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Saturday, May 14, 2005

Brain Teaser

John de Plano has just started a blog on the game Diplomacy called DiploBlogic. He provides this brainteaser for our amusement:

In a country long ago and far away there was a temple to which the people came to request the favor of the gods. In the temple there were three identical statues, and each statue could speak to worshippers on behalf of the god it represented. Though the three statues were identical in appearance, each represented a different god. One statue spoke for the God of Truth, and it always said the truth. Another spoke for the God of Falsehood, and what it said was always false. The third spoke for the God of Diplomacy; it sometimes spoke the truth, and sometimes did not.

The statues would answer any questions the people asked them, but of course different statues would give different answers to the same questions! Since no one knew which statue represented which god, interpreting the answers which the statues gave was pretty tricky, and there were a good many 'religious experts' who claimed to be able to interpret the statues' answers and who charged high fees for their services. It seemed to most people, however, that these experts usually disagreed with each other.

One day a logic student appeared at the temple and announced that she knew how to discover which statue represented which god; it could be done by simply asking each statue one question. The answers would, she said, reveal which one answered truly, which one answered falsely, and which one was diplomatic.

So she entered the temple and stood before the three statues and asked the one on the left, 'What god's statue is standing next to you?' The answer was: 'The God of Truth.' Then to the statue in the middle she said: 'Which god do you represent?' The answer was, 'The God of Diplomacy.' And finally she said to the statue on the right, 'What god's statue is standing next to you?' And the reply was, 'The God of Falsehood.'

'Aha!' said the logic student, 'That makes it perfectly clear!' She then went into business as a religious expert and soon made a fortune interpreting the answers which the statues gave to people's questions, because it soon became obvious that her interpretations were always correct.

Which statue represented which god?"

That Political Test

We posted earlier on the "Political Typology Test" from the Pew Institute. Reader jpg reports that changing nothing but party preference in his answers converted him from "Enterpriser" to "Conservative Democrat." We repeated that experiment with our own answers (including our presidential choice), but even as a Democrat we would be an Enterpriser.

The experience of jpg does raise questions about the validity of the categorization process, though. It seems self-evident that the party affiliation should modeled as one of the output variables (i.e. an effect) not an input variable (i.e. a cause). There are two categories out of eight that explicitly include "Democrats" in the name. No categories explicitly include Republican in the name. Not surprisingly, Conservative Democrat and Disadvantaged Democrat each have 0% Republicans. Even Liberals managed 1% Republican, so it seems likely you must specify your party preference as Democrat or independent to be included in that category.

There is also the previously noted failure in the questionaire to make any distinction between legal and illegal immigration. Altogether these design flaws make the study and the results considerably less interesting than they might have been.

It also seems that if you are reading this blog or Michelle Malkin's and enjoying it, you can probably save time by just skipping the questionaire and marking yourself "Enterpriser."

Plains Feeder

At Plains Feeder, PTG has a sort of 2-in-1 post. The first part is about Condi Rice, but then he shows a picture of an honest to goodness, short range nuke from the sixties, The Davy Crockett: Plains Feeder: King of the wild frontier.

The museum he links to says these babies had a range of 1,000 to 13,000 feet. It doesn't mention the explosive yield, but the idea of firing a nuke at something less than a quarter of a mile away is somehow unappealing.

Still Looking for a Motive

Friday, May 13, 2005

How You Think

This is a fun sort of test of the way we use our brains (Hat tip: Charles at Intentionally Left Blank). The test covers "how" not "how well," and obviously item 3 is terrible advice.

If you do decide to take the test yourself, we strongly recommend you don't use the html code provided. It's riddled with mistakes (essentially every tag is wrong), and has several hidden links back to the site (a dating service). Just take the numbers and run.

Your brain: 60% interpersonal, 60% visual, 20% verbal, and 260% mathematical!

Congratulations on being 400% smart! Actually, on my test, everyone is. The above score breaks down what kind of thinking you most enjoy doing. A score above 100% means you use that kind of thinking more than average, and a score below 100% means you use it less. It says nothing about how good you are at any one, just how interested you are in each, relatively. A substantial difference in scores between two people means, conclusively, that they are different kinds of thinkers.

