Uh Oh ... Boring 4

Undecidable Theories

I must introduce a notion based on Gỏdel's Proof: undecidability. What Gỏdel showed was that a well formed-formula (wff) could never be true or false if it was constructed a certain way. Gỏdel's proof implies there are mathematical statements which cannot be proven, but which must be accepted on faith, as premises, if at all. Any calculus which is capable of containing such undecidable statements is said to be "incomplete."

Being incomplete is not the same thing as being inconsistent; i.e., a theory which produces contradictions. Of course, if one insists that a theory must only produce true statements from the premises, then incompleteness implies inconsistency. The simple propositional calculus is like that: there are only true or false iterations (theorems) of the premises. But, once we generalize to the First Order predicate calculus and beyond, we cannot have both strict completeness and consistency.

First Order statements, such (a){X(a) Є Y(a,b)}, are at the heart of mathematics, starting with counting and arithmetic. Much of modern science is expressed in mathematical language, as mathematical models. For that reason, the notion of incompleteness can be extended to scientific theories. It is possible to make well-formed scientific statements in some theory, which cannot be proved true or false. This implies we can never know the whole truth of a science.

This modern conclusion disturbs a lot of people, especially those who want a certain world. Fundamentalists of every sort want to read the Good Book (Bible, Qu'ran, Rig Veda ...) and find The Answer. In the world according to ..., there are no unresolved questions or problems; everything that can be known is known according to ... Ever since Copernicus and Galileo, however, science runs away from Good Books. The divergence is most exquisitely demonstrated in the Scopes Trial, and all the other battles about evolution and science like it.

I am firmly modern. I believe everything I know is partial and temporary. I accept scientific "laws" because they work for a time, and they work better than the alternatives (if any). I don't expect to read any Final Truth in my Physics or Biology textbooks. I illustrate this with the "truth" of the evolution of eukaryotes. When I went to college in the late 1950s, it wasn't at all clear how eukaryotes came to be. When I went back to college 10 years later, it was assumed eukaryotes had evolved, somehow, from one or another obscure bacterial order (?). Later, as a research worker studying mitochondria, I became convinced eukaryotes were at least partially the result of symbiosis of several types of bacteria; the hypothesis invented by Dr Lynn Margulis. Of course, at the time, everyone scorned Prof Margulis, not least because she was a female in a "soft" science, biology. A few years later, I was made aware of the work on prions in Dr Stanley Prusiner's nearby lab, and even thought about applying for a job there. Dr Prusiner was looking for cheap help because, like Dr Margulis, he was short of research grant money. He shared with Dr Margulis a penchant for unorthodox ideas, which is 100% correlated with little or no research funding. (Unfortunately, I needed money, too.)

Today, Dr Margulis' theories are standard fare in biology textbooks. I am sure almost everyone knows about Mad Cow disease, which is caused by prions. So, what could not possibly be, is, and that is taught to willing students. The unwilling, such as the U.S. beef industry and the Bush Administration's USDA, have lost billions in sales and caused havoc in food distribution because of something that could not be.

Are Dr Margulis theories the final, true answer about evolution of eukaryotes? What exactly are prions, and how do they reproduce? Does Dr Prusiner's study of prions lead to disease treatments? How is the prion theory related to ongoing studies of Alzheimer's?

I don't know the answers to any of those questions. I don't know who does. I don't know if the underlying theories and ideas are correct, incorrect or merely somewhere in between and suggestive. In the long run, the truth of those things matters a lot. In the short run, it doesn't matter: the currently accepted "standard theory" is what we have to work with. In the middle run, we work on replacing those theories by working them hard. We make theories produce results until they run dry. That is the practical, non-fundamentalist way of looking at things.

Local Application

Good scientific theories cannot explain everything. Theories that do explain everything are subsets of the simple propositional calculus, collections of tautologies, which also mean nothing. So, whenever we hear someone explain this, that and the other thing with a "universal" theory, we are entitled to be skeptical. For example, conservatives are much enamored these days of "Markets," which are both super-glue and universal solvent for almost every problem, human and otherwise.

If neo-classical economics is a science, it cannot explain everything. It can only explain some things, within a delimited universe. In order to be good and useful theory, all the theory has to do is explain the things within its purview. It must also tell us just when it does or doesn't apply.

