Beauty of Gray

Friday, April 05, 2002


In the cafeteria during lunch, I caught a snippet from a CNN (or maybe headline news) report on the conflict between Israel and Palestine, and the reaction in newspapers around the Arab world. The reporter actually said, and I swear I'm not making this up, "But Arab regimes are finding it increasingly hard to remain neutral."

Hello? Was this Rip Van Winkle giving the report? What colossal vacuum of ignorance must this reporter only recently emerged from, dazed, shielding her eyes from the glare, to believe that Arab states have ever, for one minute in their entire existence, been anything other than virulently hostile towards Israel? Yeah, it's only just now, due to the horrible oppression of the peaceful and angelic Palestianian children, that the fair and balanced Arab regimes are being forced to reluclantly side against Israel.

Whoever was responsible for that report should be sacked and should be forced to immediate go and read all the archives of Little Green Footballs, followed by a good history of the state of Israel which covers the multiple attacks that the unbiased neighboring Arab states launched to try and destroy it and drive the Israelis into the sea. With an ignorance that astounding, I'm surprised this reporter knew which end of the microphone to talk into.

Link posted by Doug Turnbull at 3:01 PM

Quantum mechanics and postmodernism

Yesterday, Instapundit linked to this muddled mess of a column by Dave Kopel on the NRO. While the column meanders here, there, and everywhere, its main thrust is to try and refute the claims of some postmodern theorists that quantum physics, and specifically Heisenberg’s uncertainty principle, supports their philosophy. On this main point he is absolutely right, but his argument contains so many errors and misunderstandings that I couldn’t let it pass without some commentary.

Kopel argues that the postmodernists’ claims are wrong on the basis of a recent book, which puts forth an alternative interpretation of quantum physics, supporting Einstein against the standard Copenhagen interpretation. However, the interpretational superstructure that you put on quantum mechanics does not affect the uncertainty principle—it is a basic consequence of mathematics, not a matter of interpretation. Regardless, it doesn’t matter, because the uncertainty principle says nothing at all about larger issues of truth—it doesn’t say that “Everything is uncertain” or whatever other ideas the postmodernists want to shoehorn into it. It’s just a specific and narrow mathematical statement.

To understand why both the postmodernists and Kopel are wrong on this issue requires a brief explanation of what quantum physics says and what it is, and of how the uncertainty principle fits in. Basically, quantum mechanics is the science that explains phenomena at the atomic level, and at that level things behave differently than they do at the macroscopic level. Mathematically, this means that particles obey a different set of equations—rather than obeying Newton’s laws, they are described by Schrodinger’s wave equation. (Although when describing large sizes/lengths, the quantum description reproduces Newton’s laws.)

In this framework, each particle is described by a wavefunction, which gives the information which can be known about it, rather than by a position and momentum, as is Newtonian physics. When things happen to the particle (like absorbing energy, or moving in space), its wavefunction then changes.

Wavefunctions which have a well defined value for a particular variable (like energy, position, or momentum) are said to be eigenfunctions of that variable. For a given variable like energy, any function at all can be broken down into a combination of the eigenfunctions of that variable. Consider, for example, the standard Cartesian plane. Any point on the plane can be broken down into a certain value in the x direction and a certain value in the y direction—it can be described by two numbers (x,y). The breakdown of wavefunctions is similar, only in a much larger number of dimensions. Such a wavefunction is said to be in a superposition of states.

So that’s the first tricky part—a particle doesn’t have to be in a state which is an eigenfunction of a given variable. That is, there are states which don’t have well defined values for given variables. This is what Einstein didn’t like, since in the Copenhagen interpretation, once you measure a value, the particle has to “choose” one of the eigenfunctions for the wavefunction to “collapse” into. The theory becomes probabilistic, rather than deterministic.

There are rules in quantum mechanics that tell you how to determine what the probabilities are to get a particular result from your measurement, if you know the wavefunction before the measurement. The problem with challenging this paradigm is that the theory works. It accurately describes the results of experiments. And there are experiments you can do that prove a particle must be in a superposition of states, rather than having a well defined value, but when you measure that value, then this superposition disappears and the wavefunction does in fact collapse into an eigenfunction.

The next tricky part, and the essence of the uncertainty principle, is that, for some pairs of variables, it’s not possible for a particle to be in an eigenfunction of both variables. That is, the eigenfunctions are incompatible—an eigenfunction of one of the variables is a superposition of states for the other variable. Mathematically, it is impossible to specify a wavefunction that has a well-defined value for both of the variables.