Matching Summary: Each of us has different tastes. Still, I offer the following advice, which I think is obvious:
  1. Don't date someone if your interpersonal percentages differ by more than 80%.
  2. Don't be friends with someone if your verbal percentages differ by more than 100%.
  3. Don't have sex with someone if their math percentage is over 200%.

My test tracked 4 variables How you compared to other people your age and gender:

You scored higher than 81% on interpersonal

You scored higher than 81% on visual

You scored higher than 36% on verbal

You scored higher than 99% on mathematical

link: The 4-Variable IQ Test.

Thursday, May 12, 2005

Escultura and Wiles III

We have two previous posts on this topic: here and here. However, judging from the traffic on the blog and elsewhere, there is still considerable interest.

Fermat's Last Theorem (FLT) is that for the equation:
x^n + y^n = z^n
there are no non-zero, positive integers for x, y, and z that satisify it for n > 2. This was incorrectly stated in the original article in the Manila Times quoted in the first post on the subject on this blog.

The letters to the editor of The Manila Times include this letter from Roy C. Choco, dated May 10. The copious "[sic]" references were added by the paper. Considering that newspapers routinely edit letters from readers silently to remove these kinds of errors, we surmise that the media in The Philippines are every bit as receptive to constructive criticism as those in the US. Here is Mr. Choco's letter in its entirety:
"I was reading your on-line edition on Thursday (May 5) when I came upon the story about Prof. Edgar Escultura proving the proof advanced by Mr. Andrew Wiles and Richard Taylor on Fermat's last theorem was incorrect. The story is at the very least incomplete and most probably untrue.

First, according to the theory, the refutation of the proof was published in 1998 and was greeted with much discussion on the Internet. A casual Google search on the terms 'proof Fermat's last theorem' yielded websites that only discuss the proof as presented by Mr. Wiles and Mr. Taylor. No mention has been made regarding Mr. Escultura nor his supposed refutation. Did your reporter, Mr. Rony V. Diaz, even made [sic] this kind of cursory search?

Second, according to the story, Mr. Wiles conceded an error regarding his proof and will be reviewing all his proof. But the e-mail was addressed to Mr. Escultura. There is no independent verification of this 'supposed' concession was made [sic]. Did The Manila Times even tried to contact Mr. Wiles regarding this assertion by Mr. Escultura? Nothing in the article leads me to believe that asking Mr. Wiles nor other mathematicians was even considered.

Third, who even said that Mr. Escultura actually refuted Mr. Wiles's proof [sic]? Who or what body was the source of this story? Whom did this person/body/ experts/ decide that Mr. Escultura was correct [sic]? To whom should the readers actually try and validate veracity of the story [sic]?

So The Times ran a story from no-one that was verified by nobody [sic]. Is this the king of journalism [sic] that The Manila Times practices [sic]?� I expected more from your paper.
Obviously, English is not Mr. Choco's native language. However, every one of his points are right on the money. His logic is solid, and his arguments are well-constructed. Mr. Choco missed the sarcasm in the letter attributed to Wiles, but he has plenty of company on that score. Considering the language barrier, even if he suspected sarcasm, Mr. Choco probably would have hesitated to raise that in a public forum.

So what does The Manila Times have to say in response?
"The source of our information, including the letter of Dr. Wiles, was Dr. Escultura. We did not have any reason to doubt him. Escultura published his refutation of Wiles's proof and counterexamples to Fermat's last theorem in: (1) Proceedings of the Second International Conference on Dynamic Systems and Applications, Atlanta, 1995. (2) Exact solutions of Fermat's equation, Nonlinear Studies, 5(2), 1998. (3) Mathematics of the new physics, Applied Mathematics, Computation (138(2), 2001. (4) New mathematics and physics, Applied Mathematics, Computation, 139(2), 2003.

More discussions on the FLT can be found in: (1) Usenet Archives, (2) Archives of Mathforge.Net and (3) Archives of news group Sci Math, among others on the subject.

The editors who published Escultura's refutation and counterexamples are V. Lakshmikantham (USA), M. Sambandham (USA) and M. Scott (USA). Mathematicians who acknowledged and/or congratulated Escultura were R. Agarwal (USA), editor, Archives of Inequalities and Applications; G. Osipenko (Russia), editor, Electronic Journal of Differential Equations; Xilin Fu (China); L. Kusmina (Russia); V. Gudkov (Latvia). "
So we learn a couple of important things here. The letter attributed to Dr. Wiles was, as we suspected, supplied by Dr. Escultura. As Mr. Choco suspected, the paper did no fact checking at all before publishing the story. Furthermore, they still feel no need to check the critical fact of the story, namely the authorship of the purported "concession" email.

