What do Tom Finneran and Sarah Palin have in common?

“Speaker Finneran was there at the creation,’’ Ware said. “I had hoped to elicit the truth from Speaker Finneran, and instead I was stonewalled.’’

But Finneran regained his voice the day after the release of Ware’s report. He defended himself on his morning radio show on WRKO-AM.

Criminals like Finneran only talk when in their own cocoon.  No nasty questions about a system of patronage that costs Massachusetts residents so much more than just money.  Because in the end, as Billy Bulger’s son Chris stated, hey, this is the way things work on Beacon Hill.  Not to visit a father’s sins upon his son, but if anyone, he should know.  So shut up, get on with your miserable lives, and every other year, remember to vote in the “D” column no matter what.

Speaking of cocoons: does an over-reliance on a cocoon imply that Sarah Palin is a criminal?  [Now I sound like an anchor from Fox news.]  Who knows.  But she surely has something to hide.  Even Jennifer Rubin, whom I have raked over the coals in these pages for her fangirl support of an obviously unqualified candidate, believes that Palin needs to get out of her cocoon.  But just remember one thing: a candidate that gets elected from within his or her own coocon will truly give us the government we deserve.

Maybe he was brushing his teeth with Ben-Gay

Galluccio claimed he had used a toothpaste that mistakenly triggered the chemical breath test machine installed in his home. Galluccio failed the test the first time he was required to take it. Nestor scornfully sentenced Galluccio to one year’s imprisonment.

Perhaps I am too harsh on our State Reps.  But please allow me the smallest amount of schadenfraude for seeing such an idiot finally be put behind bars.  Maybe the next question we can ask ourselves is how many of our State Reps end up with a criminal record upon exiting Public Service?

The reason why the public is so angry with the TSA

In studying the media’s coverage, officials have come to conclude that a slow news week, combined with the president’s being overseas and Congress being out of session, created the perfect storm of bad coverage.

Yeah, that’s the ticket.  It’s not the fact that this stuff catches only the stupid terrorists or that it does not work against cavity bombs.  And when someone tries to set off a cavity bomb, to what sort of collective punishment will we be subjected?

An unintuitive limit

Problem: Let \(f(n)\) = the number of zeros in the decimal representation of \(n\).  For example, \(f(1009)=2\).  For \(a>0\), define

\(S(N)=\displaystyle\sum_{k=1}^{N}a^{f(k)}\).

Evaluate

\(L=\displaystyle\lim_{N\to\infty}\frac{\log S(N)}{\log N}\).

Solution: The key is to recognize that the sum \(S(N)\) is best evaluated according to how many digits are in \(N\).  As an example, suppose \(N=9\): none of the single-digit numbers between 1 and 9 have zeros, so the sum \(S(N)\) is equal to 9.  Within the two-digit numbers, note that there are 9 numbers with 1 zero [e.g., 10, 20,…,90] and the rest [90-9=81] with no zeros; in this case \(S(99)=9 a+81+S(9)=9 a+9^2+S(9)\).  For three-digit numbers, there are 3 possibilities: the number can have 2, 1, or no zeros.  There are 9 such numbers with two zeros.  Numbers with 1 zero include 101 and 110; note that there are 2 different numbers resulting from two non-zero digits and one zero digit.  Given that there are \(9^2\) combinations of digits, it is clear that there are \(2\times 9^2\) three-digit numbers having exactly one zero digit.  Finally, there are \(900-162-9=729=9^3\) three-digit numbers with no zeros.  Therefore,

\(S(999)=S(10^3-1)=9 a^2+2\times 9^2 a+9^3+S(10^2-1)\).

The pattern here is clear to the [mathematically inclined] observer:

\(S(10^k-1)=9 a^{k-1}+\binom{k-1}{1}\times 9^2 a^{k-2}+\ldots+\binom{k-1}{k-2}\times 9^{k-1} a+9^{k}+S(10^{k-1}-1)\)

or

\(S(10^k-1)=9 (a+9)^{k-1}+S(10^{k-1}-1)=9 \displaystyle\sum_{j=0}^{k-1} (a+9)^{j}\).

