Friday, August 28, 2009

No Laughing Matter

Typically incomplete piece on NPR today about nitrous oxide, aka laughing gas.

Nitrous oxide has always been a normal part of our atmosphere, "but since industrialization, its concentration has been going up," says A.R. Ravishankara at the National Oceanic and Atmospheric Administration in Boulder, Colo.

Now that synthetic chemicals are waning in the atmosphere, he wondered if other gases posed any environmental threat. As he reports in the online edition of Science magazine, nitrous oxide, a byproduct of agriculture, is a serious problem for our planet.

"There's so much being emitted, that right now, nitrous oxide emissions would be the largest ozone depleting gas emissions today, and it will continue to be in the future," Ravishankara says.

Unmentioned is the fact that there will always be some chemical that is the largest ozone depleting gas in the atmosphere. The real question is how big a problem this might be.

Ravishankara estimates that by the end of the century, we will have 4 percent less ozone in the stratosphere than we would have had before the Industrial Age, as a result of nitrous oxide.

Note the careful language: 4% less than before the Industrial Age, not less than we have right now. Total ozone depletion right now is about 3% compared to pre-1980 values. So the effect of nitrous oxide is no more than 1% over the next 90 years.

At this point the correct response, it seems to me, is sufficient interest among atmospheric scientists to keep an eye on things, and yawns and a return to our normal lives for pretty much everyone else. Looks like there's no disaster on the way. NPR doesn't take this approach, of course:

"I think that limiting nitrous oxide is going to be more difficult than, for example, limiting carbon dioxide emissions. And we know how difficult that is," she says.

That's because we need nitrogen - it's an essential part of protein. Carbon dioxide comes mostly from smokestacks and tailpipes.

"You can get your energy from other sources than carbon, but you really can't get your food from sources other than nitrogen."

We can't phase out nitrogen fertilizers, Nevison says. And studies show we could make only a modest difference if we used them more carefully.

And it's not just the ozone layer that's at issue here. Nitrous oxide also contributes to global warming - so there's another important reason to pay attention to this often neglected gas.

The implicit assumption here is that since some harm is measurably taking place, therefore we must pursue any means to mitigate it. But should we even bother trying to limit nitrous oxide emissions at the present time? This really should be an open-and-shut case: the effect is very small, the cost is very large. The faithful in the religion of environmentalism will try to persuade us that it doesn't matter, of course: Sin is being committed, therefore it must be stamped out, regardless of cost. That last sentence is particularly telling. If your case for environmental danger isn't strong enough otherwise, then by all means bring in the big gun: global warming.

The biggest problem with environmentalism (as a movement) today is that costs and benefits are never netted out. Bjorn Lomborg attempted to apply this kind of economic analysis and was summarily excommunicated for it. The IPCC does this kind of analysis on global climate change, but the results are so mild that they get no media coverage and environmentalists pretend they don't exist (or argue that the IPCC has been bought, or some such conspiracy). We should certainly take some steps to protect the environment, but people have other needs, wants, and values as well.

Wednesday, August 26, 2009

Medical Care Snafus

As the debate about health care reform rages on, I'm hearing a steady drumbeat of horror stories (from the right) about medical mistakes, insurance screw-ups, and other snafus in existing "single-payer" countries such as Canada and the U.K. These stories serve two purposes: first, they rouse fears about what a single-payer system would mean here in the United States; second, they counteract anecdotes about the failings of our own system.

Nonetheless, they are but anecdotes, and thus may not be considered "fair debate." As we say in science, the plural of "anecdote" is not "data." The problem is that comparing useful data is not easy. Here is a sample attempt, showing the U.S. leading a group of six developed nations (including Australia, Canada, Germany, New Zealand, and the U.K.) in medical errors over the two years to 2005. The most obvious problem with this survey is that it is almost entirely self-reported. Thirty-four percent of Americans reported an error next to thirty percent of Canadians. Maybe Americans are just more likely to report errors, though: such a small difference could easily be attributable to such an effect.

One aspect of single-payer that is particularly troubling is that it is very hard to sue the government. (If you think dealing with a large, profit-driven, lawyer-riddled health insurance company is tough, try the gargantuan federal bureaucracy.) Lower accountability usually results in lower standards. So while these anecdotes should not be extrapolated too literally, there is at least some reason to believe that we would in fact have more errors here if we adopted single-payer. The question is whether some of the errors that we already have due to the complexities of our different payment and care mechanisms would be reduced sufficiently to counteract the loss of accountability. It is impossible to know this without knowing more details about how a single-payer system would be implemented in the U.S., and it might be impossible even then.

