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The 2011 Ford F-100 SupernationalsWritten by on August 16, 2011 33 Years and the Best Keeps on Getting Better!
Geez, it'd been a good six years or so since I'd had the pleasure of heading out to beautiful Pigeon Forge, Tennessee, for the F-100 Supernats. My ol' pal Pat Ford was runnin' the show back then and the gathering was one that I looked forward to every year. But with my transfer back to the street rod world, business had me hitting the car shows instead of the truck shows for a while. During the time I was missing out on the Supernats a gent by the name of Charlie Cobble (the driving force behind www.autoshows.cc) had taken over the helm. Now back behind the wheel here at CLASSIC TRUCKS, the F-100 Supernationals again became one of the premier shows of the event season—and I was excited to head back to Pigeon Forge to see what I'd been missing.
Well, first of all, Charlie ended up being a super guy (just like Pat) and the show was every bit as awesome as any I'd attended in the past. The event was well put together and ran without a flaw. The well over 700 vehicles that attended were downright beautiful, and the people were as friendly as ever! It was just like old times for me with the icing on the cake being my friends from LMC Truck being the event's main sponsor—I felt as though I was literally in heaven, heck at least I was in God's country!
The show ran Thursday through Saturday and as always included countless show classes, and the most trophies, awards, and giveaways (including over $2,500 in gift certificates from LMC Truck alone) I've ever seen at any event I've ever attended. Along with Charlie, Sam Memmelo (star of the TV show Motorhead Garage) kept the crowd entertained as master of ceremonies throughout the weekend. But, aside from the large selections of classic truck industry vendors, countless trophies and awards, a really good-sized swap meet, and lots of entertainment and music, the real stars of the show were the hundreds of awesome F-100's displayed in the huge event show area.
The F-100 Supernationals has been and always will be the nation's premier F-100 show and one that any red-blooded classic Ford trucker should have on their perpetual "must attend" list each and every season! With that said, let's take a look at some of the hundreds of beautiful F-100 at this year's F-100 Supernationals. We'll be there looking for ya next year in Pigeon Forge! CT
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When such a prestigious company as LMC Truck gives its full support to an event like this you know it's gotta be a winner! It was great to see my friends from LMC Truck at the show and they were mobbed throughout the event by happy long-time customers and hundreds of soon-to-be happy trucker's as well.I got to the show before opening on Thursday only to run across a slew of Ford truckers that arrived even earlier than I. One of the first cool F-100s to catch my eye was Dan Carpenter's way-cool, in-the-weeds shop truck. This baby is just my style!And since I did get there before the vast majority I started my day by perusing the large swap meet area. As always, it was chock full of classic Ford truck parts—everything from complete project trucks to trim, moldings, bumpers, and everything in between.Roger Olive made his way to the Supernats all the way from Winter Haven, Florida, with his awesome '51 F-1. Roger's gone over the top with this baby; it has to be one of the finest F-1s we've seen in a long time.Speaking of over the top, Aaron Watkins' Powell, Tennessee-based '63 F-100 was equally impressive. It seems to me that lots of folks are beginning to build classic trucks in the style and high quality seen in the street rod world—and that's a good thing.I was really pleased to run in to my pal Mark Coleman (I met him years ago at the first Supernats I ever attended and he's a regular at the show every year). Mark's '53 is the latest F-100 he's built and each one seems to be even better than the one before.This pro street-style Unibody was a sweet truck, too. I only wish folks would take the time to fill out their window tags at shows so we magazine guys can give credit where credit is due.
I was lovin' Denny Rogers' way-cool '37 Ford. It may not be an F-1 or F-100 but it's one heck of a good-lookin' classic Ford pickup, and a great change of pace at a show filled with Effies.It's hard to believe that Billy Templeton's beautiful '56 is a driver, but it's true. Billy's F-100 sees more than its share of road time, which means Billy must spend a huge amount of time waxin' and polishin' cuz this baby is spotless!Throughout the show TV personality and hot rodder to the core Sam Memmelo not only kept everyone well informed as to each day's happenings but offered up his usual entertaining banter and joking with the crowd. Sam's one heck of a nice guy, and one heck of a mechanic to boot.I only wish I was brave enough to take one of those famous Pigeon Forge helicopter rides so I could have gotten a few good aerial shots of the show for those who're unfortunate enough to have never attended the F-100 Supernationals. This image shows just an extremely small fraction (just a line of seven out of over seven hundred) of the awesome classic Ford pickups on hand at the event. I'll tell ya, there's not an F-100 fan on the planet that should miss the opportunity to attend this show.Scott Young's Hickory, North Carolina-based '64 is a sterling example of just how cool a later-model F-100 can be. Though the '53 to '56 F-100 is the epitome of classic Ford truckin', the '60s versions are pretty darn sweet themselves, and we're loving the fact that we're beginning to see more and more of 'em these days.How's this for a bit of contrast? Lamar Gregory and Sam Stubbs' sweet '50 F-1s (Lamar's is the red custom) are both beautiful pickups. The F-100 Supernationals plays host to both the nicest stockers and hot rod pickups you'll ever see in one place, and these two babies are prime examples.Not all Effies are bright 'n' shiny. Steve Neiheisel's '55 wears its patina well wouldn't you say? The only thing I don't like about this flathead-powered F-100 is the fact that my name isn't on the title!
I told ya Charlie and sponsor LMC Truck handed out lots of awards and giveaways! I'll bet the guy at the trophy shop is lovin' those folks—as are the lucky winners.I'm not sure what I enjoyed more, checking out Jim Blandino's cool traditional hot rod-style '53 or spending time shootin' the bull with Jim himself. Jim's bright-red F-100 was one of my personal favorites.Well, there ya have it, the 33rd annual F-100 Supernationals. I wish I had more space to show the rest of the 400-odd images I shot at the show, but since I don't you'll just have to make it a point to head out to beautiful Pigeon Forge, Tennessee, for next year's F-100 Supernationals! I'll surely be there and I hope you will be too!


text: Hello people, and whatever or whoever else comes to Dragoart, this is going to be the last submission for the day and what we will be doing is learning how to draw a hippo for kids, step by step. Even though these extra-large animals are incredibly cute, they are actually not friendly at all. They may look adorable when playing in the mud and water, but don't invade their space because a hippo is a very territorial animal. I have a few hippos on the site so talking about this species again gets kind of boring. All I can really do is shut up, and let you get busy as you learn how to draw a hippo for kids. I'm not going to return today with anymore but I think you will enjoy all the tutorials that went up today. Thanks guys and enjoy!

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TransCanada, which has been waiting for White House approval for the 830,000 bpd pipeline expansion for years, expects to receive the necessary permit "by the first half of 2013," according to Paul Miller, a senior vice president in charge of oil pipelines. He spoke on the sidelines of a Houston conference.
By BEN LEFEBVRE
HOUSTON -- TransCanada Corp. still fully expects to receive
approval for its controversial cross-border Keystone XL
pipeline expansion within the next several
months, a company executive said Thursday.
TransCanada, which has been waiting for White House approval
for the 830,000 barrel-a-day pipeline expansion for years, expects to
receive the necessary permit "by the first half of 2013," Paul
Miller, TransCanada's senior vice president in charge of oil
pipelines, said on the sidelines of the Platts North American
Marketing conference in Houston.
"We anticipate to have this in service by end of 2014 or
beginning of 2015," Mr. Miller said.
The pipeline is meant to ship heavy crude oil from Alberta,
where production is expected to grow to 4.5 million bpd by
the end of the decade. But the project has gained criticism from environmental groups who say it will
spur increased production from Canada's tar sands, an energy
intensive process some groups say will cause an increase in
green house gas emissions.
Mr. Miller spoke about the pipeline after his presentation
at the conference was interrupted by an anti-Keystone protestor
who chained himself to the projector Mr. Miller had been
TransCanada has no interest in building an oil pipeline to
Canada's West Coast, because competitors Enbridge and Kinder
Morgan Energy Partners have already announced projects there, Mr. Miller said.
Instead, TransCanada might convert a natural gas pipeline to
transport Alberta's growing supply of light oil to refiners in
eastern Canada, he added.
"We're talking to refiners today, stakeholders today,
producers today, to see what the market wants," Mr. Miller
The lack of a major pipeline connecting Alberta's growing
oil sands production has pushed local crude prices down.
Western Canadian oil at the end of January was selling at a
nearly $40/bbl discount to its Gulf Coast counterpart Maya.
One thing Mr. Miller did not foresee was Canadian oil
exports out of the Gulf Coast. At least one analyst has
forecast up to 200,000 bpd of Canadian crude could head to
Europe and Asia via the Gulf Coast
by the end of 2014.
