Choice and Constraint — Introduction

Choice is an attribute we infer in others and apply metaphorically to systems that cannot choose. Constraint is an attribute that applies to any system, regardless whether it has choice.

How should we think about the choices and constraints that shape us? First I talk about the constraints. These include the political necessities for security and law as well as the civilized constraints of justice and the need for `graceful winners' and `graceful losers', and, of course, times of failure.

In any event, we need taxes and regulation. Then I back off and talk about the general characteristics of economics and the development of accounting from a very general point of view — as a form of governance. Business leads into the problem induced by the intrinsic failure of any system that excludes `external costs'. This leads us to ask how to deal with pollution, one method of which is simpler and the other more efficient.

All this brings us to the need for supra-national government, and a practical suggestion.

Success in one choice or another depends on how we influence others. Using words to influence others, rather than coercion or bribery, depends on how we think and how we make judgements.

In every event, we live within systems that replicate themselves with error and error correction. It helps to understand their general characteristics.

Political Necessities

Order, Law, Justice, Democracy

One political response to increased scale is to increase hierarchic control. Traditional China is an example: its mandarins and military ordered clans and villages. But China failed to adapt to the new technologies of the 18th and 19th centuries. Its government failed. After decades of civil war, a new government came into power in 1949. Over the past 20 years, the new government has shown remarkable flexibility. But the question still remains, how well will it adapt to conditions two and three generations from now? Or will it freeze conditions?

In politics, a hierarchical control system can succeed so long as there is little or no change, or so long as the change is easily foreseen. The main problem comes during the succession. If a family does not gain full control, as in a monarchy, competing groups may fight. Such a civil war destroys both order and law. Often in history, a family or clan gained power in a civil war, succeeded for a period, and then became excessively corrupt or lazy. These failings enabled a new dynasty to gain sufficient support to enable it to win a civil war and replace the old dynasty.

However, even with dynastic change, hierarchical political systems fail to adapt well to change: their very success causes failure. They are similar to the companies that Christensen and Raynor describe in The Innovator's Solution ¹². A company's management, its ruling group, institutes methods for employees to follow. Middle managers, the equivalent of captains and colonels in an army and of middle level civil servants, learn enough of their company's culture to prevent anyone higher up from learning about many propositions. This filtering prevents those higher up from being overloaded. Consequently, many a successful company or government carries out only actions that fit what the organization has already been doing successfully.

Christensen and Raynor suggest ways for a company to avoid losing to a smaller, but faster moving competitor that achieves success by following a process that the bigger business rejected as too small or too inadequate. Essentially, the new way means setting up a new organization within the company that is separate from the old, with different cultural values, different rewards for success, and different goals.

As a political system, democracy does the same: it enables an opposition to become the government. The opposition may well have different cultural values, different rewards for success, and different goals from the previous government.

When you view an `opposition' as a part of an overall political system, then its step into power is like the elevation of one division, previously small, into the lead of a corporation.

(As Adam Przeworski said, this means we need

Without them, the overall political system fails.)

Interestingly, the idea of a flexible political system arose before the notion of a flexible corporation. In the past, the overall economic system was presumed to include many corporations, some of which would die. Flexibility lay in the competitive, free market economic system as a whole, not in its components. The Christensen and Raynor solution enables a component, a corporation, to thrive.

Incidentally, Abraham Maslow spoke of a hierarchy of needs:

• survival,
• security,
• social,
• esteem, and then, once those are assured,
• `self-actualization'.

The sequence of order and law provide for survival and security. Justice enables a person and family both to establish a meaningful society and for people and groups to feel properly esteemed. Democracy enables a society to offer survival, security, social, and esteem, even during periods of fairly rapid change.

This analysis is optimistic, for it suggest that unless a catastrophe damages us enough or a powerful government stops or slows change, for example, by hindering innovation, democracy will survive.

Liberty and Resources

This is an hypothesis advanced some years ago by an ecologist named Paul Colinvaux¹⁴. He wrote a book on history in which he advanced an ecological metaphor for human actions. One of his theses is that elites feel both liberty and constraints sooner than others.

In an agricultural, preindustrial society the poor stay poor. But increased resources, be they from trade or conquering one's neighbors, translate to more slaves or servants for the rich. There are more opportunities for a man (and even occasionally a woman) to concern himself with non-tactical things. Moreover, it becomes feasible for the society to create a few more high status, resource consuming jobs, such as that of assistant chief priest, bishop, or chamberlain.

These people do not care to give liberty to others — certainly not to their slaves or tenant farmers; but they are interested in their own freedoms.

However, in the usual course of history, a group more than reduplicates itself. There comes a subsequent generation in which the number of elite children more than match the resources. Each child has fewer material resources. Incidentally, this is why second and subsequently born boys were forbidden to inherit a part of a landed estate in England.

Similarly, a society can only create a few new high status positions; otherwise the positions become common, and lose their status. As the number of elite children increases, it gets harder and harder to gain a `place'. So it makes sense to be more tactically oriented, more survivalist, less keen on freedoms for others like oneself, more keen on getting ahead.

We who live in the advanced industrial societies are in a similar kind of world, except there are vastly more material resources and considerably more status resources: multiple companies, multiple non-profit organizations, and multiple government bureaucracies mean more respectable positions, like that of a vice president, than ever before. (However, the number of very top positions remains the same — there is only one Prime Minister or President per country, only one president of the `largest manufacturing corporation').

So the Colinvaux model applies to us as well as to people in the past.

Eventually, of course, people get used to the level of resources they have. But this takes some time. Perhaps two generations.

During a transition period, people would consider themselves richer or poorer than they expected. And eventually act accordingly.

Graceful Winners, Graceful Losers

In his excellent book on Democracy and the Market, Adam Przeworski ¹⁶ points out that in transitions from tyranny to democracy, democracy succeeds only when the process is not undone. For success, the losers should not try to subvert the process, but go along with losing.

Likewise, the winners must also act gracefully. Otherwise the winners will persuade the losers that they have nothing more to lose.

If the losers are bad guys, they will not avoid subversion from the goodness in their hearts. Bad guys will avoid subversion only because they calculate that going along is better for them in the long run. Perhaps they will win next time. Or, in any event, they hope to gain more benefits by being good losers than by fighting.

In Iraq, at the moment, the Sunni are losers. They no longer rule the Shi'ites and Kurds. Moreover, the winners, the Shi'ites, want justice. The Shi'ites want justice for the murder and torture they suffered from various Sunni, some of whom can be identified as individuals. Quite simply, many Shi'ites would like to do unto the Sunni what the Sunni have done to them.

In the spring of 2004, some Shi'ites in Iraq, such as Grand Ayatollah Ali al-Sistani sought an election quickly. It looked to me that the Shi'ites wished to gain sufficient power to seek justice on their terms. They are a majority of the population in Iraq. No one doubts that they would win an election.

Clearly, a sense of fairness favors their seeking justice. But it is impolitic. Such action would repeat what has gone before. Instead, with the exception of a few individuals, the losers must be protected.

A democracy in Iraq needs strong institutions to prevent the winners from convincing the losers that they will have nothing to lose if they continue fighting. Enough Sunni must be convinced that it is better to go along with losing than it is to further efforts to regain the kind of power that will server to deter the Shi'ites after the US leaves; or else they must be convinced that they do have the power to protect themselves again the Shi'ites.

At the moment, the majority of people in Iraq have no reason to want institutions that limit their power and their right to seek justice. Hence, the United States occupation forces must both protect US enemies, the Sunni, and create armed forces among them to defend themselves. Or else the US must accept that it has done nothing to change the culture in the Middle East, and also has made itself look less potent and be more hated.

Put another way, the key to fair elections in Iraq is to impose countervailing forces that will, in many ways, reduce fairness.

To talk only about elections, and not about these countervailing forces, is to favor Shi'ites who have good reason to favor justice for themselves, and no experience with tolerance. If effect, such talk is to favor civil war, and its accompanying looting, torture, and murder.

Periods of Unraveling

(Much of this essay was inspired by Generations, by William Strauss and Neil Howe.)

In a `period of awakening', like the 1960s in the US or the 1640s in England, one of two things happen: either `the revolution' loses, as it did in the US, or it wins.

A `period of unraveling' follows the `period of awakening'. Both when the revolution loses and when it wins, the outcomes lead to the adoption of solutions that fail: either the solutions are a repeat and increase of the old solutions with minor tweaks, as in the US; or they are the implementation of new methods that turn out to fail in practice, as in England under the Commonwealth. At the same time, new sets of solutions are proposed, but not exhaustively implemented.

Another way to look at the `awakening' of the 1960s is to see it as a failed social revolution: `radical' suggestions were made for solving contemporary problems.

In the subsequent period of `unraveling' the Awakeners' suggestions were mostly not followed; and when they were followed, the solutions are changed on implementation to ways that are very different than originally proposed. For example, in the 1960s when people talked of cleaning up polluted sites, they did not expect the United States government to spend as many tax payer dollars on litigation as digging. Yet in places that has happened. Similarly, the people who opposed incarcerating the mentally ill in state mental hospitals did not intend to move many of the former inmates to prison. And, when space enthusiasts talked of a `shuttle' they were not expecting a design that costs more to take a kilogram into orbit than the previous, use-once Saturn launch vehicle.

Following the `unraveling' is an ensuing `period of crisis' during which the proponents of one set of solutions win; their solutions are implemented.

The losers are defeated. They lose their jobs and positions of authority, and the newspapers and other media are either scared into self-censorship or directly censored.

The period following is called a `high' by Strauss and Howe, since everything moves along in a fairly predictable fashion and even though it is heavily criticized at the time. But as soon as nostalgia has a chance to operate, the period looks good.

In the US, for example, the 1950s are called a `high', yet at the time, schooling was a problem, race was a problem, the economy was a problem, military preparedness was a problem, conformity was a problem, lack of interest by elite college students in major social issues was a problem ... although better than the preceding depression and war, the period did not appear to be much of a high at the time.

Fortunately for the US, most `highs' have been more or less benign.

But a `high' does not have to be benign; it can simply be inadequate. It has been suggested, for example, that in the mid-Victorian era, the United Kingdom went though a muted awakening that led to a muddling through of the subsequent unraveling and crisis -- not a disastrous outcome, but not as successful in the long run as people in that one-time Empire might have wished.

One might argue that the US post-Civil War high was also inadequate. The Federal government permitted whites to reimpose local racist rule in the south; it permitted major private corporations to establish near-governmental power over many areas; and when government got directly involved, it permitted private corporations to co-opt the government regulatory agencies.

It has been said that it took the 1930s to overcome the mistakes of the 1880s. Moreover, I need not remind you that the response in the 1980s to the 1930s took the US from being the world's biggest creditor to being its biggest debtor. (And you do not have to be a nationalist to regret the loss of autonomy caused by debt, merely a democrat, with a small `d'.)

[Addendum written in April 2004: in the US, we are now going through a `period of crisis'. That is why politics are so vicious and people so divided. As yet, we do not know who will win.]

Taxes and Regulation

Tax, Borrow, Scrimp

As George Washington said in his Farewell Address as the first United States president,

The simplest way to raise taxes and at the same time to disown others' claims is to run an inflation. United States arranged its governing institutions such that no one part of government can run an inflation along. Instead, the Executive branch of the government must borrow dollars from the Federal Reserve. In turn, the Federal Reserve must be willing to lend those dollars. It will only lend if the Legislative branch is willing to pay interest on the borrowings. The interest can, of course, be paid by borrowings, at least for some years. If all three groups agree, then money can be created readily. As in Japan, the cost of creating money is low. In addition to the paper work, it involves adding zeros to a computer account. This is less expensive than in the old days, when governments had to print on paper. But even then, `printing money' was cheap.

It goes without saying that inflations, especially large inflations, tend to destroy an economy. I am leaving that aside.

When a government, such as the United States Bush Administration increases spending on the military, on drug payments for the elderly, on farm subsidies, and the like, it either must borrow more or raise taxes. There is no other alternative.

The Bush Administration cut taxes, so it must borrow more. Indeed, the deficits both it and others predict go on for years. The deficits do not have the look of Keynesian counter-cyclical deficits, since they persist regardless of the state of the economy.

(In the past, some argued that the Bush Administration wanted to reduce overall government spending. It was said that the Administration had to increase military spending, but would cut back on other types of spending. However, its increases in drug payments and farm subsidies have disproved that argument. It is not a `tax and spend' administration, as people have complained about some Democratic administrations, but a `borrow and spend' administration.)

While a trusted government can borrow for a long time — it can borrow so long as its anticipated increase in revenues is larger than its anticipated costs — there may come a time when anticipated costs rise dramatically, or when the government becomes less trusted. Either problem raises the risk premium for borrowing.

An increase in the risk premium raises the cost of borrowing. Such an increase often precipitates a disownment. The terms used to describe such an action vary. A newspaper may say that a central bank stopped maintaining a `currency peg'; or it may way that a government declared a `moratorium' on certain loan payments. Regardless of the language, the action is to disown a promise once made.

Needful Government Regulation

1. that everyone have full knowledge;
2. that economic activities never enjoy or suffer externalities, and;
3. that high initial/low incremental cost production never occur.

Of course, we know that these conditions fail: people do not know everything. Cars and other `goods' release exhausts, which are external `bads'. Moreover, steel and flour mills, oil refineries, railroads, radio broadcast systems, and automobile manufacturing are examples of century-old industries that have high initial and low incremental costs.

(It cost Henry Ford a great deal of money to build his Rouge River plant, but once built, it cost relative little to manufacture an additional 100 Ford cars each year, up to a maximum.)

Products that are dependent on information, such as medicines, and products that are pure information, such as songs and software, are examples of current goods with high initial and low incremental costs.

A government can permit a market to allocate goods when people know of risks, when private and social benefits are the same, and when no industries with decreasing costs exist.