People, especially those inclined to be true believers, easily slip into another mode: using a theory to explain far more than was intended. I think this kind of behavior is most obvious in the case of the computerized Bible readers, who "discover" secret codes which are supposed to be prophetic. I view that kind of work as "advanced numerology," rooted in the ancient numerology which assigned secret meanings to numbers and collections of numbers. Such beliefs and uses, including tarot cards, the I-Ching, and birthdays, are widespread in all human societies.

Astrology and the workings of sacred calendars are based on an interpretation of astrophysics. Numerology is an interpretation of number theory. I don't believe these interpretations are true, because they take the underlying mathematical and physical theories into realms never intended by the scientific disciplines. Even though Sir Isaac Newton himself was incredibly superstitious by recent standards, (he even believed in the philosopher's stone and the alchemical transmutation of lead into gold) that does not justify usurping the limits of physics. The science itself eventually surpasses its inventors and discoverers, and finds its own level.

When conservatives use (neo-)classical economics to justify just about everything, they, like Newton, have stretched matters too far. There's nothing wrong with neo-classical economic theories, when they are applied to situations (circumstances) within their scope. Now, I don't know just how far neo-classical economics stretches, nor do I throw it out altogether. For me, it's the same with Quantum Physics, the Big Bang and a lot of other theories.

The difference is, in economics, we have a lot of politically well-connected folks who do have explanations of just about everything, which indeed do go far beyond what the underlying theory covers. President George H. W. Bush once called "supply side" ideas "Voodoo Economics," and that is a good label for the sort of thing those folks do.

Voodoo Economics

In this election year, there are some highly visible issues that fall in this category: for example, outsourcing.

According to the classical notion of comparative advantage, as laid down by Smith and developed by Ricardo, free and unfettered foreign trade is a Good Thing in consequence of the principle of division of labor. If one country can produce a certain good or commodity at a lower cost than another country, then everyone benefits from the lower cost of production as it presumably implies lower market prices. This is just the generalization to countries of arguments about the division of labor as it applies in households, farms, factories and communities.

There are several hidden assumptions in the classical argument about the division of labor, and comparative advantage. These assumptions control when the arguments apply, and when they don't.

Untaxed and Unregulated

In the first place, classical theory assumes there are no market impediments, such as tariffs or prohibitions. If country A subsidizes its breweries in order to use up excess barley, malt or hops, and exports beer and ale at below-cost prices, then breweries in Country B will be undersold. Eventually, Country B's breweries may be forced to lower prices, go bankrupt or leave the business. After some time, Country A may stop subsidizing its brews and, facing less competition, could raise prices to recover the subsidy. According to classical economists, this situation is not the result of a free market but of monopoly. Subsidies represent a cost of increasing market share in order to gain market control in an oligopoly or monopoly, so classicists oppose subsidies.

The problem is almost every country, especially First World countries, imposes some form of tax (tariff) on production and uses subsidies to control production and distribution. Every major country has regulated agriculture intensively and extensively for over 100 years. The United States and Europe pay their farmers and food processors to grow, store, buy and sell plant and animal resources. There are volumes of regulations and huge subsidies which control the production and distribution of ethanol (ethyl alcohol), which in turn controls some of the feedstock (corn, wheat, barley, hops, malt, etc). The purposes of the system are to maintain production (avoid famine), prevent rapid farm belt depopulation, use food as a foreign policy tool, provide inputs to other industries, maintain aggregate consumption, & c. There is a complex of reasons (social interactions) which lead to extensive and intensive government regulation almost everywhere in the world. This cannot be explained by the (neo-)classical economists; instead, they condemn all those practices and, therewith, ignore them.

Free for All

Another hidden assumption is "easy entry, easy exit." Classical economists believe markets allow low cost, simple access and exit. In the days of Adam Smith, or even David Ricardo, a man could invent a steam engine and become an industrial magnate. By modern standards, that seems a simple enough thing. However, the reality of past times was that very few men could afford to stay home for years tinkering with a balky steam engine until it was perfected. Very few had the capital even to open a candy or tobacco shop. Adam Smith marveled at the wealth created by pin factories and the similar works of his time, all seemingly built from very little or nothing; but, he was not a participant in the creation of those businesses.

