You know you live in an internet age when Time magazine and the Wall Street Journal do profiles on Christopher Poole, aka ‘moot’, founder of that internet fixture/virtual cesspool 4chan. The Guardian has responded as well.
Remember: Anonymous does not forgive, Anonymous does not forget, and Anonymous makes yellow vans explode:
So HBO is running an extensive multi-layered advertising campaign for its upcoming vampire tv show True Blood, based on Charlaine Harris’ book series. Between this, and the Twilight movie coming out, I’ve got to ask: why more vampires? And not even the proper conscienceless monsters of lore and Stoker, but the broody, misunderstood White Wolf/Anne Rice type? Maybe the Mexicans are right, and the emo kids that are this stuff’s target audience need to be beaten. Though, I would accept a series with an “American Vampire League” if it were instead a satire about how political correctness has reached a point that even the most ruthless, blood-sucking predators can get their own advocacy group.
I’m not exactly a fan of 60 Minutes, with its liberal biases, sloppy journalism, and uncritical, credulous reporting of various forms of quackery. Apparently, they’ve continued in that vein with another glowing report on John Kanzius’ “cancer-cure” machine, which is just an RF heater; using it to selectively kill cancer cells requires targeting molecules which bind only to the cancerous cells. The problem: such molecules exist for only very few cancers. This is the core problem of cancer treatment, differentiating the malignant cells from healthy ones, and Mr. Kanzius has done nothing to solve it. But then, this is the same machine, by the same man, that was claimed to “burn salt water,” a bit of simple radiation-powered electrolysis of water into hydrogen and oxygen, and which was hailed as a revolutionary power source by those who don’t understand basic physics, such as conservation of energy. Codesmithy made these same points over 10 months ago.
Hibernia Girl gives us a comparison between the points Irish columnist Kevin Myers made in his scathing editorial on Africa and Western aid, that has brought an official complaint from the Immigrant Council of Ireland; and those of Kenyan economist James Shikwati.
Consider the function ,
defined by the integral:
. Can we find a formula for
in terms of known functions?
First, we note that for , we have the series
. Thus
. Making the change of variable
, we find that for
,
. Now, setting
, we see
, for
.
Thus
.
Now, for the integral in each term, , we make the substitution
. Then
and
, so our integral becomes:
,
and you should recognize that last integral as the gamma function of x.
Therefore, we find:
,
and that last sum is also familiar: it is the Riemann zeta function.
Thus, we see that
Neuroscientist and author Jonah Lehrer explodes the idea of the rational voter, and that issues decide elections:
The problem, as political scientist Larry Bartels notes, is that people aren’t rational: we’re rationalizers. Our brain prefers a certain candidate or party for a really complicated set of subterranean reasons and then, after the preference has been unconsciously established, we invent rational sounding reasons to justify our preferences. This is why the average voter is such a partisan hack and rarely bothers to revise their political preferences. For instance, an analysis of five hundred voters with “strong party allegiances” during the 1976 campaign found that, during the heated last two months of the contest, only sixteen people were persuaded to vote for the other party. Another study tracked voters from 1965 to 1982, tracing the flux of party affiliation over time. Although it was an extremely tumultuous era in American politics - there was the Vietnam War, stagflation, the fall of Richard Nixon, oil shortages, and Jimmy Carter - nearly 90 percent of people who identified themselves as Republicans in 1965 ended up voting for Ronald Reagan in 1980.
He also discusses research that indicates that weather, polling place, and the “Peter Jennings effect” all, amongst many other factors, influence the way people vote. It’s definite food for thought.
As noted in this Reuters news article, the highest gas prices in the nation are found in Lime Village, Alaska. They note the difficulties of shipping to such rural locales: there are no roads, and fuel travels by barge and then small plane. And while they mention the role Alaska’s small population, and the resulting lack of economies of scale, as part of the reason for this state having the highest gas prices despite the oil being pumped out of the ground here, they fail to mention another key factor. That is the lack of refining facilities; though we pump the oil out of the ground here, it has to be shipped to California or farther to be able to be refined into gasoline, and then shipped back as gas; this, of course, adds to the price.
Charles Krauthammer has a new editorial, available at NRO, about Senator Obama’s plans to give a speech at the Brandenburg Gate in Berlin. At the core is the disparity between the candidate’s self-image and his actual accomplishments:
Americans are beginning to notice Obama’s elevated opinion of himself. There’s nothing new about narcissism in politics. Every senator looks in the mirror and sees a president. Nonetheless, has there ever been a presidential nominee with a wider gap between his estimation of himself and the sum total of his lifetime achievements?
Obama is a three-year senator without a single important legislative achievement to his name, a former Illinois state senator who voted “present” nearly 130 times. As president of the Harvard Law Review, as law professor and as legislator, has he ever produced a single notable piece of scholarship? Written a single memorable article? His most memorable work is a biography of his favorite subject: himself.
Go read the full article.
Last week we found the frequencies for the fundamental modes for the motion of n identical masses, each of mass m, connected in a line between two fixed walls by n+1 springs of spring constant k. In particular, we found that the system of differential equations reduced to finding the eigenvalues and eigenvectors of the matrix
,
where . We showed how the eigenvalues of this matrix can be obtained from those of
,
which has the same eigenvectors as . Lastly, we recall that the eigenvalues of
were given by
, i=1,2,…,n.
Note that if we have an eigenvector with corresponding eigenvalue λi, then the eigenvalue equation tells us
…
Here, we now define ; with this we then have:
, k=1,2,…,n; or, using our value for λi,
.
Consider the functions , i=1,2,…,n. First, for all our i, we have
. Secondly, we see that
.
Thus, if we let , k=1,2,…,n, then the vector
is the eigenvector corresponding to the ith fundamental mode. Note that these are sine waves of decreasing wavelength: the ith mode has i-1 zeroes (nodes) in the interval 0<v<n+1, and thus i-1 changes of phase, as we observed previously (noting the nodes via changes in relative phase). Note that our horizontal displacement of the masses as a function of time and of equilibrium position of the masses is given by the equation of a standing wave; this is particularly noticeable when n is large and i is much smaller than n. So our n mass oscillator represents a discrete model that approaches a one-dimensional longitudinal standing wave, such as a sound wave bouncing between two perfectly fixed walls.
Let us consider a function of two real variables α and β; such that
is defined and continuous for all α,β>0; and which obeys, for α≠β,
.
Does such a function exist, and if so, what is it?
Note that this exercise has three parts: First, to show that the integrand is valid over the infinite interval (0,∞); second, that the discontinuity in on the line α=β is removable; and third, to evaluate the integral, and thus find the function.
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