But when investors seek corporations with limited liability, when they desire laws of bankruptcy, when negative externalities, like thrown-away paper, litter the landscape, when the steel, automobile, and software industries exist, then governments have a job.

There are reasons for governments to regulate economies. And, in theory, governments can do the job, or at least enough of the job to help a little.

However, in practice, governments often fail. The people in governments act to promote their interests, or the interests of their associates, rather than the interests of their country. Thus, in the latter 19th century in the US, railroad companies used the Interstate Commerce Commission to prevent competition among themselves that they felt was dangerous. In the 20th century, major US food companies `captured' the US agency set up to regulate them. While the food they sold became safer, at the same time, they reduced market competition against themselves.

So the issue becomes one of governance: what institutions will enable you, a citizen, in conjunction with other citizens, make sure that your agents do as you wish?

This is a traditional `agent/principal' question, except that it is applied between politicians and citizens to rather than between employees and their managements or between civil servants and politicians who are in office.

You and others citizens are the `principals': you give the orders. In theory, your `agent' acts on your behalf.

For example, you may not know why you are feeling ill; but an agent might: in this case, he would be a medical doctor. So you `go to the doctor'. He knows more than you about medicine.

(Indeed, the medical market is enabled by a lack of information on your part and the existence of specialized information on the part of others. If you could treat yourself, you would not need to visit a doctor. Similarly, you do not know about your future health or accidents. Consequently, in the US, many people who can afford it purchase health insurance.)

If, in your opinion as a `principal', your doctor, your `agent', fails to do his job, you switch to another. If you like him, you continue to visit him. By your actions, you provide your agent with information telling him whether his actions are perceived as beneficial to you, the principal.

When you cannot switch — perhaps your doctor is the only doctor in town — or when you do not know enough to decide when to switch, your actions as a principal will fail.

Then your so-called agent will be free to do as he or she likes. He can shirk. She can maximize her income. He can enhance some other personal goal. For example (to talk about a problem a friend of mine, a nurse, just mentioned), she can help a large company convert a fatal condition to a chronic condition that can be maintained through continuing treatment rather than find a cure that implies a one-time treatment. While saving lives is good, the social cost (and private cost to you) of suffering a chronic condition is worse than the benefit, both public and private, of a cure. But the cost to you and to the public may, depending on institutional motivations, be profitable to some.

As the Nobel Prize winning economist, Douglass C. North wrote¹⁷

Moreover, it turns out that details matter: if citizens do not learn about the failings of their agents, they will not vote them out of office. This means that citizens, or their other agents such as journalists, must not only pay attention, they must not be cowed. Your other agents must tell you what is really going on. If they are cowed in any way, or if you are cowed, they or you will be poodles, not tigers.

There are more details. As Adam Przeworski says in the essay which inspired this Web page, A Better Democracy, A Better Economy,

Without these features, neither a market nor a command economy will be efficient at allocating economic resources. And without some degree of economic efficiency, neither you nor anyone else will be able to afford security, justice, or beauty.

In the present world, for example, the current population is too large to be supported by the old technologies of the past. We could, if we chose, now feed everyone on the planet. But we could not even think of doing that if we were limited to the economic efficiency of a century ago.

Economics

Tentacle City

    Met_Rate = 1 + 0.5*Mass

                     mass of each little `tent'     mass of each big `tent'

    Week one:                 10                         100

    Week two:                  4                          49

    Week three:                1                          23.5

    Week four:               dead                         10.75

    Met_Rate = 1 + 0.5*Mass

(Indeed, I don't even know your species, although a xenobiologist might infer that your home sun is a K type star from learning that your multi-faceted `bug' eyes are most sensitive at a nearly 800 nm wavelength rather than at the 560 nm or so wavelength characteristic of human color vision.)

But times of plenty are followed by times of scarcity. Are smaller `tents' more adaptable than larger `tents'? Are they more able to survive a relative short period of scarcity? Or do big `tents' enjoy so much extra fat that they can survive the downturns better?

Worse, what happens when a large `tent' discovers that it can eat a small `tent' and then also eat the smaller entity's former food?

At least you and your colleague can theorize together:

Suppose a big `tent' can easily eat a much smaller `tent', but has a more difficult time catching and eating a similar sized `tent'.

In this case, more or less similar sized `tents' will persist. Few will eat each other. But smaller `tents' will be eaten. The number of smaller `tents' will depend (among other factors) on the birth rate and the time which it takes a larger `tent' to digest a meal.

If by some chance or other — perhaps the `tent' grew up in a fertile valley or it figured out how to eat more efficiently — one `tent' becomes bigger than all the others, then it can devour everyone else. The other `tents' will die. The only survivors will be those who have not yet been eaten, either because they are too far away or because the larger one has not gotten to them.

Either one big `tent' survives, or a few. Small `tents' come into being; but all get eaten eventually.

Economic and Political Implications

Our bug-eyed monsters' fictional expedition is actually an attempt to simulate what happens with corporations in a capitalistic society such as our own.

I hope that most of you agree that the `ecological rules' I postulated are more or less accurate representations of the circumstances in which businesses find themselves.

• `Tents' must eta some food every week, and more if they are bigger.
  Businesses have fixed and variable costs.

• Small `tents' starve to death in a famine.
  Weak businesses go bankrupt in downturns.

• `Tents' enjoy lots of food during times of plenty.
  New businesses are more likely to survive in good times than bad.

• Some `tents' find that a nearby volcano erupted, and not only did not kill them, but fertilized the soil.
  Some businesses find themselves in a newly developing industry that offers many opportunities.

• Large `tents' can eat smaller ones, but may take some time to digest their food.
  Bigger businesses can take over smaller businesses, but may take a while to make good use of their acquisitions.

(If you do not accept the accuracy of these rules, I would like to hear of `rules' you think are realistic, expressed as descriptions of the circumstances in which these tentacled beings find themselves.)

Finally,

• You find that your colleague is partially wrong in thinking that all sized `tents' grow at the same rate if they feed enough.
  Often, small businesses grow faster than big ones, but some big businesses figure out how to grow fast even though they are big.

This latter issue is perhaps the most controversial question in politics and economics: I have heard some people argue that big companies can never be as efficient as small companies, because big companies are insufficiently agile. But others say that big companies have more resources, and so can do more.

As far as I can see, optimal size depends on circumstance.

For example, Christensen and Raynor ¹⁸ claim that large companies do better with what they call `sustainable' technological development, because they can afford the resources. But they also say that small companies do better with `disruptive' innovations.

Big companies lack senior managers who have an interest in the initial markets of a `disruptive' innovation because those markets must be small. Worse, a big company that is successful has created a company culture that filters out ideas that might lead to small markets because the company needs big markets. Success can only come to a big company that creates a new part of itself to avoid the processes and values that benefit the big company elsewhere.

This action is like a large `tent' budding a new, small `tent' that goes off to discover whether it can find any food growing on a recently weathered lava flow.

The political implication of this exercise is that wise anti-trust actions against both monopoly and oligopoly are required even when there are few or no `barriers to entry'. A large business or a group of large businesses may keep on growing.

I speak of `wise' action because there are times when sustainable innovation requires the large resources available to a single or to several large companies. But there are other times when one or a few large companies should be broken up into smaller entities so their managers adopt different goals and different processes.

Many say `the market will take care of it', but that is not true in all situations.

Accounting in the Middle Ages

I am not an accountant, but some years ago I read a history of early accounting ¹⁹. What struck me was that the metaphor that led to double entry book keeping was balance, and that from an outsider's point of view, it was hard to find profit.

All in all, for double entry book keeping, three new ways of thinking must emerge, one of which is balance. A second is that humans can create entities separate from themselves; they must be able to create golems, as it were. A third is that humans must think of time as linear.

In the Middle Ages, an enterprise started when a few people took a chance to support it. Perhaps, also a usurer would loan it money. The difference between the investors and the usurer is that the usurer was supposed to be paid regardless of the success of the venture, but only a fixed amount. The investors might lose — pirates or a government might seize a cargo, or a storm destroy it — or they might gain hugely.

The venture was seen as an entity separate from those who put money into it. This was a key notion. In particular, the owners are not the entity. Another key notion was balance; that idea was possible because no one yet thought in negative numbers.

A venture possesses assets, such as the ship to carry the goods, the gold to buy the silk, or the silk itself (or, more prosaically, the silver to purchase the grain). The people who put money into it are either the investors or the usurers. Investors own equity; the usurers are a liability.

Thus, the basic accounting equation:

Or, in modern and for most people, more boring, language;

    assets = liability + equity

An increase in liabilities means a bigger loan from a usurer who trusts that he will be paid back. The usurer is a creditor, a word that comes from the Latin, `trusts'.

An increase in equity means a bigger investment from an owner.

Before the invention of negative numbers, the value of the enterprise was seen as a positive number. Consequently, an increase in what the business owned, an increase in it liabilities or equity, was seen as an increase in assets.

And indeed, the more put into the business, the more are its assets. People could understand that the value of an enterprise equaled what it owes. The amount owed was a definite debt. The amount received was also definite. Indeed, if everyone was honest, the two had to equal.

The metaphor is like that of an old fashioned balance scale: on the right hand side is put the weight of the liabilities and equity, all definite. On the left hand side is put the weight of assets; also definite. Unless someone steals, the two must balance.

Moreover, balance continues on a smaller scale. During a venture, it looks as if the overall total of assets for an enterprise does not change. The composition changes, but if there is no theft, balance remains.

Suppose you exchange gold for silk. The amount of fixed assets increases. The venture gains a load of silk. The amount you must pay the seller also increases (from nothing to the value of the shipment). The values of both balance.

In modern thought, we would say that as a result of your payment, the value of cash decreases, which is a negative number. At the same time, the value of your cargo increases by a positive amount. And the absolute value of the negative number is equal to the absolute value of the positive number. This way of thinking also works, but it is more abstract than the notion of a definite debt balancing a definite gain.

Suppose your voyage is a success. You come home and sell your silk. Now the amount of gold you have increases; but its value equals the value of the silk you must give your buyers. Another balance.

Dissolve the venture: everyone receives his money, including the usurer. What is left over goes to the equity investors. The exact value of the enterprise is divided up among those who are owed money from it. Nothing is stolen. Again a balance.

Everything balances. A careless Medieval thinker, more used to brigands and predatory barons who steal, may well wonder how profit comes from balance? To understand how profit and loss occur, you must think over time. This is a third key notion. Not only must you think of what you pay for the silk here and now, but you must learn what the merchant paid months ago, and what it cost to ship it.

Put another way, rather than think of time as circular, or a spiral, a round of seasons, months, and religious celebrations, you must think of time as linear.

You must think of the Christmas last year as being very different from the Christmas of this year, even though both are similar religious celebrations of the birth of your savior. (And which is more important for you, being saved for ever and ever, or a little silk?)

Double Entry Book Keeping

[ I am not an accountant, but some years ago I read a history of early accounting. If I remember rightly, the book ended before Luca Pacioli, the `Father of Accounting', published his famous work in 1494. Or maybe I did not read more. I cannot remember the title or author of the history, only that it was published a long time ago. ]

In the beginning, double entry book keeping had two purposes:

• an informational purpose, a description of an activity;

• to provide an agent-principal mechanism whereby a principal gains more control over an agent (but not much).

As an informational tool, double entry book keeping depended on the ability to compare apples and oranges. Put another way, a medieval trader exchanged gold coins for silk. The gold and silk were compared in one way, by their monetary value, but not in others. It is famously impossible to keep warm with gold, but you can make warm socks with silk.

Double entry book keeping records only the `internal costs' of a business. It does not record `external costs', such as pollution. Such costs are invisible to a business. The only way to make them visible is for a government to to force external costs inwards successfully.

When governments are weak, or when pollution is so limited it can be ignored, businesses do not pay for external costs. In effect, they receive a subsidy from the people who suffer.

As an agent-principal mechanism, accounting enabled a principal to check whether his agent was doing as previously agreed. In the Middle Ages, the principal was usually an older man or group of men who put up the money for a venture. The agent was usually a relative or a young man hoping to marry a daughter or niece. Because of the familial connection, or because of hope, no one expected the agent to act too corruptly; the goal was to keep his corruption or his stupidity in line.

A Market for Pollutants

Douglass C. North²⁰ made the point that

This notion points out how to organize society more effectively.

To a friend, I once wrote,

To which my friend asked,

I responded in turn by saying,

Consider the problem posed by people who try to poison me and others by releasing pollutants into the air.

If our government decides that this sort of activity should be reduced, it has two choices:

1. Ban polluting emissions.

   This means telling a company that its emissions at its smokestack must be less than some value, or else the company will pay a fine. (People often think that a ban means `zero output' of what is banned, but that is not what is meant in practice, which is to reduce an output below a certain level.)

   A ban also means organizing a policing unit to check smokestack outputs and/or providing outsiders with a legally permitted mechanism to check companies' actions and take them to court if they violate the ban.

2. Organize a market to cause the various companies involved in electricity production to internalize the cost of pollution; and to penalize them for producing pollution.

   This means deciding on the total amount of the pollutant that will be permitted into the environment and setting up the legal environment that enables people and companies to write contracts regarding the release of this pollutant.

Banning is simpler than creating a market. It is simpler administratively and simpler in terms of how people think and perceive.. A ban is categorical. It is the simplest of the Guttman scales. A market requires thinking in terms of a ratio scale, which the most complex scale.

A market is difficult to create: to succeed, a country needs an administrative system that is not excessively captured by the companies the administration is supposed to regulate. It needs a reliable, quick, and honest legal system. Otherwise, the process will become a source for bribes and not do the country any good.

Suppose an electric power company owns four power plants, all burning coal:

• Two of the power plants are old and can produce 500 MW each of electricity and release 100 tonnes of ash for every N kwh produced.