"I don't know why a producer would ship to the Gulf Coast
just to bypass 5 million barrels a day of heavy oil refining capacity," Mr. Miller
Mr. Miller said that the company remained confident that the
pipeline expansion would receive approval,
even as some potential buyer's have grown more skeptical. Tom
O'Malley, chief executive for east coast refiner PBF Energy,
earlier this month expressed doubt that Keystone XL would
receive the necessary cross border permits.
Dow Jones Newswires
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Engineers and designers are highly skilled individuals. Forcing them to enter design changes using tables, forms and spreadsheets is unproductive and uneconomical, and it increases the likelihood of human error—this is the way that most instrumentation software systems currently work. For too long, software vendors have denied engineers and designers the simple practicality of a graphical visual engineering interface with "drag and drop" capability and inbuilt intelligence, ensuring changes are automatically replicated into all the associated data and databases.
Is 2016 the peak for US gasoline demand?
Too soon to tell
July 2016


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For my purposes, you may want to interpret "best" as "clearest and easiest to understand for undergrads in a first number theory course," but don't feel too constrained.
I think by far the simplest easiest to remember elementary proof of QR is due to Rousseau. All it uses is the Chinese remainder theorem and Euler's formula $a^{(p-1)/2}\equiv (\frac{a}{p}) \mod p$. The mathscinet review does a very good job of outlining the proof. I'll try to explain how I remember it here (but the lack of formatting is really rough for this argument).
Here's the outline. Consider $(\mathbb{Z}/p)^\times \times (\mathbb{Z}/q)^\times = (\mathbb{Z}/pq)^\times$. We want to split that group in "half", that is consider a subset such that exactly one of x and -x is in it. There are three obvious ways to do that. For each of these we take the product of all the elements in that "half." The resulting three numbers are equal up to an overall sign. Calculating that sign on the $(\mathbb{Z}/p)^\times$ part and the $(\mathbb{Z}/q)^\times$ part give you the two sides of QR.
In more detail. First let me describe the three "obvious" halves:
The three products are then (letting P = (p-1)/2 and Q=(q-1)/2):
All of these are equal to each other up to overall signs. Looking at the second component it's clear that the sign relating 1 and 3 is $\left(\frac{p}{q}\right)$. Similarly, the sign relating 2 and 3 is $\left(\frac{q}{p}\right)$. So the sign relating 1 and 2 is $\left(\frac{p}{q}\right) \left(\frac{q}{p}\right)$. But to get from 1 to 2 we just changed the signs of $\frac{p-1}{2} \frac{q-1}{2}$ elements. QED
The question asked for the nicest proof for a first undergraduate course. Has anyone who offered a proposal used their favorite choice in a course? (Obviously the suggestions referring to $K$-theory or Hilbert symbols weren't suggested in that spirit.) I've taught an undergrad number theory class several times and initially I gave the Gauss sum proof. But I realized afterwards that to the students this truly comes out of nowhere (it seems too magical), so I hunted around for other proofs, preferably some which build on more basic ideas that I could present earlier in the course. The Eisenstein (sine-function) proof doesn't fit that requirement, and Zolotarev seems too far-out if the students have not had group theory (which most have not). So what else is available?
There is a proof due to V. Lebesgue (not H. Lebesgue!) that is based on counting points on hyperspheres mod $p$. It can be found in Ireland-Rosen's book. For an odd prime $p$ and positive integer $n$, let
$$N_n(p) = \#\{(x_1,\dots,x_n) \in ({\mathbf Z}/(p))^n : x_1^2 + \cdots + x_n^2 = 1\}.$$
This is the number of mod $p$ points on the sphere in $n$-space mod $p$. Earlier in the course I have the students discover numerically that every number mod $p$ is a sum of two squares. That is,
$$\#\{(x,y) \in ({\mathbf Z}/(p))^2 : x^2 + y^2 = a\}$$
is positive for every $a$ in ${\mathbf Z}/(p)$. This could be shown by the pigeonhole principle, since $x^2$ and $a - y^2$ each take $(p+1)/2$ values mod $p$ and thus have an overlap. But more precisely, if you look at examples, you quickly discover that this 2-variable count is independent of $a$ when $a$ is nonzero (from a more adv. point of view, the independence is because the norm map on unit groups $(({\mathbf Z}/(p))[t]/(t^2+1))^\times \to ({\mathbf Z}/(p))^\times$ is a homomorphism so its fibers have the same size, but that is a crazy explanation in an elem. number theory course). Enough data suggest what that uniform value is for any nonzero $a \bmod p$, and then we prove that in class. With this 2-variable count we return to the hypersphere count and get a simple recursive formula connecting $N_n(p)$ to $N_{n-2}(p)$. If you let $n = q$ be an odd prime, the recursive formula involves $p^{(q-1)/2}$ plus $N_{q-2}(p)$ times a multiple of $q$, so $N_q(p) \bmod q$ involves $(\frac{p}{q})$. [Note: Although the application will use $N_q(p)$, you must think about $N_n(p)$ for general odd $n$ first since the recursion from $n$ back to $n-2$ makes no sense in general when the number of variables is only an odd prime: $n-2$ usually isn't prime when $n$ is.]
At the same time, the set being counted by $N_n(p)$ is invariant under cyclic shifts of the coordinates. On the very first problem set I have the students discover numerically that the number of cyclic shifts of an $n$-tuple is always a divisor of $n$. So when we let $n = q$ be an odd prime, $N_n(p) = N_q(p)$ is the number of constant $q$-tuples on the unit sphere mod $p$ plus a multiple of $q$. A constant $q$-tuple is basically counting whether or not $q \bmod p$ is a square. So $N_q(p) \bmod q$ is related to $(\frac{q}{p})$.
In the two approaches to counting $N_q(p) \bmod q$, one involves $(\frac{p}{q})$ and the other involves $(\frac{q}{p})$. This implies the QR relation mod $q$, which is actual equality since $1$ is not $-1 \bmod q$.
One nice thing about this approach is that it can also be used to prove the supplementary law for $(\frac{2}{p})$, by counting
$$\#\{(x,y) \in ({\mathbf Z}/(p))^2 : x^2 + y^2 \equiv 1 \bmod p\}$$
in two ways. First there is the exact formula for the count (not just mod $p$) which I mentioned before. Second, most solutions in this count come in packets of size 8 (permute coordinates and change signs to get 8 solutions out of one solution). The exceptions which don't fall into packets of size 8 (when $x$ is $\pm y$ mod $p$ or $x$ or $y$ is $0$ mod $p$) depend on whether or not 2 mod $p$ is a square (does $2x^2 \equiv 1 \bmod p$ have a solution?), and comparing these two formulas mod 8 implies the usual rule for $(\frac{2}{p})$.
Since I am able to get the students to work on ideas that are used in the proof much earlier on during the semester (one doesn't need quadratic residues to numerically look at solutions of $x^2 + y^2 \equiv a \bmod p$, for instance), this proof nicely ties together things they have seen throughout the course. So that's why this is my vote for the best proof to give in an undergrad course.
The proof involving Gauss sums always seemed the best to me. I'm going to run my own undergrad number theory students through that proof, right after we develop some experience with roots of unity.
If you remove the constraint of accessibility to students of a first number theory course, then you can avoid computations with roots of unity altogether: By Galois theory (and some knowledge of discriminants), a square root of p or -p lives inside of the cyclotomic field of index p. An examination of the action of a Frobenius element at q on this square root relates Legendre(p,q) to Legendre(q,p).
The following variant of a proof going back to V. Lebesgue and Eisenstein is due to Aurelien Bessard (2010). See also W. Castryck, A shortened classical proof of the quadratic reciprocity law, Amer. Math. Monthly 115 (2008), 550-551.
Let $p = 2m+1$ and $q$ be distinct odd primes and let $N$ denote the number of solutions of the equation $$ x_1^2 + \ldots + x_p^2 = 1 $$ in the finite field ${\mathbb F}_q$.
I'm a fan of Zolotarev's proof, although the proof by Gauss's lemma does have sentimental value.
The proof involving Gauss sums seems to be the most standard one.
There is also Tim Kuniskys proof using only basic group theory, which for me makes the theorem a bit less misterious.
I don't think anyone mentioned Eisenstein's classic proof. This presentation of it is pretty good. I find it clear and attractive, especially because it sort of avoids Gauss' Lemma (which is a clever gadget but somehow off-putting).
There's a nice proof that involves the computation of $K_2(\mathbb{Q})$ and the interpretation of $K_2$ as a universal symbol (i.e. a bilinear map $\mathbb{Q}^\times\times\mathbb{Q}^\times\to A$ for some abelian group $A$, written multiplicatively, satisfying $(a,1-a)=1$) in Milnor's book on algebraic $K$ theory. The tame symbols are interpreted as Legendre symbols, and by universality of $K_2$ as a symbol Tate claims that this proof is essentially Gauss's original argument. I suspect that this argument can be generalized to other totally real number fields, but explicit computations of $K_2(F)$ aren't very easy for large discriminants.
