Wednesday, November 17, 2004
This essay is long and boring. I almost did not have the patience to write it.
One of my favorite ways to teach complex subjects is to use analogies. Start out by talking about a simple subject, then compare it to the more complex topic. The Knight Tour problem is good for this. The problem is this: take an empty chessboard, place it on the table in front of you, situated such that there is a white square in the right-hand corner closest to you. Put a knight on that white square. Do not put any other pieces on the board. Using the traditional way of moving a knight, is it possible to move the knight such that it lands on each square on the board once and only once, and ends up on the corner diagonal to the starting point?
There are three ways to solve this problem. You could try out each possible sequence of moves. That is a bad idea, because you will not live long enough to try them all. You could program a computer to run through all the possibilities for you. That is feasible, at least, but still, it will take a while. The first two methods are called "brute force" methods, because they require a lot of effort, but are guaranteed to solve the problem. The third way, which is the way most people do it, it to try to find some kind of short cut.
In case you have not figured it out yet, I will reveal the answer here.
The chessboard is 8x8, so there are 64 squares. The knight is already on one square, so it will have to be moved exactly 63 times. The way a knight moves, it always lands an a square of the color opposite of that on which it started: if it starts on a white square, it will move to a black square:
move 1 - black
move 2 - white
move 3 - black
Note that after any odd number of moves, the knight always will be on a black square. The target square is white. The knight must move exactly 63 times, which is an odd number. Therefore, it cannot end it's tour on a white square. Thus, it is not possible to perform a knight's tour as stated in the problem.
Many problems in life are too complex to be tractable using a brute force method. Social policy problems generally are too complex to solve using brute force calculations. Therefore, a different strategy is needed. Game theory tells us this: in any game, which has two players, one of whom will win every everything, there is always an optimal strategy for both players. Note that there is no guarantee of a winning strategy; only an optimal strategy. It does not matter how complex the game is, so long as the original constraints are satisfied.
The problem is, life is not played on a grid of black and white squares; so, the Knight's Tour problem does not really tell us anything about public policy, other than that life would be easier if we got rid of all the messy stuff. It would be easier, but not very interesting. Game theory tells us that if we could always set things up so that there will be one winner, and one loser; with the winner getting everything, and the looser getting nothing, we could always find an optimal strategy.
Oddly, our political system is set up as a winner-take-all system, in some ways; and often it ends up being a two-player game. But, it never is really that simple.
Is there some kind of mathematical short cut that we can use to solve social problems? Does the knight's tour problem reveal some kind of magic strategy for setting good policy? No. The truth is, there always will be guesswork involved.
Yes, people do try to find short cuts. Tax and spend. Follow the ten commandments. Love thy neighbor. Such simplistic maxims do have their place. But it seems obvious that you cannot really expect to solve complex problems with such simple sayings.
I like my neighbors, but love? No thanks.
So what is a wonk to do? The problems are too complex for brute force calculations, and there are no simple shortcuts. There are two classes of possibilities. You can try a faith-based solution, or try a reality-based solution. This was what Ron Suskind was talking about in the NYT Magazine article, Without a Doubt:
[...] I had a meeting with a senior adviser to Bush. He expressed the White House's displeasure, and then he told me something that at the time I didn't fully comprehend -- but which I now believe gets to the very heart of the Bush presidency.The knight's tour problem is a good example of solutions emerging from a judicious study of reality. Study the board. Notice how many squares there are. Figure out how many moves will be made. Notice that the knight always lands on the color opposite to that on which it started.
The aide said that guys like me were "in what we call the reality-based community," which he defined as people who "believe that solutions emerge from your judicious study of discernible reality." I nodded and murmured something about enlightenment principles and empiricism. He cut me off. "That's not the way the world really works anymore," he continued. "We're an empire now, and when we act, we create our own reality. And while you're studying that reality -- judiciously, as you will -- we'll act again, creating other new realities, which you can study too, and that's how things will sort out. We're history's actors . . . and you, all of you, will be left to just study what we do." [...]
Od course, we can't set policy, or write laws, based upon the assumption that everyone is going to spend their lives hopping around from white square to black square. So how does one apply the empirical method to the business of running a country?
You have to start out by attaining some degree of calm acceptance, of the simple fact that we never know ahead of time how a given intervention is going to work. I know it is annoying to recognize, but it is the truth. When a law is passed, a regulation made, or a court judgment rendered, we do not know what will happen until it happens. Even then, we rely on the news media to tell us what happened, which they may or may not do.
There is a way to address this problem. It does, however, require that one dispense with faith, and settle for that much less soothing alternative: reality. This would require an entirely new approach to legislation; indeed, it would entail a compete reform of all branches of government.
It would be fair to say that am proposing a revolution. I am not a radical. No. I am habitually moderate, slightly left of center. This would not be a revolution that entails demonstrations, or explosions. It would not even be a bloodless coup d'état. In fact, it would not even require that anyone new take office. We can do it with the same blokes who are in Washington right now. Everything will still look the same. You will still see mommies kissing daddies goodbye, as the daddies get in their Ford Tauruses and drive to work.
This would not be a revolution that would change anything right away. The Republicans could still pass their tax cuts, still promote the interests of big business, still pretend to be moral champions.
But slowly, surely, things would change.
Now, put away the chessboard. We are done with it. Get out the latest copy of JAMA, or any of the AMA journals, and open it to any of the journal articles. It does not matter which one. If you don't have a journal handy, open one of the articles on the AMA website. Used a tabbed browser ; it's easier. Here's a link, to make it easier still.
Actually, if you use two monitors, open this blog entry on one, and the JAMA article on the other. (I know, this essay is for wonks, not geeks, but some people are both geeks and wonks: gonks. If you are a gonk, you've got to have two monitors (and a chessboard.)