Summing the series, we arrive at the following:

\(S(10^k-1)=9 \frac{(a+9)^{k}-1}{a+8}\).

In evaluating \(L\), observe that the limit \(N\to\infty\) is equivalent to \(k\to\infty\). In this limit, \(\log N \approx k\). We therefore get the final result:

\(L=\log (a+9)\)

Bilious Rubin

I don’t normally participate in making fun of anybody’s name: under most circumstances, people do not have control over their names and bravely go through life with them.  That said, I must make one example for Jennifer Rubin of Commentary, a persistently hypocritical blog writer on the Contentions site who is little more than – no, nothing more than – a shill for the GOP.  Of course, there’s loads of those, what makes her special?  As I will explain below, it is the sort of bile in her writing, the incredibly obvious double standards she has for people, that drives me nuts.  And someone who spews bile like this and has a last name of Rubin…I cannot resist.

Anyway, Jennifer Rubin  has been at the top of the shrieking heap against the Park51 Islamic Community Center, 2 1/2 blocks from NYC.  I’m not going to post any of her rants about it as anyone reading this post has heard it all before: the acknowledgment of the “right” to build, but the necessity to be “sensitive” to the 9/11 families [some of whom are Muslim, and others of whom support the project].  Plus, ugly questions about the funding source for the center and the personal leanings of Imam Rauf, the spiritual leader of the Cordoba Initiative, the group behind the project.  All of it is bullshit, and further commentary on it by me is a waste of your time.

No, I want to lay before you the sort of character this political marionette is or has become.  I don’t know her personally of course, so I can only judge her from her writings.  And believe me, judging from her writings, she is a unique character: an anti-Semite who accuses other Jews of being anti-Semites.  I do recognize how bizarre this charge is, and how easily it can be turned back on me.  But seriously, you must see what I mean to believe it.

I posted before about an article Rubin wrote this past January called “Why do Jews hate Palin?”  To summarize, Rubin looooves Palin because Palin loooooves Israel, despite the fact that Palin’s stated position on Israel aligns with fundamentalist Christians and Jews and is a sure path, according to every Mideast expert, to the destruction of Israel as a democracy and a haven for Jews worldwide.  Jews hate Palin in droves not because of Palin’s propensity to lie, or be divisive, or to be a dumbass.  No, Jews hate Palin because they hate who she is.  Palin is sexy, Jews like frumpy.  Palin is blue collar and has worked jobs Jews won’t touch.  Palin’s child is in the military, Jews never do that.  Palin has 6 (or 5) children, Jews never have that many kids [oog, unless their frum, then they’re OK].  Jews read, but they have been misinformed about Palin, who loved to read as a child, and they simply don’t appreciate “instinctual” leadership anyway.  O, and Palin has a Downs baby, while Jews love to abort.

If you think my interpretation of her article is extreme, it is not: people who are paid to notice these things for a living say the same damn thing.

To its credit, Commentary publishes readers’ letters, and has the author respond.  The letters chosen, of course, are chosen from the milder lot [the practice of any magazine], but the charge remains and Rubin responds:

Other readers…found in my article echoes of anti-Semitic tropes or fodder for anti-Semites, especially with respect to characterizations of “elitism” or “intellectualism.” But there is, I would suggest, nothing remotely anti-Semitic about the observation, supported by Tom W. Smith’s 2005 Jewish Distinctiveness in America: A Statistical Portrait and ahost of other data, that Jews are more educated than the population at large. Nor is there anything controversial in observing that the proportion of Jews in intellectual professions is higher than the proportion of Jews in the population. Simply observing an antipathy felt by a disproportionately well-educated, highly credentialed group for a politician with a different persona and background is not a value judgment on either half of the equation. Rather, it is a candid recognition that Palin and most American Jews simply don’t share a common perspective or life experience.