• One power plant is moderately new and can produce 1000 MW of electricity and releases 50 tonnes of ash for every N kwh produced.

• One power plant is new and can produce 1000 MW of electricity and releases 20 tonnes of ash for every N kwh produced.

The average demand for electricity from these plants is 2250 MW; the peak is 2700 MW.

Consider two ways of paying for the reduction in pollution. Please bear in mind that the consumer, namely me, you, and others, will end up paying. I have an interest in a lower electricity bill! The poorer you are, the greater the interest.

1. Ban pollution; for example, have a government agency state that the permitted pollution level for each plant be under 40 tonnes/N kwh.

   This means that three plants need to be retrofitted: the two old plants and the middle-aged one.

2. Create a pollution market by having a government agency state a total amount of permitted pollution that (as it happens) leads to exactly the same number of tonnes of pollutant entering the air per year as in the ban.

   This means that the electricity producer pays some cost when operating the middle-aged plant without having retrofitted it and a considerable cost when operating the old plants without having retrofitted them.

The question is, what is the cost to electricity buyers, to gain the same low level of pollution production?

The banning technique means that three plants will have to be retrofitted.

The market technique means, most likely, that the middle-aged plant and one of the old plants will be retrofitted. The new plant produces a low level of pollution and will sell its `pollution credits' to the other old plant. And that old plant will be turned off when power demand is below peak. The electricity customer pays less to reach the same level of pollutant output.

Generally speaking, the second method, the market technique, costs less for a given level of pollution, presuming a good government.

The reason is that different plants are built with different technologies and have different ab-initio pollution outputs and different costs of retrofitting. (As a rule of thumb, for the same reduction in pollution, older plants pollute more and cost more to retrofit than newer plants, per unit of electricity produced. New plants, for example, use different kinds of burner than old plants and build ash collectors into their exhaust systems.)

The same argument applies to `intrinsically polluting' operations, such as burning fossil hydro-carbon for fuel. If two plants are equally efficient, then the one burning natural gas will release less carbon dioxide than the one burning coal, per unit of electricity output. So the idea is to tax carbon, to encourage a switch to fuels that use less or no carbon. (I have heard it suggested that in the US, an effective `carbon tax' would increase the cost of auto gasoline by 10 or 15 cents per gallon. I have no idea if these numbers are good suggestions, but such numbers are what the controversy is about.)

If the contrast is between two 1000 MW plants, one burning coal and the other using uranium, the latter will possibly release a catastrophic amount of radiation, but the former will continually release low levels of radiation in excess of what the nuclear plant releases.

(There is uranium dust in the ash that comes out of the smokestacks of coal-fired power plants. I have been told that coal-fired power plants have been exempted from the radiation release regulations that nuclear power plants must follow; otherwise, the coal-fired power plants would be shut down on account of their low level radiation releases. An acquaintance, a public health specialist, once told me she researched just how much radiation is released and could not get good figures. I do not know if the problem has been exaggerated by nuclear power plant operators or downplayed by those who own both nuclear and coal-fired plants. As far as I know, natural gas plants do not release radiation; they do not have much if any radon in the gas, and no dust.)

The alternative to a carbon tax is to ban fuels that contain carbon, or ban types of fuel. Thus coal might be banned, but natural gas permitted.

However, such a ban immediately wastes the sunk investment into coal burning plants and means that natural gas pipelines must be built to areas which have readily available coal. The idea behind a differential tax is that it discourages new investment in the more expensive fuel and encourages more investment in and full use of plants that use the less expensive fuel.

Since I want both less pollution and lower electricity bills, I prefer the more efficient method.

This is why I favor carbon taxes and other such mechanisms that cause companies to internalize the costs of what economists call `external goods' and to penalize the companies for producing outputs that hurt me and others.

It goes without saying that if courts and government agencies become more corrupt, the market method becomes less efficient and the banning method better. If a government and its courts becomes even more corrupt, then nothing can be done, no method is efficient, and we are doomed.

Governance

Developing and Extralegal

For me, the first part of this insight comes from Edward Hugh, who described

Hugh is right. In more detail, he said

(Hugh attributes this notion to Andy Xie of Morgan Stanley, who wrote of "a global economy". Although Xie did not write of "a global developing economy", at least not as far as I could find, Xie does write of the world economy as global. Since most of the world is developing, the implication is that the economy is both global and developing.)

The second part of the insight comes from Hernando de Soto, who noted ¹⁵ that

Put together, these notions tell us that we should look at `the economy' as global, developing, and extralegal. This means that the central bank of the United States, the Federal Reserve, is wrong to focus only on US problems. It means that those who seek the rule of a single law fail when they focus on the (relatively speaking, for businesses) reliable, quick, and honest legal systems of countries like the United States.

Instead, the Federal Reserve should consider how its actions have planetary influence: if you follow this reasoning, then there is a strong argument that recent economic volatility comes as a consequence of actions made for local reasons that have global effect.

For example, in the early 1990s, the Federal Reserve kept US interest rates low to help American banks recover more readily from governmental mismanagement of Savings and Loan institutions. Consequently, large funds traveled to China, where investors hoped for a higher rate of return. That money inspired a Chinese inflation, which the Chinese government eventually crushed. For several years, this wiped out prospects of high rates of return in China. Therefore, funds traveled back to the United States, where they were invested in stocks and property, helping fuel the asset price `bubble' of the late 1990s.

Moreover, rather than expect businessmen to be able to borrow money from and settle disputes with strangers (the great benefit of a reliable, quick, and honest legal system), investors should remember that most entrepreneurs depend on family, clan, friends, or crooks. Their businesses must remain small.

On the one hand, this limitation means that local businesses will lose when competing with existing, large `Western' companies. They can never raise enough money to do otherwise.

On the other hand, this also means that the overall market, and the potential for investor's profits, will be smaller than hoped.

If you take this view seriously, the conclusion is two-fold: first, within developed countries such as the United States, people who work directly or indirectly for the nation, such as those on the Federal Reserve, should focus on the impact of their actions on the planet, as well as on the country. Since the global impacts may echo back upon them, this focus is in their own long term interest.

Second, investors should figure how to support de Soto and his programs for adapting formal law to existing social contracts rather than the reverse. This way, the investors will be able to make a higher return, in the long run.

In the short run, investors should note that only empire provides a mechanism for settling disputes among strangers, as was done for so many millennia among the Chinese. The problem with empire is that its decision makers have no incentive towards fairness. They are not paid and permanent judges, or randomly chosen juries, but managers who will help themselves, their families, and their friends by finding and accepting the largest bribes possible. Such a system favors the already rich, which is another way of saying it harms most businessmen, since most are not rich as those at the top.

Opportunity, Compassion, and Justice

Philip Bobbitt, ²¹ a man who combines legal and military ideas, argues that the next major political argument will be over the ways in which governments provide opportunity.

This means that some will succeed materially more than others; there will be many who perceive themselves and are perceived by others as losers. They will have made a mistake when they were 16, or an `Act of God' will befall them, or they will fail at any job valued by a market society.

In turn, this means that compassion will become more important politically, since enough successful people will think `there but for the grace of God go I'. Only with the growth of a strong countervailing belief will compassion become less significant.

Moreover, since people dislike free riders, and since new times mean new issues which do not fit into traditional categories, visible justice will become more important.

Opportunity implies meritocracy. It means that enough individuals find a chance to do better, and that social status and material rewards come to those who best do what society seeks. The chance to do better is not determined, or at least, not ultimately determined, by religious upbringing or by accidents of birth considered extrinsic to a person, such as wealth or race.

When people receive rewards according to their degree of success, many see the system as a whole as just and legitimate.

It goes without saying that others value different sources of legitimacy and justice: people who become rich, for example, often want to pass on their positions to their children. In so far as their children are less capabile than others, the others' opportunities must be restricted. Otherwise, the rich children will lose. If others are not overtly restricted, then the rich children must be given advantages to compensate. Thus, the rich must provide better schools for their children, whether public or private, must provide better health care, and must provide language that justifies this.

As I write this in the spring of 2004, it looks as if this emerging conflict is being sidelined by efforts on the part of Al Qaeda and its allies to beat infidels and to replace corrupt governments with virtuous governments, and by the responses of countries such as the US.

Both in the US and elsewhere, many hope to succeed by doing `more of what they should have done' rather than by doing `more of what they should be doing'. The former is a known path, and clearly some followed it well. The latter requires deciding what `should be done' and then doing it. Both deciding and doing are fraught with uncertainty.

However, over time, countries that make better military and economic use of their resources tend to overwhelm those that do not. This means a better use of all talents within a society, not just a few. Put another way, meritocracy wins wars.

So I expect that over the next generation or two, the backward looking responses of people in the US and other countries will fail. (Whether the countries will also fail is another question.)

But there are different ways for a `market state' to handle opportunity. Bobbitt identifies three:

• The entrepreneurial, in which a government acts to set people free to make their own decisions. The United States is an example.

• The mercantile, in which a government focuses on long term opportunities and social stability. Japan is an example.

• The managerial, in which a government attempts to achieve social equality. Germany is an example.

Each way handles justice differently. In the United States, and countries with the same goals, justice comes from a focus on individual rights, a belief that `acts of God' are few, and that in any event, everyone has a `second chance'. In the US, the `second chance' belief is most vividly seen in those who are `born again', an act which enables such people to disown the mistakes and accidents of their pasts.

In Japan, Korea, and the like, justice comes from a focus on stability and a ban on chaos, even when rapid material changes take place.

In Germany and the like, justice comes from a focus on social equality and on caring for those who are eager to work but cannot. The premise is that by acting this way few unemployed will become so alienated as to become criminal or addicted to alcohol or other drugs, or become active in the kinds of political movement that have caused much suffering in the past.

I do not know how countries will respond to technological changes, but think there are strong suggestions for two themes.

Consider the following change: a sharp drop in the cost of information reduplication. Right now, unless effective law enforcement raises the price, a full computer operating system and office suite on a CD costs US$1.50 - US$2.50. The cost of the machine on which to run the CD is high, but a modern computer costs considerably less than any from 50 years ago. The cost of manufacturing a CD with data on it is much less than the cost of duplicating, marketing, distributing and selling 650 megabytes in 1954.

This is a technological change with social consequences. In particular, the only way to keep the price of data high is to enforce laws against inexpensive data transfers.

Effective law enforcement costs. In schools, for example, children must be taught that it is wrong to share non-rivalrous ²² goods, like games or learning. Programming students must be forbidden to study certain topics lest they become common knowledge. If this is not done, children will grow up to favor sharing; students will learn. Police actions to hinder sharing or knowledge will lose legitimacy and law enforcement will become more difficult.

The key political factor is whether people think that a shirt that only one person can wear at one time is different from software that two people can use at the same time, or whether they think the two are similar? The latter requires the metaphorical extension of the concept of property from a rivalrous good, such as a car or chair, to a non-rivalrous good, such as software.

As far as I can see, a country that focuses on social stability, a `mercantile' state like Japan, will be less inclined to admit the turbulence that comes from lower prices. It will try artificially to keep prices high when technology permits them to drop.

On the contrary, a country that focuses on social equality, a `managerial' state like Germany, will figure that its institutions will care for those hurt by price changes, and be more against governmentally enforced high prices.

The outcome in a country that focuses on `rights', an `entrepreneurial' state like the US, will depend on how it defines legal `rights'. It could come to think that people have a right to do what they want, so long as they do not prevent others from also acting; in this case, the right will be to copy information, and the price will be allowed to drop. Or they may come to think that individuals and companies have a right to keep information from others, and government policing will increase.

Opportunity, Compassion, and Justice make for a slogan. It seems to me that one or other political party in the US should adopt it. I think that the Democratic party is better positioned than the Republican party.

The Republican party once favored fiscal rectitude, balanced budgets, small government, and individual freedom. Now it implements government deficits, unbalanced budgets, large government, and government intrusion on private lives.

The Democratic party has already made the transition to fiscal rectitude and balanced budgets. It generally favors social as distinct from economic freedom.

For an entrepreneurial, opportunity based country, the keys are fiscal rectitude and individual freedom. This favors the Democrats.

On the other hand, by `going back to its roots', the Republican party could re-adopt both these keys, and size the opportunity.

No World Government

(Some of these people, like James Webb, President Reagan's Secretary of the Navy, have referred to the US invasion of Iraq as "the greatest strategic blunder in modern memory". Others are fearful of the Bush Administration's deficits. Even when deficits profit them in the short term, they look at Federal government deficits that are projected to extend forever, and fear that the country will become weak in a generation or two. They may figure that they should embrace an organization that might help them in the long run.)

A Larger Federation

Soldier, Enemy Suspect, Criminal, Civilian

(From the United States 2001 September 14 Use of Force Resolution (Against Terrorism).)

This means that the President, or someone deputized to act on his behalf, makes the classification. The classification is based on whether the entity is thought to have

those involved.

In brief, the `Use of Force Resolution' provides a classification mechanism that is different from those used by a court. This classification mechanism enables the US government to categorize people approximately rather than precisely. It means the government can act, even in ignorance. And it means more injustice.

Sadly, the `Use of Force Resolution' provides less stringent guidelines than a traditional declaration of war or rebellion. It therefore provides for less accountability. Consequently, if the Founders of the United States were correct in their understanding of politics, and I think they were, we are more likely to see governmental tyranny than we would in a traditional war or rebellion.

It should be replaced.

Words, Money, and Guns

Words Only

Understanding Without Proof

    [If you cannot see the equation above,
    here are two ways of writing it in plain text:

        e^(i pi) + 1 = 0
    and
         i pi
        e     + 1 = 0

    Euler, by the way, is pronounced `Oiler' in English.]