At least in the U.S., if they screw up (and you're still alive), there is some recourse. In a single-payer system, there may be none. That should be reason enough not to go that route.

Tuesday, August 25, 2009

Bold, Persistent Experimentation

From a CNN article about President Obama's nomination of Fed Chairman Ben Bernanke to a second term:

President Obama on Tuesday compared Bernanke's efforts to avert a second Great Depression to FDR's "bold, persistent experimentation" to get the country out of the first one.

Lord, save us from bold, persistent experimentation. That meta-policy of FDR's was perhaps the most damaging attempt to undo the Depression (in a crowded field). The future is already unpredictable for plenty of reasons, from the weather to fads to people's animal spirits. But in order to grow, businesses need to plan for the future. Unpredictable government policies only add to their difficulties. When a government announces that it intends to be unpredictable - and there is no other way to read a phrase like "bold, persistent experimentation" - businesses are likely to react like a turtle in a hurricane: stop moving, pull in their legs and hope they're still alive when the storm is over.

Let us hope Obama was merely being rhetorical.

Democratic Speedbumps on the Road to Single Payer

The Democrats may be subverting their own ultimate goal (a U.K.-style single-payer system) by pushing single-payer, the public options, etc., right now. Taking a long-term view, our current medical care system is politically unstable. People are generally unhappy with the system; they see that it is overly complex, leaves many people out, and contains obvious waste and duplication of effort. But they also fear change. Radical reform of any type will only be popular when dissatisfaction with the status quo exceeds the fear. In the meantime, the debate rages between centralized "single-payer" plans and decentralized market-based plans.

It's pretty clear that the leaders of the Democratic Party want single-payer. Obama and his advisers have said so on several occasions. Ted Kennedy has been working towards this for decades. Howard Dean supports it. I've spoken to several committed Democrats privately and they nearly universally wish for single-payer.

The question is how they get it. Single-payer is unpopular today, and the Democrat leadership knows this. So they propose the "public option" instead. This would be a government-run insurance program that anyone could buy into, and would establish a minimum standard for private plans. But this would push us towards a single-payer system. A study by the Lewin Group showed that over 110 million people currently insured through their employers would shift to the public plan (or be shifted by their employers). That would represent over two-thirds of all privately insured Americans. Once that happens, not only would private insurers be financially gutted but voters would view a step to single-payer as a smaller reform than it currently is. We don't even have to speculate on this. Prominent Democrats have publicly announced this strategy on multiple occasions.

However, the public option is also coming under fire, because the "camel's nose under the tent" strategy is so transparent. Obama has also done a poor job selling it. He used the Post Office, of all things, as an example of a well-run competitor to privately-run FedEx and UPS! (He ignored the fact that the Post Office actually has a monopoly on first-class mail delivery and is not competitive in the reliable package delivery business that FedEx and UPS specialize in.)

So Democrats have shifted the debate to focus opprobrium on insurers. They are broadly disliked already, so this tactic may be effective. So much political capital has been spent on health reform so far that some bill is almost sure to pass.

As a result of all these factors, here's the way I see the future of medical-care insurance: This year, we will get insurance "reform" which will contain measures that will push rates higher, cause more people to lose their private coverage, and create more financial burden on states. The reform will be unpopular with Democrats, who will view it as a compromise. Republicans will be relieved to have avoided the public option. But over the next few years, the "reform" will create ever more dissatisfaction with private care. Health insurance will, in effect, be transformed into a publicly regulated utility.

Increased dissatisfaction, an increasing number of uncovered citizens, and increasing regulation all work to the Democrats' favor. They are all steps leading to the sort of ultimate goals they want: either the creation of a public option a few years hence, followed by single payer a few years beyond that, or even a direct move to single payer.

Luckily for us conservatives, a lot of rank and file Democrats don't grasp this progression or are too impatient to wait for it. They are pushing for the most radical reforms now. We should encourage these feelings. If we are really lucky, they will be so busy attacking the current push for reform from the left, while we attack it from the right, that no compromise comes to pass. With Republicans completely out of power, that is the best result we can hope for this time around.

Thursday, August 13, 2009

To Sample or Not To Sample?

For over a decade the idea of using statistical sampling instead of a straight count for the U.S. Census has been hot in some circles. Broadly speaking, Democrats have favored the method, while Republicans have opposed it.