I could have purchased a Napa valley vineyard for $22,000 about 35 years ago. In retrospect, the price seems a bargain; at the time, that was more than 2 years income for an upper middle class family. Now that vineyard is priced in the millions, but the overall socio-economic composition of Napa vineyard owners hasn't changed much. (Most of them still are successful San Francisco professionals.) In reality, the successful rarely start "with nothing." The initial investment comes from somewhere, and is often unearned; thus, the common saying that every fortune hides a crook. People commonly reminisce about how easy it was to make a fortune, ignoring how hard things used to be. Thus the myth of "easy entry."

The computer industry is often cited as a classical "rags to riches" story. The truth of this recent example is otherwise: those who could afford to play around with computers in the 1970s became wealthy. While Bill Gates, for example, was supported by his wealthy family, the rest of us could only hope for such luck. In 1976, I deeply desired to buy a computer kit for only $4,000 - about 1/4 of my gross annual salary. But, I could not and did not, as I had other duties. I always regretted that, and so did many others who had the ability but not the wherewithal, so did not become captains of industry.

These and many other stories belie the "easy entry" hypothesis. What's more, easy exit is just as much a myth. For most people, it is difficult to start a business, or get a good job. To arrive in a high paying position requires a considerable investment in education and training, as well as the accumulation of experience. As we are finding out lately, those who got PhDs in Computer Science, Physics and other "hard" sciences are not easily re-trained to be hamburger flippers. Exit from a market is almost always at a considerable loss of capital and labor.

Easy exit and easy entry are really the same thing: an assumption that capital and labor are easily and immediately transferable to some other economic activity. Today McDonalds, tomorrow NASA. In fact, capital markets are far from elastic, and people (labor) are very inelastic.

Invisible hands

A third hidden assumption underlying the doctrine of comparative advantage is that there is always a quid quo pro. If you or your country is adept at making shoes, then surely someone here must be very good at making gloves. We are all advantaged by exchanging shoes for gloves. A difficulty arises when I, or my country, do not make, or cannot provide, anything of value for your shoes. The classical view is such problems do not occur, or do not occur for long (due to easy entry).

Classical views break down, again, in the real, modern world. The poorest Third World countries in Africa and Asia could provide food in exchange for First World products. The difficulty is First World agricultural subsidies make First World food cheaper than anything even the poorest Bangladeshi or Kenyan could grow. Many Africans and Asians are explicitly denied entry into world markets by First World policies, so they have nothing to trade, no matter how much they may desire First World products. There isn't any flow of capital to Africa to develop new productive resources: the First World just isn't interested in most things Africans do, or could do.

So, my efficiency in making gloves does not miraculously provoke a market in gloves somewhere, or encourage your making of shoes. Maybe I am a rich fellow who makes gloves for a hobby, so I will even sell my gloves below cost to enforce my fashion on you. None of that helps you at all, because I don't desire your unfashionable shoes; as it turns out, I also make my own fashionable shoes in my spare time. There is no "comparative advantage."

Insatiable Demand

At the root of this last notion, that a market will always develop, is the premise that production creates enough income to buy the product. My efficiency in making fashionable gloves (as I define them) creates a tradable good, and that in itself creates a credit which enables someone to buy the good. In other words, my fine gloves will create a desire in someone to have them, so they will offer a price for them.

I find this last idea very difficult to explain or defend, as my life experience is exactly the opposite. Lots of people, including myself, do lots of things that have no value whatsoever to others. Even when entrepreneurs go to great lengths to start a business, most of the time very few or no one wants the product. The successful business is the rare exception, not the rule. Most often, all of the labor and capital invested in a new business is lost. No credit or economic expansion is created most of the time by new or increased production. At best, the notion that production somehow induces income is questionable. It requires a lot of special social and political circumstances to make it so.

I think Adam Smith proposed getting around this unlikely premise, by assuming human beings are greedy and always want something, anything. As the old Russian saying has it: 'a man is not a pig; he will eat anything.' This dim view of humanity supports the notion that there is always demand for every product, and each product has a market clearing price. In the teaching of classical economics, it is naively assumed the "market clearing price" is always positive. In our world, it could as well be negative: who wants to buy some toxic waste?