After proving this formula in a lecture, the mathematician Benjamin Peirce said

Pierce was unable to express to others the meanings which underlie mathematics, although there is no doubt that he worked with them. He was able to prove Euler's equation to his own satisfaction, but his remark demonstrates `Proof Without Understanding'.

At least Pierce could prove the relationship. I was worse: when I first heard of Euler's equation I could neither prove it nor understand it.

Fortunately, understanding is now easier.

Recently, George Lakoff and Rafael E. Núñez ⁹ argued that a mathematical idea is based on a `conceptual metaphor', an

The authors argued that mathematics consists of metaphor piled on metaphor, blended and transformed, so people often do not realize the basis of it all.

Lakoff and Núñez provided evidence that infants can see the sizes of groups of up to four objects and recognize subtraction and addition prior to the development of language. They contend that arithmetic comes from an inference-preserving extension of this ability to larger numbers.

Moreover, they argue that there are actually four `grounding' metaphors (metaphors based on experiences many of us had as children); these are:

• adding and taking away objects from a collection (playing with pebbles);

• construction of a larger whole from smaller objects (playing with blocks);

• measuring the width or height of something (by stretching our hands to the ends of the object or standing up to see how high it is);

• moving from one place to another (by crawling or walking).

These experiences provide us with four metaphors that work with arithmetic: four inference-preserving cross-domain mapping mechanisms that work consistently with each other and the world.

Measuring provides us with zero and moving backwards provides us with negative numbers. By blending these metaphors, and insisting on consistency, we get zero and negative numbers for collections, too. And then by adding new metaphors based on existing arithmetic metaphors onto existing ones, we get the `empty set' and set theory....

To quote Daniel J. Solove, ¹⁰,

These ideas change the salience of my understanding. No longer do I think of a metaphor as `merely' a figure of speech or as an aid to thinking. Instead, I have come to realize that much thought — and all abstract thought — is based on metaphors.

Look at Euler's equation:    .

The hard part is the first: the number e raised to a power with the product of the square root of minus one and pi. What is going on here?

Lakoff and Núñez argue that the expression makes sense if, but only if, we understand that mathematics consists of the metaphorical extension of familiar notions into unfamiliar areas.

First, it is straightforward to think of multiplying the number 2 with itself three times: two times two times two. The answer is eight.

The next step is to imagine multiplying two with itself some fractional amount, such as two and a half times. This is hard, since ordinary multiplication can only operate as an integral whole. However, we do know that two times two is four, and that two times two times two is eight. So if we were able to multiple two with itself 2.5 times, the result would be somewhere between four and eight. (It is approximately 5.66.) Some centuries ago, mathematicians figured out how to calculate such results. The procedures are not the same as those you follow to multiply two times two, but the idea is consistent with doing that.

It is easy to imagine multiplying a fractional number with itself: for example, 2.5 times 2.5, which yields 6.25. (Of course to understand 2.5, we need to understand fractions. Perhaps the base for that understanding comes from crawling part way to the cookie jar as a baby.)

The next step is a combination of the previous two: multiplying a fractional number with itself a fractional number of times. (Two and a half multiplied by itself two and a half times is a bit more than 9.88.)

The number e is a bit more than 2.71818. It is the number you find when you figure out a value that depends on its previous values. For example, air pressure on the surface of the earth depends on the air above the surface. That bit of air above the surface has a pressure, too, which depends on the air above it. The numbers of plants or animals in an ecology depend on the same number, with the additional constraints that the ecosystem can provide only so much food, and others will infect or eat them.

Both e and pi are fractions. You can multiply e by itself pi times — e raised to the pi power. The result is a little more than 23.14.

The square root of minus one is not a regular number like 2 or 3.15159; you cannot place it somewhere on the ancient `number line'; you cannot crawl to it going forewards or backwards. That is why, historically, it was called `imaginary'. It does not fit the ancient way of thinking about numbers. However, i does perfectly well when we think of it as a `lateral' number, as Gauss suggested. If you are crawling or walking up the ancient number line, you need to turn. Perhaps it is even better to think of i as suggesting a quarter turn.

pi, you will remember, is the ratio of the circumference of a circle to its diameter; this is another way of saying that it is the ratio of the circumference of a circle to twice its radius, since a radius is one half a diameter.

A rotation is a complete turn. By a consistent metaphor, you can think of this a crawling or walking around a circle. This means moving a distance that is twice times pi times the radius. If the radius is one, then a complete turn means going twice pi.

The distance for a half turn is one pi.

The number i is an indicator of a rotation, along a radius of one unit.

Originally, we insisted that e multiplied by itself some number of times be a result on the ancient, straight number line. But we can also talk about a situation in which we turn. Metaphorically, e can be extended to this notion, and extended consistently.

This is how i fits. It tells us to go out a unit and then crawl or walk around the circle for which that unit is the radius. The distance we are going to travel is pi.

And where do we end up? This is the beauty of the equation. We end up at the location of minus one on the ancient `number line'. When we add one to that number, the result is zero.

The key to understanding — not the key to mathematical proof, which is different — is that mathematics comes from consistently extending fundamental experience, such as crawling. Each extension is consistent with what went before, but a little different.

Mathematics provides one way to persuade others; it succeeds because others duplicate your reasoning; it fails when others do not understand the metaphors you use.

Mathematics is difficult because most people do not see the metaphors that give meaning. So all they learn is proof, which is boring when meaningless.

[ Brad DeLong inspired me to this notion by quoting Pierce. ]

What is Science?

Fundamentally, science is a form of transcultural communication. It is a way of persuading someone that one judgement is more suggestive than another. Mathematics provides one method of communication; similar observation another; and experiment a third.

Instead of trying to persuade another by appealing to common cultural understandings, or by appealing to a widely accepted authority, a scientific communication strives to generate an internal experience of some sort within the listener.

This is strong, since an internal experience is undeniable.

The advantage of science as a method of persuasion is that it is robust. If you have a good reputation, many will simply accept your assertion because of your authority. Indeed, adults almost always depend on others when forming their opinions. Others may not trust you, but are open minded; they will follow your reasoning, or duplicate your observation, or repeat your experiment.

Modern physicists are often open minded. As one correspondent said,

But sometimes the other person thinks you are wrong and will not listen. The other person may be an enemy. Communications fail.

An enemy will never accept your authority. He or she will not accept your world view. Nothing that you can say will come across. Your enemy has various reasons to think you are wrong and will not change.

Such people are unreachable, whether with scientific or non-scientific forms of communication. But their students are different. Students and other young people often `cause trouble' — they may not listen to their `betters'. They are the ones you may reach. (This is not invariable. Some cultures are so strong that very few within them change. But it is a tendency.)

One of your enemy's students may well think though the same problems as you, or make similar observations, or, most effectively for your attempt at changing minds, conduct experiments that confirm your results.

A student tends to follow his or her teacher, but if you come up with a good way to reason, a good set of observations, or a good set of experiments which student can replicate or which people the student respects can replicate, then the student may come to believe you.

Because scientific communication enables one person to recreate another's experience, it is the best form of transcultural communication yet known.

Let me be more specific: for robust communications, scientists use three method to generate internal experience in another listener.

Either

• the listener replicates the reasoning, as in a mathematical proof; or,

• the listener replicates the observations, as in astronomy or old-fashioned biology, and also reasons that there are no better alternative interpretations of the observations; or

• the listener replicates the experiment.

As I said, this method of communication fails when directed towards someone who will not listen, reason, or experiment. But in most societies, some will listen.

We can list the various ways of learning. The two most common are:

• I know culturally. For many people, this is the background of all their beliefs.

• I hear. This is the dominant mode for establishing new a belief, since it means going by authority. It includes hearsay. (Knowing culturally comes from the same mode, but people are so young when they learn culturally that they think of it as different from accepting authorities as a grown up.)

Neither of the two common methods succeed well across cultures.

The scientific ways of inducing internal experience are three fold. It is vital that the person reasoning, observing, or doing follow in your footsteps. Only by doing this can anyone be sure of replicating another's experience, and thereby checking it.

• I know from internal experience.
  Mathematical beliefs come from this, because people reason. At the same time, internal experience includes dreams, visions, and personal revelation. Many religious beliefs are confirmed by revelation. Mathematics is transcultural because people from different cultures follow the same process of reasoning and come to the same conclusions. But people from different cultures who each have revelations often interpret them differently.

• I observe.
  This includes astronomical observations. Remember, the key is that the person himself or herself makes the observations, and understands how they are made. Otherwise, the `observation' is simply a report by another: another case of I hear.

• I do.
  This includes experiment. Again, one key is that the person do the experiment, and not let another do it.

As a practical matter, most people accept new beliefs because they come from a trusted authority. Few have the resources or the time to reason, observe, or experiment. For most people, existing knowledge and technology are simply another gift of their culture. Knowledge and technology are accepted, like other beliefs.

Guttman Scales and the Structures of Social Life

This is the mathematical background to Alan Page Fiske's book ¹¹ Structures of Social Life.

Fiske argues that all social life is composed of patterns of interaction that are based on four types of scale: categorical, ordinal, interval, and ratio. The scales provide ways of perceiving, and thereby of organizing social interaction.

The four scales are not mere manifestations of a single culture, but are different primary mathematical structures. They are different axiomatically. They are transcultural.

In 1944, Louis Guttman pointed out that all forms of measurement belong to one of four types of scale: categorical, ordinal, interval, and ratio. (Actually, forms of measurement can belong to more than four, but people conflate them into these four.)

Just as Fiske's four patterns of social life are based on four types of mathematical structure, Guttman's forms of measurement are also based on different primary mathematical structures: equivalence relation, linear ordering, ordered Abelian group, and Archimedean ordered field. Indeed, Guttman's scales and Fiske's patterns are both based on the same four primary mathematical structures.

It is easy to understand Guttman scales:

You can say this stone weights twice as much as that stone, which indicates a ratio scale, but you cannot meaningfully say that one Fahrenheit temperature is twice another. That is because the Fahrenheit scale has an arbitrary zero; it is what is called an `interval scale'. But you can add ten Fahrenheit degrees to a Fahrenheit temperature.

Similarly, you can say that a captain in the Army is superior to a lieutenant but you cannot say by how much he is superior (and indeed, the `how-muchness' is irrelevant). Military ranking is `ordinal'; soldiers follow orders.

Finally, you can say that one animal is a cat and another one is a dog. A cat is in a different category than a dog.

Much progress in science comes from changing the type of scale used in a measurement. For many centuries, people said `it is cold outside', in which cold is a category distinct from hot. Then people said `it is colder today than yesterday'. This is an ordinary category. After the invention of the thermometer, it because possible to say say `it is 10 Fahrenheit degrees colder today than yesterday', making use of an interval scale. Finally, after Kelvin and Boltzmann brought us understanding, an engineer could say `the thermal energy content of this piece of iron is 0.6% less than it was yesterday', making use of a ratio scale.

As for truth: if you are using a categorical scale, you may say that a proposition belongs to the category of truthful propositions or the category of false propositions. If you use such a scale, you are not saying how much truth there is in a proposition, only that it is true, not false. Traditional logic is based on there being only two categories, true and false; it makes the mathematics simpler. The various fuzzy logics are a formal attempt to add interval or ratio scales to logic.

You can say that this first proposition is more credible than that second proposition, and that second proposition is more credible than a third. This is an ordinal scaling. In a court case, a jury may have to judge whether one person's testimony is more credible than another's, which meaning using an ordinal scale, so as eventually to place the defendant in one of the categories of `guilty' or `not guilty'.

A `prioritizing' grid is a way to order a list of items. Compare two items each and choose the one you prefer. The item you preferred over all the others has the highest rank, and so on.

Prices provide numbers that can be used in a ratio scale. In so far as prices contain all the information necessary for choice, people choose items with a lower price. But when a price fails to contain all the salient information, other factors are added — perhaps you are bothered by the pollution or the rate of discount that a low price requires.

As I said, traditional logic presumes a statement is either true or false. The metaphor for this kind of logic comes from your early experience with a cup. Either your proposition is contained, like milk in a cup, and is true, or it is outside, spilled, and is false. The categories are inside, true, or outside, false. There is no third option.

An ordinal scale is like a hierarchy of naval ranks; a captain has a higher rank than an ensign. When humans use McAllister's certainty factors they impose an ordering: they say that some propositions are more suggestive than others.

With an interval scale, you can say that three apples are more than two. But you cannot compare apples to oranges with an interval scale. For that you need a ratio scale.

For millenia, apples and oranges have been compared by price: some form of money is used as a `numeraire'. This has been customary and commonplace. `Rates of interest' enable people to compare money flows over time.

But price is only one criterion that people employ to make judgments. Sometimes they use taste. Sometimes beauty. Sometimes goodness.

In computer programs, numbers may be used to indicate the quality of the evidence for a proposition. Even though the numbers appear to suggest a familiar ratio scale, as used in measuring weight or density, the computer program often limits operations on the numbers to a more restrictive set of axioms than that used by rational numbers.

