A little fragmentation

At the request of my uncle, who helps run the Splintered Light Bookstore, I'm reading through a book entitled, Mathematics through the Eyes of Faith, which is part of "through the eyes of faith" series. I intend to write a review fairly soon, once I finish, but at the moment I just had a general comment to make about the "through eyes of faith" series. The concept of such a series seems both familiar and strange to me. Many Christians I interact with regularly are of the kind to ask the "big questions" about how faith and life connect, about how to view everything in light of the gospel, about how to bring all things under the authority of Jesus Christ. From a Christian point of view, this seems like the right mission, even if it is an enormous undertaking. Thus, in particular, many Christians are wondering how the various academic disciplines relate to the faith; hence, this series.

On the other hand, something feels a little strange about the kinds of ideas which result from this grand endeavor. Some will argue (not the book I'm reading) the rather extreme position that mathematics makes no sense outside of a Christian worldview. That would be a powerful apologetic if it made any sense to anyone other than those making the argument. Others take the more moderate approach of just trying to draw vague but highly stimulating connections between a particular discipline and Christian faith. For instance, what does Cantor's theory of infinity say about God? Does belief in a personal infinite being open up avenues of inquiry to us which may not have otherwise existed? (Such might be suggested by the very interesting book, Naming Infinity.)

But whatever ideas you might generate by looking "through the eyes of faith," the simple fact is that all disciplines, from mathematics to history to philosophy, continue onward without adhering permanently to one guiding framework. Paradigms come and go. The notion that we need to be constantly aware of how all knowledge fits into a bigger picture can be quite stifling, or at best irritating. No, I'm really not thinking about God every time I recall a result from functional analysis in order to prove a theorem about a system of partial differential equations. Asking me to explain how this new truth I've discovered relates to the gospel is, from my point of view, silly. Frankly, I don't expect mathematics to look noticeably different "through the eyes of faith" than through any other set of eyes.

I think a case can be made for a little fragmentation in our lives. This is precisely what many Christians seem to think is wrong with the secular world: we live in many different parts of reality without being integrated into a whole. But I'm not convinced this is so much of a problem. In fact, it might be worth being more intentional about this. For instance, I highly recommend that everyone make a point of fragmenting political issues from one another. Gay marriage, abortion, prayer in schools, immigration, medicare, and terrorism are all completely unrelated issues. By saying "completely unrelated" I may have made the above statement false, but if you let yourself believe that it is true for a least a little while, you might end up thinking about each issue more rationally, without allowing your views to be predetermined by the one big picture that now informs all of your beliefs. The more we are in the habit of seeing everything through a single lens, the harder it becomes to resolve our differences without entering into conflict.

We may not be willing to say that some beliefs and ideas are unrelated to faith, but perhaps we can at least say that we do not know what the relationship is. Maybe we can never know. In our vain life, sometimes we must simply be content to solve the problems which are solvable, and to leave to God the things that are mysterious. A holistic worldview is perhaps but a chasing after wind.

Bryan Caplan on immigration restrictions

This guy is fantastic.

It's a long video, so here's a brief synopsis: Most of the arguments against free immigration are based on claims that are at best exaggerated. Moreover, even if we accept all of the reasons usually given, there are cheaper and more humane ways to deal with the problems mentioned. For instance, if we're concerned about immigration lowering wages (which doesn't happen to any significant extent) or about immigrants soaking up welfare benefits (which really aren't that much to begin with) there is a simple solution: charge a flat fee for immigration (say, $30,000), or have a higher rate of taxes (say, an extra 10%) on immigrant workers. These suggestions are just concessions, of course. The real point is this: once a reasonable person has heard the facts, there really is no moral reason why he should oppose open immigration.

"What is Debt?"

That's the title of an interview with economic anthropologist David Graeber (hey that name sounds familiar) on "naked capitalism." Excerpt:

Yes there’s a standard story we’re all taught, a ‘once upon a time’ — it’s a fairy tale.

It really deserves no other introduction: according to this theory all transactions were by barter. “Tell you what, I’ll give you twenty chickens for that cow.” Or three arrow-heads for that beaver pelt or what-have-you. This created inconveniences, because maybe your neighbor doesn’t need chickens right now, so you have to invent money.

The story goes back at least to Adam Smith and in its own way it’s the founding myth of economics. Now, I’m an anthropologist and we anthropologists have long known this is a myth simply because if there were places where everyday transactions took the form of: “I’ll give you twenty chickens for that cow,” we’d have found one or two by now. After all people have been looking since 1776, when the Wealth of Nations first came out. But if you think about it for just a second, it’s hardly surprising that we haven’t found anything.

Think about what they’re saying here – basically: that a bunch of Neolithic farmers in a village somewhere, or Native Americans or whatever, will be engaging in transactions only through the spot trade. So, if your neighbor doesn’t have what you want right now, no big deal. Obviously what would really happen, and this is what anthropologists observe when neighbors do engage in something like exchange with each other, if you want your neighbor’s cow, you’d say, “wow, nice cow” and he’d say “you like it? Take it!” – and now you owe him one. Quite often people don’t even engage in exchange at all – if they were real Iroquois or other Native Americans, for example, all such things would probably be allocated by women’s councils.

So the real question is not how does barter generate some sort of medium of exchange, that then becomes money, but rather, how does that broad sense of ‘I owe you one’ turn into a precise system of measurement – that is: money as a unit of account?

By the time the curtain goes up on the historical record in ancient Mesopotamia, around 3200 BC, it’s already happened. There’s an elaborate system of money of account and complex credit systems. (Money as medium of exchange or as a standardized circulating units of gold, silver, bronze or whatever, only comes much later.)

So really, rather than the standard story – first there’s barter, then money, then finally credit comes out of that – if anything its precisely the other way around. Credit and debt comes first, then coinage emerges thousands of years later and then, when you do find “I’ll give you twenty chickens for that cow” type of barter systems, it’s usually when there used to be cash markets, but for some reason – as in Russia, for example, in 1998 – the currency collapses or disappears.

The whole interview is rather fascinating. On the whole, Graeber's argument would appear to strike a blow to capitalism as it has evolved into a modern economic theory. He sharply criticizes the tendency to view all human behavior in terms of exchange. He shows how money evolved from debt, and how debt came from the threat of violence, and how this threat of violence most often came from the State.