Don't actually read the abstract, unless you are interested in hypertension. Just look at he outline:
Effect of Antihypertensive Agents on Cardiovascular Events in Patients With Coronary Disease and Normal Blood PressureThe article is a formal description of an experiment. Notice the key element: the authors stated up from what they were trying to accomplish (Objective), how they planned to do it (Interventions), and how they proposed to assess the result of their effort (Main Outcome Measures).
The CAMELOT Study: A Randomized Controlled Trial
Steven E. Nissen, MD; E. Murat Tuzcu, MD; Peter Libby, MD; Paul D. Thompson, MD; Magdi Ghali, MD; Dahlia Garza, MD; Lance Berman, MD; Harry Shi, MS; Ethel Buebendorf, BSN; Eric J. Topol, MD; for the CAMELOT Investigators
Context The effect of antihypertensive drugs on cardiovascular events in patients with coronary artery disease (CAD) and normal blood pressure remains uncertain.
Objective To compare the effects of amlodipine or enalapril vs placebo on cardiovascular events in patients with CAD.
Design, Setting, and Participants Double-blind, randomized, multicenter, 24-month trial (enrollment April 1999-April 2002) comparing amlodipine or enalapril with placebo in 1991 patients with angiographically documented CAD (>20% stenosis by coronary angiography) and diastolic blood pressure <100 mm Hg. A substudy of 274 patients measured atherosclerosis progression by intravascular ultrasound (IVUS).
Interventions Patients were randomized to receive amlodipine, 10 mg; enalapril, 20 mg; or placebo. IVUS was performed at baseline and study completion.
Main Outcome Measures The primary efficacy parameter was incidence of cardiovascular events for amlodipine vs placebo. Other outcomes included comparisons of amlodipine vs enalapril and enalapril vs placebo. Events included cardiovascular death, nonfatal myocardial infarction, resuscitated cardiac arrest, coronary revascularization, hospitalization for angina pectoris, hospitalization for congestive heart failure, fatal or nonfatal stroke or transient ischemic attack, and new diagnosis of peripheral vascular disease. The IVUS end point was change in percent atheroma volume.
Results Baseline blood pressure averaged 129/78 mm Hg for all patients; it increased by 0.7/0.6 mm Hg in the placebo group and decreased by 4.8/2.5 mm Hg and 4.9/2.4 mm Hg in the amlodipine and enalapril groups, respectively (P<.001 for both vs placebo). Cardiovascular events occurred in 151 (23.1%) placebo-treated patients, in 110 (16.6%) amlodipine-treated patients (hazard ratio [HR], 0.69; 95% CI, 0.54-0.88 [P = .003]), and in 136 (20.2%) enalapril-treated patients (HR, 0.85; 95% CI, 0.67-1.07 [P = .16]. Primary end point comparison for enalapril vs amlodipine was not significant (HR, 0.81; 95% CI, 0.63-1.04 [P = .10]). The IVUS substudy showed a trend toward less progression of atherosclerosis in the amlodipine group vs placebo (P = .12), with significantly less progression in the subgroup with systolic blood pressures greater than the mean (P = .02). Compared with baseline, IVUS showed progression in the placebo group (P<.001), a trend toward progression in the enalapril group (P = .08), and no progression in the amlodipine group (P = .31). For the amlodipine group, correlation between blood pressure reduction and progression was r = 0.19, P = .07.
Conclusions Administration of amlodipine to patients with CAD and normal blood pressure resulted in reduced adverse cardiovascular events. Directionally similar, but smaller and nonsignificant, treatment effects were observed with enalapril. For amlodipine, IVUS showed evidence of slowing of atherosclerosis progression.
I propose that we write laws, and enact administrative rules, the same way as the authors designed their study. Say up front what you are trying to accomplish, how you propose to do it, and most importantly, say how the results will be assessed. Enact all laws and regulations for a specified time period. When it comes up for renewal, look back at what you said you were trying to accomplish, apply the measurements, and see if you actually accomplished what you claimed were your goals. Simple. If the goals were not attained, the legislation has to be rewritten before it can be reenacted.
It may not sound revolutionary, but think about it. It would change everything.
Except: it relies upon politicians to be honest. In order to work, the politicians would have to state honestly what they are trying to accomplish with the legislation. Is such a think possible? Is there a way to force politicians to be honest? Probably not. But there might be a way.
In fact, there is a precedent. Remember all the news we've seen lately, about the way the FDA regulates pharmaceutical companies? It is a bit misleading. Although there are plenty of problems in the FDA, there are some things that they do correctly and effectively. One example is the way they enforce the marketing of medications and health-related products. It is illegal to make a health claim about a product, if that claim cannot be substantiated. This is different from other kinds of truth-in-advertising laws, in which the prosecutor must prove the claim to be false. With health claims, the burden of proof is on the person making the claim. He or she must be able to show that the claim is true.
This is ironic, in a way. Sure, health products can do a lot of harm, if they are promoted improperly. But even the worst drug on the market is nowhere near as dangerous as a bad piece of legislation. A bad drug can kill thousands of people, but a bad law can kill millions. Why is it that we insist on legal protection against false advertising of drugs, yet allow politicians to run around saying all kinds of crazy things about proposed legislation?
I propose that politicians be limited in what claims they can make, when they are promoting a new law, or a change in a rule or regulation. They should have to prove that what they are saying is true. It should not be up to wonks and gonks to prove that the claims are false.
It is clear -- abundantly so -- that we cannot rely on the news media to keep them in check. Bloggers do their best, but it does not seem to help much. So let's put away the journals, put away the chessboard, put away our faith. Those things all are useful, but they do not lead to good policy. What leads to good policy is honesty and an empirical, systematic approach to government. Let's join the reality-based community.
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