Without the "confession" from Wiles of his "error," there's really no story here. Dr. Escultura has been publishing his work on the topic for years in the places cited above, on his own web site, and in The Manila Times. The whole "sizzle" of this story is the Wiles "concession." It absolutely required a verification that the letter was actually from Wiles and that he was in fact abandonning his previous positions on the topic.

We don't suggest that Dr. Escultura faked the email, in fact we are certain he did not do so. However, it is not enough to "trust" him on this. Spoofing an email to make it appear to come from someone else is easily done. It's quite clear no one has checked the email header for evidence of spoofing.

Furthermore we don't believe for a moment that this email letter represents any sort of acknowledgement by Dr. Wiles that Dr. Escultura has refuted his work. We doubt that Wiles had anything to do with the letter, but it is absolutely clear that whoever wrote it was not doing so out of respect for Dr. Escultura's work.

As for the references cited for the work itself, postings on MathForge or Usenet groups prove nothing at all, as will be obvious to anyone who has read such groups. Conference proceedings are not peer-reviewed publications. Math is not our field, so we are not familiar with the journals "Applied Mathematics, Computation" or "Non-Linear Studies," but we have no reason to doubt their legitimacy.

If you're scoring this at home, that's Choco 1, Manila Times 0.

Some other discussions on this topic can be found here and here.

Wednesday, May 11, 2005

Omaha Election Results

Tuesday was election day in Omaha, Nebraska's largest city (some would say "only"). Incumbent mayor, Mike Fahey, easily defeated challenger, Dave Friend, with 60.7% of the votes. All but one member of the City Council was re-elected. Full results here.

The turnout was pathetic, just 24.6% of registered voters. Lincoln's City Council Election last week managed 29.3% without a mayoral contest. While that was nothing to write blog home about, it looks good compared to Omaha's miserable showing.

Political Test

We've noted before that real world political views are much more diverse than the liberal/conservative one dimensional picture we are generally presented with. So we are always happy to see signs of recognition of the richness of the political landscape.

This political "Typology Test" (via Michelle Malkin) is a bit of fun. Their system breaks people up into 8 different politcal groups via a short questionaire.

N.B.: The questions on views on immigration make no distinction between legal and illegal immigrants. This obviously skews things, and it's a serious flaw with the whole thing. We'd venture to say that most people view legal immigrants and illegal immigrants quite differently, and one can only assume the cause is political correctness run wild.

Abe's category.

Too Many Blows to the Head

There may soon be a new simile in American English: "dumb as a Huffington Post," because "dumb as a post" just doesn't say enough. Ryne, on his blog, has a pointer to this gem from Jim Lampley, called The Biggest Story of Our Lives. Apparently, he has some association with boxing, which could explain a lot:
"At 5:00 p.m. Eastern time on Election Day, I checked the sportsbook odds in Las Vegas and via the offshore bookmakers to see the odds as of that moment on the Presidential election. John Kerry was a two-to-one favorite. You can look it up."
Let's see, that would be about the time the inaccurate exit polls were all over the blogosphere and the media. Why would anyone want to bet on Kerry to win at that point?
"People who have lived in the sports world as I have, bettors in particular, have a feel for what I am about to say about this: these people are extremely scientific in their assessments. These people understand which information to trust and which indicators to consult in determining where to place a dividing line to influence bets, and they are not in the business of being completely wrong."
The objective of the oddsmakers is always to get equal amounts of money on each side of the bet. The house rakes in the commission with no risk, because there is no exposure to the outcome. The losers pay off the winners. If the money starts to flow disproportionately to one side of the bet, they raise the odds until it equalizes again. [Jim, in case you're reading this, "disproportionately" means "unevenly."] They do need to stay on top of those kinds of trends rapidly to avoid exposure, but they don't try to predict the winner, just how people will bet. It's incredible that someone who passes himself off as a sports "expert" would not know that.
"Oddsmakers consulted exit polling and knew what it meant and acknowledged in their oddsmaking at that moment that John Kerry was winning the election."
It's hard to tell for sure, but we don't think he's suggesting the oddsmakers ran their own exit polls. We didn't hear anything about another set of exit polls from oddsmakers existing, let alone giving the same flawed results as the ones the network pool commissioned.