Democrats expect to gain from using sampling, since traditional methods tend to undercount Democratic constituencies: minorities, illegal immigrants, and transients. And for the same reasons, Republicans expect to lose. So their respective support and opposition aren't surprising. Naturally, their public reasoning cannot be so self-centered.

Republicans base their formal opposition in part on the U.S. Constitution, which states: "The actual Enumeration shall be made within three years after the first meeting of the Congress of the United States, and within every subsequent term of ten years." The word "Enumeration" contains an implicit demand that each person be counted. The 14th Amendment includes similar language: "Representatives shall be apportioned among the several States according to their respective numbers, counting the whole number of persons in each State..." (emphasis mine). However, I find this line of argument unpersuasive. While an "enumeration" can mean a "list or catalog", it can also mean a "reckoning or count". While the former definition would exclude sampling, the latter would not. The phrase "whole number of persons" might be more persuasive, except that that phrase is pretty clearly used to void the original text's treatment of slaves: "Representatives and direct Taxes shall be apportioned among the several States which may be included within this Union, according to their respective Numbers, which shall be determined by adding to the whole Number of free Persons... three fifths of all other Persons." So the meaning of the Amendment is that every person shall be counted equally, i.e. there will be no more three-fifths rule.

Some Republicans also object that sampling can make the census less accurate. This is a better argument, since if true it is devastating to the whole basis of sampling. Technical Report 537, by Brown, Eaton, Freedman, Klein, Olshen, Wachter, Wells and Ylvisaker of the Department of Statistics, U.C. Berkeley, goes into great detail on the legal issues, techniques, and potential problems with sampling. The possibility that sampling will reduce accuracy is raised: "Will proposed adjustments to the census take out more error than they put in?" Unfortunately, the question is left unanswered: even these professors are unsure whether sampling will satisfy its intended purpose. The paper also points out that one problem sampling is meant to address - undercounting of certain groups - could be solved without sampling: "Census figures could be scaled up to match the demographic analysis totals for subgroups of the national population defined by age, sex and race (Section V). The people in a demographic group who are thought to be missing from the census would be added back, in proportion to the ones who are counted—state by state, block by block."

On the pro-sampling side, one of the most vocal supporters is Dr. Kenneth Prewitt, director of the Census Bureau from 1998-2001. He argues that sampling will be more accurate than a direct count, although Tech Report 537 seems to cast some doubt on this. Another point he makes is that the federal government government already uses statistical data for policy-making all the time. This point, though, is easily refuted. The Census Act as amended in 1976 states:

...except for the determination of the population for purposes of apportionment of Representatives in Congress among the several States, the Secretary shall, if he considers it feasible, authorize the use of the statistical method known as "sampling" in carrying out the provisions of this title. [emphasis mine]

The emphasized portion was the basis of the U.S. Supreme Court's 1998 decision in "U.S. House of Representatives v. U.S. Department of Commerce, et al.," which upheld the principle that sampling should not be used for apportionment.

My own take on the debate is that the Constitution demands that an accurate count be made by any means. I do not believe that a direct count is required. The census is a critical part of our representative democracy, though (which is why it is covered in our minimalist Constitution at all), and it is important that it be simple and transparent. The appearance of bias or political machination would erode civic trust in the most representative of our federal legislative bodies. A direct count that was just slightly less accurate than some other technique (sampling or something else) might still be favored due to its transparency.

The concerns raised in Tech Report 537 lead me to conclude that any improvement in accuracy from sampling would not be sufficiently great or certain enough that we should use it for the census. But future developments could change this balance: direct counts could become far less accurate (for some reason) or indirect counts far more accurate.

Tuesday, August 11, 2009

Krugman and Stross: Making America More Like France

After their conversation, the floor is opened to questions from the audience. The first goes something like this:

One of the things that science fiction used to promise us was that robots would do all the work and one of the social problems we'd have to deal with would be what to do with all the leisure time. Do you think the fact that we're still working 40 hours a week is a technical issue, a social issue, an economic issue, or what?

One thing notable about Krugman is that I think he really does know better. He's a very accomplished economist. He knows that free markets, free trade, etc. really do bring enormous value to great masses of people. But he's also become a totem for the left, so he can't be entirely honest. I think this is why his answers are such careful nonsense. He starts out:

The stuff that can be automated is at this point still quite limited. We used to need to have 90% of the population tilling the soil just to feed us. At this point in the United States there are fewer farmers than there are playing World of Warcraft.