This is, of course, garbage.  Yes, the document she cites goes into the themes she mentions, but there is a huge difference.  Smith’s document, at 154 pages, is a carefully written sociological study [and, at the risk of attaining my wife’s ire, I must point out it lacks, despite heaps of table of results backing the conclusions, no decent summary of the statistical validity behind those conclusions] whose validity is does no use here to question.  David Harris, the head of the American Jewish Committee who published the survey, says the following:

Why should we care about all of this—other than for “bragging rights” or a parlor game? We care because the numbers reveal an underlying strength of the American Jewish community: Despite our declining share of the overall American population, a high intermarriage rate, and a growing geographical dispersion, Jews have been able to retain a distinctive profile which bespeaks a unique core Jewish identity. Furthermore, Jews have embraced certain broad values, such as belief in the importance of education and in expressive individualism, that seem to have resonance for other Americans as well.  Why should we care about all of this—other than for “bragging rights” or a parlor game? We care because the numbers reveal anunderlying strength of the American Jewish community: Despite ourdeclining share of the overall American population, a high intermarriagerate, and a growing geographical dispersion, Jews have been able to retain a distinctive profile which bespeaks a unique core Jewish identity. Furthermore, Jews have embraced certain broad values,such as belief in the importance of education and in expressive individualism,that seem to have resonance for other Americans as well. [Emphasis mine.]
That is, Jewish identity is something of which the American Jewish community should be proud.  Further, it is meaningful that American Jewish values have become American values as well.
The importance of this statement cannot be overemphasized with respect to Rubin, whose article bemoans these values because, let’s face it, it makes her an outlier with respect to her hero-goddess Palin.  She turns these values on their head as negative and anti-American.  That her article was published in Commentary and not the Occidental Quarterly is surreal.
Now, for my cri de coeur.  Peter Beinart, who has  stood up and questioned the role of American Jewish leadership in its stewardship of young Jewish Americans’ values, wrote with regard to the Park51 project:

And oh yes, my fellow Jews, who are so thrilled to be locked arm in arm with the heirs of Pat Robertson and Father Coughlin against the Islamic threat. Evidently, it’s never crossed your mind that the religious hatred you have helped unleash could turn once again against us. Of course not, we’re insiders in this society now: Our synagogues grace the toniest of suburbs; our rabbis speak flawless English; we Jews are now effortlessly white. Barely anyone even remembers that folks in Lower Manhattan once considered us alien and dangerous, too.

To which Rubin, of all people, writes:

As for Beinart’s second paragraph, it is an unfortunate example of the bile that can be splattered on Jews by Jews, with nary an eyebrow raised by elite opinion makers. Had Pat Buchanan, to whom Beinart lately bears an uncanny resemblance, accused Jews of walking with Father Coughlin, or had Al Sharpton (before becoming part of polite liberal company) referred to Jews as “effortlessly white,” I imagine all sorts of elites would be throwing a fit. But now it is par for the course.

I imagine she writes this with a straight face, for she clearly feels she has acquitted herself of the same accusation laid onto her by her intellectual superiors.  [I also love her use of the word “bile”.]  But all Beinart is pointing out is that the language used by many Jews is exactly analogous to that used by their former tormentors in years past.  And Beinart is not the only one to make this observation as well.

So, on the one hand, Rubin uses an anti-Semitic canard to someone who is attacking anti-Semitic language in discourse regarding American Muslims.  On the other hand, she is happy to take findings from an AJC report about “Jews” [ill-defined, but I assume they know of whom they speak] and turn them on their head to expose the other-worldliness of those values because they result in a severe dislike of Sarah Palin.

Anyone not lobotomized should only read Jennifer “Bilirubin” Rubin’s yellow journalism with derision.

Hoisting the world by a string

Problem: I have a rope, it fits around the equator exactly once. I add 10 cm to the rope, attach the ends, and pull up. How high off the ground can I pull the rope?

Solution: The length \(L\) of the rope before adding the 10 cm is \(L=2 \pi R\), where \(R\) is the radius of the earth and is about \(6.4 \times 10^6\) meters.

After adding the 10 cm, you give the rope a stretch in the center.  When the rope is stretched to full tautness, the result will be most of the rope hugged against the equator, with 2 straight pieces, each tangent to the equator.  Thus, we have the right triangle as pictured above.  We are interested in solving for the height \(h\).

