclear winter”

Plastics revolutionize material culture, create extensive ocean pollution

Tens of thousands of man-made chemicals created and disseminated

Electronics revolutionizes communication and becomes the primary information storage medium

All technology becomes dependent upon electricity

Consumerism and the necessity of growth becomes a dominant global force

Free trade and air travel link all people economically

Muslim radicalism erupts

Growing migration of populations displaced by war

Lifetime Two: 1865-1940

Height of Nationalism and Colonialism

All science is integrated around seminal discoveries in physics

Western countries are electrified

Coal-based railroads and steamships revolutionize transportation

Petroleum-based technology revolutionizes transportation again (automobiles and aircraft)

Modern medicine matures, extending life expectancy

Russian Revolution, WWI

Lifetime Three: 1790-1865

Industrial revolution becomes a dominant force

Coal-based technologies arise

Middle classes expand in Europe and America

Darwin undermines the foundation of religion

Nationalism and Colonialism growing

Most of eastern U.S. deforested

Lifetime Four: 1715-1790

European Enlightenment

American and French revolutions

Early industrial revolution

Lifetime Five: 1640-1715

Newton revolutionizes physics and invents the calculus

Louis XIV guides France to its apex of power and sets the stage for its decline

Wars in Europe continue

Lifetime Six: 1565-1640

Galileo and the rediscovery of experimental science

Luther triggers the Reformation, which leads to the wars of religion

Age of Elizabeth and Shakespeare

Descartes revolutionizes philosophy and mathematics

Spanish are the dominant power in Europe

 Lifetime Seven: 1490-1565

Late Renaissance

Voyages of discovery

Destruction of Pre-Columbian civilizations and their written history by the Spanish

Lifetime Eight: 1415-1490

Ottomans conquer Byzantium

High Renaissance in Europe

Lifetime Nine: 1340-1415

Black Death kills one in three Europeans

Schism fractures the Catholic Church

Tamerlane invades middle Asia

Rise of Ottoman Empire

Early Renaissance

Lifetime Ten: 1265-1340

Islam in retreat, under attack in east and west

Late Middle Ages in Europe

Nation states arise in Europe

Increased contact between East and West

 Lifetimes 20-10: 515 – 1265

Feudalism dominates for 500 years in Europe after Germanic invasions

Catholic church becomes the predominant power in Europe

Medieval revival of European culture

Origin and explosive expansion of Islam

Golden age of Islamic science

Lifetimes 30-20: 235 BC to 515

The Roman Empire replaces the Roman Republic and disintegrates after 500 years of dominance

The invasion of the Huns sets off the Great Migration of Germanic tribes into Europe

Christianity arises and becomes the dominant religion in Europe.

Roman culture survives in the Byzantine Empire

Lifetimes 50-30: 1735 BC to 235 BC

Written history arises in China

Urban civilizations arise in India and Meso-America

Classical Greek culture

Alexander the Great reaches India

Roman republic arises and conquers Italy

Deforestation for agriculture, ship-building and fuel begins, continuing to the present

Lifetimes 75-50: 3610 BC to 1735 BC

Invention of writing and recorded history

First civilization – Sumer, c. 3,300 BC

First Egyptian dynasty c. 3,100 BC

Harrapan civilization arises in the Indus Valley c. 2,600 BC

Pre-literate civilizations arise in Meso-America

First Chinese dynasty c. 2,000 BC

Lifetime 100-75: 5,485 BC to 3,610 BC

Pre-literate civilizations arise in Iraq, Egypt and Pakistan

Lifetimes 150-100: 9,235 BC to 5,485 BC

End of the last glacial period

Invention of agriculture and animal husbandry

The first towns appear

Lifetimes 200-100: 12,985 BC to 9,235 BC

Humans colonize North America via the land bridge across the Bering Strait.

As occurred elsewhere soon after colonization by humans, nearly all the megafauna in the Americas become extinct.

Lifetimes 500-200: 35,500 YBP to 12,985 BC

The last of our close relatives, the Neanderthals and Denisovans, disappear, after interbreeding with modernt humans

Humans colonize the entire earth except for the Americas, Antarctica, and some Pacific Islands

Lifetimes 1,000-500: 75,000 YBP to 35,500 YBP

Fully mature language evolves

The first confirmed evidence of art occurs

Modern humans (Homo sapiens) colonize Eurasia, Australia and some Pacific islands

Lifetimes 100,000-3,000: 7,500,000 YBP to 225,000 YBP

The lineage of African great apes leading to humans, their ancestors and cousins (Hominins) splits from the lineage leading to Chimpanzees and Bonobos (genus Pan); Gorillas and Orangutans had split off earlier

Numerous Hominin genuses and species arise, a few of which are ancestral to humans (no one knows which ones)

Members of the genus Homo migrate out of Africa at various times. Homo erectus Hominins migrate into Middle East, East Asia and India about 2,000,000 YBP

Stone tools and fire are invented

Upright posture frees hands to use projectile weapons, giving Hominins a crucial advantage in hunting: attacking from a distance

Early form of language develop

Lifetime 870,000: 65,000,000 YBP

A great extinction event triggered by a comet impact results in extinction of dinosaurs (except birds), allowing the dominance of mammals

Lifetime 2,100,000: 160,000,000 YBP

Origin of flowering plants resulting in major increase in atmospheric oxygen, allowing the evolution of large terrestrial animals

Lifetime 7,200,000: 540,000,000 YBP

The “Cambrian Explosion” populates the seas with macroscopic organisms, the ancestors of all our phyla of animals

Soon thereafter, animals, plants and fungi move onto land

Lifetime 28,000,000: 2,100,000,000 YBP

The “Great Oxygen Event” occurs when enough oxygen accumulates in the atmosphere to cause a massive extinction event and the evolution of oxygen-dependent organisms

Eukaryotes, much more complex but still microscopic organisms, form by the merging of specialized prokaryotes and viruses.