Here is a table of Guttman's scales and Fiske's patterns:

                     Scales of Measurement
                     ====================

  Scale       Basic Empirical    Permissible Statistics    Examples
                Operations         (invariantive)

              Name of mathematical
                structure
--------------------------------------------------------------------------

Categorical   Determination of   Number of cases      Assign model numbers
(or Nominal)     equality        Mode                 Specify species of
                                 Contingency             animal
              Equivalence           correlations
                 relation


Ordinal       Determination of   Median               Hardness of minerals
                 greater or less Percentile           Quality of leather,
                                 Order correlation       lumber, wool
              Linear ordering      (type O)           Pleasantness of odor


Interval      Determination of   Mean                 Temperature
                 equality of     Standard deviation      (Fahrenheit and
                 intervals or    Order correlation        Celsius)
                 differences        (type I)          Calendar dates
                                 Product-moment
              Ordered Abelian       correlation
                 group


Ratio         Determination of   Geometric mean       Length, weight, density,
                 equality of     Coefficient of          resistance
                 ratios             variation         Loudness scale (sones)
              Archimedean         Decibel
                 ordered field       transformations

From:

Mathematics, Measurement, and Psychophysics, by S. S. Stevens,
in Handbook of Experimental Psychology,
S. S. Stevens, Ed.,
1951, Wiley, New York

See also:

A Basis for Scaling Qualitative Data,
by Louis Guttman,
1944, American Sociological Review 9:139-150

Introduction to Logic,
by Patrick Suppes,
1957, Van Nostrand, , New York

Measurement and Man,
by S. S. Stevens,
1958, Science 127:383-389

Measurement: the Theory of Numerical Assignments,
by Louis Narens and R. Duncan Luce,
1986, Psychological Bulletin, Vol. 99 No. 2, p. 166-180

Structures of Social Life: The Four Elementary Forms of Human Relations,
Alan Page Fiske, 1991,
Free Press,
ISBN 0029103452

Groups and Rings

Certainty Factors

A certainty factor expresses how accurate, truthful, or reliable you judge a statement. It is your judgement of the evidence.

People have always made judgements. Nowadays, people use computers to help them. Many current computer programs enable people to analyze probabilities and `what if' situations more readily. `Certainty factors' go a step further; they enable computers to combine degrees of certainty to gain more confidence, but never to become completely sure.

Traditional logic is binary: either a proposition is true or it is false, either black or white. However, we live in a world of gray — or of even more colors. The advantage of binary logic is that it is relatively simple. The disadvantage is that it sometimes fails to match reality. (Students have trouble with traditional logic, but nonetheless it is simpler than more modern logics.)

Currently, computers use traditional logic internally. However, some computer programs, especially financial programs, try to model a more complex environment than one in which some facts are known to be true and others are known to be false. All financial programs, for example, handle interest rates, which are a way of combining a preference for the present with uncertainly about the future.

I am confident that over the next generation, we will see more computer programs come to rely on logics that are gray. There are two parts to such an action: one is the sensing part, which assigns a value to whatever is perceived. The second part is the method of combining multiple values.

`Certainty factors' provide a way to combine several sensed values.

In the mid 1980s, David McAllister developed a metric for `certainty factors' for use in an `expert system' (a type of computer program).

A certainty factor is used to express how accurate, truthful, or reliable you judge a predicate to be. It is your judgement of how good your evidence is. The issue is how to combine various judgements.

Note that a certainty factor is neither a probability nor a truth value.

Consider the expression `George is suffering from hypoxia'.

Based on warnings given to pilots, we would speak of there being `strongly suggestive evidence' that George is suffering from hypoxia when he is flying in an unpressurized airplane at 4,000 meters (13,000 feet) and his judgement, memory, alertness, and coordination are off.

Note, we are not saying "there is an eighty percent chance that George suffers hypoxia"; that is a probability estimate. We are talking about our judgement of certainty. You may be able to generate statements of probability, such as: "80% of US Air Force student pilots will fail to maintain altitude within 100 feet when they fly higher than ... meters without supplementary oxygen, and this will indicate they suffer from hypoxia." But this is a different sort of statement than one involving certainty factors.

In this example of uncertainty I am taking the information that I was taught as a student pilot and creating from that a mechanism for diagnosing hypoxia. I don't know the probability that a person of my health and age will suffer hypoxia at 4,000 meters but I do know the symptoms, which, however, may be weak, or have other causes.

In McAllister's scheme, a certainty factor is a number from 0.0 to 1.0. A phrase such as `suggestive evidence' is given a number such as 0.6; `strongly suggestive evidence' is given a number such as 0.8. The person making the judgement uses the scale more or less as an ordinal scale in which one item trumps another. The numbers are used in a metric to permit a computer to make calculations.

McAllister's rules for combining certainty factors are such that you can add new evidence to existing evidence. If the evidence is positive, this increases your certainty, as you would expect. But you never become 100% certain.

Continuing our hypoxia example: George tells us that he feels wonderful. This is `suggestive evidence' that George suffers from hypoxia. (Pilots are warned of this: "if you feel euphoric, consider hypoxia: you may be flying too high without oxygen, or suffering carbon monoxide poisoning from a broken heater." Of course, there are many good reasons to become euphoric when you fly; hypoxia is insidiously dangerous.)

McAllister defined the rule for adding two positive certainty factors like this:

    CFcombine (CFa CFb) = CFa + CFb(1 - Cfa)

I.e., reduce the influence of the second certainty factor by the remaining uncertainty of the first, and add the result to the certainty of the first.

In our example, the altitude and loss of judgment are strongly suggestive evidence, with a certainty factor of 0.8; and euphoria is suggestive evidence, with a certainty factor of 0.6. The combined certainty factor is:

                .92     =  .6 + .8(1 - .6)

(Incidentally, it does not matter which factor you start with first:

       .8 + .6(1 - .8)  =  .6 + .8(1 - .6)  = .92

Both sequences produce the same result.)

McAllister also has rules for adding two negative certainties, and for adding a positive and a negative certainty. A negative certainty is the degree to which you are certain a case is not so.

The rule for adding two negative certainties is simple: Treat the two factors as positive and negate the result

    CFcombine (CFe CFf) = -(CFcombine (-CFe -CFf))

The rule for adding positive and negative certainty factors is more complex:

    CFcombine (CFg CFh) =  (CFg + CFh) / (1 - min{|CFg|, |CFn|})

Thus, if your certainty for an instance is 0.88 and your certainty factor against it is 0.90, the result is:

               -.17     = (.88 - -.90) / (1 - min(.88, .90))

                        =   -.02 / .12

I.e. take the difference, and then multiply that value by the reciprocal of one less the smallest remaining uncertainty.

These three rules provide an interval scale for certainty factors.

You will note that you cannot say that a certainty factor of 0.8 is twice the certainty of 0.4; the rules of this metric only involve those of addition and subtraction that I have shown, no others.

An Exercise Using Certainty Factors

As I said earlier, a certainty factor expresses how accurate, truthful, or reliable you judge a statement. It is your judgement of the evidence.

It goes without saying that people have been making judgements from the beginning. The key to McAllister's certainty factor formulation is that it enables a computer to calculate a combination of certainty factors.

Certainty factors are a hybrid: for humans, they are an ordinal scale in which people specify an uncertainty that is more or less suggestive; for computers, they make up an interval scale consisting of numbers such as 0.6 and 0.4; and for calculation, they provide a ratio scale.

In McAllister's methodology, people express their judgements with phrases such as `suggestive', `strongly suggestive', or `weakly suggestive' and computers use numbers.

When a mechanical sensing element operates, a human programmer attributes different certainty factors to different measurements. Thus, you can imagine a sensor that detects just a little carbon monoxide in a cockpit's air: the output would be labeled as `slightly suggestive'.

Here is an example of certainty factors that is both topical and controversial. (One reason I picked this exercise that there are differences among people in how they judge one statement or another.)

First, I express the certainty factors for several statements; then, I pull them together in a computer calculated combination. Also, I briefly mention probability analysis, which I think is better for some questions. Finally, I will contend that the notion is especially suited to floor vacuuming robots, and the like, and there is where we will see the most use of the concept.

Several Certainty Factors

In the past, the following statement was highly controversial but it is now, I think, only mildly controversial.

In decades past, left-leaning liberals and Democrats considered the statement truthful. They told me that US policy was a failure and that the failure would come to haunt the country.

However, others told me that they thought the policy helped the US. They favored support for the Saudi government. However, I think that by January 2002, the United States government as a whole, including members of the Bush Administration, came to hold the same view as many Liberals and Democrats did in the past.

My judgement of the accuracy and truth of the statement is that it is `strongly suggestive'.

And as for whether the United States government as a whole believed the statement in January 2002: I think that, too, is `strongly suggestive'.

Here is a controversial statement:

One person told me that a single generation is too few, that a change would take many generations. Others have suggested that a change could come in less than a month, most likely from the election of a different President in the US.

In my judgement, the statement is `suggestive'. The vast majority of people around the world may well change their opinions quickly. But too few will act to stop those who have dedicated their lives to recreating a Caliphate by, among other actions, defeating the US.

However, I think this statement is better analyzed using probabilities rather than certainty factors. It is an assertion about the future. Further on I talk more about probabilities.

Here is another statement:

Initially I thought there was little controversy about the preceding statement, but I discovered that some thought that US spying was going well.

In my judgement, the validity of the statement is `suggestive'.

Now, a different statement, not about US spying itself, but about what the US government thought in January 2002:

In my judgement, the reliability of the claim is `suggestive'.

I think the truth of this statement is `strongly suggestive'. Also, I think the US government believes this equally.

This is quite different from the statement that

Some people think this is `strongly suggestive'. They combine this with a statement that they think is `suggestive', namely that

On the contrary, I think there is `suggestive' certainty for the opposite of this latter statement, that Americans cannot be so persuaded. So I figure the first statement is irrelevant.

Probability Analysis

Earlier, I pointed out an assertion about the future, and said that I think it is better analyzed using probabilities:

This is an assertion for which probability analysis is a better tool than certainty factor analysis. The judgement is not so much about the accuracy, truth, or reliability of existing evidence, but about the likelihood and magnitude of something happening in the future.

Here are two more assertions to illustrate probability analysis and its political consequences.

How likely and how important is the chance or probability:

How likely and how important is the chance or probability:

US conservatives tell me they worry about the former: they claim that in November 2003 the US made a deal with Iranian theocrats to gain peace in the short run by favoring certain Shi'ite groups in Iraq. (This claim requires a certainty factor judgement; I think the evidence it occurred is `highly suggestive'. At that time, Shi'ite military groups did not engage in guerilla warfare against the US. In addition, I think there is `suggestive' evidence that the US government began to renege on this agreement in the early part of 2004. Grand Ayatollah Ali al-Sistani asked that the US stage elections before creating institutions to protect Shi'ite enemies from the Shi'ites.)

The conservatives fear that an agreement between the US and Iranian theocrats, if kept by both sides, will mean that the US will not be able to create institutions to protect the losers in a war from the vengeance of the winners, and that as a consequence, there will be no fundamental change and the US will be in danger over the long run.

US liberals and privacy advocates worry about the latter; they fear that merged databases will make it easy for crooks to bribe, blackmail, or bamboozle police or other government officials. They fear that crooks will use such information to rob or otherwise hurt individuals or companies. And they fear that crooked people in government will misuse their positions.

Three More Certainty Factors

Here are three more statements. I do not think any are particularly controversial:

A few people from Moslem countries wish to weaken the US.

Advances in technology have enabled the militarily weak to kill many people at lower direct cost than in the past.

In my opinion, the evidence for the first is `suggestive' and for the second and third statements is `strongly suggestive'.

(The last statement comes from the observation that the attacks of 11 September 2001 directly cost Al Qaeda less than $500,000.00 and the lives 19 operatives. This was less expensive directly to the attacker than the cost of an attack causing the same damage in World War II.)

Combining Certainty Factors

The key to David McAllister's method is that certainty factors can be expressed as numbers and combined by computer.

Here is a table of the relations:

As a reminder, here again are the rules for combining certainty factors:

To add two positive certainty factors, add one to the second, the second having been reduced by an amount that depends on the size of the first:

    CFcombine (CFa CFb) = CFa + CFb(1 - Cfa)

To add two negative certainties, combine the two factors as if they were positive and negate the result:

    CFcombine (CFc CFd) = -(CFcombine (-CFc -CFd))

To add positive and negative certainty factors, sum the two and divide the result with one less than the minimum of the absolute values of the factors:

    CFcombine (CFe CFf) =  (CFe + CFf) / (1 - min{|CFe|, |CFn|})

Let us combine statements. I am going to express them according to how I think the US government thought in January 2002:

`strongly suggestive' = 0.8

(As I said earlier, I think this statement is better analysed as a probability; but suppose someone thinks of it as a current judgement.)

`suggestive' = 0.6

    CFcombine (CFa CFb) = CFa + CFb(1 - Cfa)

                        = 0.8 + 0.6(1 - 0.8)

                        = 0.92

The combination tells us that I think it is highly certain that the US government thinks that previous US policy failed and that it will take a long time to make it a success for the US.

Now let us add four certainty factors. We do this two by two. Note that we can make the calculation in any order; the result comes out the same:

`suggestive' = 0.6

4. The US government believes that its covert anti-terrorist actions are incompetent.

`suggestive' = 0.6

5. A few people from Moslem countries wish to weaken the US.

`strongly suggestive' = 0.8

6. Advances in technology have enabled the militarily weak to kill many people at lower direct cost than in the past.

`strongly suggestive' = 0.8

I did the calculations using Emacs Lisp. Here I combine statements 3 and 4, statements 5 and 6, and their results:

    (+ 0.6 (* 0.6 (- 1 0.6)))
        which is 0.84

    (+ 0.8 (* 0.8 (- 1 0.8)))
        which is 0.96

    (+ 0.84 (* 0.96 (- 1 0.84)))
        which is 0.9936

Just to show that the order in which you combine these factors is irrelevant, I combine statements 3 and 5, statements 4 and 6, and their results:

    (+ 0.6 (* 0.8 (- 1 0.6)))
        which is 0.92

    (+ 0.6 (* 0.8 (- 1 0.6))) 0.92
        which is 0.92

    (+ 0.92 (* 0.92 (- 1 0.92)))
        which is 0.9936

This suggests that as of January 2002, US government strongly believed that:

You probably came to a conclusion without needing the mathematics. The exercise is simple. But computers, which use these calculations, are more stupid about judgements than people.