It's definitely not the easiest to understand, but at the moment, it's my favorite.
A great proof, inspired by Zolotarev's paper mentioned above, can be found in a very nice paper by Duke and Hopkins. http://www.math.ucla.edu/~wdduke/preprints/duke-main.pdf.
Gauss' original inductive proof is the most natural proof to me. It is a computationally based induction on the maximum of the two primes p and q, and is far and away the most natural. Here, natural does not mean easy or elegant. It means a proof that arises naturally from the numerical patterns. Gauss computes the special cases of quadratic reprocity in a table in the back of his "Disquisitiones" from which it is fairly easy to guess which numbers are residues or non residues of given prime. He carries out the examples of p=2,3,5, 7 and the patterns start to show clearly. He gives an induction proof for some of those cases, indicating the structure of the general induction proof.
Admittedly, Gauss, himself, looked for other proofs. Nevertheless, the first proof shows WHY the theorem is true in a way which the subsequent clever proofs do not.
There was some discussion above about how the proof with Gauss sums is hard to motivate. I disagree, but the motivation involves a little more (mild) algebraic number theory (i.e., Galois theory, algebraic integers, characteristic zero...) than appears in the shortened proof in Serre's book on arithmetic.
(This is of course well-known to number theorists, but I'll write up the full argument just in case somebody has only ever seen the more magical presentation with Gauss sums before.)
Let $p,q$ be odd, distinct primes below.
1) $\mathbb{Q}(\zeta_p)$ has Galois group $(\mathbb{Z}/p\mathbb{Z})^{\times}$, and therefore contains a unique subfield of degree $2$ over $\mathbb{Q}$. It's straight-forward to compute (without knowing what a Gauss sum is) a non-trivial element of this extension with rational square: it's the Gauss sum $G=\sum \left(\frac{a}{p}\right)\cdot(\zeta_p)^a$.
2) By construction, $G^2\in\mathbb{Q}$. What is it? It's easy to see from the formula above that $|G|^2=p$. Moreover, also by the formula, the complex conjugate $\overline{G}$ equals $G$ iff $p=1\mod 4$ and $\overline{G}=-G$ iff $G=3\mod 4$. Therefore, $G=\pm \sqrt{p}$ or $G=\pm\sqrt{-p}$ depending on the residue class of $p$ modulo $4$.
This is the major upshot: we have a very convenient expression for (a variant of) $\sqrt{p}$ now.
3) Note that $G$ is an algebraic integer. Therefore, we can reduce it modulo $q$. Since $\mathbb{Q}(G)$ is a quadratic extension of $\mathbb{Q}$ (namely: $\mathbb{Q}[\sqrt{\pm p}]$), the induced extension of $\mathbb{F}_q$ is an extension of degree $\leq 2$.
4) Is this extension $\mathbb{F}_q$ or the unique quadratic extension of $\mathbb{F}_q$? Well, it suffices to check whether or not $G\in\mathbb{F}_q$. To do this, you can use the Frobenius at $q$. It's easy to see in this way that $G^q=\left(\frac{q}{p}\right)\cdot G$ (by the formula for $G$). So the extension has degree one if $\left(\frac{q}{p}\right)=1$ and degree two if $\left(\frac{q}{p}\right)=-1$.
5) But since we know that $G=\sqrt{\pm p}$ (again: depending on the residue class of $p$ mod $4$), we see that we can give a second answer to the question in 4): $G$ defines an extension of degree $1$ if: a) $p=1\mod 4$ and $p$ is a quadratic residue mod $q$ or b) $p=3\mod 4$, $\sqrt{-1}\not\in\mathbb{F}_q$ (which is the same as $q=3 \mod 4$) and $\sqrt{p}\not\in\mathbb{F}_q$.
6) Comparing the answers to the above questions, we see that $q$ is a quadratic residue mod $p$ if and only if the conditions from 5) are satisfied. But these are exactly the conditions from quadratic reciprocity.
Gauss' original proof is to be in Gauss' Disquisitiones (English translation published by Springer): the residues -1 and +1 on pages 72-73, the residues +2 and -2 on pages 73-77, +3 and -3 on pages77-78, residues +5 and -5 on pages 79-82, +7 and -7 on page 82...the general law of reciprocity is stated on page-87-88, and the proof is carried out on pp 88-98.
There is a very fine presentation of the Gauss' general inductive proof in the textbook Introduction to Number Theory by Daniel E. Flath, on pages 77-80. I have given this proof (Gauss' treatment of the residues +2, -2, +3, -3, and Flath's version of the general proof) repeatedly in my classes in the University of Costa Rica and the students have responded quite positively.
Finally it can also be found in Mathews, Number Theory, but uses properties of the Jacobi symbol. Gauss used and stated these properties, but did not introduce a separate definition, and of course never used the Legendre symbol.
Kevin Brown has a nice expository article Jewel of Arithmetic
and Franz Lemmermeyer has compiled a list of all published proofs
both of which are worth a look.
Edit: I just thought I'd add that there are 224 published proofs in Franz Lemmermeyer's list, and if you are using frames and if your institution subscribes to the online version of Mathematical reviews or Zentralblatt, then the reviews will appear in one of the frames.
I learned the following proof from Jean-François Mestre, it is a variant of Zolotarev's.
For every prime number $p>2$, let $T_p\in\mathbf Z[X]$ be the monic polynomial such that $T_p(X+1/X)X^{(p-1)/2}=(X^p-1)/(X-1)=1+X+\dots+X^{p-1}$. The complex roots of $T_p$ are $x+1/x$, where $x$ is a primitive $p$th root of unity. The same holds in any field of characteristic $\neq p$. In a field of characteristic $p$, the only root of $T_p$ is $2$, with multiplicity $(p-1)/2$.
Let $p,q$ be two odd prime numbers, with $p\neq q$.
The resultant $\mathop{\rm Res}(T_p,T_q)$ of $T_p$ and $T_q$ is an integer. Since these polynomials have no common root, this integer is non-zero.
Since these polynomials have no common root in every field, in particular modulo every prime number, this integer is $\pm1$.
Compute this resultant modulo $p$. One gets $\mathop{\rm Res}(T_p,T_q)\equiv (-1)^{(p-1)(q-1)/4} T_q(2)^{(p-1)/2}\equiv (-1)^{(p-1)(q-1)/2} q^{(p-1)/2}\pmod p$. Consequently, $\mathop{\rm Res}(T_p,T_q)=\epsilon \left(\frac qp\right)$, with $\epsilon=(-1)^{(p-1)(q-1)/4}$.
Similarly, $\mathop{\rm Res}(T_q,T_p)=\epsilon \left(\frac pq\right)$.
Now, $ \mathop{\rm Res}(T_p,T_q) = (-1)^{\deg(T_p)\deg(T_q)} \mathop{\rm Res}(T_q,T_p), $ hence the quadratic reciprocity law.
I don't really know who discovered this proof, but it's interesting. It is taken from Prof. Ram Murty's website:
The easiest to understand line by line are the elementary proofs that go through Gauss' Lemma, and are likely to be seen in any elementary number theory book. I've never actually liked these proofs personally and prefer the one at the start of Serre's "A Course in Arithmetic" for a proof without many technical prerequisites (finite fields only from memory).
Edit: Less elementarily, one could argue that any 'best' proof will necessarily be adelic, proving that the product of the Hilbert symbols over all places at rational arguments is 1. For a geometric example of such an argument, I'm going to throw out arXiv:0804.2142 and references therein, primarily because I don't know if there exists an analogous argument using a central extension of GL_1 in the number field case.
I think my favorite proof that's accessible to undergrads is Eisenstein's proof using the sine function. If we raise the bar on the prerequisites though, my favorite proof (the one that I would give if someone demanded a proof!) is the one using basic algebraic number theory and Galois theory. That's largely because this is a family of ideas that is useful for much more than "just" proving quadratic reciprocity.
Several people above have mentioned the proof above using Gauss sums. In a recent assignment for our Galois theory course, we were asked to prove quadratic reciprocity using Galois theory. I would like to remark that in determining the fixed field of degree 2 over $\Bbb{Q}$ corresponding to the subgroup of index $2$ in $\textrm{Gal}(\Bbb{Q}(\zeta_p)/\Bbb{Q})$, one does not need to know about Gauss sums. Instead notice that $\Bbb{Q}(\zeta_p)$ is the splitting field of $x^p -1$, so that the discriminant of this polynomial $(-1)^{p(p-1)/2}p^p$ is in $ \Bbb{Q}(\zeta_p)$. The discriminant can be computed easily using the Vandermonde determinant and some knowledge about power sums.