The trick of greed motivates buyers and sellers in the classical world. Smith made a psychological assumption about homo sapiens sapiens, which may reveal why people act as they do in the marketplace. However revealing, motivation is not the same thing as proof of a theory. It only suggests how or why people may act, but does not make them do so. Greed and its supposed consequences appear in many places in the classical theory; it is the economist's daimon ex machina.

Pure Marguerite

There are many more hidden assumptions on which the neo-classical edifice was built. There are also many schools of thought all claiming Adam Smith, Ricardo and Malthus as their spiritual fathers. All of these schools started by believing in the seemly magical economic works. Perhaps one of the attractions was the "Newtonian" mathematical models built by Ricardo and his successors. Those models give a factory manager or stock market speculator seeming perfect insight into the workings of the market. The promise of infallibility almost always seduces, as from that power all else is obtained: riches, social status, political power, sex and the rest. It is the eternal story of Faust.

The trouble is, the models don't really work without human intervention. They have to be tweaked. For example, market researchers and propagandists have to be hired to prepare the market for a product. When people are sufficiently conditioned (brainwashed), the product is introduced and sells the requisite number of copies. This, of course, encourages all concerned to greater belief in the power of the economic theory or model. While it is appropriate to believe in a system that produces the desired results, I think it is clear the economic model is only one part of its success.

One popular neo-classical school is the Monetarists, founded by Prof Milton Friedman. Dr Friedman's insight was that inflation is entirely a monetary phenomenon. He conjectured that problems of an inflationary economy would be corrected by appropriate control of the money supply. He invented a number of measures to discover money flow and money supply. All of that work was in the 1960s. A decade later, the opportunity arose to put Dr Friedman's theories to work during the OPEC-induced inflation of the 1970s. Dr Friedman's followers were also in charge of economic affairs during the Reagan Administration.

Unfortunately, monetarism didn't work in controlling the hyper-inflation of the late 1970s. Thus were born the Reaganite "supply-siders," who adapted monetarist views to the political desires of the wealthy for tax cuts. The result of that combination was the huge deficits of the Reagan-Bush years. Monetary policy did not prevent or correct the deep recessions of 1981-82, or 1991-1995.

Dr Greenspan is a sometime and somewhat follower of Dr Friedman. He tried applying the monetarist theorems to the 2000-2003 recession, but the recession didn't go away. What Dr Greenspan's low interest rates did accomplish, however, was fuelling a housing bubble that mainly benefited households with annual incomes over $75,000.

Perfect Candide

Classical and Neo-classical economic theories are not inherently wrong. They do seem to work in those situations in which their premises apply. It is a great temptation to take those ideas and run with them, which is exactly what professional economists have done. In the late Victorian era, the same misuses of economic theory were prevalent with respect to Newtonian physics. People, including physicists, felt everything was explained and explainable. Newtonian ideas were believed to encompass the Universe; a sort of cocoon in which denizens of the Gilded Age felt assured of their complacency.

During the Gilded Age, and in Edwardian England before Word War I, people felt that everything was for the best, in this, surely the best of all possible worlds.

In that same age, following the American Civil War and the Franco-Prussian war, James Clerk Maxwell, Thomas Edison, Alexander Graham Bell and many others theorized about, and put to work, electricity. It was shown that electro-magnetic fields are the same thing as light waves, which did not mesh well with Newtonian views. Later, Michelson and Morley destroyed the conventional, Newtonian view of the world in their experiment. This led to the Lorenz transformations, which were an ad hoc "fix" on Newtonian mechanics, and a little later, in 1905, to Einstein's Special Relativity and Photoelectric effect.

Why mention this little piece of socio-scientific history? Because, during the very time people came to believe the truth of Newtonian physics, and derived from it a world view, that physics was creaking, cracking, falling apart. I believe we have come to the same place today about "economics," and probably some other things as well.

Sustainable ≠ Conservative

I introduce another notion which I think should be at the base of economic theories; viz., sustainability.

This is really the same sort of idea as "conservation" in physics. It simply means the sum of all inputs and outputs nets zero. (The closed integral over the space of some function equals zero.) Nothing is created and nothing is destroyed. A sustainable economy is just a conservative economy; meaning everything is recycled. In such an economy, no new resources are required to keep things going, and no special efforts are required to remove waste products.