How then can capitalism be a necessary condition for a free society, as Milton Friedman so forcefully argued? Well, I think the answer is not to turn to Friedman but rather to Hayek. Many of Graeber's points are good reminders that classical liberals and libertarians can't just construct a society axiomatically from principles such as property rights, without regard for history. But this just leads me back to The Fatal Conceit, which addresses precisely the question of how civilization evolved into the extended order which now holds together by the forces of the market.

While it would certainly be much nicer to think of the "invisible hand" emerging from peaceful developments in human civilization, we need not reject a system merely because of its origins. In fact, that's the whole point of evolution: it may be a grueling process, but what emerges is not the same as what went into the process. For instance, the State may have established money as a way to exercise power over its citizens. However, this is certainly not the only function which money has come to serve. The ability to use existing artifacts for purposes other than those originally intended continues to be a major source of innovation and progress. Under the term "artifacts" we may include both physical objects and abstract artifacts, such as social conventions and morals.

Graeber's point that not all human interaction is exchange is well-taken. Hayek's argument certainly does not rely on this myth. Rather, his argument is that exchange was the vehicle through which interactions with people we don't know could take place. So, for instance, when Graeber says, "Communism is in a way the basis of all social relations – in that if the need is great enough (I’m drowning) or the cost small enough (can I have a light?) everyone will be expected to act that way," Hayek would respond that this works just fine in a situation where you can actually see all the needs. If, however, you want a system in which people all over the world can benefit from the vast human potential that exists scattered among people who have no way of knowing anything about one another, the only system that we know of is that of exchange.

Hayek said that the one contribution he made to the science of economics was to point out how the price system worked as an abstract signal to regulate extended cooperation. If the price system had been intentionally designed for that purpose, he said, it would have been the most astonishingly brilliant achievement of mankind. As history shows, the real story is not so pretty, but the end result is still worth keeping.

That's not to say that the current understanding of debt and money must remain constant. Indeed, we never would have advanced as far as we have without changes in our cultural norms. In a world where so much debt is sovereign debt, I think it's worth taking seriously the idea of debt forgiveness, and what a fresh start could mean for the global economy. We're playing a dangerous game. Libertarians ought to take this very seriously: we can't pretend to live in a world where "property rights" are a fixed concept, and we need to understand the relationship between debt and coercion.

Since I find what he says so profound, I'll let Graeber have the last word on this:

Since antiquity the worst-case scenario that everyone felt would lead to total social breakdown was a major debt crisis; ordinary people would become so indebted to the top one or two percent of the population that they would start selling family members into slavery, or eventually, even themselves.

Well, what happened this time around? Instead of creating some sort of overarching institution to protect debtors, they create these grandiose, world-scale institutions like the IMF or S&P to protect creditors. They essentially declare (in defiance of all traditional economic logic) that no debtor should ever be allowed to default. Needless to say the result is catastrophic. We are experiencing something that to me, at least, looks exactly like what the ancients were most afraid of: a population of debtors skating at the edge of disaster.

Irrational Voters

Here's an entertaining talk (part 1 of 6) from Bryan Caplan on "The Myth of the Rational Voter":

The overall point is troubling, but not unexpected: yes, it does actually make a difference how uninformed the public is about political matters. For instance, Caplan cites research showing that anti-market bias is markedly more prevalent among voters who are less informed about the facts. Those who count as "informed" here are of course not universally libertarian free market ideologues, but there are things on which people educated in certain areas can actually agree, regardless of ideology. (One comment I found interesting, but again not surprising, was that most economists are moderate Democrats, who believe in many free market policies in spite of their left-wing views.) As a result of the gap between informed and uninformed, many people support irrational policies (for instance on tariffs or what have you) even when they hurt us.

If you get to the end, you'll hear him start to talk about prescriptions. One idea is to have voters tested on basic knowledge before they vote. I understand why this is controversial, although I think people are a little too biased against this. Another idea is to "work on our communication skills"--for Caplan, this means that economists in particular should work on making basic economics presentable to the public. I grow weary of this idea. It's something we in the academy talk about endlessly, but we have very few concrete ideas about how to do it. Just as there are very few incentives for the average person to learn what experts know, so there are also very few incentives for academics to go out of their way to make key ideas popular.

In the long run, we absolutely do need ways to limit democracy. There is no question that if popular ideas are always allowed to become policy, democracy will ruin itself. In my opinion, this strengthens the argument for limited government. The argument goes like this:

1. If people are to have government ruling over them, it ought to be by the people's consent. That is, it ought to be democratically chosen.
2. If a society is going to be healthy, it must be protected at times from imposing its own irrational beliefs on itself.
3. Therefore, a healthy society ought to have a democratically elected government which is limited in its powers.

If we reject point (1), we end up with authoritarianism. If we reject point (2), we end up with chaos. The average American believes very strongly in point (1), but many people are eager to reject point (2), which ironically leads to more and more coercive actions by government.

Candidate for change

What is the one thing the President of the United States can actually do in office? For all the policy questions candidates have to answer in debates and forums, very few of those policies can actually be put into practice directly through the Executive branch of government. The vast majority of these policies are enacted through laws made in Congress.

But there is one thing which fundamentally depends on the President, especially at this point in our history: the military. After all, he is, you know, Commander in Chief of the armed forces. If a U.S. President decided that the best thing after all would be to pull back from Iraq and Afghanistan, that would actually make a guaranteed difference--unless, of course, Congress actually declared war, which it hasn't done in...65 years?

And that's exactly what Ron Paul would do first as President:

In other words, Ron Paul is probably the only candidate who would be able to change anything substantial about what government currently does, because he is the only candidate who has staunch beliefs against our current foreign policy.

Bringing our troops home would, by the way, save us on the order of $500 billion per year.

Ron Paul is often cast as a fringe candidate with views too far outside the mainstream for the average voter. But let's face it: if Ron Paul were President, most of these views wouldn't matter, because he wouldn't be the one making laws. The way I see it, then, we ought to elect him in 2012 because on the one issue that he could influence most, he is in favor of much needed change.