We proceed by considering the rope after the addition of the 10 cm which will now be denoted as \(\Delta L\).  When pulled up, the rope hugs the earth outside the points of tangency.  Denote the points of tangency on the earth as corresponding to an angle \(\theta\) from the vertical, and the length of one of the two sections of rope not attached to the earth as \(y\).  The following relation holds:

\(L+\Delta L=2 (\pi – \theta) R+ 2 y\),

where

\(y^2=(R+h)^2-R^2=2 R h+h^2\).

Use the fact that \(L=2 \pi R\) and \(\theta=\tan^{-1} \frac{y}{R}\), and define \(w=\frac{\Delta L}{2 R}\) and \(z=\frac{y}{R}\).  The above equation is then rewritten as

\(w=z-\tan^{-1}z\),

where we must solve for \(z\).  Of course, this is a transcendental equation that cannot be solved exactly, but it is clear that, since \(w\) is very small, then \(z\) must also be small, and we can get places by expanding the transcendental function in a series:

\(z-\tan^{-1}z=\frac{1}{3} z^3-\frac{1}{5} z^5+\frac{1}{7} z^7-\ldots\)

The best way to use this series is to consider the first term, with all higher-order terms being some error:

\(z-\tan^{-1}z=\frac{1}{3} z^3+O(z^5)=\frac{1}{3} z^3 \left [ 1+O(z^2) \right ]\).

Then, to lowest order, we obtain the following:

\(z=\left ( 3 w \right )^{\frac{1}{3}} \left [ 1+O(w^{\frac{2}{3}}) \right ]\).

Now, to lowest order,

\(z=\sqrt{2 \frac{h}{R}} \left [ 1+O \left ( \frac{h}{R} \right ) \right ]\),

so that we now have an approximate solution and an error estimate:

\(h=\left ( \frac{9}{32} R \Delta L^2 \right )^{\frac{1}{3}}+O\left [ \left ( \frac{\Delta L^4}{R} \right )^{\frac{1}{3}} \right ]\).

Note that the solution involves the radius of the earth, which is a very large number compared with the rope extension of 10 cm.  The result will then be surprisingly large; the first-order term is, using the values given above, about 26.2 meters.  The error term, on the other hand, is on the order of 0.001 meters, or 0.1 cm, and can safely be called negligible.  However, for larger extensions, we can simply expand the series solution further until the error estimate is within acceptable bounds.

The ADL is a joke, and Peter Beinart is right

A long, long time ago, in a galaxy far, far away…[August 19, 2007, to be exact]

I wrote my first Facebook note, taking aim at the Anti-Defamation League for firing a local leader named Andrew Tarsy.  Why?  For carrying out the ADL’s mission in Watertown, MA, of “secur[ing] justice and fair treatment for all.”  In this case, the Armenian community, which had declined to take part in the ADL’s programs because Abe Foxman, the head of the ADL, continued to insist that the massacre of 1.5 million Armenians at the hands of Turks in 1915 did not constitute a genocide.  Given that the ADL is expert at such things, you would imagine it would stick up for the historically harassed Armenians, whose quest for justice has been roundly trivialized.  But, no such luck.  In fact, the ADL roundly fought hard against any efforts on part of the Armenians to have the historical record corrected.

Why?  Because Turkey, in 2007, was a friend to Israel.  And friends of Israel can never do wrong.  Foxman “consulted Elie Wiesel” and invoked Morganthau the Senior in performing the bee-like dance that required him to help our Turkish friends avoid the Genocide label.  [Of course, never mind that Raphael Lemkin, the originator of the term “genocide”, was motivated by the…, um, genocide of the Armenians to invent the word “genocide”.  Lemkin, by the way, was a Jew whose life would be horribly affected by a genocide against his own people.  The whole brutal story can be read in A Problem from Hell by Samantha Power.]]