 Lifetime 50,000,000: 3.700,000,000 YBP

Life arises, probably in many different forms, until one chemical system becomes the standard template for all subsequent life

All life for the next 2 billion years consists of prokaryotes – bacteria and bacteria-like “archaea”, along with viruses

Lifetime 61,000,000: 4,600,000,000 YBP

The sun ignites at the center of a rotating disk of dust, ice, heavy elements and gas, in a quiet “suburb” between spiral arms of the Milky Way Galaxy

The earth, other planets, and countless larger and smaller fragment coalesce from the rotating disk

Large and small fragments bombard the earth. One the size of Mars strikes a glancing blow to the earth, and the resulting debris coagulates into our moon.

The bombardment gradually tapers off over half a billion years, until the earth cools enough for liquid water to form; it is uncertain where the water came from

 Lifetime 183,000,000: 13,700,000,000 YPB

The universe expands abruptly from a tiny kernel in the “Big Bang” and the “Cosmic Inflation” that immediately followed, all within an infinitesimal fraction of a second. Or at least that what cosmologists thought last week.

After the “Dark Ages”, stars begin to form and our galaxy begins to coalesce, a process that continues to the present

  Next Lifetime: 2015-2090

I see the next lifetime as a climactic episode of dramatic change in human civilization and global ecosystems. Nobody knows what the world in 2090 will be like, but it is certain that it will not remotely resemble that of 2015. It is extremely unlikely that it will be as comfortable, populous and orderly.

Essay I on Function: Does Reality Have a Purpose?


Leaving aside ceremonial dinners and mathematical expressions, “function” is a synonym for purpose, or is the role something plays, whether by itself or as part of a larger assembly. So if we substitute “role or purpose” for “function” we will not be far off. My ultimate goal is to explore the concept of function in the context of architecture, but in this first essay, I want to explore function in the context of nature.

Does the sun or a rock or the atmosphere play a role or have a purpose? Well, if you believe that this land was made for you and me, then the sun functions to light and heat us, rock provides us with building material, and the atmosphere delivers oxygen to breathe and protects us from ultraviolet radiation. If you adopt the Enlightenment notion of a clockwork universe, then each has a function as part of God’s grand clock that he wound up and let run according to the Newton’s laws. Einstein had such a view of God; he was certain God made orderly, logical laws, and didn’t at all like the uncertainty that is fundamental to the theory of quantum mechanics he helped formulate.

A modern scientific point of view rejects such ideas. Stars and rocks and gases are things that emerge naturally, given the laws of physics. You can trace cause and effect step by step back to the big bang, beyond which for the moment we are blind. If you want to interject a deity, you can be a Deist and have God set off the Big Bang or design the laws of physics, but I don’t think this kind of deity would satisfy many people’s spiritual needs, although it seemed to satisfy Einstein. For today’s science, there is no one behind the scenes deciding what comes next. Arguments on the subject continue unabated; I stake my claim on the side of materialism.

A role or purpose needs context. To define the role or purpose of a rock, you need to have some kind of goal, for example, making a rock wall. When you set a goal, everything in the universe suddenly has a role or purpose relative to the goal. Rocks, yourself, tools, a plan, and a location all have essential functions, while the Andromeda galaxy takes no part, and the sun functions to keep you warm while you work and to provide light. Invent a goal, and function follows; if there is no goal, nothing has a function.

But does this line of thinking apply to life? It seems natural to think of one’s heart as having an essential function, doing its part to keep you alive so you can reproduce. Richard Dawkins argued in “The Selfish Gene” that it is your genes that have the goal, and you are just the vehicle they use to make more of themselves (as a chicken is an egg’s way to make another egg, or a scholar is a library’s way to make another library).

I maintain that we have invented the goal. Genes don’t have goals, they are just doing their thing, even if it seems to us that they “want” to persist into the next generation. It is a compelling metaphor, but it is just that: a gene is the pathway through time taken by the atoms that make up the gene, a part of the unfolding evolution of our universe.

The injection of purpose, intention, role, agency, goals and the like into our thinking about things is probably essential for understanding. We seem compelled to personify things, to think of them as if they were people, applying our hyper-developed social skills as a tool for understanding. In this way, we endow objects and events with an essence, a thingness that helps us makes sense of the world.

This is a highly useful tendency (which is no doubt why it evolved), since on our planet, nature clumps into identifiable objects and events. But our planet is highly unusual: very little of nature clumps into identifiable objects and events, important as these are to us. Most of nature consists of undifferentiated aggregations of dust, gas, plasmas, particles and fields. Only a few percent of the mass of the universe is in the form of what we call matter. But we didn’t know that when our mental equipment evolved. It was tuned to a pre-scientific world.

Nature doesn’t have a purpose, and being a part of nature, neither do you. This idea creates cognitive dissonance, so we seek meaning and purpose in our lives: it’s the only way we can avoid existential despair. But when we try to find out how nature actually works, we need temporarily to abandon our search for meaning and purpose and accept reality as it presents itself.