Big Numbers - Weaver

Living

A Billion, a Trillion, Whatever

Michael T Kaufman

From the New York Times, October 18.

Well, what is the difference between this, that, and the other?

A trillion was an expression more akin to zillion, gazillion and jillion.

The concept of a trillion has shifted in recent weeks from a fuzzy, imprecise and somewhat abstract notion into a hard-edged number like, say, 47 or 254 or 7,453.
Indeed, because of the Long-Term Capital Management fiasco, trillion has become the next big thing. (Of course, the federal budget passed $1 trillion several years ago, but nobody pays attention to it.)
Before this recent shift in consciousness, a trillion, at least in everyday usage, was an expression more akin to zillion, gazillion and jillion. It was a way of connoting scads, heaps, plenitude and humongosity. In this it was like a light year. No one ever experienced a light year and no one ever saw a trillion anything. It was a poetic concept like all the stars in the heavens and all the grains of sand on the beaches.
But when Long-Term Capital Management's troubles became newsworthy in early October, it was reported that the firm had entered into "exotic financial transactions" valued at $1.25 trillion. Derivatives and forward contracts might not be universally comprehensible, but the basic image conveyed by the news stories was not at all meant as an abstract concept, like stars in the Milky Way. Anyone who plays poker could understand it; a group of people, a very finite group of people, were sitting around a table and making bets trying to win a pot worth $1.25 trillion, a figure even more impressive when it is represented like this: $1,250,000,000,000. That is quite real. It is so real it is scary.

If somebody distributed $1 trillion equally to all 240 million Americans, they would give more than $4,000 to every person.
For perspective, it may be useful to note that if somebody wanted to distribute $1 trillion equally among all 240 million Americans, he would have to dispense more than $4,000 to every man, woman and child.
Putting a dollar sign in front of very big numbers tends to make them real, though this does not always work for other units of wealth. For example, one can go to the Numismatic Museum in New York and gaze at the quintillion pengo note that circulated in Hungary during a period of hyperinflation after World War II. Despite its 18 zeros, six more than those of a trillion, it is not really awe-inspiring. Even in the heyday of the pengo, one probably couldn't get much for a trillion, or quartillion or quintillion of them.
But there is a lesson here. Dollars, like pengos, fluctuate over time. And just as there are forces of inflation and devaluation affecting currencies, so there are semantic shifts in the numbers that come to be associated with money. Take millions and billions, which were as mythical as trillions were before Long-Term Capital helped make them a household concept.
There was a time when a million dollars was a pretty high standard. Telling somebody they looked like a million was considered a high compliment. Similarly, a millionaire was a rare species, generally depicted in cartoons as a cigar-smoking person in a top hat. Now, according to "The Millionaire Next Door," a best seller since it appeared in 1997, there are 3.5 million of them. That's 3,500,000, households. Though this is not exactly a dime a dozen, it is not one in a million either.

A person with a net worth of $1 is closer in wealth to a person with a net worth of $50 million than the one with $50 million is to the person with $1 billion.
And within the last decade, some people began to be designated as billionaires. This has led to some confusion between the categories, notably the assumption that millionaires and billionaires are related subspecies who graze together. This is a fallacy that may be made clear by the following facts: A person with the net worth of $1 is closer in wealth to a person with a net worth of $50 million than the person with $50 million is to the person with $1 billion. Much, much closer. After all, the person with $1 is only $49,999,999 behind the millionaire, while the millionaire is $950,000,000 behind the billionaire.
This co-mingling of truly fat cats and the merely plump has long bothered John Allen Paulos, a Temple University mathematician who has written entertainingly about mathematics in everyday life. He advocates using scientific notation to describe the rich instead of the indistinct millionaire or multimillionaire, which could mean anyone who possessed more than a million or less than a billion (which the British refer to quite correctly as a thousand million).
Paulos thinks exponents would help put the very rich in their appropriate places. For example, if one were to read about a 6 x 10⁷ centerfielder, one could immediately determine that this was a $60 million variety of millionaire. A 3 x 10⁶ adolescent baby sitter would be established as a $3-million member of the phylum. And so forth.
Greater precision could also be achieved by borrowing from Indian usage. Indians, who number at least 8 x 10⁸, have an increasingly useful word -- crore -- which means 10 million. And should the time come when the currently awesome trillion turns out to be small potatoes, there is the googol, which is the number 1 followed by 100 zeros, or 10¹⁰⁰. And if that's not enough, there is the googolplex which is 10 to the power googol.