In other words, the most fundamental characteristic of Ron Paul as a presidential candidate is that he is anti-war. I happen to agree with many other things he believes in, but even if you don't agree with him on anything else, peace might just be a principle worth supporting.

Now you see why the Republican party establishment hates him so much. This ain't no George W. Bush.

By the way, beside Rick Perry, Ron Paul is the only veteran in the presidential race; he was a flight surgeon during Vietnam.

"How Obamacare is Destroying Accountable Care Organizations"

That's the title of an article from Forbes. Excerpt:

“Accountable care organizations” is the health wonk phrase du jour. Obamacare’s advocates point to its support for ACOs as one of the important cost-control initiatives in the law. Except that, like nearly everything about Obamacare, the truth isn’t so simple. It turns out that the government’s idea of an accountable care organization is completely unworkable, to the point where nearly all leading health providers have declared it dead on arrival.

It turns out these organizations are already being tried--under the Medicare Advantage system, which is a privatized system. But just to make the invisible hand a little more visible, the government insists on spending hundreds of millions of dollars to try out their own version. Only, the government model doesn't seem to be as popular; I wonder why?

On March 31, Donald Berwick’s Centers for Medicare and Medicaid Services issued 427 pages of proposed rules and regulations that will govern how ACOs will operate.

In May, ten groups that participated in an ACO pilot program called the Medicare Physician Group Practice Demonstration, including leading centers like Dartmouth-Hitchcock, Geisinger, and the University of Michigan, told CMS in a letter that it would be “difficult, if not impossible” to participate in Obamacare’s ACO program, due to its incessant federal micromanagement and high start-up costs.

Once again, ladies and gentlemen, your tax dollars hard at work.

The future of education

If a revolution in education production is possible, this is it:

"Humanizing the classroom"--with technology, incidentally. It's more than just humanizing the classroom; it's individualizing education. Educators have always been searching for ways to give each student the chance to move at her own pace; now that opportunity is readily available.

A colleague of mine is actually trying this method with her calculus class. Apparently you can make your own video lectures, which she has done, and she is assigning the lectures as homework. Then the entire classroom experience is for the students to work on what used to be homework. I'm really excited to see how it goes for her. I'd be willing to try this teaching method in the future; I sort of wish I'd thought of it before we started this semester.

And this is all thanks to YouTube...and a former hedge fund analyst. Spontaneous order, indeed.

Newcomb's Paradox

From Wikipedia:

A person is playing a game operated by the Predictor, an entity somehow presented as being exceptionally skilled at predicting people's actions. The exact nature of the Predictor varies between retellings of the paradox. Some assume that the character always has a reputation for being completely infallible and incapable of error; others assume that the predictor has a very low error rate. The Predictor can be presented as a psychic, as a superintelligent alien, as a deity, as a brain-scanning computer, etc. ...

The player of the game is presented with two boxes, one transparent (labeled A) and the other opaque (labeled B). The player is permitted to take the contents of both boxes, or just the opaque box B. Box A contains a visible $1,000. The contents of box B, however, are determined as follows: At some point before the start of the game, the Predictor makes a prediction as to whether the player of the game will take just box B, or both boxes. If the Predictor predicts that both boxes will be taken, then box B will contain nothing. If the Predictor predicts that only box B will be taken, then box B will contain $1,000,000.

By the time the game begins, and the player is called upon to choose which boxes to take, the prediction has already been made, and the contents of box B have already been determined. That is, box B contains either $0 or $1,000,000 before the game begins, and once the game begins even the Predictor is powerless to change the contents of the boxes. Before the game begins, the player is aware of all the rules of the game, including the two possible contents of box B, the fact that its contents are based on the Predictor's prediction, and knowledge of the Predictor's infallibility. The only information withheld from the player is what prediction the Predictor made, and thus what the contents of box B are.

So which do you choose?

The paradox is that there are two lines of reasoning which both appear to be "rational," yet produce opposite conclusions. The first is this: since the Predictor has already placed the money in the boxes, my decision has no effect on whether or not B has $1,000,000. I should choose both boxes, since that will give me more money than if I only chose one. The second line of reasoning is this: the Predictor is never (or almost never) wrong, so I should choose just box B, because if I choose box B then it will be $1,000,000.

A couple of interesting observations. First, it seems to me to make all the difference in the world whether or not you're the one actually making the choice. If I were observing someone else make the choice, I would think, "Gosh, I hope for his sake that he's the type to take just box B, because then surely he will make more money." But if I'm the one who has to choose, well, it's hard to make such a statement about myself.

There's an interesting discussion about the paradox here, although it's a bit long. The perspective taken there is an appealing one, in my view: rationality ought to win. It's no excuse for the rationalist to say, "I choose both because this is the most logical answer; I cannot help the fact that I am rational and therefore wasn't given the option of making $1,000,000." If that's what it means to be rational to you, then rationality isn't going to get you very far.

Another interesting question: what if the Predictor tells you the money is for charity? Does that change the rationalist's reasoning? Logically speaking, it shouldn't.

I'm adding this to my list of lovable paradoxes, because yet again we have an example demonstrating how reason is insufficient for making decisions. Sometimes logic is an obstacle to being rational.

The politics of peace

If I could sum up my objection to both the right and the left in American politics, it would be to say that both movements believe that progress is made fundamentally through conflict. Conservatives believe that progress is made through protecting "Western culture" or "American values" and by defeating the enemies of freedom; hence going to war and violently defending our borders are often necessary components of progress. For liberals, progress is made by winning the inherent conflict between the rich and the poor, or between the privileged class and the underprivileged class, or between the majority and the underrepresented minority. This also manifests itself occasionally in violence, as for instance when labor unions in the past have violently coerced workers to fall in line with their policies. But even if violence is not as welcome on the left as on the right, coercion is, whether in the form of taxation or bureaucratic regulations.

The fundamental reason I am a libertarian is because I believe that progress is not made primarily through conflict, but through peace. Competition has been overemphasized in expressing the value of free markets. Yes, competition protects the consumer in a free market, but the kind of competition we're talking about is not a zero sum game, because free exchange means mutual benefit, and mutual benefit means a net positive for society. Free exchange is not only the natural result of peace, but it also helps to create peace. People who benefit from one another are not likely to soon become enemies. Nor can friends do anything but freely exchange, since the very nature of friendship is to desire mutual benefit.