Of course, on planet Earth, there is no such economy, nor can there be as long as economy is about living things. In the first instance, almost everything alive on this planet depends on the Sun. Every square centimeter of this planet is illuminated, and life forms depend on it. While there are some bacterial forms living miles underground or in deep oceans, human life and human economies start with sunlight. Life feeds on an energy gradient, by transforming photons into electrons, and then into chemical reactions. The degradation of energy means there is waste. For us, there is always food and garbage.

Nonetheless, we can ask whether our lives are, or should be, conducted within limits that do not "destroy" the planet. This question takes many forms, and depends a lot on what we mean by "destroy."

The Living Earth

Before we set some limits on the destruction of the planet, consider the geological and evolutionary history of our planet. Earth coalesced out of gas and particles swirling about our proto-star, and grew larger due to many collisions with bodies in nearby orbits. One of those last collisions was particularly horrendous, creating the Earth-Moon system about 4.5 BYA (billion = 10⁹ years ago). After another 500 million years or so, the first living things appeared on Earth, somewhere in the 3.8-4.1 BYA range.

Our oldest ancestors were born into a living hell. They must have been tough, because they colonized every square millimeter of the planet's surface, all of the oceans, and miles and miles of underground rock. In the process, they created Gaia, another hypothesis I think is true. Gaia is mother Earth, the Earth living things changed to suit themselves. Can anyone doubt that today's conditions are vastly superior for today's living things than what we think they were in the beginning?

All of the transformations of Earth required energy, and all of that energy came from just three sources. First was the gravitational energy released in the formation of the planet. Much of that energy is still trapped in Earth's iron core, which is still white hot by our standards. Some of that energy is trapped in Earth's rotation and its magnetic fields, as well as in the Earth-Moon system and the tides.

Secondly, the Earth is also heated by the radioactive decay of those trans-uranic elements trapped in the mantle. The melting of the core and stratification of the solid Earth due to gravity and radioactivity result in heat flow from the interior to the surface. That heat is seen in the surface convection we call "continental drift," and in many other natural wonders. The processing of solid materials over billions of years has brought to the surface the chemicals needed to support life. The heat brought to the surface allows chemical reactions to take place which are essential to life. It appears, initially, living things depended entirely on the geochemistry of this planet, not the sun. This is still so in the deepest oceans and fissures in which we find living things.

Later, today's all important third source arrived: sunlight. In the early (T-Taurus) stage of star formation, photon production is poor and intermittent. Planets are not well illuminated until hydrogen fusion becomes well regulated in the parent star, which results in photosphere heating and "blow-off" of a star's formative shroud. When the solar environment is clarified, surfaces of the remaining bodies begin receiving insolation. As the star gets older, its temperature rises and so does the temperature of its solar system. All of those factors, and the timing of solar evolution, were helpful to our life forms in evolving out of purely chemical dependencies. Today, almost every living thing on this planet's surface directly or indirectly requires sunlight.

In the course of evolution, Earth's life forms changed Earth to suit themselves (again, the Gaia hypothesis). They did not do this in small ways. All of Earth's free oxygen was and is created by plants. The availability of fixed nitrogen depends on specialized bacteria. Forests induce a climate suitable to themselves. All parasites and predator species ultimately depend on the lowest of the low: algae and bacteria. Despite their great accomplishments, living things cannot be stretched too far, as was shown 65 MYA (million years ago). Then, an asteroid crashed into Yucatan, created a worldwide "nuclear winter" which wiped out the dinosaurs, and wrote its story in the KT boundary. That accident enabled mammals, and thence our species, to walk on this Earth.

Some Limits

Looking at the long sweep of geological and biological history, it should be clear nothing on Earth stays the same very long. The planet and its passengers are in a restless interaction to make themselves comfortable. So, in thinking about "sustainable" human economies, we have to recognize that sustainable cannot mean "the same," or stasis. People enjoy the same liberty with their environment as all other organisms: they remake it to suit themselves. Keeping things as they were is not, in itself, a valid goal of "conservation" and not a useful guideline in measuring "sustainability."