A Floor Vacuuming Robot:
  machine-made observations combined with human evaluation

Over time, more observations will be made by a machine. The observations can be classified into statements with associated certainty factors. The statements will not be about politics. More likely they will be like this:

    Combine the first two certainty factors:
      (+ 0.8 (* 0.4 (- 1 0.8)))
        which is 0.88

    Combine that result with the third:
      (+ 0.88 (* 0.5 (- 1 0.88)))
        which is 0.94

A floor vacuuming robot could use sensors that are programmed to translate noisy and poor quality observations into statements such as `looks elliptical with weakly suggestive reliability', and then combine several such statements into results on which it can act.

In this case, the programming would lead the robot to decide (with a strong certainty factor of 0.94) that the object it detected is an old silver coin that should be picked up rather than vacuumed up.

Yes, you could program the robot to make the same decisions using fuzzy logic and probabilities. My contention is that for this kind of action, humans will consider certainty factors more understandable than probabilities. It will be easier for humans to figure out what the robot will do.

An expert will not need the `crutch' of certainty factors; the expert will understand fuzzy logic and probabilities. But the expert is not the key here. From the point of view of a company selling a floor vacuuming robot, most sales will be to the majority who purchase robots without bothering to check how many coins they vacuum.

The key is to persuade the latter, the majority of buyers, that the purchase will be safe and do its job. The people who persuade the majority will be a late portion of `early adopters'. These people will not be experts. They will not harm their own cause by causing others to think `it is good for them, but not for me'. Instead, if the task is not too time consuming, and fairly comprehensible, these `early adopters' will investigate how the robot works, either by putting coins and the robot in the same room, or by reading the robot's rule set, or both. In this circumstance, certainty factors make for a simpler rule set than fuzzy logic or probability.

This is how an `early adopter' will convince himself that the robot is not too stupid, and rather than vacuum the floor himself, he will let the robot do it. And his example will persuade others.

The Nature of Self-Replicating Systems

Von Neumann Machines

In the late 1940s, John von Neumann first suggested a modern, robotic self-replicator. Moreover, he calculated how much information a self-reproducing entity would require. This meant figuring out what parts a machine needs if it is to reproduce. He estimated that the minimal size of a self-replicator's `blueprints' or `genome' is 25 – 150 kilobytes.

By extending von Neumann's notion metaphorically, we can think more readily about societies, economies, ecologies, and the origins of life.

Economies, for example, reproduce themselves; in that sense, they are von Neumann machines. But people work in economies; economies do not reproduce without human help.

As yet, no one has built a von Neumann machine. Right now, you could build a device that assembles different kinds of large, identical components or `modules' into duplicates of itself. Perhaps some factories that use robots to make robots already do this. Unfortunately, the modules themselves must be manufactured in some other way. I do not know whether they can yet be manufactured purely by self-directed robots. In any event, current investors, whether government or private, would have to spend a huge sum to build the first instance of such a manufacturing system.

We humans are entities that consume `modules' that are not identical — some foods taste differently than others. Reproduction from large, non-identical, breakable `components' is difficult. That is what a von Neumann machine that works with `regular sized' components will have to do. For example, it will mine ore that is an ill-defined mixture.

Very small, `nano-sized' von Neumann machines are as yet impossible to build. If built, these as-yet imaginary, `nanotech self-assemblers' would put together atoms. These are small, identical, unbreakable components. Molecules are not identical because the atoms of the same kind that make them up may have different weights. For example, carbon atoms comes in two different stable weights. Not counting the different weights of oxygen, the carbon dioxide that plants inhale comes in four different weights. Plants prefer the lighter carbon. However, small molecules are often similar, or similar enough, and are made from unbreakable atoms, so they are important. Large molecules may not only weight differently, but fold differently.

Although we cannot yet construct them, we do know that `nano von Neumann machines' exist: we call them `bacteria'.

The first human-made `nanotech self-assembler' may be `soft' and work in water, like a bacterium, or may be `hard' and involve diamond, as in Eric Drexler's 1986 book ¹ Engines of Creation.

For any kind of von Neumann machine, a basic question is how much can the system reproduce? Can it reproduce itself entirely, or only partly? The fraction is the system's `closure'. A closed system reproduces all it parts. An open system fails to fabricate some of itself. For an open system to continue, some parts must be imported from outside. A farm or factory need not be fully self-reliant but can be partly open. On the other hand, a complete natural ecology can only be closed.

According to a 1980 NASA study, simple, contemporary bacteria have a complexity of about 10 million bits. The NASA study proposed a device to operate on the moon. In that environment, the lunar von Neumann machine might require 10 – 150 gigabytes of `genome' and even then it might not be fully self-replicating; it might lack `parts closure'.

Since humans must build the first von Neumann machine, efficiency and cost are issues. It is no good building a von Neumann machine that makes worse use of your land than existing farms and factories. And you cannot build one you cannot afford.

Aspects of a von Neumann machine

Like any living entity, a von Neumann machine must eat, which means it must gather energy and other inputs.

In order to eat and live, a von Neumann machine must be able distinguish useful inputs from poisons; it must be able to see (or smell, taste, feel, or hear) potential food.

This means the machine not only needs appropriate sensors, but the ability to understand and act upon the information. It needs eyes, a brain, and hands.

In a small, `nano' von Neumann machine, thermal motion brings atoms and molecules to a site. Most often, only the appropriate atom or molecule settles in the site. Most others do not fit. (The others that do fit create variations.)

Unless you think of the process of `fitting' as a combination of sensing, analysis, and action, you will not consider these entities as having `eyes', `brain', or `hand' at all. However, the process is similar, but more condensed: input that fits is both identified (perhaps wrongly) and accepted by that action.

The inputs, whether energy or material, must be transformed to enable the original von Neumann machine to continue and to enable that machine to reproduce.

In order to continue, the machine must be able not only to provide itself with enough food — enough energy and materials, it must also be able to ward off illness — to defend itself, and to heal itself — to repair itself.

Moreover, the machine must be able to dump materials and energy it no longer uses. It must be able to excrete. Some of this excreta will be useless to us. It will be `pollution'. We will want other excreta, manufactured `goods'. This will be what we humans say the machine `produces'.

All in all, a von Neumann machine has a minimum of nine different aspects:

• Energy and material inputs, or `food',

• sensors, or `eyes, ears, and nose',

• processors, or `brains',

• effectors, or `arms', of various types. These are hands that gather materials, perhaps by mining, or are solar collectors that transform light into electricity. Effectors manufacture new systems, repair old systems, defend the machine and its parts, and move materials and energy that is no longer needed out of the machine, as excreta (some of which may be what human harvest).

• Effectors need to make use of internal transport and communications, a `circulatory system'. Although in some ways, an internal transport and communications system consists simply of different kinds of effectors, people tend to categorize transport and communications differently.

• Similarly manufacturing, or `metabolism', takes place because of effectors, but people think of a `metabolism' as different. This includes the `metabolism' or manufacturing needed to reproduce.

• In order to maintain oneself, or reproduce descendants, `blueprints' or a `genome', design data must be kept.

• The border may simply be the line dividing the machine from the rest of the universe, a concept, or it may be a `skin' with barriers or other effectors that serve as defense.

• Finally, a machine produces outputs, including waste heat, and materials. Humans will dislike some outputs, the `pollutants', and will like others, the `economic goods'.

A von Neumann machine can reproduce exactly or with errors. Even though errors are common, it is possible to reduce the end number through appropriate `error correction' techniques.

Natural selection requires that descendants show variation, either as the result of sex or reduplication errors. When reproduction is accompanied by error or variation, the set of re-duplicated descendants includes a mix of entities. Of that mix , a few will more tightly reproduce the design of the original manufacturer and others will more loosely reproduce that design.

Those descendants that do better in the circumstances in which they find themselves — which may be different from the original circumstances — will be more likely to reproduce themselves into another generation, and thus, probabilistically speaking, be more likely to pass on their design data to their descendants.

On the one hand, the `error' or `variation' aspect of reproduction is important, since it means that different circumstances are met by von Neumann machines with different capabilities. For natural selection to succeed, new instances with different capabilities must appear.

On the other hand, the amount of `error' or `variation' cannot be too great, since circumstances seldom change dramatically and if the `error' or `variation' is too great, too few of the different entities will reproduce. Hence, internal error correction mechanisms must operate.

Humans may not want machines with new capabilities. Hence humans may well design machines with very strong internal error correction mechanisms. In addition, humans are not likely to introduce auto-variation mechanisms or sex, and they are likely to produce tests to make sure that newly produced machines are similar to older ones.

But without humans around, you may end up with a mechanical ecology like that described in James P. Hogan's 1983 science fiction novel Code of the Lifemaker ².

Build with Unbreakable Components

In human societies, sacred postulates are also unbreakable. They may be replaced by others, but they cease to be sacred when shown to be false. That is why the better ones cannot be falsified, but only replaced.

Laws also are built from unbreakable components, like the admonition not to murder your neighbor. And like complex organisms, the nature of the unbreakable component may be come irrelevant as the body of law becomes more complex, which occurs when the question circles around the legal definition of `neighbor'. Is the person breaking into your house at night a neighbor or a thief? What rights and obligations do you have towards him?

The as-yet imaginary, human-made, extremely small self-replicators, the nanotechnological self-assemblers will work with atoms.

Although the first human-made, nano-sized self-assemblers may have a complexity no larger than a very early proto-bacterium, a complexity of 25 – 150 kilobytes, I expect them soon to become as complex as more recent bacteria, and perhaps more so.

Entities stop becoming more complex, stop becoming more prey to rot, only when the complexity or rot kills enough of them.

Darwin's Five Laws of Evolution

As Ernst Mayr pointed out ³, Darwin's notion has five parts, only one of which was accepted by all the evolutionists of his time: that part was the conclusion that the world is neither constant nor recently created, nor does it pass through cycles which repeat, but that it changes and that entities that live on it change, too.

Darwin's colleagues rejected various other components of his theory, either because they flew in the face of cultural beliefs, because of lack of conclusive evidence, or because of some combination of factors. However, in the time since Darwin first proposed his hypotheses, all five components have been proved in simulations, observations, and experiments.

Hence rather than call Darwin's ideas a theory or group of theories, it is better and more conventional to refer to them as natural laws. They are, after all, as well established as Newton's Laws, which we all know, are broken under certain circumstances, but which hold well enough.

Darwin's Five Laws are:

1. Evolution as such

   Evolution as such comes from the understanding that the world is not constant. It was not recently created; it is not cycling. The world changes. Moreover, the types of entities that live on it also change.

   A change in entities contradicts the `common sense' notion that different animals and plants each had its own `essence'. This notion has been prevalent in Western society since the ancient Greeks. Its implication was that one species could not change to another any more than a triangle could change to a square.

   You only had to look at a cat and a dog and ask how one could change into the other. Nowadays, we do not think of a cat changing into a dog, but ask about a common ancestor of both, from a time long before cats and dogs appeared.

2. Common descent

   Common descent is the understanding that every group of living entities that we know of on this planet descended from a common ancestor.

   Common descent occurs because one lineage would, willy-nilly, be a little more prolific than another, and would thereby wipe out the other. So only one survives.

   (Prions are an exception. These are proteins of a particular shape that catalyze other proteins to take on the same shape. Prions are not life in the usual sense of the word although they are self-replicating. Similarly, no one thinks of an economy as living in the usual sense of the word, even though an economy can reproduce it itself, too.)

   Rather than ask how a cat could change into a dog, we ask how a previous ancestor of both could give birth to an animal that is slightly more suited to the wolf way of making a living than to the feline profession. (Ecologists call plants' and animals' ways of surviving and reproducing in the world their `niches'. These are what we humans call our `professions'.)

   The answer is straightforward: one animal's blueprints vary from another. The word `blueprints' stands for the record that some people in the latter 19th century called `germ plasm', and that modern people call DNA. That error or variation enabled an adult who was born with that variation to live more like a wolf or modern dog than its parents or more like a cat.

   This understanding, by the way, answers the age-old question, `which came first, the chicken or the egg?' The egg came first, because it contains the part that changed. The egg was laid by a non- or pre-chicken entity; the egg grew up to be a chicken.

   The chicken comes first only when adults can change and can pass on that change to their children. This latter form of change is called Lamarckianism. Human culture is invented by grown people and passed on by parents to their children. It is Lamarckian. But the looks and actions of animals, at least those without culture of their own, are passed on genetically. A parent's action does not influence the looks and actions of the child. Only changes in the egg change the child.

   At the time Darwin wrote, many evolutionists still thought of animals and plants as being like humans. They asked whether an adult proto-giraffe could stretch its neck to reach higher leaves, and pass on a longer neck to its children, much as human parents pass on a language to their children.

3. Multiplication of species

   Multiplication of species is the understanding that species either split into or bud off other species. Because different ecological niches provide different ways for an animal or plant to live — provide different `professions' — and because blueprints do not copy perfectly, different plants and come to fill different niches, with different shapes and behaviors.

   Often multiplications occurs after some members of a founder species becomes isolated from the rest. Those of their descendants who are adapted to the new place are more likely to survive compared to those who are adapted to the old conditions.

4. Gradualism

   Gradualism is the understanding that changes take place through a gradual change of population rather than the sudden production of new individuals.

   `Gradual' is a relative word. In discussions of `punctuated equilibria', I have heard people talk of one species replacing another in the `blink of an eye'. What they meant was a time period that is many times as long as written human history. The `blink' might last 100,000 years. In human terms, this is a long time. But in geological terms, 100,000 years is short. Hence the use of the phrase. But to humans, a change over 100,000, or over merely 10,000 years, seems gradual.

   Put another way, gradualists claim that it is unlikely that starting tomorrow at 9 am, all humans born would possess green skins and lay large, hard shelled eggs.

5. Natural selection

   Natural selection is the understanding that individuals in every generation differ from one another, or, at least that some of them do. In every generation some individuals survive and reproduce better than others. Their genes multiply.

   This is the key idea: natural reproduction is not perfect.