From his very first example, it sounds like automation isn't limited at all! Less than 1% of the population of the United States is involved in agriculture. That's a two-orders-of-magnitude improvement in productivity. So what are those 89% of people who used to farm doing? At first, manufacturing:

And in manufacturing, we have very few people working assembly lines now, and yet manufacturing output is a lot bigger than you might think, even in America, despite all the de-industrialization. But we have not found ways to have robots doing most of the things that involve interacting with complex physical environments.... Go out for an early morning walk and you'll see lots of short men from Central America taking care of the garden, right? Things that involve actual physical labor, most medical procedures, technology has done very little so far to be labor saving.

I can scarcely believe this is an economist speaking. Those "short men from Central America" are not going around with garden shears and push mowers - they're using gas-powered edgers and riding mowers, and they're using them because - guess what? - they save labor! The same number of men can do more in less time with that technology. The same is true in medicine in a different way. Remember my grandfather who was laid up in bed for six weeks? That's six weeks of lost labor from him, plus his care while in the hospital. With me, I lost one day of work and didn't spend a single night in the hospital. That's a huge labor savings.

Krugman makes up for it a bit with a good followup point:

Human wants tend to be infinitely extensible: it's not as if there's a fixed amount of stuff we want. If people had been willing to stop at a 1955 standard of living, we could all be working 20 hour weeks, but in fact, one way or another, people wanted more.

Correct. We are much more productive, but we also want more stuff. Furthermore, the premise (that we haven't gained in leisure time) is wrong. Krugman again:

In the United States, up until about 1970, we did take part of our gain in productivity in the form of increased leisure time: shorter work hours, growing vacations. And that did actually continue in Europe, but in the United States it just stalled, and we still are taking on average about two weeks of vacation.

Right again, sort of. At the beginning of the 20th century, it was not uncommon to work 60-80 hours a week, with no vacation. Americans have made a different trade-off between leisure and stuff than Europeans, but that's all we can really say. But Krugman is only "sort of" right because Americans working full time actually get an average of 3.9 weeks of paid vacation and holidays per year. The French get an average of 7 weeks. It's worth remembering these numbers when both he and Stross start exaggerating them later on.

Stross perhaps goes a bit too far here: "If you want Utopia, just move to France. Thirty-five hour working week, 8-10 weeks vacation a year, and their overall productivity is equal to anyone in America." Aside from the fact that Stross's numbers are wrong, the problem is the mandatory nature of vacation. In America, you have at least some choice about your leisure/work balance. In France, the work week and vacation time is mandatory. That's Utopia? Maybe in America we prefer to work more and take more expensive, shorter vacations than the French. Is this obviously a bad idea?

But do we have a choice in America? A later questioner brings this up and Krugman has more to say:

Effectively it's not possible for an individual to say, "All right, I think 20 hours of work a week is enough to provide everything I want." The world is not geared to 20 hour work weeks, there are all kinds of signaling aspects. There's an element where people want you to prove that you're committed, and so you can't actually work humane hours, because if you do then you must not really care. So what you do in a place like France is that there are 35-hour legal work weeks, there are mandated vacations, all of these things which enable them to collectively move to a position of working shorter hours and some indication that that does lead to more personal satisfaction.

So the 40-hour work week we have in America is inhumane, but the 35-hour weeks in France are humane? I admit I don't get it. The average Frenchman works 25-30% fewer hours per year than the average American. This is far less than the difference between the average American today and the average American a century ago. Krugman is just riffing to a receptive audience here.

And does it lead to more personal satisfaction? There may be "some indication" that it does, but there is also plenty indication that it does not. The world map of happiness shows the U.S. ranked 23rd out of 178 nations surveyed (and the highest-ranked really large nation). France comes in 62nd. "Industry is the enemy of melancholy," said William F. Buckley. Why should we assume that more leisure equals more happiness?

If an individual American wants to work less and earn less, then I certainly hope he can find a way to do so, even if that means emigrating to France. But I equally hope that we don't try Krugman's proposal of "collective action" to force us all to do so. Americans are choosing to forego even the vacation time they do get, so it isn't like we're chafing for more and being thwarted by our corporate paymasters.

Krugman and Stross: Intellectual Property

Krugman brings up the topic of intellectual property: "Even though the Internet is all old hat, we still haven't seen the economics of it play out. One of the big problems is we don't know how do people get compensated for producing information when it can be...." He doesn't get to finish the sentence, but I assume he meant it to go something along the lines of: "...copied easily and cheaply everywhere in the world instantaneously."