The most famous such pair is position and momentum. The uncertainty principle simply says that the better you know the value of one of these variables, the less well you know the value of the other. If you try to make up a wavefunction that has a pretty narrow range of available momentums, then its spread in space must be large. And vice-versa.

As I said, this is a fundamental consequence of the mathematics, and can be rigorously proven. No matter what interpretation, Copenhagen or otherwise, you put on quantum mechanics, the uncertainty principle will still be there, and will still be just as true. And it doesn’t say anything about absolute truth or knowledge—it says something much narrower—that there are pairs of values which you cannot know both of arbitrarily accurately. But you can know one, or the other. And the uncertainty here is incredibly small, so that it really has no effect whatsoever on the behavior of things at the human level, or our ability to know or predict things about them.

Addendum: for those who are interested, the mathematical proof of the uncertainty principle relies on the commutator of the two variables, [X, P] = XP – PX. If this is non-zero, if you get a different value when you measure X then P, than you do measuring P then X, then the two variables have an uncertainty relationship—it’s just the mathematical version of the statement above, that a particle can’t be in an eigenfunction of both variables at one time.

Link posted by Doug Turnbull at 1:30 PM

Thursday, April 04, 2002
More on CAFE

Megan McCardle responded via e-mail to my previous item and gave me some pointers towards studies on the effects of CAFE. (This is why somewhere on the list of rules to live by, below "Never go up against a Sicilian when death is on the line," but above "Always bet against a Bob Knight coached team in your NCAA pool," is "Don't argue with economists about cost-benefit analyses." They're usually right, and have the studies to prove it.) The idea I wrote about, the phenomenon of driving increasing as a result of increased fuel efficiency, partially defeating the purpose of reducing gasoline consumption, is called the “rebound effect,” and there have been some studies of it.

The numbers I found (or at least saw quoted, here and here) indicate that a 10% increase in fuel efficiency would cause an increase of around 2% in the numbers of miles driven. So there’s some effect, but it doesn’t look huge. More interestingly, however, as the report at the second link above discusses, the cost of extra miles driven is not limited to the extra fuel consumed. There are substantial additional costs: increased congestion, increased road and parking costs, and an increase in the number of crashes. Of course, these additional costs do not change the fact that CAFE reduces energy consumption and so addresses the problems of conservation and energy independence. But factoring in these additional costs makes CAFE standards seem much less appealing.

The report argues, and I agree, that a better approach is provided by methods that reduce overall mileage. This reduces fuel usage and also gives benefits in all the areas mentioned above where CAFE standards impose additional costs. So while the CAFE standards are of the “two steps forward, one step back” variety, additional gas or road use taxes provide double benefits: “two steps forward, one more step forward.”

Perhaps the best simple approach would be to increase gas taxes, which reduces overall traffic and attendant problems, does a better job at accurately pricing car use to pay for externalities like road use and parking. Such a tax would also encourages people to buy fuel efficient cars. (Stay tuned to Live from the WTC, where some features on the benefits of gas taxes are promised.)

Unfortunately, it doesn’t seem like such a tax is politically feasible right now. Republicans would oppose it on general principle, since it is a tax increase. That alone would be enough to kill it, but Democrats are also unlikely to rally behind it since it is a regressive tax and it would likely be opposed by the Teamsters, who still have some pull with many Democratic candidates. Conservation groups would support it, but they don’t seem to have the clout to line up Democrats behind such a proposal, especially one that would be unpopular with the public.

Other such transportation demand management solutions, which limit overall mileage, include graduated insurance rates based on miles driven, HOV priorities, improved public transit, and work-at-home/telecommuting programs.

Anyway, after looking into it further, I still support improved CAFE standards, but after reading about the secondary costs, not nearly as strongly as before.

If you’re interested in the issue, I’d definitely recommend this report, which I linked above. It is a good introduction to the CAFE issue and to various other market based ideas to reduce fuel consumption. The whole issue is an interesting lesson in the law of unintended consequences, and the way in which some seemingly obvious solutions (like CAFE standards) can have hidden costs or consequences that make them much less appealing. I argued a similar point in a previous post about attempts to reduce congestion simply by building more roads. It’s the obvious solution, but for non-obvious reasons it isn’t a particularly effective one.

Link posted by Doug Turnbull at 9:30 AM

Tuesday, April 02, 2002
CAFE and gas consumption

Megan McCardle has an interesting post on CAFE standards and their effect on gas consumption over at Live from the WTC (which you should be reading and I should have linked by now. Soon, though.) Anyway, she brings up the point that CAFE standards have a hidden perverse incentive, since by improving fuel efficiency they actually encourage people to drive more, keeping gas consumption relatively steady. She goes on to say

CAFE is useless at reducing our oil consumption, because the evidence is that households use a sort of straight-level budgeting process for gas consumption -- raise fuel efficiency, and people drive more until they're at the same oil consumption as before. Which is what has happened with cars in the US -- according to my energy guru, our gasoline consumption hasn't dropped at all since CAFE was introduced.

