April 30, 2010

I didn't know why time it was

 S = k \, \log_{e} W

If you have a glass box divided by a partition with a small hole in the partition...let's say the box is one cubic foot...and in that box you have 2,000 molecules of air (let's hope it's tempered glass), you would expect, because of the random motion of molecules banging around in the box and finding their way through the hole, that over time the number of molecules on each side of the partition would be equal. If you make two observations of the box over a period of a half hour, and in one of those observations you "see" that there is one molecule on the left side and 1,999 on the right; and in the second observation you notice that there are 999 on the right and 1,001 on the left, you naturally assume that the second observation occurred later than the first.

What do you mean by "later?" That's what Ludwig Boltzmann couldn't let go of, and so, like any good mathematical physicist, or student of probabilistic mechanics who wanted to be known as the founder of rigorous thermodynamic theory, Ludwig came up with the formula above, which lays it all out. His grandfather had been a clock maker in Berlin, so perhaps it was natural for Ludwig to wonder not only what time it was, but why time it was.

Our sense of the passing of time is based upon a random increase in disorder in all things physical. Boltzmann's great insight was that the glass box arranges itself the way it does because of the laws of chance, of aleatory development. There is precisely one arrangement for all 2,000 molecules on the left and none on the right. There are 2,000 arrangements for one molecule on the left and 1,999 on the right, one for each molecule taking its turn as Han Solo. There are almost two million for two on the left and 1,998 on the right. There are about 1.3 billion for 3 on the left, 1,997 on the right. For 1,000 on the left, 1,000 on the right, there are about 2 x 10 raised to the 600th power. So the odds favor the roughly even distribution, in the same way that you expect 10,000 coin flips to produce about 5,000 heads, 5,000 tails, even if the first seven or eight flips are all heads.

Thus, the statistical basis for entropy. The formula above is on Boltzmann's tombstone in Vienna, and some scientists believe the formula belongs in the same category of breakthrough as Einstein's formula for E or Newton's laws of motion. I've been reading about him in Sean Carroll's From Eternity to Here, which is all about Time, in all its manifestations. Carroll is a Caltech physicist who seems to have picked up some of Richard Feynman's gift for mixing the sublime with the ridiculous, such as quoting Bill Murray's Peter Venkman from "Ghostbusters" when he wants to make a heavy point: "Move back, I'm a scientist." Or quoting from "Annie Hall," as when little Alvie Singer becomes worried about the expanding universe and his (Jewish) mother tells him sternly, "What has the universe got to do with you? You're in Brooklyn. Brooklyn is not expanding."

I actually take a great deal of comfort from the realization that chance lies literally at the bottom of everything, that we know what time it is because disorder and randomness keep increasing, and have since the Big Bang. It shows up everywhere. Feynman's own example was typically brilliant and evocative: you're on a tropical beach and it suddenly begins to rain, torrentially. You grab your towel and run for cover. The towel is a little "less" wet than you are, so at first you're able to dry yourself a little with the towel, but after a minute or so, you're simply trading the dampness of the towel for the dampness of your body in a pointless exchange of water. That's entropy, the point of equilibrium.

Thus, the more energy you expend during your life, the greater the trail of disorder in your past (where it belongs). That seems about right, doesn't it, when you think about the lives of marvelously energetic and accomplished people. Their lives are often a mess. Jimi Hendrix, Wolfgang Amadeus Mozart (another Austrian entropic), Jim Morrison, Vincent Van Gogh, all burning brightly, all dying too young. Maybe they just knew something the average mortal does not: we're actually meant, by Nature, to unravel, or even, as the greatest writer of all time, who himself died at the age of fifty, put things,

O, that this too too solid flesh would melt
Thaw and resolve itself into a dew!

Even Feynman died too young, if you ask me. Any state of the world is the poorer for not having Richard Feynman in it, a disordered and expended state. One might think of the entropy of democracy, for example: a room with 2,000 people, and one side, at the lectern, is Richard Feynman, and on the other are 1,999 people...

April 27, 2010

A modest proposal for solving the California pension problem

The facts are stark, as relayed by the Los Angeles Times:

The state of California's real unfunded pension debt clocks in at more than $500 billion, nearly eight times greater than officially reported.