Stross has fascinatingly contradictory ideas about this:

As for the intellectual property, I try not to get too worked up about it.... [W]hat we're looking at with copyright today is a smoking hole in the collective landscape....

(Sure, why get worked up about a mere smoking hole in the collective landscape?)

We can't simply wave a magic wand and change the copyright laws to something sensible.... Now the best thing I've been able to come up with is an idea for doing this is a tax on bandwidth.... The tax goes into a pool which is then distributed to content creators on the basis of some kind of sampling or rating mechanism that's sampling the traffic that's going across the network. How to enforce this, let alone deal with it internationally is mind-numbingly don't-go-there... but at least it has the one supreme advantage that if you have such a regime in place, you can legislate that if you've paid your tax, you are then immune from prosecution for copyright violation. [emphasis mine]

This is just trading one intractable problem for another one, though. If you could enforce an international tax on bandwidth, trust the sampling agencies, carry out the disbursement of funds correctly and inexpensively, and so on, then it all sounds great. But frankly, just changing copyright laws sounds simpler, or at least no harder.

Krugman suggests an analogy to financial ratings agencies:

When the ratings agencies originally came into existence they would produce a book of ratings and people would buy the book and that was how they made their revenue. And that has long since been impossible, [because] people tend to disseminate the ratings too easily, so nobody buys the books so they had to find a different revenue stream. And some decades back the source of the revenue stream [changed so] that issuers of assets would pay the ratings agencies to rate their assets.

[N]ow the question is, what do you do? And everybody looks at this and says, "This is a terrible way to do this." But then the question is how are you going to fund the rating agencies? And there is a certain number of people who say, "They should be public." They should be the BBC. But in America of course, well that wouldn't work, it'd be government. So we can't use that.

Typical Krugman: every time a problem seems hard, he thinks we should just fob it off on the government. Here's an alternative: get rid of the ratings agencies. Do we really need them? We already have very effective ratings of financial assets: they're called prices. Ratings agencies might just be fossils left over from a time when information was expensive, trading was thin, and capital flowed sluggishly. All that has changed.

Krugman and Stross: Artificial Intelligence

Krugman next asks Stross a good question: "Do you think that true AI [artificial intelligence] is [likely] anywhere in my lifetime?"

Stross's response is to say that we already have it to some degree: grandmaster-level chess-playing computers, expert medical diagnosis systems, self-driving cars, etc. But he doesn't quite mention what I wish he had, which is that general intelligence is a whole different animal. Writing a program to solve a single problem like playing chess may be computationally challenging, but it's not intelligence. Krugman gives him a good lead-in to this topic:

[W]hen I took computer science... the instructor told us all that by getting chess-playing computer programs we'd learn a lot about the nature of consciousness, and we ended up learning a lot about the nature of chess.

That's probably inevitable when focusing on a specific problem like chess. It's pretty clear that Deep Blue (the chess supercomputer that beat Kasparov in 1997) was not simulating the thought process of an actual chess grandmaster in any meaningful way. This subject is incredibly deep, more so than I want to go into right here. Stross does mention one interesting quote from Edsger Dijkstra: "The question of whether a machine can think is no more interesting than the question of whether or not a submarine can swim."

I'm not sure I agree with Dijkstra on this one. What he seems to mean is that problems of definition overwhelm what you really want to talk about, so that the question becomes meaningless. But one could take him to mean that a submarine is a mechanism to accomplish the same task that swimming accomplishes for living things. If so, then analogously an AI computer should accomplish the same tasks that thought accomplishes for living things. Clearly we do not possess such an AI today - our best computers only accomplish tiny subsets of what our brains can do. But the question is certainly more interesting that definitional ones about whether submarines "swim."

Krugman and Stross: Network Economics

The next interesting topic (skipping over some less interesting ones) is on the economics of distribution networks - right up Krugman's alley. Stross leads off:

But going a step further, there's a huge inefficiency in these hub and spoke models of distribution and shipping stuff long distances. If you can produce stuff locally, and distribute it locally, that gives you a huge advantage.

Er... really? Actually, transportation costs have dropped by orders of magnitude (a point Stross himself made earlier), to the point where they are a fraction of the retail cost of most goods. This didn't used to be the case. Whole cities used to spring up along rail lines or rivers or canals because the transportation cost along those corridors was so much lower than anywhere else, and the low-cost corridors were scarce enough that a lot of commerce was packed into any particular one. These days if you need, say, a computer shipped from Asia and can wait a couple of weeks, it comes - extremely cheaply - by sea to a port, then by truck to a distribution center, and then by smaller truck to our doorstep. There are still low-cost corridors, but they are both ubiquitous (highways and roads) and very cheap. Even if you need that computer more quickly, it can shipped by air in a day or two; the cost of air freight has dropped very rapidly.

