William Krehm

One thing should be made clear. As great as the financial scandals have been, they are not the trunk story line of the skullduggery that has brought down the American model. They are mere symptoms of a deeper swindle. That by-product – palpable body counts – of course, is easier to quantify than the cause. But suppressing key information, including crucial cuts of our history, and substituting a twisted version of the setting, is what made possible the financial malfeasance. Send to prison all the miscreants who cooked the books and made off with the boodle, but leave in place the underlying web of fiction, and it will all start over again in no time flat.

That achievements of all the venturesome attorneys and reporters are significant only because they alert us where we must do further digging. And with persistence – for each disclosure leads to the next more astounding one.

That is why The New York Times (28/02, "Once Upon a Time, a Restless CEO" by David Leonhardt) deserves our applause.

"Welcome to story time in corporate America. The old story went like this: the chief executives were in such demand that they were apt to jump ship at any moment. The next story is already emerging. It says executives will begin quitting in droves if boards force them to hold on to their company stock in an effort to tie the executives’ pay to their company’s long-term health.

"The storytellers have most often been the executives and the recruiters and pay consultants they hire. By suggesting that the job market for chief executives is fluid, the tales of executive wanderlust have conveniently offered an economic rationale for enormous executive pay. The evidence, however, is about as impressive as the wardrobe of the emperor in that other fairy tale.

"The job of CEO is fabulously attractive, allowing somebody to lead thousands of people, often in an organization where they have spent years. Few people leave voluntarily before they are ready to retire. Surprisingly few have even been willing to leave one corner office for another elsewhere.

"Since 2000, a year in which executive turnover spiked, 77 of the 200 biggest companies have hired a new boss, according to Pearl Meyer & Partners, a compensation consulting firm in New York. How many of those companies had to do so because their CEO took another job? Two. Most departing chiefs retired and remained on their company’s board, according to news accounts. A good number were forced out.

"Yet many companies, including USX and Verizon, lavished their executives with so-called retention bonuses. Dozens of others cited retention to justify big pay packages, even – as was the case at Enron recently – when the executives could hardly expect to be sought-after candidates for other jobs."

Senator John McCain, Republican of Arizona, has proposed requiring top executives to hold all their company stock as long as they are in their jobs. Congress is unlikely to adopt the plan, but some analysts think that boards of directors might enact milder versions of the policy on their own. Executives have begun to fight the effort, saying that talented leaders would quit after the stock price had risen, sell the stock and find new work.

"If boards are wise, though they will realize that finding a new company to run is not easy. Bank One and Citigroup already have stock-holding rules for top executives, and neither has suffered an exodus. Boards and investors simply have to decide that they will not bend to executives’ wishes as often as they did in the slap-happy 1990s."

There is enough religion of a tattered sort about our economy to warrant reaching to the Old Testament for guidance. There we note that rather from the Temple, the greatest prophets came out of the desert. No surprise then that Chairman Greenspan’s much awaited utterance on the economy should be found wanting (The Wall Street Journal, 17/07, "Greenspan Issues Hopeful Outlook as Stocks Sink "by Greg Ip). Despite his unhappiness with the situation, his analysis was essentially an inside job.

"Saying an ‘infectious greed’ had gripped business in the late 1990s, he warned that breakdowns in corporate governance could undermine the trust necessary for an efficient market. That prospect threatened to ‘significantly erode the economy’s impressive gains in productivity.’ He praised the Senate’s sweeping legislation aimed at shoring up accounting standards and corporate governance, and noted that even without congressional intervention companies such as Coca-Cola have voluntarily begun to record their stock-option grants as expenses. With inflation now low, he said Fed officials are sticking to their current stance until they see evidence that obstacles to growth ‘are dissipating enough to allow the strong fundamentals to show through more fully."

In those few remarks there are enough windows left open for the miscreants to be back at their games in no time flat.

What, for example, is "inflation"? This he sees as low enough for the Fed not to raise interest rates – unlike his headlong Canadian counterpart. If prices were flat despite the increased government measures against terrorists, with so much run-down infrastructure in our cities, the neglect of our educational, health and social services, that would surely indicate not a victory over "inflation" but actual deflation. Prices would have fallen far short of what is necessary to replace the public investment being used up. The monumental hanky-panky disclosed in our greatest corporations’ books must have left holes in society’s balance sheets as well. And what really lurks behind the term "productivity" that serves as ground base for the Chairman’s optimism? Statistically that is the total amount of all goods and services divided by hours worked, or wages and salaries paid. Though a causal relationship between numerator and denominator is implied, it isn’t necessarily there. For example, the spoliation of the environment and the degrading of our social services will not be recognized in the numerator of the productivity ratio. Whatever economists don’t want to recognize, they declare an "externality." Wasn’t that what Enron and Global Crossing did with much of their debt and deficits? How much of Mr. Greenspan’s celebrated "productivity" is actually just bad bookkeeping?