I believe in open borders, non-interventionist foreign policy, free trade with all nations, and minimal regulations on private affairs. In other words, I believe the purpose of government is to promote peace in all facets of life. The reason I believe this is that I think the goal of human civilization is a world in which humans don't look at one another with suspicion, and I think the first step toward this goal is to first drop our own suspicion of others.

The politics of conflict can never be satisfied; on the one hand there always seem to be more people threatening to undo our culture, and on the other hand there always seem to be more greedy people who prey on the weak. At some point, wisdom demands that we drop our weapons and seek peace with our enemies, even if this means losing what feels like the battle for justice.

Is it possible that Americans will ever give up the conflicts which have driven our political ideologies? On the answer to that question may rest the fate of civilization as we know it.

What about the minimum wage?

Nothing says "I'm a cold-hearted capitalist" like saying the minimum wage should be abolished.

...But it really should.

There is a simple, sound economic argument against the minimum wage, and those who reject the argument, no matter how intelligent they might be, are really being quite irrational. That is because we let our instincts get the best of us. We ask ourselves, isn't a worker better off if he is paid enough to live on? The answer to this question is obviously "yes." But that isn't the question. The question is, how does a higher wage for some workers affect others?

The clear, irrefutable wisdom of the economists is this: a minimum wage will cause overall low-wage employment to go down. This hurts unskilled workers--not the workers who actually are working, mind you, but only the workers who can't find work because it isn't available to them.

The video below is from Milton Friedman's "Free to Choose" series (the link is here), and it is primarily about labor unions, but it also features a vigorous debate (second half of the video) about the minimum wage:

As Walter Williams points out in the video, the minimum wage law is really a law that says, "If you are unable to produce labor worth $X an hour, you are not allowed to work." It is difficult for the average person to see a minimum wage law as a violation of workers' rights, but in fact it is. It is, unfortunately, a belief in the mythical power of words that leads us to think that declaring a minimum wage actually improves the lot of poor people. As Milton Friedman points out, why wouldn't we just declare the minimum wage to be $200 an hour?

However, before you conclude that I really am, after all, a cold-hearted capitalist, consider my alternative. Instead of a minimum wage, why not simply subsidize wages using a moderate wealth redistribution plan? If the wages of a laborer really are too low to be considered living wages, the best plan is to subsidize those laborers until they can find better work.

Under this plan, instead of a minimum wage, there would be a "target wage." If workers happened to have wages below the target wage, the government would pay a certain proportion of the difference. For instance, the federal minimum wage is currently $7.25 an hour. We would need to make the target wage a little higher for my scheme to work, so let's make the target wage about $10 an hour, and have the government pay 50% of the difference between a person's actual wage and this target wage. So if a person got hired at, say, $4 an hour, he would in fact be paid $7 an hour once the subsidy is included. Even a person whose wages were desperately low would still get at least $5 an hour with the subsidy.

This scheme would mean two things: (1) workers would probably have more opportunities to find a job, any job, and begin acquiring skills, and (2) workers would have greater freedom to choose between employers based on factors other than wages--perhaps someone would rather start working at a small business for lower wages than work at Wal-Mart. There is a third benefit which goes to us as a society: the taxpayers would be subsidizing productivity. Given that you usually get more of anything you subsidize, isn't it a positive thing to subsidize employment rather than unemployment?

Overall, this plan would be moderately progressive, taking a little bit from the rich to give to the poor; but it would also be a little more consistent with Econ 101 and with the principle of freedom of contract between employer and employee.

Consumer expectations

Here is episode 7 of Milton Friedman's series "Free to Choose." In it Friedman argues for ending the power of government institutions to control which products we are allowed to buy. He argues the consumer self-regulation is a more powerful, non-coercive way to provide goods in such a way that properly balances safety with value.

Fast forward to the discussion at the end of the video. One of the problems that I think is really worth thinking about is mentioned at the end by a representative of automobile safety regulators. She says that now that cars have been subject to certain regulations for so long, consumers have a certain standard, anything less than which would not be tolerated. That is, if government were to suspend these regulations, producers would probably not depart from them, anyway, because customers would still demand them.

I'm inclined to agree with this analysis. Indeed I hesitate to take either her side or Friedman's in the debate, because I'm not sure we're really working with the right principles. Friedman wants to make the point that no one has the right to tell consumers what to buy. But he also seems to want to make empirical claims about the results of a free market. Can he have both? It appears to me that if you use a certain preset target as an empirical measure of market effectiveness, then you've implicitly rejected the normative principle about personal rights.

Indeed, the fundamental argument for a free market is that it allows society as a whole to unconsciously calculate the relative value of infinitely numerous objectives. Safety and the preservation of life are only two objectives out of thousands that a person has. The free market is supposed to coordinate the thousands of interests of every individual with one another, allowing them all to flourish simultaneously to the maximum possible extent. Obviously not all objectives can be reached equally well, or even at all.

But if there are certain objectives embedded into the public consciousness, especially regarding the preservation of human life, what is the possible response? It seems entirely possible that coercive power will often be taken not as coercive, but as a breath of fresh air, if you will, or a sort of wake up call reminding us of something we wish we had thought of all along. Regulations on automobiles will cause consumers to realize, yes, we really do want seat belts and air bags in all of our vehicles. We really were so foolish not to have demanded this earlier. Once the idea is implanted into the public consciousness, it completely changes the market.

It would be interest to run a sort of experiment on the public at large. Introduce a regulation on some business, say on automobiles, but don't let anyone in the public know about it. Then see how many consumers object to it: for instance, how many would demand the car company sell them a cheaper vehicle with less gas mileage? Now then, wait a few years until the regulation becomes totally standard. Then get rid of the regulation, and just see what happens. It would be fascinating to see whether consumer expectations could be so altered by coercive power that their "individual preferences" would actually conform to a forced standard.

If that were the case, and I suspect in many ways this is undeniably the case, it would make the case for a free enterprise system much more difficult on empirical grounds. If the system is designed to coordinate the various interests of individuals, it becomes much harder to recognize success when in fact it is so easy to change the interests of individuals using subtly coercive means.