However, even if the transportation cost is low, it is still a cost that does not need to be paid if the item is produced locally. So is there an advantage to local production? For some goods (milk, let's say) there is because of spoilage. But for many goods the production cost is simply far lower elsewhere than near wherever you happen to be. Modern economies involve thousands of products, the production of each of which involves dozens or hundreds of intermediate goods, raw materials, etc. There's an extremely complex interchange of materials. The odds are very good that not all of these goods will be most efficiently produced locally. There are economies of scale in most production, after all: instead of having ten separate factories, it's usually more efficient to have one factory with a tenfold greater capacity. But that one factory has to be in one place, which means it isn't in all those other places; if you want the goods that factory produces, you have to ship them there.

This isn't really complicated or mysterious. Which is why I'm mystified that Krugman (Nobel Prize-winning economist) has such a weak response to Stross:

That's by the way one of the mysteries — we don't quite know why there's so much stuff being shipped long distances.... Why were they traveling and — better still, when you're flying between Cleveland and Atlanta, what is it that Cleveland has that Atlanta needs? What is it that Atlanta has that Cleveland needs? Actually, what is that Atlanta has that anyone needs?

Surely Krugman understands comparative advantage? Even if Cleveland produces everything more efficiently than Atlanta, Atlanta must have some good that it is comparatively best at producing next to Cleveland, and that is what Atlanta will tend to export. But Krugman's elitist tendencies get in the way. Perhaps he is playing to his Canadian audience: they enjoy hearing a joke at Atlanta's expense. In a nutshell this has been Krugman's career since become an opinion journalist: he trades on his (impressive) academic economics background to get people to listen to his vacuous, ill-thought-out biases and prejudices. He really should know better.

Stross, incidentally, comes to Krugman's rescue here:

I reckon that complexity, the number of different components, the number of different specialties that you need to run a modern, high tech civilization has mushroomed by orders of magnitude over even the past 50 years. And all of this stuff is really small, very, very specialized, there's only a very few people who do it in one place and it has to get shipped about even though it looks similar.

That's right. The science fiction author is teaching economics to the Nobel Prize-winning economist.

Krugman and Stross: Future Shock

Moving on to the topic of "future shock", Stross suggests that religious fundamentalism is a response:

People don't like rapid change when it's applied to them against their will, when it's coercive, and when people don't like something, an external stimulus, they tend to kick back against it. Religious fundamentalism boils down very largely to one thing: certainty in life.

There are several problems with this thesis. One is that "progress" (generally defined) has been ongoing since... well, really since time immemorial, but the most obvious point to date it from is the Industrial Revolution. Once that got started in earnest, each generation saw a clear rise in living standards and technology from the previous one (prior to this point, technology advanced slowly enough not to be disruptive during a single generation). But religious "fundamentalism", by which I assume Stross means a rejection of the Enlightenment and return to safe religious dogma, has not risen in step.

A second problem is that Krugman and Stross just finished saying in the prior segment that we haven't seen much rapid advance in technology if the past fifty years - that it has flattened out. But if that's true, then where's the shock?

A third problem is that their terms are horribly biased. "Religious fundamentalism" is really a poor name for the general movement to reject the Enlightenment. This movement can be traced back to the Romantics at the start of the 19th century, and continues into Postmodernism. But when Krugman is talking about "religious fundamentalists", he's not talking about that. He conflates (a) Islamic fundamentalism, which traces back at least to the Wahhabi movement, and probably could be traced pretty easily back to the point at which the Islamic clearly was losing supremacy to Christendom (the Battle of Lepanto in 1571? the siege of Vienna in 1683?); (b) Jewish orthodoxy, which he claims has been on the rise recently among an "amazing number of relatives of [his]"; and (c) Christian (mostly Protestant) fundamentalism, which he traces back to the rise of radio in the 1920s. Is it really possible that each of these really reflects "future shock"? They seem amply explained by other mechanisms. Maybe future shock is some sort of meta-mechanism underlying everything, but Krugman and Stross are not at all convincing that this is the case.