A few responses. First, I'd be interested to see the evidence that people really budget for gas as she says, because I'm skeptical. It seems to me that the amount of driving can be broken down into a first, relatively constant amount for the daily commute and errand running, and a second flexible amount for vacations and other non-essential driving. Fuel efficiency and gas cost can have a slow effect on the first value, making people more willing to take a long commute to work, but I don't think this is a strong phenomenon. Living in an urban area, the driving factor in suburban sprawl is property costs, and the primary brake on it which makes people want to live closer is commuting time, not the cost of gasoline used for commuting. So I'd hold that the baseline is relatively independent of CAFE standards.

Then, the question is, does improved fuel efficiency cause the second amount to increase enough to offset gas savings in the first? I'm fairly skeptical, but could be convinced. But it seems that, first of all, optional driving is a relatively small percentage of the total driving people do, and improvements in fuel efficiency would then only cause a change (switching from something else to driving) in behavior for a small percentage. So you're down in the small percent of a small percent, which might be 1% or so. While CAFE standards are improved by 10-20%.

The second point is even more questionable--that the lack of change in fuel consumption is proof that CAFE standards don't decrease fuel consumption. The old saw that "correlation doesn't imply causation" is well known. It seems to me that this is an example of the converse, "lack of correlation doesn't imply lack of causation." If there are other uncontrolled variables that are changing, you can't isolate out the effect of the single variable (in this case CAFE standards) of interest. Or, to put it another way, you can't prove (or at least not with the simple data Megan mentions here--there are probably more detailed studies that might be more conclusive) that gas consumption wouldn't have been even higher than it is today if CAFE standards had never been implemented. So they might be reducing gas usage, but other factors are increasing gas usage, so the net result is a wash.

What are some of the possible culprits? First, have gas prices changed since CAFE was introduced? Second, has the introduction of CAFE standards actually improved the average fuel efficiency of vehicles on the road? One of the main arguments for revising CAFE standards is that, since they were introduced, the light truck vehicle class has become more and more prevalent with the increasing popularity of SUVs, and such vehicles are held to much lower standards. And third, this time period has seen an increasing suburbanization of the country, increasing averaging commute distances, and with it average gas consumption.

While it's certainly true that CAFE standards alone are not a solution to US dependence on foreign oil, but nothing is. And right now, it seems to me that improving (increasing?) CAFE standards are a modest but nonetheless positive step that can be taken to ease that dependence and reduce the rate of US consumption of the ultimately non-renewable resource of the world's oil supply.

Link posted by Doug Turnbull at 2:18 PM

Economics of catering

So, I've been busy lately with preliminary planning of our wedding, and we are getting increasingly close to accepting the grim conclusion that it is literally impossible to have even a modest wedding and reception for under $10,000. This is with around 100 guests, no wedding dress, no cake, using her church, and a simple hall rather than an opulent downtown hotel.

What really burns me up is the cost of the food. I have a question that I was hoping someone out there could answer. So if there's anyone with experience in the catering field, or an economist who isn't busy writing about steel tariffs or CAFE standards, please drop me a line. Why is it that we can go to one of the top restaurants in the city--Morton's, say, or Legal Seafood--and have a nice meal, selecting from dozens of menu choices, including a glass of wine, for $50 a piece, yet it costs as much (and usually quite a bit more) to get a caterer to deliver forgettable banquet style rubberized chicken and bland pasta, with little or no menu choice?

This just doesn't make sense to me at all. I know there are some additional catering costs (food trucks, portable cooking/heating gear, etc.) But the caterers also don't have to pay rent. There aren't any more wait staff per capita, and the service in general is usually not nearly as good for catered meals. So what gives? Why can a restaurant do a far superior job at a far lower price? And should I quit my job to become a caterer, retiring after 5 years to a life of ease and luxury?

Update: Megan McCardle (of Live from WTC) wrote in to point out the, obvious in retrospect, explanation that caterers must charge more because they have to make their profits on far fewer meals than restaurants. Caterers typically serve only a single meal in a day, and most of their business is also concentrated on weekends and during the warmer part of the year. As a result, their profit margin per plate has to be a lot higher than a sit-down restaurant, and hence the higher, elopement-inducing prices.

Link posted by Doug Turnbull at 9:20 AM

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