I conclude, then, with a frank admission: I simply do not know how to defend liberty. I am actually rather sure that personal autonomy is, to a greater extent than we will admit, an illusion. But I am even more certain that we are arrogant and foolish to think that there is any fully justified basis on which "we as a society" can cause greater prosperity through comprehensive schemes, such as regulations on industry. In general, I suppose I am just a pessimist with respect to human reason. The more we learn, the more we ought to realize we don't know.

Food for thought

Ron Paul's predictions from the past decade on the housing bubble, the economic crisis, the wars in Iraq and Afghanistan, Osama bin Laden, and the expansion of federal government.

What if people had been listening to this guy earlier?

What does it mean to be infinite?

Taking a break from my intensely political posts to write about mathematics again. I'm going to teach an honors class this fall which will deal with some advanced topics like set theory and cardinality, which deal with basic questions like, what is the size of a set?

I've been thinking about such questions ever since I ran into the possibility some years ago that math could have evolved without counting. You see, sets in mathematics are inherently discrete constructions. They consist of elements, each element being perfectly distinct from all the other elements. The size of a set can only be measured, then, by counting the number of distinct elements. You can tell if sets have the same size by matching elements together; if one set is bigger than another, you'll always have some elements left over in that set. Just think of boys and girls at a dance; if every boy has found a girl partner and there are still girls left over, obviously there are more girls than boys.

But counting isn't the only way we think of size. You can tell one object is "more" than another in several ways. Visually something could just be bigger than something else. One cup could have more water in it than another cup--just compare the height of the water in matching containers. One object could be heavier than another--just use a balance. None of these comparisons require actually coming up with numbers. "More" and "less" still have meaning even if there's nothing distinct about a given quantity.

I have written before about how the mere ability to distinguish two things can conceivably lead to an idea of discrete elements, thereby leading to counting, thereby leading to all of classical arithmetic, etc. But that seems pretty unnatural.

What I thought about doing instead was a thought experiment, built on the premise that mathematics develops with commerce. For this thought experiment we will want to assume that very different resources are being traded than what we are accustomed to. We count things because we have so many resources which can be conveniently counted--you know, cows, chickens, ears of corn, that sort of thing.

Everyone's down on education

From the Onion:

Despite years of putting up with underperforming teachers, overcrowded classrooms, and a gradually deteriorating educational experience, American students reluctantly announced Tuesday that they would be giving the nation's public school system yet another chance this fall.

Saying they would "probably kick themselves later" for deciding to enroll once more in a system that has let them down time and time again, millions of American children agreed to put up with their schools' insufficient funding and lack of adequate arts and science programs in hopes that administrators might finally start providing a nurturing, or at least tolerable, environment in which to learn.

The rest goes as you'd expect.

If people generally agree that the American public school system is such a failure, why does nothing change? Why do we still see our performance come out so low on international rankings? Why do we still see such a high achievement gap? Most of all, why are people generally so unhappy with the system?

Here's a suggestion for how to improve schools: stop hiring education majors. Or at least, stop hiring only education majors. Need a math teacher? Hire someone with a master's degree in math. How about science? Even someone with a bachelor's in chemistry, physics, or biology could probably do a world of good. Particularly at the high school level, my feeling is that endless lists of courses in pedagogy just really aren't that important for teachers who specialize in a subject.

There are plenty of people out there who would make brilliant teachers, precisely because they'd taken the time to master a particular subject. It takes a great deal of confidence to get up in front of people and teach them a lesson. What better way to have confidence in your teaching ability than to have a rich understanding of the subject extending beyond the material being presented? We all know that a teacher's enthusiasm for a subject improves the students' ability to learn it, and likewise a teacher's anxiety about a subject greatly harms the students' ability to learn it.

This is really a very simple, practical way we could start improving public schools immediately, and in fact it's already being done in charter schools. Private schools have always been free to do this. Why not public schools? I have no idea. Sometimes political realities are just incomprehensible. I guarantee you, it's not about the children.

If we're going to fix education, it might just have to be the hard way: demanding more charter schools, or taking the homeschooling option (without being exempt from paying taxes to fund public schools, I might add). The political process is broken. Indeed, I find it a little difficult sometimes to distinguish the Onion's reports from reality:

Grateful for another opportunity to amend its past administrative blunders, the Department of Education was quick to promise it wouldn't let students down this time and would do all it could not to mess everything up again.

"We want to thank all of our students for this vote of confidence," Education Secretary Arne Duncan said in a special televised press conference. "We are seriously going to work harder than ever before this year and make some real changes. I promise. Students will not regret giving us this chance."

"That being said, funding is a little tight right now, so try to keep your expectations within reason," Duncan added.

"The One"

Ron Paul's latest campaign ad picks up on a label more often applied to Barack Obama, at least during the 2008 campaign. Of course, any time someone talks like this about a particular politician, it sounds pretty weird. In this case, I think it's fun because (a) Ron Paul is legitimately not mainstream, and (b) he actually is the most consistent politician that anyone can name.

Is he "The One"? Well, who cares. It's just fun to support the anti-establishment figure.

We need space aliens to get fiscal stimulus

That's what Paul Krugman says:

Question: if economic activity is focused on solving a problem that doesn't exist, does it really improve the economy?

Common sense tells us no; Paul Krugman tells us yes. The Nobel Prize winner is surely quite brilliant, but sometimes brilliance goes a long way in justifying things that make no sense.

World War II, it is said, got us out of the Great Depression. Just because World War II forced everyone to be employed doesn't mean it added value to the economy. Obviously the opposite happened: people died, and resources were spent on things which have no value except during war time.

So what did get us out of the Great Depression? It turns out there is an explanation that rejects both the New Deal and World War II as possible cures. Robert Higgs argues that 1946 was the turn-around year, owing not to the government spending during the war, but rather to a renewed faith in personal property rights and investment opportunities--the New Deal was over, and so was the war, both of which drew resources away from the civilian economy.

I am not an economist, but I am a firm believer in drawing conclusions about important political issues using good morals and common sense. If someone suggests that a deception may be useful in stimulating the economy, there's something wrong with his theory. If someone suggests that war can be good for the economy, there's something wrong with his theory. If someone suggests that digging random holes in the ground is "better than nothing," there's something wrong with his theory. All of these are violations of either our morals or good common sense, or both.