Since the square root of the discriminant is a product of differences of roots, it too is in the splitting field. Hence we see that $\Bbb{Q}(\sqrt{\pm p })$ is the unique subfield of index 2 contained in $\Bbb{Q}(\zeta_p)$, depending on whether $p \equiv 1$ or $3$ mod $4$.
Keith Conrad remarked above that in the usual proof using Gauss sums, we need to show that $1 \equiv -1 \mod(p\Bbb{Z}[\zeta_p])$ gives us our desired contradiction, or that $2/p \in \Bbb{Z}[\zeta_p]$ gives a contradiction. I believe one can do this without invoking anything about integral bases. Instead we can say by Proposition 5.1(iii) of Atiyah - Macdonald that $2/p$ is integral over $\Bbb{Z}$ and since $\Bbb{Z}$ is integrally closed in its field of fractions (the proof of which can be rephrased entirely without any commutative algebra) this forces $2/p$ to be an integer. But by assumption $p$ was a prime not equal to 2 so this is a contradiction.
I found this connection with linking numbers very fascinating and this discussion of generalizations.
A nice proof was given by Dirichlet (see Dirichlet P.G.L., Lectures on number theory). Poisson summation proves that (see also Davenport, Multiplicative number theory) $$S(q)=\sum_{k=1}^qe(k^2/q)=\dfrac{1+i^{-q}}{1+i^{-1}}\cdot\sqrt{q}.$$ Together with multiplicative property $$S(pq)=\left(\dfrac{p}{q}\right)\left(\dfrac{q}{p}\right)S(p)S(q)$$ it proves the law: $$\left(\dfrac{p}{q}\right)\left(\dfrac{q}{p}\right)=\frac{1+i^{-pq}}{1+i^{-p}} \cdot\frac{1+i^{-1}}{1+i^{-q}}=(-1)^{\frac{p-1}{2}\cdot\frac{q-1}{2}}.$$
I recommend Gauss's third proof with modifications by Eisenstein. In my opinion, it is by far the clearest and most straight-forward proof of Quadratic Reciprocity even though it is not the shortest. The proof makes no use of any mathematical discipline other than elementary number theory. That is, it uses no abstract algebra or combinatorics. Its charm is that it uses the greatest integer function in an advanced way in place of any advanced theory. The proof uses the greatest integer function to express a variety of number-theoretic concepts and statements involving integers mathematically. Then, using properties of the greatest integer function, the proof works with these concepts and statements concretely (by manipulating them mathematically) to achieve the result. Gauss invented the greatest integer function for his third proof of QR in 1808 for this very purpose. Since it was long and messy, it was simplified by Eisenstein in 1844.
How a proof is presented by the author is also important. In my online text, "A Mathematical Analysis of the Greatest Integer Function", I include a full treatment of QR. For Gauss's third proof, I used Dence. His book, "Elements of the Theory of Numbers" is an advanced text and I felt that his presentation of the proof contained gaps. While his presentation might be appropriate for his objectives and target audience, I felt that it would seem more like an outline to undergraduate students. For this reason, when rewriting the proof, I took three measures to provide clarity. I put a lot of effort into closing every gap and providing a thorough explanation for certain parts, which accounts for a lot of its length. Since the proof has many components even after modifications by Eisenstein, I organized it by dividing it into sub-objectives and providing sub-proofs for each. I also include all three lattice-point diagrams with a numerical example in full detail. So, if you want to savor Gauss's third proof with modifications by Eisenstein, then you want to read my online text at www.greatestintegerfunctionresearch.org. My online text is also an excellent resource for various topics in number theory and analysis and is chockfull of original research.
Well, I certainly don't know all the different proofs presented here, but the "natural", unoriginal and very elementary one you'll find p. 77-78 of Hardy and Wright "Theory of Numbers" (4th edition) is assuredly quite pleasant to teach...


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Start Selling! - AutoVue Enterprise Visualization Solutions
By jose.fernandez-stoll on Oct 13, 2009
Calling All Partners!
You can now start reselling select AutoVue EVS products as an Oracle Remarketer. Please contact your local distributor for more information.
Remarketer Authorized Value Added Distributor Contact List
Good Selling.
Jose Fernandez-Stoll
Worldwide Alliances Consultant, Remarketer Program


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A 3-D carbon nanotube mesh enables rat spinal tissue sections to reconnect in culture.
Genome Digest
April 24, 2014|
What researchers are learning as they sequence, map, and decode species' genomes
Covering the life sciences inside and out
April 24, 2014|
What researchers are learning as they sequence, map, and decode species' genomes
April 24, 2014|
A marine cyanobacterium possesses astounding genomic diversity, yet still organizes into distinct subpopulations that have likely persisted for ages.
April 16, 2014|
The extra chromosome behind Down's syndrome can impact transcriptional regulation beyond chromosome 21, a study finds.
April 11, 2014|
Considering "targeted therapeutics" in the face of intra-patient heterogeneity.
April 10, 2014|
A little-studied protein appears to be a critical part of the perplexing channel that prevents cells from bursting.
April 9, 2014|
Study finds that prediagnosis obesity is predictive of poor prognosis, even among patients who have a molecular marker associated with better disease outcome.
April 7, 2014|
People who report having enjoyed amphetamine are more likely to have gene variants associated with protection against attention deficit-hyperactivity disorder and schizophrenia, a study shows.
April 4, 2014|
Lynne Quarmby's love of the natural world inspires her to explore beyond her cell biology lab through art.
April 1, 2014|
Shared sequences within the brain lipid-metabolism pathway between Neanderthals and modern Europeans highlight questions about how these genetic similarities arose.
March 28, 2014|
A neuroscientist studies the brains of tango dancers in an attempt to understand interpersonal connectedness.


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On Thursday, November 7 Cassia Spohn, Foundation Professor in the School of Criminology and Criminal Justice at Arizona State University, presents research from a National Institute of Justice funded study in which Spohn and colleague Katharine Tellis investigated police and prosecutorial decision making in sexual assault cases. The study uses quantitative data on sexual assaults reported to the Los Angeles Police Department and the Los Angeles County Sheriff's Department in 2008, and qualitative data from interviews with detectives and deputy district attorneys.Cassia Spohn is a Foundation Professor in the School of Criminology and Criminal Justice at Arizona State University. She is the author or co-author of five books, including The Color of Justice: Race, Ethnicity and Crime in America and How Do Judges Decide: The Search for Fairness and Equity in Punishment. A sixth book, Policing and Prosecuting Sexual Assault: Inside the Criminal Justice System will be published in 2013. Her research interests include prosecutorial and judicial decision making, the intersections of race, ethnicity, crime and justice, and sexual assault case processing decisions.
Links:[1] https://www.z2systems.com/np/clients/vera/eventRegistration.jsp?event=307
[2] http://www.nsvrc.org/states-territories/new-york
[3] http://www.nsvrc.org/event-type/trainings


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Wow! It works great and softens clothes too! Review by SHAWN
I was skeptical as well, and it sat around my laundry room for a while before I had the guts to try it. I saw the comments from others on this site and decided it was time to give it a try. Wow, I am amazed! The real dirty clothes came clean and I cannot believe how soft the clothes are! Love it! Goodbye detergent! (Posted on 7/26/2015)
Amazing Funny Looking Ball Review by Texas Karen
I had a smell in my washer or dryer that I couldn't
identify or get rid of, no matter what I tried. This Funny Looking Ball got rid of it in 1 load! Clothes smell so clean and fresh, I just shake my head. (Posted on 3/12/2015)
Hot Tub Review by Kevin
I throw one of these mineral balls in my hot tub every 4 months and it keeps the water sparkeling clear and clean. I have two tubs and it really does work great. (Posted on 10/30/2014)
I was skeptical like the others - but I LOVE... Review by LH
I was skeptical like the others - but I LOVE THIS LAUNDRY BALL! My clothes come out clean and soft! I am happily surprised! I am buying some for my adult children for Christmas! (Posted on 12/15/2013)
Was skeptically but purchased this for a lot... Review by JT
Was skeptically but purchased this for a lot of reasons; soap expsensive,coupons, free shipping etc. I rehab wildlife and wash towels all the time and BOY are they dirty!! Tried this and couldn't believe it. Just folded them and am AMAZED how clean and fresh smelling they are. Was afraid to smell them because of the feces and other smells that go along with rehab. They are supposed to continue to make laundry better once residual soaps are removed. I will be using these forever! But..being a wise shipper, I will purchase the 2-pack. Stocking stutters for all my kids! (Posted on 10/31/2013)
I was skeptical. But I'm also a "gadget"... Review by TP
I was skeptical. But I'm also a "gadget" guy. Seemed like a reasonable price to experiement with. If it doesn't work, well, I've spent a lot more for items that turned out to be garbage. I'm happy to say this was money well spent. Wow! I am blown away by how great this little gadget works. Don't know how or why. Just know it works great! (Posted on 2/23/2012)
This is a very good product that works well... Review by TAW
This is a very good product that works well and leaves your laundry clean and softer than using fabric softeners.Your lent trap in dryer is far less with this product and dry time is also cut on avg. 10+ minutes due to no detergent residue. Over all this is a cost saving product.