   People make considerable efforts to ensure that human copies are perfect. Inexact copying indicates a failure of the scribe or bug in the program.

   In natural reproduction, children may be similar to their parent if they bud from that one parent and if no stray cosmic ray changes their DNA and no DNA enters their cell from another.

   More sophisticated plants and animals have two parents. These are species with sexual reproduction. In this circumstance, children come from mixtures of the two parents' genetic material. This mixing induces variation among the children.

   Some of those children will do better at one or other niche and consequently will be more likely to survive and propagate whatever enables it to survive and propagate better.

   The environment in which plants and animals reproduce is defined by the world around each plant or animal: and part of that world consists of other entities of the same type. Put another way, plants and animals must survive and reproduce in a world with others of their own type. The others will be the same species, with similar skills and talents.

   This means that selection occurs within a species even when the rest of the environment does not change. (Incidentally, when characteristics like perceived health influence sexual choice, the process is called `sexual selection'.)

   Increased intelligence sometimes increases survival and reproduction. David Brin suggested this in 1982 ⁴. Doubtless, others enjoyed the same insight earlier.

   For example, a female peahen will have more healthy offspring (probabilistically speaking) if she is able to identify a peacock that is more healthy than its peers. This task requires more intelligence than not being able to make the identification.

   A side effect of this process is that some lineages should gain certain features, such as intelligence, even without changes in the non-lineage part of the environment. Not all lineages will gain these, since alternative ways to survive and reproduce also exist. But some lineages will.

   This means that if the dinosaurs had survived, we humans might not exist. Instead dinosaur-descended beings might exist in our stead and these beings might also communicate symbolically, as we humans do in language.

   Interestingly, Ernst Mayr ⁵, among others, does not accept this line of reasoning, and therefore argues that high level intelligence is a happenstance rather than an outcome that may well occur on any living world on which complex life survives for long enough.

   Well, to be more precise, I think Mayr does accept this reasoning, but in his writing he focuses primarily on a different argument, that involving `purpose'. Evolution lacks purpose, but many people think otherwise, either because humans act according to purposes, or because their beliefs suggest it.

   The requirement for lengthy survival poses barriers. As Peter Douglas Ward and Donald Brownlee point out ⁶, planets endure catastrophes that are frequent over the eons. A stable sun, like ours, grows brighter as it ages. The inward side of a solar system's `habitable zone' moves outwards. This makes a `runaway greenhouse' as on Venus more likely. If the planet starts out closer to the inward side of its habitable zone than earth, the planet may die before complex life has time to evolve.

   Or microbes may consume so much carbon dioxide and other `greenhouse' gases that rather than overheat, the planet may freeze. The freeze may kill every living being on it before volcanic eruptions increase the supply of greenhouse gases which warm the planet.

   Or major volcanic eruptions may poison the land and sea, or asteroids may strike. Or a science fiction theme may turn out to be true: an intelligent species builds von Neumann machines for war and at least one reproduces with an error that causes its descendants to attempt to kill all biological life, not just their makers' enemies.

   As a practical matter, complex life may be rare, even if simple life is common.

Differing Virtues

As Den Beste said, in any ecology, a period of non-competitive growth comes first. This period lasts so long as unfilled space remains. For plants and animals, `space' means niches, for businesses, it means markets. For humans it means empty land suitable for colonization. In this period, virtue is the deciding factor (virtue meaning `most fitted to the environment'). Those that do best expand the fastest.

But the deciding capability, the `limiting factor', changes when all niches are filled. Then, lack of faults becomes key. In a `full' ecology, or `saturated' market, a plant, animal, human society, or product will be able to reproduce only so long as it can survive competition with others of its own kind.

With competition from similar entities, the ecosystem becomes zero-sum.

Consider the initial human settlement of Europe, Asia, and the Americas. Prolific and peaceful humans range widely over an empty territory. They cooperate with each other. But when these people meet thugs, they will be killed, unless they learn to kill.

`Empty territory' means, of course, `empty' at the level of the ingressing humans' technological and pathological capabilities. Thus, in the 1500s, the Spanish conquered what is now called `Latin America'. The Spanish had steel and their soldiers knew about deceit and double-dealing. The first European settlers in Massachusetts, the Pilgrims, found that before they arrived in 1621, most of the indigenous people had died. The indigenous peoples had caught disease from the many Europeans who had visited the shores for fishing or from people who caught diseases indirectly from the distant Spanish. European settlers were accustomed to these diseases. Some of their children died; but other European children fell ill, recovered, and enjoyed immunity as adults.

Put simply, whether it be a plant, and animal, a human society, or a commercial product, an entity with a great virtue may do well so long at it does not have to compete with others of its own kind. But when it does compete, if its virtue has nothing to do with intra-species survival, it and its kind will die.

Societies as Von Neumann Machines

Although you can think of von Neumann machines as ecologies or species, human societies fit the criteria, too. On the one hand, this notion is straightforward and obvious; on the other hand, by thinking of societies as von Neumann machines, we can think differently about them than usual.

Let us go back to human beginnings: the earliest societies taught their children how to duplicate, more or less, what the elders did, both to support themselves physically, with food, clothing, and shelter, and culturally, with religion, law, and humor.

We can think of a society metaphorically as a ship with a crew, a `ship of state', or as an animal, such as a bear, or as an uncle. Likewise, we can think of a society as a complex, self-reproducing machine with sensors, blueprints, energy requirements, and effectors; or in more biological language, with eyes and ears, with a genome, with food requirements, and hands.

Moreover, we know that inexact duplication leads to evolution (or extinction). Humans pass on genes through sex; they pass on knowledge and culture through words and actions. Consequently, in a social von Neumann machine inheritance is both Darwinian and Lamarckian. `Memes' are important as well as `genes'.

Ancient societies took a long time to replicate: they reproduced themselves once per generation, with some parts taking longer, such as shelters. They added little from century to century. Mostly, people replaced what was worn out.

In the modern world, we do not think merely of reproducing a society, but of adding to it: of adding cultural and built goods to it, and of reducing its bads, such as pollution and injustice.

As of 2000, the fastest self-replicating social systems are economies that duplicate their economic output in seven years, a 10% per year growth rate. This sort of number is not exact: along with the goods that are measured to double in seven years come bads, which are often not measured.

A von Neumann machine consists of parts. These can be used to analyze the various parts of an economic and social system:

• The central processor, or `brain'

  In a economic or social system, the `brain' of a von Neumann machine consists of the people who make the decisions that influence the whole society, such as poets and engineers, a few generals, a few of the rich, and some politicians.

  In science fiction novels, writers have suggested societies in which computers make many or all the decisions.

• Sensors, or `eyes, ears, and nose'

  In society, sensor information, what you see, hear, smell, taste, and touch, is transformed into reports for others. In the past, reports were almost always anecdotal. They were stories. Sailors and spies told stories about their adventures abroad. People at home told of the conditions and situations with which they were familiar.

  Nowadays, some reports come as statistics about production and surveys of people. Collection and presentation can be, although it often is not, designed to reduce the dangers of bias and selection.

• Blueprints, or `genome'

  A society reproduces itself by reproducing its religion, ritual, law, methods of cultivating land, making shelter and clothes, by reproducing its knowledge, habits, and characteristics, as well as by reproducing its physical embodiment, whether people or houses.

  In the past, much information resided in ritual and tacit knowledge, or else in a mysterious biological inheritance. Nowadays, more is known and more is written explicitly.

• Internal transport and communications, the `circulatory system'

  Paths, roads, railroads, telephones, shipping lanes, and the Internet all make up the `circulatory system' of a modern country. In the past, roads were few and paths perilous. Only shipping was relatively inexpensive and then only over the past 10 millennia.

• Manufacturing, or `metabolism', ways of growing food, building, and making

  Each era has its own technology. 2000 years ago, drinking vessels were made of bronze. They were called `bronzes'. But as glass making become more widespread, people began to shift to drinking `glasses'.

  Over the past two centuries, manufacturing technology has changed and changed again. Now, many items cost less to produce. Most people like this increase in material wealth, even when it comes with new forms of injustice and new or more imposing pollution.

  (Often people in a government or ruling circle choose a method that is not so unpleasant for them, but is dreadful for ordinary people. People in a ruling circle, for example, may figure that they will always live in rooms with filtered air, and not care about the air pollution that sickens ordinary people.)

  Another side effect has to do with conceptions of justice. Not all, but a part of a feeling of justice comes from what people learned as children: the `right way' to act. With changes in technology, the `right way' can become the `wrong way'. Thus, in the past, many people lived in villages. In a village the way to ensure economic and social security is different from the way to ensure it in a city. The patterns of the one do not scale to that of the other.

• Borders, or `skin', the barriers against outsiders

  At the end of World War I, the victors created several new countries in Eastern Europe. One method — one that did not always succeed — was to draw a national border along a linguistic border. Differing languages do present a barrier, as do differing rituals and customs.

• Effectors, or `arms', which can build or make

  In the past, people used fire and wind and human and animal strength. Although fire was important to the non-human ecology, neither fire nor wind had as much impact on society or the economy as human and animal action to grow food and make clothing. And neither human nor animal action had much impact on the world.

  Now, modern technology provides for vastly different and more powerful effectors, like bulldozers. Already, humans move about as much earth each year as nature does with wind and water.

• Energy sources, or `food'

  Most past energy sources, such as grain for eating, hay for horses, or wood for burning, gained their energy through `low energy density' transformations. All had to be grown.

  Many modern `alternative energy sources' are similar: the sun's rays, wind, waves ... Only uranium fueled nuclear power plants and as yet unbuilt hydrogen or hydrogen-boron nuclear fusion plants are alternatives that make use of `high energy density' transformation.

  But mainstream contemporary energy sources, oil, natural gas, and coal, have `high energy densities'. (Their beginnings did not; but that is so long ago, few think of them.)

• `Pollution', or excreted material

  Human excreted material is not necessarily polluting. But it has to be handled with care, for without good sewer systems, people fall ill from infection.

  The materials excreted from the non-human part of our von Neumann machines are worse. No one has yet figured out how to make much use of the side effects of agriculture, of metal mining and refining, of logging, or of burning coal, gas, and oil. The only remedy seen so far is to figure out a different way of doing the job, or of not doing the job.

  In the old days, the side effects could be as bad as they are now. The ancient deforestation of the Mediterranean region was as bad as recent deforestation. But most side effects were too small to cause much trouble. The `bads' could go into the river and be diluted, or into the air. A smaller area was deforested. Nowadays, the amounts of bad are large.

In old times a society might survive without full `parts closure' — it could gain new ideas, new techniques, and new blood from a neighboring but different society. In the present, in so far as you think of the Earth as being made up of various von Neumann machines, each society enjoys even less `parts closure'. But if you think of the present Earth as one segmented, but entire von Neumann machine, we either enjoy complete `parts closure' or we are dying.

In so far as we are mining coal, oil, and natural gas, and not engaging in sustainable activities, we are dying. We are a von Neumann machine that cannot quite reproduce itself exactly, but which can reproduce itself well enough to carry on for a time.

The process of dying can go on for a long time. One generation can succeed another. I remember moving to a new house when I was young. On its land, my father found an old dump with car parts in it. He learned the story and told it to me: a previous owner had kept taking apart his car. Every time he did this, he also put it back together again. But each time, he found leftover parts. Those he threw in the dump. But the car kept running. Whatever he threw out was not really necessary. The car lasted a good long time. But, eventually, it stopped.

A Species is Not an Organism

Sometimes, I speak of a species as one organism. But it is not. A species is a collection of organisms that evolved according to Darwin's Five Laws.

Nonetheless, sometimes the `one organism' metaphor is useful. Just as an organism needs to eat and reproduce, so does a species.

Sadly, the metaphor may also be misleading. A friend of mine recently employed the metaphor to argue against human wars: just as one leg in a human should not fight the other, so one country should not fight another. According to the metaphor, humanity as a species was like a single organism.

However, under various circumstances, species' virtues are different from organisms'.

This is not to say that metaphors cannot be useful. They are. More to the point, we often understand and experience one kind of thing in terms of another.

More abstractly, George Lakoff and his collaborator, Rafael E. Núñez, ⁷ wrote in reference to mathematics that metaphors are a

The key is to separate the map from the territory: to understand that much of our understanding comes through metaphor, and that metaphor is useful, but also dangerous.

Just as it is useful to think of either a single human society or a group of human societies as a von Neumann machine, it is useful to think of an organism or a species the same way. It is easier to think more clearly about an imaginary self-replicating, robotic factory than to think of your own society or of your food supply.

When you imagine an ecology as consisting of many self-replicating, robotic factories ⁸, the mapping is straightforward. Each biological organism is equivalent to a self-replicating, robotic factory, or equivalent to two such factories that must cooperate to reproduce.

The correspondence is somewhat less straightforward when you imagine a complete species as a von Neumann machine. The correspondence becomes even more distant when you imagine a complete ecology, made up of many species, as one self-replicating, robotic factory.

But we can imagine:

For ecologies on the Earth, the primary source of energy is the sun, although a few organisms rely on chemical energy from volcanic vents in the ocean. Predators makes use of the secondary source of energy, which consists of those entities that have gained their energy from the sun or chemicals, directly, as in the case of herbivores, or indirectly, as in the case of carnivores. This sequence is an `energy chain'. (In most ecological texts, the `energy chain' is called the `food chain'.)

Likewise, we can note that an ecology contains its instructions or blueprints to reproduce itself in the genes of the various organisms that make up the ecology. The data store is distributed.

Does an ecology possess a central or distributed processing unit? This is a big question. People who speak of `Gaea' often presume it does. Certainly, ecologies respond to changes in their environment: for example, parts of it die when glaciers come. Clearly, a freeze, like the development of `Snowball Earth' before the Cambrian, kills many.