Which brings me to current events, and we can now guess where this is heading.  Fast forward to June 2010, and here we have Turkey, who has been acting in a rather hostile way toward its old friend Israel.  The Gaza flotilla, for example, was Turkish in origin; the IHH which ran the operation is Turkish; and Turkish PM Recip Erdogan, rather than wondering how Turkish citizens sailed off for a hostile encounter with an ally, is making serious threats.

So, who knows how this will play out.  But what interests me is the integrity of our Jewish-American institutions, like the ADL.  And, gee, what do you think would be the position of the ADL on the Armenian genocide today?  Hmmmm…:

Today, far from being an asset for Turkey, the American Jewish community appears to becoming a potent foe of Turkish interests in Washington.

On Tuesday for example, the Anti-Defamation League issued a press release calling on the State Department to designate the IHH, the Turkish charity that helped organize the free-Gaza flotilla as a foreign terrorist organization. In Turkey, the IHH has been praised as a group of peace activists and humanitarians.

“In terms of the Jewish community and Israel, neither one of us wants to throw it away and hope it is not over,” Mr. Foxman said. “But every day there is another provocation. Every day the Turkish government goes out of its way to be insulting to Israel and another link is broken.”

Morris Amitay, a former executive director of AIPAC who has also represented Turkey, was more blunt.

“If someone asked me now if I would try to protect Turkey in Congress, my response would be, ‘You’ve got to be kidding,'” he said.

So, watch out for the Armenians now getting Congress to finally recognize their genocide by the Turks in 1915.  Because, for the ADL, truth and justice only means being on the right side of Israel.  And Peter Beinart is dead right: our American Jewish institutions have failed us.

Danny Ayalon can go fuck himself

Danny Ayalon is the Deputy Foreign Minister of Israel.  Both he and his boss, a racist from the Yisrael Beitanu [Israel Our Home] party named Avigdor Lieberman, represent an unfortunate trend of Israel being seen as less and less likable to its allies.  But it is Ayalon who is in my line of fire this week, for several reasons.

Ayalon made the news last month because of an incident which a skilled diplomat could have handled discretely and in a dignified manner.  Turkey, with whom relations with Israel have been going down the tubes, had one of its stations broadcast a program with anti-Semitic themes.  A quiet complaint and message of understanding the balance between freedom of expression and placing Jews in danger would have been appropriate.  But Ayalon, representing an increasingly tone-deaf Israel, made a mess of things:

Footage of Mr Ayalon urging journalists to make clear the ambassador was seated on a low sofa, while the Israeli officials were in much higher chairs, has been widely broadcast by the Israeli media.

He is also heard pointing out in Hebrew that “there is only one flag” and “we are not smiling”.

In an interview with Israel’s Army Radio on Tuesday, Mr Ayalon was unapologetic.

“In terms of the diplomatic tactics available, this was the minimum that was warranted given the repeated provocation by political and other players in Turkey,” he said, according to Reuters.

One Israeli newspaper marked the height difference on the photo, and captioned it “the height of humiliation”.

That, however, is not even my main problem with him.  Massachusetts Congressman Bill Delahunt is part of a contingent of Democratic lawmakers in Israel, traveling as part of a mission sponsored by liberal lobby group J-Street.  I will say that I have been warming to J-Street, although I do not like the arrogance of its identification as “pro-peace, pro-Israel”.  [So is the Zionist Organization of America…it just has vastly different definitions of these terms than does J-Street.]  Standard protocol is that such a delegation, if desired, may seek out an audience with Ministry officials.  However, Alayon, because he feels that J-Street is not in fact “pro-Israeli“, has locked the delegation out from any such meetings:

“We were puzzled that the Deputy Foreign Minister has apparently attempted to block our meetings with senior officials in the Prime Minister’s office and Foreign Ministry – questioning either our own support of Israel or that we would even consider traveling to the region with groups that the Deputy Foreign Minister has so inaccurately described as ‘anti-Israel,'” Delahunt continued.

“In our opinion this is an inappropriate way to treat elected representatives of Israel’s closest ally who are visiting the country – and who through the years have been staunch supporters of the U.S.-Israeli special relationship.”