(Posted on 11/2/2011)
When I bought this item for my wfe as a... Review by RWB
When I bought this item for my wfe as a stocking stuffer at Christmas, she laughed at me. "Your a Chemical Engineer and you thought this would work" she said, "You must be getting senile in your old age". But she tried it...and loves it. She sprays Shout on stains but uses no detergent or softener. She's even tried it, successfully, on things she never thought would ever come clean or bright. But she did have a question I couldn't answer. How do you know when you've reached 1000 washings? Do the pebbles go away? (Posted on 4/13/2011)
My wife and my mother uses this laundry ball... Review by AJN
My wife and my mother uses this laundry ball for 2 years and I'm always coming back to reorder more. It's the best thing ever created! Clothes come out smelling fresh and clean it's awesome! Saves us alot of money on laundry soap too. (Posted on 2/3/2011)
bought these and then waited forever to... Review by PR
bought these and then waited forever to begin trying them out. omg. what a miracle! our water is so terrible. hard. stinky. had to use only cheer, never anything else. had to use twice the recommended amt of the expensive brand of softener liquid and THEN use dryer sheets too. used a ball in maybe 2/3 the amt of water level.. my washer is oversized. never have my clothes been so soft. and I swear that they dry faster. is this because of no soap and softener residue in the clothes? I am going to get them for all my grown kids and grandkids. (Posted on 9/29/2010)
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The Trib reports:
As legislators weigh impeaching Gov. Rod Blagojevich and federal prosecutors prepare to indict him on corruption charges, his acting chief of staff and a deputy governor will be keynote speakers Wednesday at an "Ethics in the Workplace" seminar for some 200 state employees.
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A case study is at hand for speaker and audience. Will they use it?
I guess they can skip the part about Why This Seminar Is Necessary.
Awkward? Orwellian!Btw, has there ever been a more ridiculous public figure than Roland Burris, the senator that nobody wants, chosen by the process that nobody likes?
I'd say the governor is slightly more ridiculous. Mr. Burris has an air of stupendous dignity that offsets his predicament--and his foolishness in accepting the offer.
I have to agree with Peggy -- Burris is a strong candidate (cf. his pre-engraved cemetary monument and his self-titled children), but it's hard to beat Blagojevich for the Most Ridiculous title. That press conference where he quoted Kipling in defense -- nay, in praise -- of his own integrity? Incredible.
To be filed under - you can't make this stuff up.
I truly believe that Blagojevich has an undiagnosed and/or untreated mental illness. His behavior has been erratic and inexplicable almost since he assumed office. His grasp of reality often seems tenuous at best.
Before we go to the medical model, and diagnose a debilitating malady aren't there alternative possibilities: for example, he's a jerk; or he is not very bright; or he's in a state of mortal sin, or.... well, fill in.
I don't see what is ridiculous about an African-American, legally appointed to the Senate by the sitting Governor of Illinois who has been convicted of no crime I am aware of being physically threatened and barred from his legal entry into the Senate building on trumped-up charges of improper documentation by the all-white Senate Democrats. I guess African-Americans need not apply to the Democratic caucus unless they come bearing three-quarters of a billion dollars as the President Elect did. What a sad day for America.
Is Mr. Burris perhaps guilty of hubris?
MAT, you're aware that the president-elect was elected to the U.S. Senate, aren't you? And that, during that Senate race, Bobby Rush opposed him in favor of a wealthy white man?http://www.suntimes.com/news/commentary/1363433,CST-EDT-edit06a.article
MAT: the notion that opposition to Burris's appointment is racially motivated is plainly ridiculous, from where I sit.
"Before we go to the medical model, and diagnose a debilitating malady arent there alternative possibilities: for example, hes a jerk; or he is not very bright; or hes in a state of mortal sin, or. well, fill in."Sure, he's got a share of the usual maladies that afflict politicians in Illinois. But in his case there is something else there. In instance after instance it seems he lives on another planet. Almost to a person, members of the legislature don't know what to make of him and have found they can't work with him. He's thoroughly alienated both parties and even members of his own family (i.e. his father-in-law the Chicago alderman). Illinois state government has never been a watchword for efficiency or effectiveness, but even by Illinois standards, the government has never sunk this low. In many ways, it's simply stopped functioning.He boxed as a youth. Maybe he got hit in the head too many times.
I view Illinois politics in the spirit of high farce (maybe too many Royko columns as a Young Person), and Blago certainly doesn't disappoint. That Kipling reading nearly did me in. I hope he reads does it more, maybe makes it a regular feature of his news conferences. I could suggest the last four lines from "The White Man's Burden":Comes now, to search your manhoodThrough all the thankless yearsCold, edged with dear-bought wisdom,The judgment of your peers!Anyway, I forgot about that Obama-Bobby Rush thing. When Rush was on TV supporting Burris, he looked, to put it kindly, somewhat feeble. Is he more with it than he appears?
MAT,I would be in agreement with you completely if you had left out the racial stuff. There is simply no justification for "playing the race card" on this one.Blagojevich is under a major political cloud, but he seems to me clearly to have the authority to appoint Burris, and to the best of my knowledge, there is no legal reason for the Senate not to accept him. Also outrageous was the Illinois Attorney General's attempt to get the state supreme court to remove Blagojevich on the grounds that he was "disabled." If this is how our lawmakers regard the law, then heaven help us.On 60 Minutes this week, I saw a report about prosecutors charging drunk drivers who cause fatal auto accidents with murder. It was appalling. I am all for extraordinarily harsh treatment of drunk drivers, whether they cause fatal accidents or not, but I object to getting "creative" with the law. (By the way, if they want to make causing a fatal accident while drunk equivalent to murder, it doesn't make any sense unless they make drunk driving into something like attempted murder.) Another case that comes to mind is the despicable woman who pretended online to be a teenage boy, charming and then dumping one of her daughter's former friends, resulting in the duped girl committing suicide. I wish there had been some applicable law that would have allowed them to throw the book at her, but it is disturbing to see the authorities in effect say, "What that person did was reprehensible. Let's figure out some charge to bring against her."
Re: Blago, Illinois pols, and ethics - I do have to say this, though - it seems whenever I travel and buy the local paper, whatever state in which I happen to be sleeping that night is mucking about in its own scandals and ethics infractions. I guess it's endemic to politics. Was it ever thus, everywhere? Or is it true that people are fundamentally disconnected from those who run our governments?
It could be really awkward if the Senate refuses to seat Roland Burris and doesn't refuse to seat Al Franken.http://online.wsj.com/article/SB123111967642552909.html
Both of these events (Franken won't be seated) confirm my view that Harry Reid should go as majority leader. Really!


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KILLEEN (October 3, 2012)--A Killeen teacher will find out on Sunday if he is the winner of a statewide weight loss competition, sponsored by H-E-B.
Contestants are competing in the 2012 Slim Down Showdown for a chance to win $10,000 or a $5,000 fan favorite prize.
Donnis Hamilton, 37, of Killeen has been competing against 24 other contestants in the program that includes a five-and-a-half day wellness lesson along with weekly coaching.
The Slim Down Showdown is lasts 16 weeks.
Participants also must be willing to share their journey and blog about their experience, an H-E-B spokesperson said.
At 445 pounds, Hamilton told competition organizers before the program began that he has trouble keeping up with his 3-year-old son.
He said he has considered weight loss surgery but added that it doesn't help when you don't learn to break bad nutritional habits.
The program began in June and will wrap up Sunday in conjunction with the fall Siclovia, a free San Antonio event hosted by the city and the local YMCA.
Overall winners will be announced at the Grand Finale celebration in San Antonio.
"I am not in it for the money. I am in it because it offers something I have not gotten yet. I have not gotten training… Give a man a fish; you feed him for a day. Teach him how to fish; you feed him for a lifetime," Hamilton said.


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Children's Vaccines Health Center
Dec. 13, 2011 -- Girls and young women who are vaccinated against human papillomavirus (HPV) appear to be no more likely than those who are not vaccinated to engage in sexually risky behaviors, a CDC survey finds.
HPV is the most common sexually transmitted infection in the U.S., with an estimated 6.2 million new infections each year.
Two types of the virus, HPV 16 and HPV 18, are responsible for 70% of cervical cancers. HPV also causes genital warts and can lead to cancer of the cervix, vagina, vulva, penis, and anus.