So no, I don't trust Krugman on this. We don't need space aliens.

(HT: Sheldon Richman and Mary Theroux, who has another post about WWII here.)

In Defense of Ron Paul

The political blogosphere is depressing. Part of the reason for that is what I think of as the tyranny of pragmatism. Asking for realistic solutions all the time has the tendency to favor the status quo. Our sense of realism is almost entirely shaped by what we've tried before. It's only when our sense of frustration with the status quo reaches critical mass that we're willing to consider something ideologically pure, impractical, radical.

That's why I'm just going to indulge myself in a little optimism about the "Ron Paul Revolution." After all the times I've heard Paul speak, I've never found a more consistent politician. His belief in personal freedom protected by limited government extends into all areas of politics, from free market economics to bringing our troops home from Afghanistan and Iraq.

There's something deeply ironic about the political idea of individual liberty. The message is that individuals free from coercion can produce a complex social order that acts for the benefit of everyone, without the guidance of superior elites. But we humans need figureheads to get messages heard. In other words, we can't avoid having a political elite, whether it's people like Barack Obama or George W. Bush or Ron Paul. Right now, Ron Paul sits just outside the mainstream. Because I can't think of a figurehead who espouses more consistently the political principles I believe in, I'm afraid I'm just going to have to be one of those annoying fans of his.

It's worth mentioning that Ron Paul was a very close second in the Iowa Straw Poll. Fox News, of course, focused on Bachmann and barely gave two words to Ron Paul. At least Bill Maher likes him.

The search for pro-life intellectuals

Students for Life of America has an interesting little blog post on the difficulty of finding an academic advisor for a pro-life group on a college campus.

Advisors of student-run groups are a necessity at most colleges and universities in the U.S., since they, theoretically, help with administrative logistics, resources, and almost always help get your group “official” recognition by the university administration. But the growing number of student pro-life groups who are unable to find a sponsor are shining a light on a whole new injustice.

If you can’t find a professor willing who is pro-life or willing to stand up for their beliefs, your constitutionally protected right of speech is silenced.

...

The fact is, plenty of professors may not have the time, willingness, or courage to sponsor student-run pro-life groups, no matter what their views, and this poses a real threat to the exposure of the pro-life movement to young people across the country.

From personal experience, I wouldn't say an academic advisor is all that essential for actually doing things, but this probably varies from school to school. Whatever the case may be, I suppose one could call it an injustice that student groups are not allowed to exist without a faculty representative, even when such a representative is unavailable. Each school will have its own policy on this, but the best policy would be one that favors free speech and allows even fledgling student groups to organize themselves on campus.

But frankly, that is neither here nor there. SFLA is missing something huge in terms of long-term strategy: sooner or later, we're going to have to get to the root of the problems faced by pro-life student groups. I don't care what kind of gains the pro-life movement makes in national public opinion polls; as long as 90% of professors on college campuses remain resolutely pro-choice on abortion, the United States will never see Roe v Wade overturned. It is not enough for SFLA to protect students from the intellectual climate on these campuses. In the long run, we have to define the intellectual climate.

Charles Darwin on the Creator

Occasionally in Origin of Species Darwin mentions God, in ways that seem in some sense to defend his character. For instance, there's this quote from Chapter V:

He who believes that each equine species was independently created, will, I presume, assert that each species has been created with a tendency to vary, both under nature an under domestication, in this particular manner, so as often to become striped like the other species of the genus; and that each has been created with a strong tendency, when crossed with species inhabiting distant quarters of the world, to produce hybrids resembling in their stripes, not their own parents, but other species of the genus. To admit this view is, as it seems to me, to reject a real for an unreal, or least for an unknown, cause. It makes the works of God a mere mockery and deception; I would almost as soon believe, with the old and ignorant cosmogonists, that fossil shells had never lived, but had been created in stone so as to mock the shells living on the seashore.

And then there's this (rather lengthy) quote from Chatper VI, which comes in the middle of explaining how the eye may be the product of incremental changes:

It is scarcely possible to avoid comparing the eye with a telescope. We know that this instrument has been perfected by the long-continued efforts of the highest human intellects; and we naturally infer that the eye has been formed by a somewhat analogous process. But may not this inference be presumptuous? Have we any right to assume that the Creator works by intellectual powers like those of man? If we must compare the eye to an optical instrument, we ought in imagination to take a thick layer of transparent tissue, with spaces filled with fluid, and with a nerve sensitive to light beneath, and then suppose every part of this layer to be continually changing slowly in density, so as to separate into layers of different distances from each other, and with the surfaces of each layer slowly changing in form. Further we must suppose that there is a power, represented by natural selection of the survival of the fittest, always intently watching each slight alteration in the transparent layers; and carefully preserving each which, under varied circumstances, in any way or in any degree, tends to produce a dinstincter image. We must suppose each new state of the instrument to be multiplied by the million; each to be preserved until a better one is produced, and then the old ones to be all destroyed. In living bodies, variation will cause the slight alterations, generation will multiply them almost infinitely, and natural selection will pick out with unerring skill each improvement. Let this process go on for millions of years; and during each year on millions of individuals of many kinds; and may we not believe that a living optical instrument might thus be formed as superior to one of glass, as the works of the Creator are to those of man?

Adam Smith showed how the market may be the product of human action, but not of human design. Darwin showed how biological evolution may be the product of divine action, but not of divine design.

Charles Darwin on "Chance"

Although the theory of evolution is now progressed far beyond Darwin's original work On the Origin of Species, I thought it would be interesting to read through it, for historical perspective, and to round out my education (I never did learn very much biology). I'm not finished, but a couple of things have caught my eye that I wanted to write down.

Many people take issue with Darwinism based on the general idea that it promotes chance over design, thus making the universe out to be chaotic and purposeless. But that's not how Darwin himself wrote about it. Chapter V is framed by the following statements:

I have hitherto sometimes spoken as if the variations--so common and multiform with organic beings under domestication, and in a lesser degree with those under nature--were due to chance. This, of course, is a wholly incorrect expression, but it serves to acknowledge plainly our ignorance of the cause of each particular variation.

...