That's the finding from a study released Monday by Stanford University's public policy program, confirming a recent report with similar, stunning findings from Northwestern University and the University of Chicago.

To put that number in perspective, it's almost seven times greater than all the outstanding voter-approved state general obligation bonds in California.

Why should Californians care? Because this year's unfunded pension liability is next year's budget cut to important programs. For a glimpse of California's budgetary future, look no further than the $5.5 billion diverted this year from higher education, transit, parks and other programs in order to pay just a tiny bit toward current unfunded pension and healthcare promises. That figure is set to triple within 10 years and -- absent reform -- to continue to grow, crowding out funding for many programs vital to the overwhelming majority of Californians.

How did we get here? The answer is simple: For decades -- and without voter consent -- state leaders have been issuing billions of dollars of debt in the form of unfunded pension and healthcare promises, then gaming accounting rules in order to understate the size of those promises.

This report was immediately attacked by CalPERS and other California employee pension managers on a number of substantial grounds. First, the report originated at Stanford. The gravamen of this criticism is, to wit, those people at Stanford think they're so smart. Alas, they are pretty smart, which is why the second argument is perhaps more substantial: it's just damn embarrassing to be talking about such a thing in public.

One might say that California has a problem with "shadow inventory," along lines similar to the housing bubble. In my own county, the local rag reported that, effectively, the payroll for current employees must be multiplied by 1.5 to get a sense of the true obligation, and this means that the county is way, way underwater. The unfunded medical expense obligations for retirees is so astronomical that the county pension managers convinced the actuaries not to include the figure ($348 million) in official calculations of the shortfall, lest we frighten the children and small animals. All of this is occurring at a time when real property taxes are in decline, a principal source of state and local funding, because of the magic of Proposition 13, which permits homeowners to keep apace of their declining house values by petitioning for a decrease in taxes. And, of course, California has the highest official unemployment rate in the country, another drag on revenue. Ah, it's a hardy witches' brew we've got on the cauldron here in the Golden State!

Some recovery in the pension funds has been achieved over the last year courtesy of the gamed stock markets, whereby the Federal Reserve lends money to Primary Dealers at ZIRP for them to place bets in the market and buy the spread of Treasuries (earning, say, 3% by lending the Fed's money back to the Treasury), in a defiance of Perpetual Motion Machine Theory. This delusionary market has escaped serious scrutiny so far because it's just complicated enough to defy Senatorial scrutiny. Plus, who wants to play the part of Alice at the Mad Tea Party? (Speaking of which, I did not think it was possible to make Goldman Sachs look good on national TV, but the Senate panel managed to do so. I'm now thinking along the lines, thank God we have smart investment bankers because we sure have stupid legislators. In essence, the Senatorial inquisition, led by the orotund Carl Levin, appears to argue only that Goldman should never short any security in a proprietary trade where it sells a long position to a "customer." This is the only point the Senators can wrap their heads around, because they read it in Matt Taiibi. This is just stupid, and a misunderstanding of securities law. )

But back to California - the solution is obvious. For each area of state activity that is short-changed by diversion of current budget to pensions, a pension recipient, where able-bodied, will volunteer to serve in the afflicted area, compensated by an existing pension. For example, retired Department of Motor Vehicle employees (to the extent that one can tell when they're "retired") will teach Classics and European Diplomatic History at the Berkeley or Los Angeles campuses of the University of California. Libraries will be kept open by drawing on the ranks of retired Department of Transportation truck drivers, who will choose new books for the stacks and serve as librarians. State parks can be staffed by retired Franchise Tax Board employees, who could use the fresh air. This crazy quilt approach, I would predict, will result in no decline in the overall quality of service, and will be colorful and exciting.

It might seem impracticable, of course. Yet I think, in the long run, it is far more reasonable than the alternative, which is to heavily raise taxes in order to continue paying for retired employees. That will result in a general taxpayer revolt, which is why the cowardly legislature and pension managers choose to shoot the messenger (Stanford in this case, admittedly an inviting target) rather than deal with reality, which is extremely unpalatable.

As an actuarial, mathematical, exponential matter of fact, however, it seems highly doubtful that California's pension plans can possibly cover the massive shortfalls through investment acumen alone. It's going to be a real mess, but that's why I'm here. To be in the solution, not the problem.