With the approval of the first vaccine to prevent HPV infection in 2006 and the second in 2009, concerns emerged that vaccination might promote sexually risky behaviors.
Results from the CDC survey suggest these concerns may be unfounded, but researcher Nicole C. Liddon, PhD, warns against over-interpreting the findings.
Liddon is a research scientist with the CDC's Division of Adolescent and School Health.
"This survey represents a snapshot in time, and we cannot rule out the possibility that the HPV vaccine leads to sexual risk taking," she tells WebMD. "But this should help calm concerns of parents and (health care) providers to some degree."
HPV Common in the Sexually Active
Among non-vaccinated girls and boys, infection with HPV is very common following initiation of sexual behavior.
By one estimate, 24% of teenaged girls in the U.S. between the ages of 14 and 19 and 45% of women in their early to mid-20s are infected with HPV.
For this reason, vaccination efforts target girls who are not yet sexually active. Current recommendations call for vaccination of girls and women ages 11-26 with the Cervarix or Gardasil vaccine. The Gardasil vaccine is also approved for use in boys.
In an effort to examine vaccine coverage rates and whether being vaccinated against HPV has any impact on behavior, Liddon and colleagues examined survey data from more than 1,200 young women between the ages of 15 and 24.
The women were participants in a CDC-sponsored survey examining sexual and reproductive health issues among teens and young adults.


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6 Supposedly Ancient Traditions (That Totally Aren't)
Nothing shuts down a person's higher reasoning functions quite as fast as the word "tradition." If it was good enough for our ancestors, it must be good enough for us, damn it!
Unfortunately, some of the most "ancient traditions" still followed today come from people who knew this, and just made them up off the top of their head.
#6. The Pledge
The Tradition:
According to this ridiculously schmaltzy video, this video with a hilariously ironic choice of music and 90% of the people in states beginning with the letter A, the pledge is an inviolable American tradition. Given the massive hissy-fit that erupts any time someone tries to change a single word, you'd think the version you grew up reciting was written into the constitution after the Founding Fathers watched a giant bald eagle fuck every letter into Plymouth rock.
An image that would bring a tear to Captain America's eye.
How Old It Actually Is:
The idea of pledging allegiance to the flag was basically an early viral marketing gimmick. It was first published in 1892 in a wildly popular children's magazine named The Youth's Companion. The much-bitched-about "under God" was only added to the pledge in 1954.
Who Made It Up:
Daniel Ford, the man who ran The Youth's Companion, dreamed of putting an American flag in every classroom in the country.
The man loved him some America.
Within a year, 30,000 flags had been sold. Our calculators tell us that comes out to $300,000, which was a lot more impressive a sum in 1892. The man who actually wrote the pledge was a former minister named Francis Bellamy. He was a Socialist (aka, a dirty commie) whose stated mission was to create in America's youth a habit of automatic reverence and utter loyalty to the country. He even came up with an original salute for children to give while reciting the pledge...
Things got awkward around '41.
The decision to add "under God" was made at the height of America's brief flirtation with paranoid schizophrenia, otherwise known as McCarthyism. Congress felt the pledge, like most people at the time, just wasn't American enough. How were these children standing around the American flag, pledging "allegiance to the flag of the United States of America, and to the republic for which it stands" to know that they weren't in the Godless Soviet Union? Thus, Congress added God to the pledge, and every generation who passed through a public school after 1954 was transferred into a flawless vessel of patriotism.
#5. Bushido - The Ancient Code of the Samurai
The Tradition:
For centuries, the samurai and their spiritual descendants followed "the way of the warrior," living lives governed by its tenets of honor, strict devotion to one's master and, above all, self sacrifice. This ancient tradition helped make World War II a hell of a lot scarier, since, according to the Internet, "Kamikaze pilots used the samurai and their code for inspiration ... Just like the samurai, kamikaze pilots had no fear of death, and were honorable men that were loyal to their country."
How Old It Actually Is:
The idea that samurai are either loyal to their country or eager to die in battle is approximately as old as Walt Disney. Bushido as a coherent ideology only dates back to 1905.
Who Made It Up?
The whole thing started with an honest, if retarded mistake by a historian named Nitobe Inazo, who based his 1905 book Bushido: The Spirit of Japan on rules written for samurai. This is the equivalent of reading a high school handbook and determining that teenagers live by a strict code of attending class, and turning weed dealers in to the cops.
According to Karl Firday, professor of history at the University of Georgia and author of a bunch of really smart books on Japan, aside from laws that they were told to follow, the history of the samurai is notable for a complete lack of evidence that they were any more happy to die in battle and even a little bit loyal. It's entirely possible that a warrior sacrificing his life was seen as noble, but that's no different than the European code of chivalry which also made room for honorable suicide. In fact, the evidence paints a picture of samurai that looks more like a modern professional athlete than what we see in our martial arts films. They'd fight and kill for you as long as the money was right. When it wasn't, they'd switch sides, and slice the word "for" clean out of the previous sentence.
So if Japan was one big game of "fuck your buddy with a sword" and Europe was the land of the noble warrior falling on his, how did a bunch of Japanese pilots find themselves swan diving at air craft carriers while saying prayers to the medieval equivalent of Terrell Owens?
As it turns out, our modern concept of Bushido developed as a method of social control. The Emperor and the Imperial Army and Navy wanted something that would boost their men's fighting spirit. When Nitobe Inazo sucked at his job badly enough to write that "the way of the warrior is to die," they all just sort of nodded and said, "Yep, that's the way of the warrior alright!"
#4. Islamic Fundamentalism
The Tradition:
The boogeyman that replaced the specter of communism in the hearts of terrified Westerners, Islamic fundamentalism seems to come from another time. They rage against science, Western ideals and the basic rights of women. That's why you hear people on Fox News claiming that Muslim world is stuck in the Dark Ages.
"You can't use reason with these people. They only understand shadow puppets."
How Old It Actually Is:
Actually, the Middle East's clock stopped around the same time as the one at Marty McFly's high school in the 1950s. If the Arab world was really still stuck in the Middle Ages, everyone would be a lot better off.
Who Made It Up?
During the period the the Western world thinks of as the Dark Ages, when Europeans were busy murdering each other over matters of religion and superstition, Islam was cool as a cucumber. At the time, Islamic regions were actually more accepting of Judaism and Christianity than most of the Christian world was of Judaism and other types of Christianity. Long before the Italian Renaissance, the Islamic Empire realized the Greeks and Romans had been on to something with this book learning stuff, and used this realization to revolutionize astronomy, literature, physics, philosophy and architecture. Still bored, they went ahead and invented algebra and modern medicine too.
"George Washington invented numbers! We call them Arab numerals to mock them!"
The antiquated practices many Westerners associate with modern Islam are actually a relatively recent development. Reporting from Saudi Arabia for The New Yorker, Lawrence Wright interviewed an older Saudi man who reminisced about the good old days when men and women used to be able to celebrate weddings together. While it might seem weird to Westerners used to hearing stories of ankle length hemlines following the words "Back in my day... ," in the Middle East, when grandparents miss the good old days, they're often talking about a place that was far less up its own ass.
"We had books. And the orgies! Don't get me started on the orgies ...
It wasn't until the 1950s that fundamentalist Islam started gaining influence, and outdated, dying traditions like the veil saw a spike in popularity. That's when followers of a fringe 18th century scholar Mohammed Al Wahab began to take Islam back to basics, which in this case meant an imaginary past where women were treated like shit and all the pesky "progress" of the last 1400 years never happened. During his lifetime, Wahab was taken about as seriously as Pat Robertson is taken today in the West. But in the 1950s, Wahabi Muslim thinkers like Sayyid Qutb started to urge total separation between Islam and the West, arguing that the outside world had "nothing else to give humanity."
Oh really, Qutb?
Qutb and his fundamentalist contemporaries inspired a new generation of radical thinkers, who took this "fuck the West" mentality a few steps further, resulting in a Middle East that is far less progressive than the Dark Ages they're supposedly stuck in.
Some people shouldn't be encouraged to "shoot for the stars."
See, as tempting as it might be to divide history into the bad guys and the good guys, civilizations tend to evolve more like the Batman franchise, kicking ass part of the time, and reaching unspeakable, ass backwards lows that would embarrass their ancestors at others. Muslim people were doing algebra while we were burning women for having funny birthmarks on their face. They just happen to be going through their Batman and Robin phase.


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The Patient-Practitioner Relationship in Acupuncture (9783131488411)
Publisher: Thieme
Binding: Paperback
by Leon Hammer
Profit from a wealth of experience in interactions with your patients!
The Patient-Practitioner Relationship in Acupuncture is written for acupuncturists and practitioners in the fields of alternative medicine searching for:
The Patient-Practitioner Relationship in Acupuncture is written for acupuncturists and practitioners in the fields of alternative medicine searching for:
effective ways of connecting better with their patients in all their diversity, and the skills necessary to guide patients through emotional, psychological, and spiritual difficulties as part of the healing process.