Ayalon has clearly associated himself with the rabid right.  The combination of this tone-deaf outlook and utter incompetence as a diplomat is making for an explosive combination.  How dare he insult a delegation from the United States because their politics do not dovetail with his!  It is men like Ayalon that will be the downfall of Israel.  For that, he can go fuck himself.

Meanwhile, Michael Oren, in contrast to his dumbass administration colleague, is wisely making peace with J-Street.  Good for him.

An improper double integral

Problem: Evaluate the following double integral.

\(I=\displaystyle\int\limits_{-\infty}^{\infty}dx\int\limits_{-\infty}^{\infty}dy\; e^{-x^2-y^2-(x-y)^2}\)

Solution: This problem was taken from the collection “Berkeley Problems in Mathematics“, Problem 2.3.3.  Two solutions are given, neither of which are close to [stylistically] mine, which I give below.

First, change to polar coordinates; that is, \(x=r \cos \theta\), \(y=r \sin\theta\).   Using the Jacobian \(dx\,dy=r\,dr\,d\theta\), we get

\(I=\displaystyle\int\limits_{0}^{2\,\pi}d\theta\int\limits_{0}^{\infty}dr\,r\;e^{-2\,(1-\sin \theta\, \cos \theta)\,r^{2}}\)

Or…

\(I=\displaystyle\frac{1}{4}\,\int\limits_{0}^{2\,\pi}\frac{d\theta}{1-\sin \theta\,\cos \theta}=\frac{1}{4}\,\int\limits_{0}^{2\,\pi}\frac{d\theta}{1-\frac{1}{2}\sin \theta}\).

Now, there are two ways I can think of to go about evaluating this latter integral.  First, we can Taylor expand and hope for the best; it turns out that the resulting series converges to something well-known, but you have to be an expert at recognizing such things.  [I so hate solutions that require a deus ex machina like that.]  The other way is to convert to complex variables and use the Residue Theorem. [I’m afraid, however, if you are not familiar with the Residue Theorem, then we are back to a deus ex machina. But one has to draw the line somewhere, I guess…]

So, consider the following integral:

\(J(a)=\displaystyle\int\limits_{0}^{2\,\pi}\frac{d\theta}{1-a\,\sin \theta}\;:|a|<1\).

Observe that

\(\displaystyle \sin \theta=\frac{1}{2 i}\left (e^{i \theta}-e^{-i \theta} \right )\).

The trick is to recognize that we are integrating over the unit circle \(C\).  if we let \(z=e^{i \theta}\), and transform to an integral over \(z\), then the result is the following:

\(J(a)=-\displaystyle\frac{2}{a}\,\displaystyle\oint\limits_C \frac{dz}{z^2-i \frac{2}{a}\,z-1}\).

Recall that a residue of a function \(f\) at \(z=z_0\) is equal to

\(\mbox{Res}(f;z_0)=\displaystyle\lim_{z \to z_0} (z-z_0)\,f(z)\),

with the Residue Theorem stating that, for a function \(f\) having simple poles \(\displaystyle\{z_n\}_{n=1}^{N}\) within the simple closed curve \(C\), then

\(\displaystyle\oint\limits_C dz\,f(z)=i\,2\,\pi\,\sum\limits_{n=1}^{N} \mbox{Res}(f;z_n)\).

To compute \(J\) using the Residue Theorem, we must compute the roots of the quadratic in the denominator of the integrand.  These roots are at

\(z=z_{\pm}=\displaystyle\frac{i}{a}\left (1 \pm \sqrt{1-a^2} \right )\).

Note that \(\displaystyle |z_{+}|>1\), so that we need only consider the root \(z_{-}\).  Hence,

\(J(a)=-\displaystyle\frac{2}{a}\,i\,2\,\pi\,\frac{1}{z_{-}-z_{+}}=\frac{2 \pi}{\sqrt{1-a^2}}\).

Finally, the result is

\(I=\displaystyle\frac{1}{4}\,J \left (\frac{1}{2} \right )=\frac{\pi}{\sqrt{3}}\).