From an outside point of view, the response is not necessarily very intelligent. When the planet cools, fewer entities transform carbon in the air into molecules that eventually sink into the ocean. Since volcanos continually release carbon dioxide, the amount in the atmosphere increases. Eventually, the `greenhouse effect' leads to warmer times. (I don't know how much of the increase in carbon dioxide and other greenhouse gases comes from biological action or from the non-biological weathering cycle. Both go on at the same time. From a human point of view, these changes are slow, taking millions of years. Rapid climate change — taking mere decades — appears to come from non-biological events like the collapse of the North Atlantic thermohaline circulation.)

In any event, a biological response suggests that the processor within an ecology is at least as smart as that of a human thermostat: not very smart in human terms, but enough to do a job.

But, as I said, the metaphor (or model, if you prefer that term) must be used carefully. In a system with distributed data stores, those data stores that survive end up living longer than those that do not. (This sentence sounds like a tautology. Nonetheless, it contains the key insight of Darwin's Laws.) Consequently, the carriers of different data stores will fight each other when the resources are insufficient to support both. Those that do not fight, do not live so long. Their blueprints do not stay around, so they become more and more a minority.

On the other hand, when a new ecological niche opens up, regardless of reason, there is no need for carriers of different data stores to fight; indeed, they are all more likely to survive when they cooperate. So we should expect to see intra-species cooperation as well as intra-species hostility. The blueprints for cooperation will also continue.

The latter concept, intra-species cooperation, corresponds well with the `single organism' view of a species. But the former notion, intra-species hostility, does not.

Other

Quotations from
"Ecology, Meaning & Religion"
by Roy Rappaport

Here are a few quotations from Roy Rappaport's book, ¹³ Ecology, Meaning and Religion, along with notes of my own.

These excerpts come from notes I made in July and September 1980 — more than 20 years ago. I purchased the book in June of that year, and found it hard to read. It was full of long and convoluted sentences. Consequently, I felt I had no choice but to make excerpts and notes.

Text within double quotation marks should be an exact copy of what Rappaport wrote; text within single quotation mark is paraphrased.

Often I realize that Rappaport explained much when he wrote that `the unfalsifiable supported by the undeniable yields the unquestionable.'

Page references are to the 1979 paperback edition, ISBN 0-913028-54-1 ¹³.

Ecology, Meaning and Religion
Roy Rappaport

Rituals bring into being certain states of affairs. "When authorized persons declare peace in a proper manner, peace is declared whether or not the antagonists are persuaded" to comply. (p 189)

In addition, these states of affairs are judged according to criteria that are provided by rituals. If "a man is properly dubbed to a knighthood and then violates the code of chivalry, ... we do not say that the dubbing was faulty," but that the knight is faulty. The state of affairs created by a ritual is judged "by the degree to which it conforms to the stipulations of the ritual." (p 189)

A descriptive statement, on the contrary, is "assessed by the degree to which it conforms to the state of affairs it purports to describe." A yellow house is accurate described only if the house is indeed yellow. The two sources of criteria are "exactly inverse." (p 198)

Rituals create conventional states of affairs and conventional understandings. Magic is the extension of the process "beyond the domain of the conventional in which it is effective into the domain of the physical in which it is not." A war can be ended by a properly conducted ritual of peace, but a drought cannot. However, the two domains are hard to distinguish: "People do occasionally die of witchcraft ...." (p 191)

A ritual does not only establish social convention, it establishes acceptance. By taking part in a ritual, the participants tell themselves and others that they are willing to go along with it. Going along with the ritual implies public acceptance of the conventions established by the ritual. Acceptance, in turn, brings with it the obligations entailed by the convention. (pp 193 - 194)

By performing a ritual, the participant "indicates to himself and to others that he accepts" the ritual. No other form of communication does this. A myth, for example, can be recounted as 'entertainment, as an edifying lesson, or as doctrine,' but to recite a myth is not necessarily to accept it. (p 193)

Public participation does not demand belief. Belief is an inward state not visible to witnesses. The participant in a ritual may have doubts: a priest, for example, may have doubts about his faith and may transcend them to perform a ritual. (pp 194 - 195)

The social order is not based on "invisible, ambiguous and private" sentiments; it depends on the "visible, explicit, and public" actions of a person. "Action is socially and morally binding." Consequently, disbelief does not destroy the social order created by ritual, although it does hurt it. (p 195)

Violations of the social order do not destroy it either: violations are considered to be faults of the person rather than errors created by the ritual. (p 195)

Since the invention of agriculture, it has been possible for rulers to force social conventions upon unwilling people through the control of strategic resources such as irrigation water. Prior to agriculture, this may have been more difficult because hunter-gatherers could wander away. Ritual may have been the primordial means by which pre-agricultural peoples ordered their social life. (p 197)

Not all social conventions are created by force or ritual. Some may emerge from everyday behavior or usage. For example, it is likely that the word "stone" evolved without being established by ritual. However, ordinary usage cannot establish conventions about gods which have no behavioral or material referents; and it is difficult to establish conventions about aspects of life that arbitrary, dangerous, emotionally charged, or require cooperation with others, "such as sex, leadership, and service to the group." (p 196)

[Descriptive and sacred messages]

Descriptive messages must be able to vary according to variations in the states of affairs that are described. A row of houses is described by saying that the first is green, the second is red and the third is white. It is meaningless to say that the first is green, the second is green and the third is green. The description must vary according to the various colors of the houses.

Sacred messages, on the other hand, are invariant. They are always repeated in the same way, time after time. The Shema, for example, has been repeated for centuries: "Hear O Israel, the Lord our God, the Lord is One." In a descriptive message, such invariance would be meaningless; but in a sacred message, such invariance implies certainty. (p 209)

In addition, the most sacred parts of a liturgy have no material references. Consequently, the assertions are neither verifiable nor falsifiable. Because such assertions can neither be verified nor falsified they are held to be unquestionable. The illogic of this does not disturb the faithful. 'Sanctity is the quality of unquestionableness imputed by a congregation to postulates in their nature neither verifiable nor falsifiable.' (pp 208 - 209)

In ritual, unquestionableness is transferred from the most sacred postulates to conventional states of affairs. This helps to create acceptance for a particular social order. This is a process of fundamental importance. The association of a particular social order with an ultimate sacred proposition certifies the 'correctness of conventions, the legitimacy of authorities and the truthfulness of testimony.' (p 211)

Social adaptation is aided by the lack of material references in the invariant parts of ritual. Since the invariant parts of a ritual do not have material references, their meaning, other than that of being certain, is mysterious. Consequently, past interpretations may be in error. Proper people may re-interpret the meaning of sacred propositions to adapt to new physical states of affairs. (see "Sanctity and Lies in Evolution," same book, p 233)

[Public acceptance, private belief, and the numinous]

Ritual requires and implies public acceptance. Although private belief is not required, it helps. 'The numinous, when it is experienced, supports acceptance with belief.' A numinous experience compounds the emotions of love, fear, dependence, fascination, unworthiness, majesty and connection. It does not have any particular references, but 'is powerful, indescribable, and utterly convincing.' (p 217)

[The unfalsifiable, the undeniable, the unquestionable]

Sacred postulates are unfalsifiable and numinous experiences are undeniable. 'In ritual, the unfalsifiable message of the liturgy partakes of the undeniable quality of the numinous: the most abstract and distant of conceptions are bound to the most immediate and substantial of experiences. The unfalsifiable supported by the undeniable yields the unquestionable. This transforms the dubious, the arbitrary, and the conventional into the correct, the necessary, and the natural.' (p 217)

[Types of information: indexical, canonical, efficacious]

Different kinds of information are transmitted in a ritual. One kind is 'indexical.' It is about the 'current physical, psychic, or social state' of a participant. A rash is an index of measles; a dark cloud is an index of rain. An index is caused by, or is a part of, that which it indicates. In the extreme case, an index is identical with what it indicates. (p 179)

Indexical information is transmitted in both human and animal rituals. It is transmitted both to the participant himself and to others. (All kinds of information are transmitted both to the self and to others. In a ritual, the self is often a very significant receiver.) (p 178)

Indexical information inverts the familiar qualities of sign and signified. Usually, a sign is as insubstantial as the word "stone," and the signified is as substantial as the "stone" itself. But an indexical sign is substantial and the signified is insubstantial. A Goodenough Islander transmits the insubstantial and abstract notion that he is a man of importance, influence, or prestige by giving away a large number of yams and pigs. The yams and pigs have substance. (p 181)

Although it is possible to deceive with an indexical message, it is more difficult than with the use of insubstantial signs. A man could say with words that he has influence and could lie about it. Pigs and yams, however, are trustworthy evidence. (p 180)

In some human rituals, 'canonical' information is transmitted as well as indexical information. Canonical information is not encoded by the participants of a ritual although it is transmitted by them. Canonical information is found by the participants already encoded in the liturgy as invariant sacred messages. The Shema is an example; so is the information implicit in a Maring ritual: "Deceased Ancestors persist as sentient Beings." (p 179)

Indexical messages refer to the here and now; canonical messages do not. The conventional states of affairs created by rituals are a third class of information which might be called 'efficacious' (a term that is not used by Rappaport).

Participation in a ritual is an indexical message of acceptance. The canonical message is supported by the undeniability of a numinous experience. The canonical message sanctifies the efficacious message that creates a state of affairs. Efficacious message may be re-interpreted and changed to adapt to changing physical states of affairs.

Ambiguity is a fault of everyday language that is usually eliminated by context. The context of a canonical message may enhance ambiguity by suggesting yet more references. Ambiguity destroys the meaning of a description and creates meanings within a liturgy. 'A ritual sign may refer to all its significata at once and derive its meaning from a union of them all.' In ordinary communications, ambiguity prevents a message from being understood unless the ambiguity is resolved. The contrary occurs with canonical messages. "That which is noise in ordinary language is meaning in liturgy." However, the meaning of that which is derived from a concatenation may "be so abstract, complex and emotionally charged as to be ineffable." (p 204)

While the canonical message of a ritual may be ambiguous, the ritual itself may impose unambiguous distinctions on ambiguous differences. For example, "a Tahitian lad decides ... around the age of twelve to have himself supercised, thus making clear his transition from the status of child to that of _T'aura'area_." The process of maturation is slow, continuous and obscure; the ritual summarizes the decision as a simple yes or no signal. (p 185)

In both canonical and efficacious messages, the signal is different from the signified, 'the map is not the territory.' In an indexical message, the part stands for the whole or the whole stands for the whole; the sign is part of, or is the signified. The map is the territory. (p 206)

[Formality]

In addition to participation, formality is an aspect of all rituals. Also, rituals are usually decorous, 'stylized, stereotyped and repetitive. They require the proper persons, occasion, place, and time.' (pp 175 -176)

Don't Put All Your Eggs in One Basket

From Software Freedom: An Introduction

`Global Warming', a Bigger Danger If Natural

In July of 2003, US Senator James Inhofe said that

and that current climate change does not come from human activity.

I hope he is wrong — most scientists think he is wrong — because if he is right, this means that it is important to act immediately to restrict humanly produced greenhouse gases, and to do so strongly, in order to try to compensate for damaging and costly natural changes. The mainstream, `anti-global warming' advice gives us more time and requires less effort.

The greenhouse gases whose output we can determine to some extent are: carbon dioxide, methane, the nitrous oxides, and the chlorofluorocarbons.

The Senator says that current human inputs of these greenhouse gases do not have much effect, even though they are known to have some influence. If he is right, then to protect us against more natural disasters, we will have to reduce greenhouse gases even more than most scientists suggest. If the tool is weaker, we have to act more strongly. That is the best we can do.

Otherwise, people in Senator Inhofe's home state of Oklahoma, as well as elsewhere, will suffer from droughts, floods, storms, cold spells, and heat waves. (I think it is well understood that no one will notice a small change in average temperature, but everyone will notice, and pay for, worse weather.)

Over the past half century, I have seen a change in local weather — right now, I live only a short distance from where I grew up, so the differences are not geographic. In particular, I have noticed that in winter we tend not to suffer long periods with temperatures below 0 degrees Fahrenheit (-18 degrees Celsius) the way we did 40 years ago. This is not to say that we do not suffer cold, just that the cold is less. Similarly, some recent winters were heavy with snow — as one would expect, since there is more moisture in warmer air. At the same time, I have noticed that a few recent winters have been so warm that we have had more rain than snow.

Summers are different, too. Rather than a few days of very hot and humid weather, we sometimes suffer several weeks of such weather. Other summers seem to have more rain than in the past.

As far as I can determine, it is true that the amount of carbon dioxide in the atmosphere is increasing. I believe the reports. In particular, I have seen a multi-decade graph of the amount of carbon dioxide in the atmosphere. The amount goes up and down depending on the season: the northern hemisphere has more land and people than the southern hemisphere. This makes a seasonal difference. But the graph as a whole shows an upward trend.

Clearly, natural variation occurs. The Medieval maximum and the Little Ice Age are famous examples. Senator Inhofe talks about them. More recently, temperatures fell from the 1930s to the 1960s or 1970s. Senator Inhofe has a point. Natural variation has an influence. I simply hope he is wrong for the present change. I hope that the people who complain about humanly produced greenhouse gases are right.

Otherwise, if Senator Inhofe is right, we will have to do more to protect ourselves. Because of technological changes and increases in population and knowledge and better communications, current human society will not bear climate changes as uncomplainingly as people did in the 12th century.

Interestingly, as a practical political matter, Senator Inhofe, who otherwise supported the US Bush Administration, is going directly against it. At least, that is the conclusion I gain from his statements.

However, Senator Inhofe himself does not come to the same conclusion. Rather than fear drought, flood, storm, cold, or heat, he suggests that we do nothing, and that the US avoid

I do not fathom his reasoning. Neither our technology nor the numbers of our people are Medieval.

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