A final problem is in the assumptions: people don't like change when it's coercive. I think that can be simplified to: people don't like being coerced. But regardless, what does that have to do with technology? Technology doesn't coerce. If a person doesn't want to use a computer, he doesn't have to. There is social pressure, sure, but that is not coercion. I think some people may not like technology (or more properly: that which it represents, i.e. the Enlightenment) and react against that, but that is not what Stross was saying. Coercion in our lives might be coming from the large faceless corporation we work for, or the enormous governments we fund with our taxes. But that isn't future shock.

Krugman and Stross: The Pace of Technology

Their first topic is technology: Where are our flying cars?

[Stross] Actually, flying cars are a really bad idea, if I can just go off on a tangent. Your flying car is great, what about your neighbor's flying car when his 15 year old son gets into it and tries to impress his girlfriend in it?

Indeed. Krugman talks a bit about kitchen technology:

If you walked into a kitchen from the 1950s it would look a little pokey, but you'd know what to do. It wouldn't be that difficult. If someone from the 1950s walked into a kitchen from 1909 they'd be pretty unhappy — they might just be able to manage. If someone from 1909 went to one from 1859, you would actually be hopeless. The big change was really between 1840 and the 1920s, in terms of what the physical nature of modern life is like.

I don't know enough about mid-19th century kitchens to judge this, but let's take it as given.

A few points worth mentioning. First, of course not all areas of life will develop the way we envisioned fifty years ago. Second, of course they won't all develop at the same pace. They vaguely touch on these points. But what they don't mention is that some areas have advanced far beyond what we envisioned fifty years ago: medical technology, for example. My grandfather had his gall bladder removed surgically in the 1950s. He was bedridden for about six weeks, recovering from the large incision made in his abdomen. I had my gall bladder removed laparoscopically in 1998. The procedure was done on a Friday. I was back at work on Monday, and was able to resume full physical activity within a week or so. Many medical procedures done today would have been inconceivable fifty years ago.

I'm not even mentioning microcomputers, the most obvious unexpected advance. Or cellular phones. One way to grasp how recently cell phones have transformed our lives is to think of the sit-com Seinfeld. How many plots would have been short-circuited by a simple cell phone call or text message?

Even in the products they use as examples - transportation, household goods - there has been huge progress. Things cost much less than they used to, when measured in terms of how many hours we must work in order to buy them. Stylish products of a type that used to only be affordable to the upper class are now available at Target. (And new forms of style have supplanted them at the high end. There is always a high end. But the gap is surely far less than it once was.) Kitchen devices may be functionally equivalent to 1950s devices, but they are as a rule more energy efficient and more reliable. Aircraft may not be hypersonic, but they are more fuel efficient and safer; the same goes for cars.

When we are plucking low-hanging fruit from the tree of technology, the pace of invention may seem tremendous because every new advance rushes to market. But when the advances get less obviously beneficial (say, the "improvement" from regular cars to flying ones), markets resist. We could certainly build a flying car now, at some price, but why? Who would buy it? And as Stross pointed out, aren't there serious safety issues? In many fields that seemed hot during the golden age of science fiction, the technology really has continued to improve, but mass market acceptance hasn't been there. The products just aren't needed.

Krugman and Stross on the Future

At the "Anticipation" World Con in Montreal, Paul Krugman (Nobel Prize winning economist and columnist for the New York Times) and Charles Stross (Hugo-winning science fiction author) discussed what the future will look like. In the next few blog posts I will dissect their remarks, pointing out a few things I think they missed and a few cases of Krugman being outrageous.

Derbyshire Math Problem of the Month

I'm trying to resist writing too much about one of my nerdy loves - math - on this blog, but every now and then I will give in to temptation. This is one of those times.

One of my favorite and unexpected phenomena in mathematics is when a general case turns out to be easier to prove than a specific case. This is counterintuitive, of course: usually, specific cases are easier. One famous example is Fermat's Last Theorem (which states that for n>2, there are no non-trivial integer solutions to the equation xn + yn = zn). It's quite easy to prove this for the specific case n = 4. But the general case resisted all efforts at proof for hundreds of years (until Andrew Wiles finally succeeded in 1994).

The problem we're looking at today is simple to state. Consider the following pattern:

1 + 2 = 3
1x2 + 2x3 + 3x4 = 4x5
1x2x3 + 2x3x4 + 3x4x5 + 4x5x6 = 5x6x7

Prove that this pattern continues.