We can safely assume that the oddsmakers, to the extent they were looking at exit polls, were looking at the same ones as everyone else. So since everyone at that point thought Kerry was on the way to a massive win, what a surprise: the odds reflected that opinion.
"And he most certainly was, at least if the votes had been fairly and legally counted. What happened instead was the biggest crime in the history of the nation, and the collective media silence which has followed is the greatest fourth-estate failure ever on our soil."
So the actually voting and counting at thousands of locations, supervised by officials from both parties was faked, and the small sample polling done by a few people at a few places is reliable!
"Many of the participants in this blog have graduate school educations. It is damned near impossible to go to graduate school in any but the most artistic disciplines without having to learn about the basics of social research and its uncanny accuracy and validity."
The wording here suggests that other HuffinPosters have told him this, and we can believe them, because they've been to graduate school. Some of them have even taken social science classes!

We particularly love the part about "social research and its uncanny accuracy and validity." This guy should be doing standup comedy instead of boxing.
"We know that professionally conceived samples simply do not yield results which vary six, eight, ten points from eventual data returns, thaty's [sic] why there are identifiable margins for error. We know that margins for error are valid, and that results have fallen within the error range for every Presidential election for the past fifty years prior to last fall. NEVER have exit polls varied by beyond-error margins in a single state, not since 1948 when this kind of polling began. In this past election it happened in ten states, all of them swing states, all of them in Bush's favor. Coincidence? Of course not."
Exit polls have not been in use in presidential elections for 50 years. According to Zogby in this article, that began in the 1970s.

We're fairly certain Lampley would not be able to explain the meaning of the "margin of error" of a poll in a statistically correct way. In essence, it means that if the poll were run again the same way there is a 95% chance the results would be within the stated "margin of error." This assumes "normal" distribution of error, and it only really deals with sampling error. Any bias in the sampling methodology of a poll or in the way the questions are asked can greatly affect the results. Badly done polls exceed the stated margin of error all the time, and even the best polls are expected to exceed it 5% of the time.

Since all the polls were done by the same group of pollsters and the results shared by all the media outlets, there is really only one set of polls here. Voter opinions were sampled at a relatively small number of places that were known in advance (although "secret"). Could Kerry operatives have gotten access to location information and deliberately skewed the exit polls to give Kerry a bounce? It's unlikely, but more plausible than the nationwide vote-fraud conspiracy Lampley is peddling.
"Karl Rove isn't capable of conceiving and executing such a grandiose crime? Wake up. They did it."
Just think, if only Karl had be clever enough to cook the exit polls while he was at it, his scheme would have been completely undetectable!
"The silence of traditional media on this subject is enough to establish their newfound bankruptcy."
I'm not sure why the traditional media's bankruptcy is "newfound." We've known about it for years. Evidently Lampley just found it.
"The revolution will have to start here. I challenge every other thinker at the Huffington Post: is there any greater imperative than to reverse this crime and reestablish democracy in America? Why the mass silence? Let's go to work with the circumstantial evidence, begin to narrow from the outside in, and find some witnesses who will turn. That's how they cracked Watergate. This is bigger, and I never dreamed I would say that in my baby boomer lifetime."
Hmmm. The "mass silence" involves a lot of talking and writing about this dead horse, especially given the complete lack of evidence. "Every other thinker on the Huffington Post"--Talk about an exclusive group. We'll bet they can all fit in one compact car, perhaps even a two-seater. What kind of odds can we get on that bet?

Update 5/11: Ryne has an update on Byron York fisking Lampley's post. This was done right on the Huffington site itself. Evidently, we have at least one "thinker" on there, so we have a driver for the car.

Tuesday, May 10, 2005

How Is Europe a Model?