Dr. Hammer bases his work on the universally accepted and fundamental role the therapeutic relationship plays in the practitioner's ability to heal and his lifelong observation that both the patient and the practitioner benefit from this vital relationship.
Drawing from his long and extensive personal and professional experiences and writing in an easily understandable and at times anecdotal style, the author avoids psychological jargon as much as possible. The material is presented independent to pathology and is organized into two parts: The first part outlines the basic tenets of the therapeutic relationship, and the second, main part presents individual, issue-oriented chapters addressing the varied life situations, personalities, and emotional reactions with which the acupuncturist or practitioner is confronted in everyday practice.
Let this handy reference become your constant and reliable companion on your path to:
enhancing your propensity and innate talents to heal, improving your therapeutic skills within the scope of your practice, and gaining confidence in your interactions with your patients.
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Domesticated Foxes, Drooling Pugs and Mike
NPR Fox/18"x24"/oil on panel
Domesticated Foxes, Drooling Pugs and Mike
NPR Fox/18"x24"/oil on panel
I'm an avid NPR listener and was really happy to get a call from them to participate in their 2012 calendar. Every year they choose 12 artists to illustrate each month. My piece was based on one of my favorite RadioLab episodes called "New Nice" which was about a Russian geneticist who domesticated the fox. After several generations of selective breeding, he was successful in creating a gentler, human-friendly pet fox. I was really proud to work on this piece for an organization that I get so much inspiration from. The 2012 calendar is available for purchase from NPR.
Katie Burk, the designer for the NPR calendar, came up for the American Illustration Show and gave us a signed Carl Kasell (Wait, Wait, Don't Tell Me) pillow. If you listen to NPR, you know the voice of Carl Kasell. What a neat gift. Thank you Katie!
Pug Drool/18"x24"/oil on paper
It's no secret I'm a dog person. And I've always been a fan of Bark magazine. This Pug painting was for an article called "Drawn to Dogs". It was a about a professional cat-sitter and self proclaimed cat-lover who fell in love with a pug while dog-walking him in NYC.
Mike/14"x20"/oil on paper
And this piece was for Reader's Digest Asia. It was a true story about a man named Mike who was kidnapped and buried alive for 5 days. Ants were biting his hands and eyelids while he was buried in small box in the ground. He lost 23 pounds but was eventually rescued by a inquisitive cop.
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Lafayette Service Center
Rachel possesses seventeen years of progressive nonprofit leadership experience. She developed a passion for nonprofit youth service as a counselor at the Acadiana Children's Shelter and the Acadiana Shelter for Girls in Lafayette, Louisiana. She continued her work in the nonprofit industry as a Membership Specialist & Membership and Training Director with Girl Scouts Bayou Council where she was recognized for her efforts in membership growth and retention. Rachel strongly believes that an environment focused on accountability and a commitment to professional excellence is the foundation to customer service and satisfaction.
Drawing on her previous experiences as an employee with Bayou Council, Rachel was promoted to Chief Operations Officer – Direct Services for Girl Scouts of Louisiana – Pines to the Gulf where she played a key role in the successful realignment of the Girl Scout organization in the state of Louisiana by effectively working to help merge three legacy Girl Scouts Councils serving 12,000 members and 42 parishes. As Chief Operating Officer – Direct Services, Rachel was chosen to lead the council in its strategic learning and planning initiative through participation in Girl Scouts of the USA Strategic Learning Pilot Program lead by Willie Pietersen (Reinventing Strategy) at the Columbia School of Business in New York. Recently, Rachel was chosen to participate in the National Human Services Assembly Executive Leadership Certificate Program in collaboration with Arizona State University's, Arizona State Lodestar Center for Philanthropy & Nonprofit Innovation, Indiana State University's School of Public and Environmental Affairs, and the Lilly Family School of Philanthropy's Fund Raising School.
Rachel has been deeply entrenched in service to her country and community. She is a United States Army Veteran who was stationed in Hanau, Germany where she was awarded the Army Achievement Medal for outstanding support services during Operation Desert Storm. She has served as an AmeriCorps member where she provided services to Habitat for Humanity, Louisiana Coastal Restoration efforts as well as mentoring at risk youth in middle schools and Lafayette Parish Teen Court in Southwestern Louisiana. Rachel has also served as a United Way of South Louisiana Campaign Volunteer Chair, United Way of Iberia Campaign Volunteer, and as a member of the Acadiana Violence Prevention Task Force.Rachel holds a Bachelors Degree of Arts with a Major in Sociology and lives in Lafayette, Louisiana with her husband and daughter who is a Girl Scout Cadette.


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Radiologic Sciences
Register for DMI 49 this Spring 2016
This course is open to all students.
Program Overview
The Radiologic Sciences Department of City College of San Francisco offers two full-time programs in either Diagnostic Medical Imaging (DMI) or Radiation Therapy Technology (RTT). The curricula are designed so that a student will accomplish the following two goals:
1.) Satisfy the requirements for graduation from the College with an
Associate Degree in Science with a major in either Diagnostic Medical
Imaging or Radiation Therapy Technology
2.) Upon program completion, the graduate will be qualified to take
the national credentialing examination administered by the American
Registry of Radiologic Technologists (www.arrt.org) and upon passing receive
national and state certification. Since 2006, 100% of the graduates of
the Diagnostic Medical Imaging program have pased the examination on
the first attempt. Since 2010, 100% of the graduates from the
Radiation Therapy Technology program have passed this examination on
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Both Programs are accredited by the Joint Review Committee on
Education in Radiologic Technology (www.jrcert.org), 20 North Wacker
Drive, Suite 2850, Chicago, IL 60606-3182.
Contact: firstname.lastname@example.com
These Programs require separate applications and a student must be accepted into the Program prior to enrollment. Each Program has pre-requisites which must be completed before an application can be considered. Please refer to the Information Packet below for details.
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Carbro, you are destroying one of the last of my illusions! I guess, however, your statement is also true of HEIRS to thrones and other kinds of office. A short story about the Siegfried and his ladies from the point of view of the Queen might be very interesting.
Of course, history is rife with heads of state with significantly sub-genius IQs.
How important are Odile's 32 fouettes?and what do they add to the ballet?
Posted 12 February 2007 - 10:11 AM
Posted 12 February 2007 - 11:00 AM
....Of course, history is rife with heads of state with significantly sub-genius IQs.
While Great Leader Stalin did not attend Maya's performance with Chairman Mao, Vladimir Putin did accompany guest G. W. Bush to the Nutcracker. And President Bush did invite the American Ballet Company to perform Nutcracker at the White House. It is good that our leaders can take a break from the pressures of State.
Posted 12 February 2007 - 11:38 AM
She said she liked to emphasize the similarity between the two Swans, because, after all, how stupid do you think Siegfried had to be?
Now that I come to think about it, I'm kind of hazy on this bit. Does Rothbart cast an Evil Spell on the court, the Queen Mother and/or Siegfried? Or does Odile have to do most of the spadework herself, as it were, which is what the fouettes are in aid of?
Posted 12 February 2007 - 12:11 PM
That would depend largely on the production. In ABT's McKenzie staging, there's little doubt that Rothbart runs the show, but I think that is a very anti-traditional take.
Does Rothbart cast an Evil Spell on the court, the Queen Mother and/or Siegfried? Or does Odile have to do most of the spadework herself, as it were, which is what the fouettes are in aid of?
Since Odile is Rothbart's daughter, it seems logical that she'd have a few magic powers of her own.
Posted 12 February 2007 - 12:20 PM
Of course, history is rife with heads of state with significantly sub-genius IQs.
Oh ouch!
Posted 12 February 2007 - 12:36 PM
Posted 12 February 2007 - 02:50 PM
I don't know, they've become a tradition, like it or not. It's kind of like the penchee ending to the White Swan pdd. It wasn't always like that, as footage from anything before the 1970s show. But now audiences have come to expect it, and it fits the music so well, so anything other than the penchee looks funny.
Ive spoken to people who dont know ballet at all, but two things they do know are Swan Lake and the 32 turns, and theyre disappointed on those occasions when they dont get them.
Speaking for myself, I enjoy seeing them unless theyre really botched, although if they are left out I wont demand my money back.
Posted 12 February 2007 - 03:54 PM
As far as the type of fouettés goes, I do have to say I find the Cecchetti way boring, as the type of movement it produces is too slow. I like a smaller rond de jambe that emphasizes second (but I don't like going directly to second). And I would prefer some restraint in Swan Lake as opposed to Don Q, Kitri, &c. A double on every 8th turn looks nice, anything much beyond that strikes me as vulgar.