Our ignorance of the laws of variations is profound. Not in one case out of a hundred can we pretend to assign any reason why this or that part has varied. But whenever we have the means of instituting a comparison, the same laws appear to have acted in producing the lesser differences between varieties of the same species, and the greater differences between species of the same genus.

In other words, we only perceive natural selection as due to "chance" because it occurs in systems of so many constituent parts that we cannot possibly know how they all relate to one another. Or better, "chance" is simply an expression of our ignorance, not nature's chaos.

Darwin's assumption is a very modern one: there must be some underlying principles which are both comprehensible to humans and universally applicable to what humans perceive in nature as distinct objects. Creationism, by contrast, asserts that the existence of the several species is fundamentally inexplicable: God spoke, and the species came into being, and that's as far as we can go. I consider both of these ways of thinking to be in tension throughout the history of Judeo-Christian thought. On the one hand, God's inexplicable intervention into history is central to the message of Scripture, particularly on Mount Sinai and at the resurrection of Christ. On the other hand, God's faithfulness, sovereignty, and wisdom are also essential parts of his character, and creation is thus characterized as fundamentally driven by principles which are comprehensible to human beings.

Can we therefore say that Darwin's idea is thoroughly unbiblical? True, it goes beyond the creation account in Genesis, as some would say attempting to see the "story behind the story." But if one were to completely forbid this kind of attempt from Christian thought, would we not have to give up all talk of the Triune existence of God, seeing that we do not ever see this explicitly spelled out in Scripture? Indeed, most Christians see the Trinity in the first few lines of Genesis: the Spirit is present in the "wind," and the Son is present as the Word of God speaking all things into existence (cf. John 1). Is this not also an example of seeing the "story behind the story"?

One final point: discovering the underlying principle does by no means remove all mystery from the universe. Even in light of modern genetics, there is no way we will ever be able to predict the long-run outcomes of evolution, as it is driven by countless tiny variations of which we will never be fully aware; much less can we possibly conceive of their future use. Because the process is so far beyond our control, we may thus call it a matter of "chance," but only if we are so inclined for reasons other than the facts themselves.

How exactly does it pay to be fat?

Via Tyler Cowen, I found this article entitled, "It Pays to Be Fat." The thesis:

After controlling for all other attributes that contribute to wages (an individual’s job experience, firm size, region in which they reside, occupation, sector, full or part-time employment, health, education, age, and whether or not they have young children) the author finds that married men and single women both have a wage rate that is positively related to the their Body Mass Index (BMI) – the heavier they are, the higher the wage they are paid. Single men and married women have the opposite experience – they are penalized for their weight -- the heavier they are, the lower the wage they are paid.

Their explanation is somewhat provocative, but a few things seem a little off to me. First, how can you control for "health" when you're comparing people based on level of obesity? Isn't being obese considered "unhealthy"? I'm not sure how exactly this control works. Suppose it means that a thin woman would have to be unhealthy in other ways in order to be considered equal in health to an overweight woman. Perhaps certain causes of lack of health, such as smoking habits, could contribute in some way to lower wages? This may be grasping at straws.

But secondly, what I'm more concerned about is that part of their explanation explicitly states that "heavy women recognize that they may not marry or have the advantage of living in a dual income household. They therefore invest more in their jobs so that they get closer to that standard of living they might have had they married." Um, so, if you don't control for different levels of investment in work, how can you possibly claim to detect some sort of "discrimination"? Either this explanation is false, as it has already been controlled for under "level of experience," or this explanation is true, and there's no discrimination going on.

This stuff becomes news just because it's provocative. I have my doubts about how much sense it really makes. Given how the article ends, I guess it really was just meant as a joke, anyway:

So, there you have it. A new cause for public outcry – slender, single women are under-rewarded in their employment. They should get together with the single, overweight men and demand fair treatment. I doubt it would improve their wages, but it could make for an interesting dating scene.

Maybe I should go into politics?

A NYT article suggests some scientists are tired of being left out of the public arena:

When asked to name a scientist, Americans are stumped. In one recent survey, the top choice, at 47 percent, was Einstein, who has been dead since 1955, and the next, at 23 percent, was “I don’t know.” In another survey, only 4 percent of respondents could name a living scientist.

While these may not have been statistically rigorous exercises, they do point to something real: In American public life, researchers are largely absent. Trained to stick to the purity of the laboratory, they tend to avoid the sometimes irrational hurly-burly of politics.

Hat tip goes to Tyler Cowen, who hopes to see a cultural shift toward higher respect for scientists.

One thing he didn't notice about the article was this amusing paragraph:

Daniel S. Greenberg, author of the 2001 book “Science, Money and Politics” (University of Chicago Press), said in an interview that he thought the odds of success [at making scientists more involved in politics] were “pretty poor,” in part because of the widespread belief that such activity is inappropriate for serious researchers or taints their objectivity. He pointed to the presidential election of 1964, when scientists organized opposition to Barry Goldwater, the Republican candidate. Goldwater was defeated, but, Mr. Greenberg said, the effort left many researchers feeling “we have sullied science.”

I didn't know about this organized opposition to Barry Goldwater before. It makes sense, of course. It's just a little bit ironic, since one of the most prestigious scholarships for undergraduate science students is named after him:

The Barry M. Goldwater Scholarship and Excellence in Education Program was established by Congress in 1986 to honor Senator Barry M. Goldwater, who served his country for 56 years as a soldier and statesman, including 30 years of service in the U.S. Senate.

Oh, what a world we live in.

Who's misreading Adam Smith?

So in an attempt to open my mind to different viewpoints (applause, please), I've been following Think Progress for a while, only to find out what I already knew: bloggers tend to be really biased. It's okay to have certain principles, of course. Some people refer to having an opinion as "bias;" I don't. What I mean by bias is simply the ability to take information and use it solely for your own purposes, rather than seeking to modify those purposes. Take, for instance, this post about "John Bolton's Misreading Of Adam Smith." In it, Ali Gharib criticizes John Bolton for taking a single quote from Wealth of Nations and using it to drum up support for the conservative cause. Bolton is quoted as saying this:

Adam Smith wrote in The Wealth of Nations that “the first duty of the sovereign, that of protecting the society from the violence and invasion of other independent societies, can be performed only by means of a military force.” Today, failing to protect our national security inevitably endangers our economic prosperity by making us vulnerable to global adversaries.