We often hear people talk about "The European Model," meaning the generous welfare net, worker protections, generous vacations, short work weeks, "free" education, and "free," universal healthcare. Generally, when they call it a "Model," it's with a sense of admiration. The Wall Street Journal's Brian M. Carney has different idea (subscription link only): - Europe Hasn't Outgrown 'That '70s Show': "Given that Europe's streak of economic underperformance can now be measured in decades, perhaps a better question to ask is: Why does anyone think that a system of generous welfare benefits, high taxes and harsh restrictions on hiring and firing would ever produce anything like a dynamic, growing economy? Why does anyone assume that there is such a thing as a 'European model,' rather than just a collection of ill-conceived policies having a predictably depressing effect on the economy and job creation?"
Indeed, the old-line Continental, European countries have been stuck with anemic growth and massive unemployment ever since Jimmy Carter brought the same to the US. The problem is all those benefits cost beaucoup d'argent, which means high taxes to pay for it. The massive spending/tax burden on business and labor and the generous incentives for not working produce (surprise!) lots more people out of work. That leads to higher spending, and around and around the drain we go...
"In 1965, government spending as a percentage of GDP averaged 28% in Western Europe, just slightly above the U.S. level of 25%. In 2002, U.S. taxes ate 26% of the economy, but in Europe spending had climbed to 42%, a 50% increase. Over the same period of time, unemployment in Western Europe has risen from less than 3% to 8% today, and to nearly 9% for the 12 countries in the euro zone. These two phenomena are related; in a country with generous welfare benefits, rising unemployment increases government spending rapidly.

But here a third element enters the picture, creating a feedback loop that explains why the Continent will never regain the halcyon days of postwar growth. As spending goes up, higher taxes must follow to pay for those benefits. But those taxes, usually payroll taxes, must be collected from a shrinking number of workers as jobs are cut. This in turn increases the cost of labor and decreases the benefit of working rather than collecting unemployment or welfare checks. As Martin Baily, a former head of Bill Clinton's Council of Economic Advisers, has described, this can lead to a spiral of rising taxes and falling employment, especially when welfare payments are high, as they are in most of Western Europe.

The result is predictable -- more jobs are lost, the tax base shrinks, and taxes must go up further to pay for yet more welfare benefits, making work less attractive and not working more attractive."
Laws that make it almost impossible to fire a worker, mean that businesses are very reluctant to hire anyone at all. The work hours a French or German employer gets out of a worker in a year is massively lower than American and Japanese employers get from their workers. It's hard to see how the European chemical industry is going to survive the massive costs of regulations already on the books that will require extensive testing of every chemical in commerce.

The European system is a "model" like the idea that every woman can have a high-powered career as a go-go corporate executive, while also being the perfect stay-at-home-mom for six children is a "model." More like a pipe dream, really...

UPDATE: The full version of the article is now available on the free, site.

Monday, May 09, 2005

Wiles, Escultura, and Fermat

We posted last Thursday about this story in Don't Let Me Stop You: Math Wars. Briefly, Dr. Edgar Escultura, a mathematician in The Philippines believes he has refuted some work of mathematician Andrew Wiles of Princeton Univ. The math at issue is a proof, by Wiles, of a 350-yr-old "theorem" of mathematician Pierre de Fermat.

A bit of an international kerfuffle has ensued, as Escultura received a letter, purportedly from Wiles, which was published in The Manila Times with a reply from Escultura. The thesis of the newspaper report is that Wiles' letter had "conceded an error in his proof," admitting that Escultura is correct.

However, as we pointed out last Thursday, the Wiles letter is clearly dripping with sarcasm. The full letter is in the previous post and the Manila Times article, but consider these excerpts:
Also I'd like to have the address of the guy who let you get a PhD 30 years ago. I'd like to discuss few things with him...[elipses in original]
Translation: "How in the heck did you ever get a PhD?"
Your work is incredible, I read all of it just yesterday and let me tell you I respect you.
Translation: "Your work is so simplistic that I read all of it in one day." There's more, but you get the idea. This is not a letter graciously conceding an error, and it does not say an error has been found. It only says:
I am going to review all my 'proof' which I am sure is wrong (thanks to you!).
Coupled with the rest of the letter, this is not an admission of error.

Now this letter may not have been written by Andrew Wiles; it well could be a forgery. Someone could be playing a joke at Prof. Escultura's expense. It is crystal clear, however, that this is not a case of Wiles admitting Escultura has caught him in an error.

Today the Manila Times article is still posted, without any follow up or correction. It's hard to believe that no one has pointed out the obvious sarcasm by now. Perhaps there is a cultural difference between the Philippines and America that makes the sarcasm less apparent.