The ongoing collapse of our economies will not be set aright by the automatic workings of the economic cycle. Economics began as a stab at a science, but it was also an instrument of advocacy and power. Over the past century the power element has completely taken over. Behind a forbidding screen of misapplied mathematics, the governance of the world has been surrendered to speculative capital. Packaging the future of which they have little knowledge and incorporating it into stock market valuations, the desired end-result is obtained. A clear case of garbage in and billions of fictitious dollars out.

The law of the deregulated stock market is that stocks must perform to substantiate the rate of increase of stock market valuation monetized in advance. The result tends to the pattern of the exponential curve: the rate of increase of the rate of increase must equal the rate of increase already attained. If it fails to, the price takes a dive. It was due to this striving to exponential increase that earnings per share were replaced by revenue per share, and revenue redefined to include expenses, and capital often to include debt. The atomic bomb was proved successful when it flattened Hiroshima. In a similar sense their exponential compulsion proved successful when it flattened the world’s stock markets. All that was implicit in the model. That is where research on the causes and cures of our disaster must begin.

In my book Towards a Post-Autistic Economy I have dealt with the necessary switch to pluralistic price theory. This would bring onto society’s balance sheets the cost of unpriced services, the amortization of public investment, the cost of repairing the damage inflicted on the environment and on human capital. The price effects of government spending for such purposes – or the debit run up by not attending to such matters – must not be confused with real inflation, i.e., an excess of market demand over available supply. It must instead be considered as "structural price rise." Today all such vital matters are ignored as "externalities." In effect then we have been trying to steer our complex world by a rogue discipline. Here I wish to suggest a valuable resource for dealing with this nightmare: the introduction of courses in the history of mathematics in university economics curricula.

A few of the benefits that would accrue:

• It would breed a reverence for the human mind in its quest of knowledge. That would help protect society against the degrading of mathematics by economists to a pitch for peddling stocks and bonds.

• One of the greatest of all challenges faced by mathematicians was handling the black magic of infinity. That is the precisely the altar at which conventional economists worship. Whenever a zero appears in the denominator of the ratio of two rational numbers, mathematicians found themselves in difficulties. If the numerator were a real number other than zero – the value of the ratio becomes infinity. Using the infinity concept often yielded remarkable results, but it could also lead to wrong answers. It was only towards the end of the 19th century that mathematicians developed a rigorous way of dealing with the infinitely large and the infinitesimally small. Georg Cantor and others achieved this in a way as remote as possible from the "number-crunching" that constitutes economists’ entire bag of tricks today.

Numbers can be viewed either as absolute values (cardinal) having no particular sequence; or in a distinct order (ordinals). Studying the infinity concept in their cardinal aspect leads nowhere – there is no way of encompassing infinity by simply adding up or subtracting – i.e., by number-crunching. However, if you line up the odd numbers as ordinals – 1, 3, 5 and the even ones 2, 4, 6, etc., directly below, and tick off a number in the upper series against one in the lower, you have proved the equivalence of the sums of the even and the odd numbers. But the numbers in the odd series (if you leave out zero) are individually less than the corresponding ordinal number in the even. That doesn’t matter: you can go on adding numbers to both series at the far end of the process – that is the essence of infinity. What is of key importance is the one-to-one correspondence of the individual terms – the essence of "set theory" that became crucial in dealing with this and many other problems in mathematics. Cantor singled out a cross relationship between the even and odd ordinal numbers. Instead of trying to walk the problem step by step to infinity, he allowed the relationship to cover the endless mileage to a sound proof. Thus the infinity of the even numbers equals that of the odd numbers or for that matter of all numbers, odd and even. Cantor, indeed, went on to prove that there was more than a single order or "power" of infinity. (He designated them by the first letter of the Hebrew alphabet "Aleph" with a numerical subscript). Thus for each irrational number there is a rational number to the left of its decimal point and an infinity of other numbers to its right – that is what makes it an irrational number. It cannot be expressed as a simple ratio of two rational numbers. So the irrational or "transcendental" numbers, are infinitely more numerous than the infinite sum of the rationals. The most familiar of these transcendental numbers is "π," the ratio of the circumference of a circle to its diameter.