It is clear that President Obama does not agree with Smith’s wisdom. Obama’s policies are jeopardizing not only our national security and economy, but our constitutional sovereignty too.

That is why I have been considering running for President.

Gharib, in turn, uses Smith in the following way:

Other than providing for defense and a robust justice system, Smith wrote that the duties of the sovereign also include setting up “public institutions and public works” for:

facilitating the commerce of the society, and those for promoting the instruction of the people. The institutions for instruction are of two kinds: those for the education of youth, and those for the instruction of people of all ages.

Smith clearly indicates that other duties of the sovereign include educating the populace — possibly up through the university level — and paying for infrastructure projects that keep commerce strong, “such as good roads, bridges, navigable canals, harbours, etc.”

In short, Smith believed not only that governments should shoulder responsibility for the first duty of defense, but for other public projects as well. And how should governments pay for all of this, according to Smith? Well, with a progressive tax:

It is not very unreasonable that the rich should contribute to the public expence, not only in proportion to their revenue, but something more than in that proportion.

So, which side is misreading Adam Smith?

Omar al-Bashir is at it again

If the genocide in Darfur was not enough, now Omar al-Bashir is dropping bombs on South Kordofan. According to the BBC,

Although South Kordofan is north of what will soon be the international border [between Sudan and the newly formed South Sudan], it is home to many pro-south communities, especially in the Nuba Mountains, some of whom fought with southern rebels during the long civil war.

In other words, the North-South conflict is sadly not over.

The Save Darfur Coalition has released a video calling us to action:

You can take action through this link: http://bit.ly/SKaction

The political blog-o-sphere is full of chatter about very complicated, subtle issues, such as economics, climate change, and health care. This issue, by contrast, just isn't that complicated. A nation that cannot find peace under its own government is a nation deprived of basic justice. The only question is whether our leaders are willing to do anything about it. See the link above for more details.

More brilliant social commentary from Failbook

see more Failbook

Please tell me there's a parody video being made right now.

The US has lost its "AAA" credit rating

Boo hoo. Here's Reuters' report:

The United States lost its top-notch AAA credit rating from Standard & Poor's on Friday in an unprecedented reversal of fortune for the world's largest economy.

S&P cut the long-term U.S. credit rating by one notch to AA-plus on concerns about the government's budget deficits and rising debt burden. The move is likely to raise borrowing costs eventually for the American government, companies and consumers.

"The downgrade reflects our opinion that the fiscal consolidation plan that Congress and the Administration recently agreed to falls short of what, in our view, would be necessary to stabilize the government's medium-term debt dynamics," S&P said in a statement.

Probably this is bad for the economy in the short run, but overall, I think there's something healthy about this. It shows that there are checks and balances working on the government from outside. For instance:

Obama administration officials grew increasingly frustrated with the rating agency through the debt limit debate and have accused S&P of changing the goal posts in its downgrade warnings, sources familiar with talks between the administration and the ratings firm have said.

It's nice to know that government still has to answer to people outside of itself.

Unfortunately, this fiscal crisis (as crises tend to do) has had a perverse effect on our political process. In truth, it ought to be during times of plenty that we seek to restore fiscal sanity. It ought to be when the economy is booming that the government seeks to eliminate waste and make difficult long-term budget decisions, which are even more costly to make during a recession. Tragically, it's only now that the private sector is doing poorly and unemployment is high that people are just scared and angry enough to think about fiscal responsibility. It shouldn't take a crisis to make us think about these issues.

Perhaps Alex Tabarrok's "Unbalanced Budget Amendment" is the right idea: make government get a surplus during times of plenty, precisely so that we can go into debt during a recession. Does this not accord with our basic sense of morality? In times of plenty, save for the future; in times of need, be generous with what you have. Now it seems like we have the opposite: government spends a lot when the nation is prosperous, and then it tightens up when things are most desperate!

It will be the undoing of our democracy if we can't figure out how to regulate government's behavior so that it doesn't behave in such an adolescent fashion.

"Evangelicalism Without Blowhards"

That's the title of a recent NYT editorial by Nicholas Kristof. (HT: DZ) Excerpt:

IN these polarized times, few words conjure as much distaste in liberal circles as “evangelical Christian.”

That’s partly because evangelicals came to be associated over the last 25 years with blowhard scolds. When the Rev. Jerry Falwell and Pat Robertson discussed on television whether the 9/11 attacks were God’s punishment on feminists, gays and secularists, God should have sued them for defamation.

...

Those self-appointed evangelical leaders come across as hypocrites, monetizing Jesus rather than emulating him. Some seem homophobic, and many who claim to be “pro-life” seem little concerned with human life post-uterus. Those are the preachers who won headlines and disdain.

But in reporting on poverty, disease and oppression, I’ve seen so many others. Evangelicals are disproportionately likely to donate 10 percent of their incomes to charities, mostly church-related. More important, go to the front lines, at home or abroad, in the battles against hunger, malaria, prison rape, obstetric fistula, human trafficking or genocide, and some of the bravest people you meet are evangelical Christians (or conservative Catholics, similar in many ways) who truly live their faith.

I’m not particularly religious myself, but I stand in awe of those I’ve seen risking their lives in this way — and it sickens me to see that faith mocked at New York cocktail parties.

One remark that I thought was particularly interesting was this one:

Centuries ago, serious religious study was extraordinarily demanding and rigorous; in contrast, anyone could declare himself a scientist and go in the business of, say, alchemy. These days, it’s the reverse. A Ph.D. in chemistry is a rigorous degree, while a preacher can explain the Bible on television without mastering Hebrew or Greek — or even showing interest in the nuances of the original texts.

In context, what this comment indicates is how progressives see a link between expertise and ability/desire to help others. The more enlightened you are, the better equipped you are to save the world. Evangelicals, by contrast, are apt to see the gospel as a story of God using common people to do extraordinary things. I think this difference might be the biggest contributor to the "God gulf" to which Kristof refers.

The way I see it, on either side of the gulf is a sort of triumphalism that needs to be avoided. Changing the world through intellectual prowess and changing the world through "one heart at a time" are equally presumptuous goals. The only way to bridge the gap, in my view, is to learn to say those three little words which we all find so hard to say: I don't know.