End Times: Inaudible Whimpering

Once, back in 1983, the magazine Scientific American (acting through one of its then columnists, Douglas Hofstadter), ran a contest to win a million dollars.

The rules could not have been simpler. Simply address a postcard to the magazine, and send it in. If only one card was sent in, that lucky person would win the entire prize -- one million dollars. But if there were more than one entry, the prize would be equal to $1 million divided by the total number of entries.

Thus if 100 people sent in cards, the lucky winner drawn would receive $1,000,000 / 100, or $10,000. And if 10,000 people sent in cards, the winner drawn would receive $100. Whatever the prize, it was guaranteed to be paid by the magazine itself. There was only one catch -- the amount to be paid had to be paid in legal tender, i.e., in lawful money of the United States.

Oh, and there was one other simplification of the rules. You might want to send in 100 entries yourself, or perhaps 1,000 entries, in order to increase your chance of being drawn as the lucky winner. In 1983 postage, that would have cost you thirteen cents per entry, or $13.00 or $130.00, depending on whether you sent in 100 or 1,000 postcards. So the contest devisers announced that any number of entries could be submitted on a single postcard -- just write the number of entries you were submitting on the card.

After the contest closed, it turned out that some entrants had submitted cards with extremely large numbers written on them -- ten to the 30th power, ten to the 100th power (a "googol"), or even a googolplex, which is a googol raised to the 100th power. That is the quantity ten to the hundredth power raised itself to the hundredth power -- a fantastically large number, way larger than any known physical quantity (e.g., the number of electrons, or of fundamental particles, in the universe).

So who won the contest?

No one, of course. The amount of the prize, as defined by the contest rules, was $1 million (i.e.,10⁶ dollars) divided by n(10^100)100, or an amount far smaller than the smallest measurable volume in the space of the known universe. (That space is defined by the Planck length cubed, or 4.222 x 10^-105 cm -- a number which is easily seen to be way larger than  1/n(10^100)100cm³.) Needless to say, the United States does not have any money of a denomination that small, and so the prize could not be paid out to anyone, regardless of whose card was drawn, and regardless of how many entries were written upon it.

And the point of the contest? To show that individual greed would win out over rational communal strategy every time. The phenomenon is called a "largest number game," or a "luring lottery."

In other words, it would have been in the interest of those who heard about the contest (mainly, the readers of Douglas Hofstadter's column in the magazine) to agree to limit their entries, so that the prize award to any one of them would be maximized -- after which, if they all agreed, the winner might split his takings among them.

(Of course, the rules forbade overt collusion. And even then, any strategy to violate the rules was not likely to pay off handsomely. If, say, 30% of 1,000,000 Scientific American subscribers saw the column and colluded to send in just one entry for the benefit of all, then each colluder would receive [assuming all collusion provisions were honorably followed] exactly $3.33. And if anyone outside the scope of the collusion agreement submitted a postcard with a large number of entries, the reward would soon vanish to the diminishing point.)

So what, finally, did the "contest" demonstrate? Why would any rational person take part in it, given human behavior's natural response to its terms and conditions -- to act in such a way that maximizes one's own chances of winning, but at the same time thereby ensures that no one will win anything?

For a present-day answer to that question, consider the current relief bill for "Hurricane Sandy damages" that is just now passing Congress. By all accounts, it is loaded with local pork (the great majority of which is not even for any areas affected by Hurricane Sandy). Indeed, the amount of the pork is said to be around 80-95 % of the total legislation of $60+ billion.

(Historical note: take this current legislation as an index of how far we have slid down that slippery slope identified by President Grover Cleveland in 1887. In vetoing an equivalent relief measure voted by Congress that year -- to aid farmers in Texas stricken by drought -- he asked the timeless question: "If the Government supports the people, who will support the Government?")

Just how can this be? you ask. I thought legislators had agreed to vote for no more pork. And just who made that agreement?  Congress. It's called a "Continuing Resolution" -- to keep government operating at its current level. There's been no "new" spending in that sense until now, even though we were still spending at least $40 billion each month over what we take in. 

Right you are -- or were. If Congress never met and did nothing this month, we would still be in a situation where the Government would be spending $40 billion more than its income -- thanks to the passing of previous continuing spending resolutions by an ever-compliant Congress. We have, indeed, gone in just five years from a government with a mandated budget to one that is unconfined, and simply spends freely. Every 90 days or six months Congress authorizes further spending at the same level as before, but without adopting any budget.  (Congress adopted the last national budget in 2008, to cover the last fiscal year of the George W. Bush administration.)

As just noted, the problem is that, authorized or not, the government has been spending $40 billion more each month than it has in income (revenues). And now, in just the first month of 2013, Congress is passing a bill that will add another $60+ billion of mostly pork to that spending, which is already way beyond our means. Meanwhile, the President has, by executive fiat, raised the salaries of everyone in government -- to the tune of another $1 billion per month. On top of that, he is brazen enough to ask Congress  to "remove" the debt ceiling, so that there would be no limit whatsoever upon the amount his  administration could borrow from year to year.

All this adds up to the conclusion that the United States of America is now conducting a "largest number game," which will herald its fiscal demise. The short-term winners are those who take home the bacon (pork) to their States right now, but in the longer term, we are all bound to lose. The government, at this rate, will inevitably run out of "other people's money" to spend -- because there are more and more demanding that it spend (other people's) money on them.

The current members of Congress, and their constituents, evidently do not care. They are acting just like the people in the Scientific American contest who sent in postcard entries with impossibly large numbers written on them. Even though their actions guaranteed that no one could eventually collect the prize, they could not refrain from trying to "win" by the easiest means, no matter what a rational strategy may have suggested.

Congress, thus, has now instituted a lottery -- with your (and the Chinese government's) money. The winners send their Congressional representatives back to vote for more -- until there will be no money left, so that in the end, all of us must lose. As a result of our borrowing more than we take in, year in and year out, the countries who have historically been willing to lend us money will come to see that this is a sucker's game. And then the lending will stop.

Even if the lending from other countries stops, however, the Federal Reserve can still step into the breach, and buy all of the government's bonds. After all, it has an unlimited checkbook, which by design it can never overdraw. But if the Fed is the only entity buying government bonds, that means that the money it "pays" each month for those bonds becomes worth less and less -- and inflation takes off, eventually (and inevitably) to become hyperinflation. (The more inflation increases, the more money government has to borrow to spend, and the more the government borrows to spend, the more inflation increases. It is, perhaps, the original vicious circle.)

So that is where this government, and this Congress, are headed. But as noted above, there can be no ultimate winners in this luring lottery. Short-term, perhaps -- but long-term, no. And if there can be no long-term winners, then what happens to those profiting in the short term?

Answer: they lose as well, just as if they had not won anything. The money they gained at everyone's expense becomes worthless -- not even worth the cost of the paper and ink it will take to print it.

Unless this vicious circle can be voluntarily halted, the outcome is inevitable.

But the voices calling for a halt -- just like the voices of those who said "do not send in any postcards to the Scientific American lottery" -- are below the threshold of audibility.

And thus we shall come to our end -- not with a bang, but with an (inaudible) whimper.