I suggest you make reading the article “The Deadweight Loss of Christmas” by Joel Waldfogel a new personal tradition. It is available for example, courtesy of the Wall Street Magazine.

The basic idea of the article is simple. Giving people stuff ought to be less efficient than giving people cash in the same amount that the stuff cost. The reason is that typically people could choose to buy the same thing they got as a gift if that is what they really wanted, but with the cash they also have other options.

The article claims that the inefficiency of giving in-kind is considerable since in many cases people would prefer to spend the money on other things. In other words, people did not like their gifts.

Explaining exactly why such an apparently inefficient tradition as Christmas gift giving has managed to survive is an interesting problem. Of course the obvious alternative, of people just giving each other money, might seem a little silly, despite the attempts of Hollywood mafia movies to make it cool.

Of course the sum is convergent, as can be seen by comparison with the Basel series for example.

Wolfram does compute a numerical approximation to the sum it claims diverges. This approximation is accurate I think. Maple however refuse to compute more than 2 digits of the sum.

One can quite easily see however that it can be approximated as with an error of size . With the help of this one can compute the sum more accurately than Maple wants to do.

The lesson is that we can not quite let computers do all the thinking for us yet.

So when I came up with another name that involved a poor mathematical-political pun I deciced to change the name. Thus I am now the Free Algebraist.

The blog is not quite dead. I actually have a couple of ideas for blog posts. We’ll see if and when I get the energy to actually write them.

Let be the sequence of partials sums, ie . Form a new series with . It turns out that the new series always is divergent despite the fact that the terms are much smaller.

I will give a proof, following Knopp’s amazing book.

If the do not converge to zero there is nothing to prove. So suppose they do converge to zero. I will show that the partial sums of the new sum grow like the logarithm of the partial sums of the original sum. We note that so has the limit .

We have that and now it is an easy exercise to show that this converges towards .

Thus not only does the sum diverge, we have an estimate for its growth in the case that the terms go to zero.

I had not remembered to what extent Polonious is a fool and comic character .

But watching Hamlet again also made me recall a wonder concerning Ophelia’s death I have always had. Did she really commit suicide?

Would not the king and queen find it convenient that she stopped going around and causing rumors? Certainly she would be an embarrassment for the Danish court.

And is it not rather suspicious that the queen can give such a detailed description of Ophelia’s death, yet gives no indication of any attempts to save her life? Probably I have read to many novels by Agatha Christie and John Dickson Carr but I have always been convinced that Ophelia was murdered.

But imagine that we only now that the curve integral is zero for circles of two different radii, and . Can we still conclude that is analytic?

The answer turns out to be yes, unless the ratio is equal to the ratio of two positive zeros of , the Bessel function of the first kind and order 1.

I found this statement in an exercise in Gamelin’s textbook on complex analysis.

Carr was an American author who lived in the UK for many years and most of his stories take place there.

His books are excellent entertainment but not much more. They are not filled with insightful social commentary, excellent character portraits or poetic language. But they brilliantly plotted and utterly engrossing. (At least many of his books are. Some of his later works are quite weak.) And if you think the main goal of literature is to entertain, as I do and Carr did, then his works fulfill their goal admirably.

I have not read them all but many of his most famous ones. Of those that I have read I think that “The Judas Window” is perhaps the best. To be sure, “The Hollow Man” is a classic, but the solution to it, and some of Carr’s other books, is perhaps too complicated. The solution in “The Judas Window” is simple and immensely understandable on the other hand. The reader is also given clear hints to it, making it feel like you are being taunted by the author. Certainly “The Judas Window” is an excellent introduction to his authorship for new readers.

That Carr was something of a conservative is clear from his books. But his exact political views are non-too-clear based only on them. He seems to have viewed attempts to upset the established social order with suspicion. He does not appear to be religious though and does not appear to have any problem with extra-martial sex. Compared to Christie, who wrote at the same time as him, his books deal with sex in a franker fashion. (Which is not to say that they are sexually explicit in any way.)

At least one of his later books, “Papa-la-Bas”, makes him come across as a complete reactionary who thought the wrong side won the civil war. His other books are rarely that reactionary however, and his historical fiction typically does not glamorize the past.

The main offense against contemporary political correctness would probably be that his main characters are typically male and middle class.

Unfortunately these type of scientific reports is almost always poor research. Perhaps there is a religious or anti-religious motivation to some of this research that biases the results*.

But the main problem with these type of reports is scientific arrogance. Frequently they ignore what historians have learned about the proposed story, such as whether it is likely that there is any basis in fact.

The article PZ Myers discusses seem to make that mistake as well. There is no discussion of what history can tell us about the proposed crossing. In fact, historians are not certain that any Israelites fled Egypt (though it is surely plausible) and much less that it was an appreciable number. In fact, the idea that a large of number of people came from Egypt to Palestine is contradicted by the archaeological evidence.

The paper does not discuss this, nor whether a small event could have been magnified in the retelling. Certainly, disregarding the question of whether anything similar to the crossing of the sea happened, it seems just from the text of Exodus that there were several version of the story circulating.

What is unusual is that is has been published in a reputable scientific journal. I wonder if they had any archaeologists or historians act as peer reviewers.

*Surprisingly to me, a religious motivation seems quite common. I would expect that a Biblical literalist who thinks the Israelites really crossed the sea would not want to explain it away as a natural occurrence.

Even worse is that the search engines do not disregard things like the list of recent posts that you frequently find on blogs. Thus occasionally you might get hits on essentially every post every written on the blog, even though only a small fraction actually mention the word you are searching for.

Rather the interesting question is what the post says about Myer’s prejudices. Specifically when he complains that the Supreme Court is “packed with Catholics” he is engaging in stereotyping about the group of Catholics. It is of course true that there are many Catholics on the Court but it far less clear that there is any connection between that and the judicial outcomes Myers dislikes.

Myers’ problem is with the fact that a number of justices are conservative or more accurately originalist. This has very little to do with their Catholicism. They themselves would deny a connection between their judicial opinions and Catholicism. And any observer can see that the Supreme Court majority is not on some path to reshape the US according to Catholic moral theology.

They have for example voted to allow the death penalty, despite the fact that the death penalty is immoral according to Catholic thinking. This is probably the clearest example but there are other areas where one could also find a conflict between Catholic thinking and Supreme Court rulings. Thus, the broad free speech guarantees secured by the Supreme Court even for example blasphemy and pornography strikes me as something that the Vatican would hardly applaud.

I thus think Myers phrasing was indeed a result of biased thinking and not rational thought. This is the problem with the overly harsh rhetoric that Myers sometimes engages in. Not that it scares away moderates but that it is not conductive to clear thinking.