That eliminated errors in the handling of infinity by some of the very greatest mathematicians. Obviously what economists stand in need of is a method that would protect them against their mistaken ways of handling endless economic growth. That is the ultimate source of the current crisis We could learn from mathematics how to put the voracious beast of infinite growth on a leash.

There are other powerful tools that economics could borrow from mathematics.

An important one is the method of "reduction to absurdity." The model to be tested is assumed true, and then the implications of that assumption are studied. If this leads to the conclusion that the assumption is not true, we have disproved it in the most rigorous way. Its refutation is found within it. This was the method that of the Greek geometers developed almost two thousand years ago. Euclid’s book on geometry was widely used as a standard textbook right into the last century.

This method of reductio ad absurdum cries out to be applied in economics. For example, it would be easy to prove with a pencil and paper that you cannot stabilize prices and the economy by continuing to increase interest rates until they flatten out our price indexes. For interest rates add to the cost of everything produced: they extract wealth from the economy for the benefit of a class that directly produces nothing. Eventually that must lead to the breakdown of the economy and society itself. Instead of arriving at this proof with a pencil and paper, right-thinking economists chose to have society act it out at a devastating cost. And now that the reductio ad absurdum disproof of that model has come crashing on our heads, they still persist in not recognizing it.

Mathematicians have been ever less concerned with specific numbers than with the internal structure of a mathematical model. At the beginning of the 19th century, "group theory" revealed the essence of any mathematical model in terms of its inner patterns of symmetry and asymmetry – whether it was valid if read backward or not. Identical patterns of this sort were found to extend to the most different fields of mathematics, so that it became possible to solve problems in the most seemingly dissimilar areas at one crack.

Our economists do just the opposite. They assume that an asymmetric model can be flipped over and read backward. Thus, because, other things being equal, market prices will rise if demand exceeds supply, they take for granted that if the price level has climbed it means that there is too much demand, i.e., "inflation." But in the mixed economy that has developed since World War II, the price level can go up for quite other reasons. When anybody moves from a town of 10,000 to New York City, he doesn’t expect his living costs to stay the same. How, then can we expect the price levels to stay flat when humanity is making a similar move? Many other such things create a growing layer of taxation in price. Economists handle this by putting it under the table – just as Enron did many of its liabilities. Even a limited knowledge of the history of mathematics would expose such evasions.

Above all, nobody should allow herself to be intimidated by a few mathematical symbols. What is needed to refute the abuse of mathematics by economics, is a "defensive" grasp of mathematical principles to penetrate the aggressive false mathematics upon which most conventional economics is based. Much of that can be gotten from an understanding of what mathematics can and cannot do. It is a discipline that contributes nothing factual to our understanding of anything but of mathematics itself. What it does do, gloriously, is reveals the implications of the premises fed into a model. If those premises clash with the reality studied, we know that the claims of that model are counterfeit. Thus the whole notion of a self-balancing market is based on the assumption that all actors in our economy are of such tiny size that nothing they do or leave undone individually can influence the result. That in the age of Enron, Microsoft, and General Electric, is clearly nonsense. You can therefore dismiss such models out of hand.

There are few mathematical principles that cannot be explained in perfectly accessible language for the reader with little mathematical background. A course in the history of mathematics for economics students would be of immense use in training economists to examine critically whatever is put before them.1

Today governments and central banks are clearly at their wits’ end to explain the grotesque results that have ensued from their "solid fundamentals."

1. A highly readable work on the subject is James R. Newman’s four-volume The World of Mathematics (New York: Simon and Schuster, 1956).

In my recent Towards a Post-Autistic Economy – A Place for Society at the Table (COMER Publications, 2002, p. 165), I outline a simple way of designing policy in gradualist steps, by pairing dosages of generally desired effects for a joint zero-influence on the public treasury – i.e., cutting interest rate costs to the Treasury by shifting a limited amount of federal debt from the chartered banks to the central bank, and at the same time curtailing the government’s revenue to an equal amount by reducing the regressive Goods and Service Tax. The immediate total effect on the Treasury will be a wash, but the bonus will appear when the consequences of these measures work their way throughout the economy. After the effects of the first dosage of such paired policies has been assessed, it can be repeated – with the same two countervailing factors, or quite different ones. This is an application of Gaussian modular congruence, but it is not necessary to know that to appreciate its enormous potential in getting society out of its present dilemma. Keynes grazed the idea when in his "General Theory" he remarked – "We send Denmark cookies and they send us cookies. Wouldn’t it make more sense if we exchanged recipes?" It would certainly decongest all channels of communication, cut down pollution, and needless bustle.