It's useful to turn this into a little "math-speak" before going any farther. We use the symbol "!" (read "factorial") to indicate the product of sequential integers. For example, 4! = 4x3x2x1 = 24. This only works for positive integers (there are ways to define "factorial" for other numbers, but they are well beyond the scope of this blog). It's pretty easily to express products like the ones in the problem above using factorials: 5x6x7 = 1x2x3x4x5x6x7/1x2x3x4 = 7!/4!. There's one other thing about factorials that needs to be said, and that is that 0! = 1. Don't worry too much about why this is so (one way to see it is the following relation: 3!/3 = 2!, 2!/2 = 1!, 1!/1 = 0!).

So we can rewrite the problem like this:

1 + 2 = 3
2!/0! + 3!/1! + 4!/2! = 5!/3!
3!/0! + 4!/1! + 5!/2! + 6!/3! = 7!/4!

But what about that first equation? From looking at the other two, it looks like we can write it like this:

1!/0! + 2!/1! = 3!/2!

And it fits. So the pattern can be written in a nice ordered way using factorials. We need to show this:

n!/0! + (n+1)!/1! + (n+2)!/2! + ... + (2n)!/n! = (2n+1)!/(n+1)!

It's worth looking at this for a minute or two and seeing how, if you substitute n = 1, 2, and 3, you get the three equations we've been writing down thus far. What we need to do is show that this works for any n.

So here's the interesting part: it turns out that this last equation is tough to prove directly. But a more general equation is pretty easy. Here's the more general one:

n!/0! + (n+1)!/1! + ... + (n+k)!/k! = (n+k+1)!/k!(n+1)

If we can show this is true, then setting k = n gives us the equation we want to prove.

First, suppose k = 0. Then our general equation says:

n!/0! = (n+0+1)!/0!(n+1)

That looks OK.

Second, let's look at that general equation again:

n!/0! + (n+1)!/1! + ... + (n+k)!/k! = (n+k+1)!/k!(n+1)

Suppose it's true. What happens if we add another term?

n!/0! + (n+1)!/1! + ... + (n+k)!/k! + (n+k+1)!/(k+1)! = (n+k+1)!/k!(n+1) + (n+k+1)!/(k+1)!

The right-hand side can be simplified:

= (n+k+1)!/k!(n+1) + (n+k+1)!/(k+1)!
= (n+k+1)!(k+1)/(k+1)!(n+1) + (n+k+1)!(n+1)/(k+1)!(n+1)
= [(k+1) + (n+1)] (n+k+1)!/(k+1)!(n+1)
= (n+k+2) (n+k+1)!/(k+1)!(n+1)
= (n+k+2)!/(k+1)!(n+1)

(I went through that pretty quickly, but almost all of the hard parts come from the fact that (n+1) times n! = (n+1)!, for example, 8x7! = 8!. That fact comes straight the definition of factorials.)

But take a look at that simplified right-hand side. We've just showed this:

n!/0! + (n+1)!/1! + ... + (n+k+1)!/(k+1)! = (n+k+2)!/(k+1)!(n+1)

which is just the general equation for k+1 instead of k. And that's good, because now we've inductively proved the general equation. See, we showed it worked for k=0, and then we showed that if it works for k, then it must work for k+1. So if it works for k=0 then it must work for k=1, which means it must work for k=2, and so on, ad infinitum. It works for all k. In particular, it works for k = n. And that's what we needed to show.

Monday, August 3, 2009

Gatesgate: The Photo

I don't have much to say about the Beer Summit, but the American Thinker had some ideas about an official White House photo that has been making the rounds.

Sergeant Crowley, the sole class act in this trio, helps the handicapped Professor Gates down the stairs, while Barack Obama, heedless of the infirmities of his friend and fellow victim of self-defined racial profiling, strides ahead on his own. So who is compassionate? And who is so self-involved and arrogant that he is oblivious?

Eh. Maybe I'm revealing something unpleasant about myself here, but I have to admit that I don't get this controversy. Obama and Gates are supposedly friends. Maybe Obama knows that Gates can get down steps like those just fine with his cane, and hates being helped - I've certainly known plenty of slightly infirm folks with that sort of fierce independence. Maybe two seconds before the picture was taken, Obama was checking to make sure his friend was in good hands. Or maybe Obama is really as arrogant as he's being described.

We really don't know from the picture. Obama acted on insufficient information when we said that the police acted "stupidly" when dealing with Gates, but the American Thinker is committing the same error here. In both cases, the symbolism struck a chord with the viewer's ideology, and this resulted in jumping to an unwarranted conclusion.