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	A trillion was an expression more akin to zillion, gazillion and jillion.	The concept of a trillion has shifted in recent weeks from a fuzzy, imprecise and somewhat abstract notion into a hard-edged number like, say, 47 or 254 or 7,453. Indeed, because of the Long-Term Capital Management fiasco, trillion has become the next big thing. (Of course, the federal budget passed $1 trillion several years ago, but nobody pays attention to it.) Before this recent shift in consciousness, a trillion, at least in everyday usage, was an expression more akin to zillion, gazillion and jillion. It was a way of connoting scads, heaps, plenitude and humongosity. In this it was like a light year. No one ever experienced a light year and no one ever saw a trillion anything. It was a poetic concept like all the stars in the heavens and all the grains of sand on the beaches. But when Long-Term Capital Management's troubles became newsworthy in early October, it was reported that the firm had entered into "exotic financial transactions" valued at $1.25 trillion. Derivatives and forward contracts might not be universally comprehensible, but the basic image conveyed by the news stories was not at all meant as an abstract concept, like stars in the Milky Way. Anyone who plays poker could understand it; a group of people, a very finite group of people, were sitting around a table and making bets trying to win a pot worth $1.25 trillion, a figure even more impressive when it is represented like this: $1,250,000,000,000. That is quite real. It is so real it is scary.
	If somebody distributed $1 trillion equally to all 240 million Americans, they would give more than $4,000 to every person.	For perspective, it may be useful to note that if somebody wanted to distribute $1 trillion equally among all 240 million Americans, he would have to dispense more than $4,000 to every man, woman and child. Putting a dollar sign in front of very big numbers tends to make them real, though this does not always work for other units of wealth. For example, one can go to the Numismatic Museum in New York and gaze at the quintillion pengo note that circulated in Hungary during a period of hyperinflation after World War II. Despite its 18 zeros, six more than those of a trillion, it is not really awe-inspiring. Even in the heyday of the pengo, one probably couldn't get much for a trillion, or quartillion or quintillion of them. But there is a lesson here. Dollars, like pengos, fluctuate over time. And just as there are forces of inflation and devaluation affecting currencies, so there are semantic shifts in the numbers that come to be associated with money. Take millions and billions, which were as mythical as trillions were before Long-Term Capital helped make them a household concept. There was a time when a million dollars was a pretty high standard. Telling somebody they looked like a million was considered a high compliment. Similarly, a millionaire was a rare species, generally depicted in cartoons as a cigar-smoking person in a top hat. Now, according to "The Millionaire Next Door," a best seller since it appeared in 1997, there are 3.5 million of them. That's 3,500,000, households. Though this is not exactly a dime a dozen, it is not one in a million either.
	A person with a net worth of $1 is closer in wealth to a person with a net worth of $50 million than the one with $50 million is to the person with $1 billion.	And within the last decade, some people began to be designated as billionaires. This has led to some confusion between the categories, notably the assumption that millionaires and billionaires are related subspecies who graze together. This is a fallacy that may be made clear by the following facts: A person with the net worth of $1 is closer in wealth to a person with a net worth of $50 million than the person with $50 million is to the person with $1 billion. Much, much closer. After all, the person with $1 is only $49,999,999 behind the millionaire, while the millionaire is $950,000,000 behind the billionaire. This co-mingling of truly fat cats and the merely plump has long bothered John Allen Paulos, a Temple University mathematician who has written entertainingly about mathematics in everyday life. He advocates using scientific notation to describe the rich instead of the indistinct millionaire or multimillionaire, which could mean anyone who possessed more than a million or less than a billion (which the British refer to quite correctly as a thousand million). Paulos thinks exponents would help put the very rich in their appropriate places. For example, if one were to read about a 6 x 10⁷ centerfielder, one could immediately determine that this was a $60 million variety of millionaire. A 3 x 10⁶ adolescent baby sitter would be established as a $3-million member of the phylum. And so forth. Greater precision could also be achieved by borrowing from Indian usage. Indians, who number at least 8 x 10⁸, have an increasingly useful word -- crore -- which means 10 million. And should the time come when the currently awesome trillion turns out to be small potatoes, there is the googol, which is the number 1 followed by 100 zeros, or 10¹⁰⁰. And if that's not enough, there is the googolplex which is 10 to the power googol.