While change is allowable, and may even be a good thing, beyond a certain point it is undesirable. Surely we do not wish for another asteroidal impact, the bubonic plague, poisoning the waters, or burning all the oxygen. It is fairly well known what is required to continue life as we know it on this planet. It is not as well known what are the interactions between the many life forms, but we do know all of the life forms together create and maintain the conditions which make life possible for all. So, one upper limit on what we may do, assuming we value our lives, is that which will destroy everything.

If changing nothing is not likely or desirable, how much change should we tolerate? This, it seems to me, is the real question of conservation and the foundation of sustainable economics.

We are creatures of the surface, largely dependent on sunlight for our existence. So, to begin with, one limit on our activities has to be average insolation. We can exceed that limit locally and for a while, but not indefinitely, barring the introduction of novel energy resources (such as fusion power). The energy available from insolation is not solely ours to appropriate. Some of that energy has to be allocated to other species, particularly those on which we prey; e.g., wheat. In turn, the general living environment must be sufficiently sustained to allow on-going human activities. Without stating details, there is some maximum amount of energy our species can appropriate strictly for itself. Using more than that amounts to eating ourselves out of house and home.

One of the statistics we need to know (it does not exist!) is just what the rest of the ecology requires. We already know what energy the sun and earth provides. We need to know what portion can never be ours.

Change

A major complication is the ever-changing ecology of our planet. As indicated above, there is no "status quo" which can be referenced. In addition, we don't really know how evolution responds to change. We do know organisms adapt or die. We know that adaptation depends on pre-existing characters. We just don't have any idea which characters will become dominant, and which fatal, under evolutionary pressure. For those reasons, we cannot predict what happens to our "environment" when humans intervene.

Since ancient times, human societies have changed the environment in the most extreme ways. I believe there have been several episodes of land overuse, eventually resulting in environmental collapse. The Great Dust Bowl in the United States during the 1930s is a vivid, documented recent example. Similar things are thought to have ruined several ancient civilizations in the Middle East. The ruined soils of the Italian latifundia required Rome to get its food overseas, so were a strong motive for the Empire. Studies of environmental breakdown are useful in setting limits on what can be appropriated, and what sorts of abuses must be avoided and repaired.

Despite our propensity for abuse, we do have the right to change the environment to suit ourselves, just as all other life forms do. As intelligent beings (I hope), we must ask ourselves how much change is allowable?

I think we should proceed carefully, and experimentally. It is probably best to avoid sudden, large scale changes. Instead, we should try new things a little at a time. We should do this sensitively, with as much awareness of ecological interactions as possible.

Resource Costs

On the basis of such experimentation, it should be possible to determine the COST of resource allocation. That is the cost of using the resource, including the cost of ameliorating harmful side effects.

Coal itself, for example, is not free (although the classical economists assume so). There are the usual costs of extraction and cleanup, which are already accounted in modern mining practices. But, there are additional costs, so far unaccounted. There is a limited supply of coal, especially low sulfur coal, so there is a depletion cost. There may be costs to maintain the local environment and ecology, while mining operations go on. There are the eventual costs of environmental degradation due to the shipment and burning of coal. There are the ill effects of coal dust on lungs, acid rain on lakes, and carbon dioxide on the climate. There are the unknown effects of mercury and radioactive isotopes released into the atmosphere, waters and soil by burning coal.

All of those effects need to be accounted, together with the positive effects, when calculating the cost of energy or other products derived from coal. The same considerations obviously apply to oil, iron, nickel, and aluminum. Although we don't like to think about it that way, the very same considerations apply to the production of wheat, rice and all the other crops as well as the raising of farm animals.
 

Getting Nowhere

Political wars are being waged over these issues. I believe a lot of the hostility of the combatants is due to inappropriate accounting of the costs. Classical economics is being used to disguise the true cost of what corporate interests are doing. Environmentalists avoid making any cost assessments at all, since they hope to succeed by appealing to your sense of "rightness."

We also have the usual power struggle, which has to do with who is in charge, and who gets the plum.

If this is all that continues to happen, I predict we will go the way of the dinosaurs. The way to change this is to come a new understanding of economics, starting by re-evaluating what resources really cost. In order to do that, we need to come to a much better, scientific understanding of just what is "sustainable."