On the math bulletin board,, Escultura joins in on this thread started by an anonymous jokester on April Fool's Day with this post:
It appears the search for a proof to Fermat's Last Theorem, a 350-year-old problem that has puzzled the greatest intellects in mathematics since its conception, is back underway. Professor Jack Vincenza of Iowa State University took out Andrew Wiles' proof for one last look "on a hunch," a 'hunch' which turned out to be fatal for Wiles and his beloved 'proof.'

"I remembered that the handwriting on one of the long divisions was nearly illegible and the ink was a little smeared," Vincenza said in a press release. Vincenza was tipped off by a conversation he overheard from a bathroom stall where Wiles and a student of Wiles were chuckling about 'pulling a fast one on all of those sorry S.O.Bs.' After working out the long division, Vincenza noticed the mistake. Wiles had, intentionally it seemed, not carried a '3.' "I've been waiting for an opportunity to bring that bastard to his knees for 11 years now," Vincenza said.

Wiles, who responded from Kuala Lumpur where he was preparing to sky surf between the Petronas Towers, said, "I'll show him and prove the Riemman hypothesis. Damn! I'll prove everything if I have to. Shit, I'll carry that three right to his door."

Prof. Escultura's reply two days later missed the April 1 aspect of the first post. Another poster cites the Manila Times article.

The Sassy Lawyer also has a post on this, along with several comments, including this one which is right on the money:
"Carla commented on 05-09-05 at 04:34 AM :
From the sarcastic letter from 'Wiles' (or someone purporting to be Wiles) and from what I've heard from other mathematicians, I think this is a hoax. Wouldn't something this revolutionary be cited by the scientific community? Not just in discussion groups but by professional bodies."
We take no definitive position on Wiles' proof vs. Escultura's refutation, lacking the necessary expertise. However, it's hard to see how Escultura's examples counter to the theorem in his own number system can be said to disprove Wiles' proof which is done in the standard number system. At most it would seem such examples could refute the proof in Escultura's number system. The MathForge thread contains links to Escultura's websites for those who want to read more about his theories for themselves.

Sunday, May 08, 2005

Free Iraqi Thanks Tony Blair

Ali at Free Iraqi has another inspiring post. He includes the full text of President Talibani's letter to British Prime Minister Tony Blair, which is a great read. Ali also adds his own warm feelings for our British friends in general, and PM Blair in particular, and a personal story from the Saddam-days. Ali admires Talibani as well, and feels a democratically-selected, Kurdish president is a great symbol of the new Iraq and the future.

This is a post that will really warm the cockles of your heart. Both Ali and Talibani's notes are must reads, and you get a two for one at Free Iraqi with this one.

BTW: Ali changed the URL of Free Iraqi, so follow the link above and then update your link to him (or add one).

Hitchhikers Guide to the Galaxy

Last night Tycho, Viper, and I went to see The Hitchhiker's Guide to the Galaxy. We all loved it, and we highly recommend it. Both Tycho and Viper had read all 5 books of the "trilogy," while I had only the old BBC series to go by.

I'm told I missed some levels of the humor due to lack of adequate literary preparation, and some reviewers have claimed that a grounding in the books is essential to maximum enjoyment. Perhaps I would have liked it even better in that case, but don't let a lack of knowledge of the books deter you from seeing it, if you are a fan of wacky sci-fi.

Just dive right in, and remember--Don't Panic.

Lincoln City Council Election Results - Epilogue

Here are a few final thoughts on last week's election for the Lincoln City Council.

To the winners, Ken Svoboda, Robin Eschliman, and Dan Marvin, we offer our congratulations. Best wishes for a term of good government on the Council. We do want you to work together with the rest of the Council in making the needed "tough choices" to get the budget under control.

To Mark Koller: we offer our condolences for a well-fought campaign that fell just a little bit short. We think you would almost certainly have made the "top 3" except for the oddities caused by the 4 vs. 2 party split in the candidates. We hope you will consider another try for office in the future.

For Shawn Traudt: we note that making the second round as a newcomer is a significant accomplishment, and it is something to build on. If you do run again for public office, we suggest answering any and all questions about your past legal troubles with something like, "That was all thoroughly discussed in 2005. What I really want to talk about is..." We appreciate your efforts in overcoming your youthful mistake and your forthright willness to discuss it. However, excessive focus on that issue distracted voters from your main message.

For Terry Werner: we hope you will not let the door hit you on the way out.