Posted 12 February 2007 - 07:37 PM
Posted 13 February 2007 - 02:26 PM
However in some versions it's still omitted. For instance in the recent video with Svetlana Zakharova the Bournmeister version was used and the last fouettes become supported pirouettes.
Posted 13 February 2007 - 02:44 PM
I think it's a bit more than that. For historical reasons I also don't like steps being altered or substituted. So many changes have crept into Swan Lake over the years that it's becoming increasingly difficult to know how much of the original choreography remains. At least we know for certain that the 32 fouettés were present in Petipa's original, so let's not hurry to toss them out.
It's kind of like the Spessivtseva solo of Giselle. Yeah it wasn't always there, but now it's become of the Giselle tradition.
Posted 14 February 2007 - 07:12 AM
For the record, I represent mid-level ballet-watchers and I like the 32 fouettés. And I'm with Mel; if the dancer can't do them, she ought not be cast.
Posted 14 February 2007 - 07:35 AM
Truthfully I don't see why any dancer with the technical ability to do Odette/Odile can't just learn to churn out 32 fouettes! It it not a super human trick, It can be taught.
Forgive the bad pun, but somehow I feel this discussion has come full circle. If there is a consensus, it is that the fouettes are both fun and irreplaceable. In that case, Vipa's advice is best. It is true I've seen videos of corps members performing spectacular fouettes (Zhong-Jing Fang!)there is no shortage of dancers who can do them. Meanwhile, I'll continue to enjoy some of the dancers who can just barely get through them.
Posted 14 February 2007 - 08:21 PM
RE: The 32
Yes it's a tradition passed down from Legnani (sp?) days, and I do like traditions. Multiples work if they enhance the musical accent, but not to excess, not as a gymnastic exercize, and not as a gloat at the audiance to "look at me, look at me, the great dancer" instead of a mesmerizing act of centrifigal force like a whirlpool or "black hole" drawing Siegfried and the Court's attention and attraction to her. I too remembe Plisetskaya and being surprised she avoided them, and guessing why that was so, and not missing them.
When I was at Tokyo Ballet, O/O was performed by two different dancers, because each had strengths they wanted to show off and weaknesses they wanted to avoid. I didn't see too much a problem because it was better to see them do well, than not when performing a difficult step, but it did negate the "twin" aspect of the plot I mentioned above.
Posted 14 February 2007 - 10:01 PM
I've encountered this comment on the musical reference more than once, and no doubt Petipa intended Odile's port de bras to mirror Odette's in the window. But it's worth remembering that Tchaikovsky wrote this adagio for the first act, when neither Odette nor Odile were on the scene yet. I may seem musically obvious to us, but Tchaikovsky didn't conceive it that way.
the poor swan vainly trying to attract his attention in the window--which is why almost concurrently with that image, and musically in the score, Odile imitates Odette's 'swan arms' to capture Siegfried's attention.
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14 Comentarios
4,8 en abril 01, 2016
So enjoyed our stay in the Granddaughters Cottage! Miss Beth graced us with a most delicious breakfast and heart felt stories. So looking forward to staying here again. Such a memorable experience. Thank you again, Miss Beth. Sue & Cathy
4,8 en marzo 25, 2016
My husband and I met up with another couple in Jefferson so we rented both rooms at Chez Lafayette. Both rooms were beautifully decorated, clean and comfortable. The garden/courtyard was very pretty. Breakfast made by Beth who was a gracious host was delicious. I would definitely recommend this B & B to anyone who wants an outstanding B&B experience.
5 en enero 22, 2016
B&B is located in the downtown area so you can walk for antique shopping and food. Beth was a very gracious host and provided an excellent breakfast. Accommodations were cozy and comfortable. Will definitely stay there again when we come back to Jefferson
3,2 en diciembre 11, 2015
Stayed during the annual Candlelight Tour of Homes. Location is convenient to all downtown attractions and a short drive to this year's homes (was on the tour once in the past). Friendly atmosphere. Stayed in the ''Granddaughters' Cottage" which had plenty of space for three of us.
4,6 en noviembre 18, 2012
Chez Lafayette provided a cozy home away from home for our getaway. Granddaughters' Cottage allowed for privacy, while our hostess, Mrs. Crawford, prepared a delicious meal and opportunity for pleasant, interesting conversation during breakfast. We were within walking distance from any points of interest.
5 en octubre 03, 2012
Our hostess/owner, Beth, was very hospitable! This town has so much to see and to -- our stay was superb!
5 en julio 31, 2012
We stay at Chez Lafayette Bed and Breakfast, every year. Sometimes twice a year. We stay in the cottage. It is always so nice and clean. Beth makes you feel so right at home. She cooks the best gourmet breakfast in the world. Chez Lafayette is the best bed and breakfast in Jefferson, TX.
5 en julio 30, 2012
Chez Lafayette is a favorite of ours. Ms. Crawford has a beautiful house filled with antiques, and is such a gracious hostess. Everything you need is there waiting for you, and the breakfast is to die for! We have stayed here twice and plan on coming back. Very. very nice!
5 en julio 29, 2012
The Chez Lafayette is a very cozy B&B right near down-town and in walking distance of Jefferson's main attractions. We really enjoyed Parker's Chamber which is a very cozy room with a comfortable bed and private entrance which opens to the front porch where we sat and drank coffee and watched the squirrels play in the morning. There is also a really nice flower garden on the side of the house not to be missed. Our host Beth, was very gracious and welcomed us with some homemade chocolate candy that was just sinful & made us a wonderful breakfast the next morning. I highly recommend the Chez Lafayette to anyone looking for a peaceful getaway! David & Katie Ziegler
5 en julio 27, 2012
My wife and I visited Chez Lafayette at Christmas. The home was beautifully decorated and the innkeeper was very welcoming. Her breakfasts are amazing! We stayed in the guest cottage and it was roomy and private. The location is perfect for walking to shops and dining establishments. We will definitely return for another visit.
5 en julio 27, 2012
Chez Lafa yette is a great place to stay in Jefferson -- walking distance to antique shops and restaurants. The breakfast was wonderful and in addition to the nice rooms and lovely parlor, this home also has a beautiful garden for visitors to stroll through and a welcoming front porch with ample seating.
5 en julio 26, 2012
My stay at Chez Lafayette was by far the most memorable I ever had! In addition to the cleaness, the food was to die for! I will definetaly book my next stay in Jefferson, Texas with Ms. Beth Crawford!
5 en julio 26, 2012
Chez Lafayette is the B&B of choice for me and my wife when we are in Jefferson. Its central location next to the city library and only a block or so off of downtown makes it the perfect place to experience all that Jefferson has to offer. Although it only has two rooms, one in the main house and a larger room detached and in back of the main house, the hospitality is that which one would expect from a much larger operation. The innkeeper, Beth Crawford, provides unforgettable gourmet breakfasts and is a wealth of information about this quaint, historic town. I've stayed at several B&Bs and hotels/motels in Jefferson, but for the last six years, this is the only place I now stay.
5 en julio 25, 2012
I have stayed at Chez Lafayette three times within the past 18 months and it will be the only place I will stay in the future when I visit Jefferson. The property is ideally situated so you can park your car and walk to all the shops and restaurants in old town Jefferson. Beth, the innkeeper, is a wonderfully charming hostess and you can't beat her gourmet breakfasts. She is also very familiar with the town and surroundings so she is full of good information. There is one room in the main house with a private bath, in which I have stayed during my past visits. The room is very comfortable, clean and inviting. The cottage out back is equally as nice and is perfect for a girls trip; it is a bit larger and has multiple beds. Whatever the occassion, you can't go wrong with Chez Lafayette.


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In general I don't really know where the flag queue goes or if it's apart from the closed question queue. So I'm not sure if there is further value in flagging a question already voted to close.
What is meta?
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Generally, there is no need to flag a question immediately after voting to close it. In the vast majority of cases, there will be other community members who happen to be looking at a question and voting on it as they deem appropriate, without ever requiring intervention from a moderator.
However, in certain cases it may be worth flagging a question which you've voted to close if you don't believe it'll ever receive enough votes from the community to be closed, such as:
That's where a flag will come in handy, as a single moderator will be able to handle the closure with a single vote.
There are also special cases, such as if a question is good but off-topic on one Q&A site but would belong on another, and any other case that would warrant a detailed description (such as abusive behavior, lengthy comments, or other issues). Those are OK to flag, but make sure you're specific in your flag description to help us understand what's happening.
Conversely, please avoid flagging questions that you've voted to close if they are likely to be closed by the community (e.g. relatively new questions, questions in high-traffic tags, etc) and don't need moderator action. Otherwise, by the time a moderator gets to them, they'll probably already have been closed, and often not require further action. If there are too many of these flags, they become noise and can potentially get in the way of other flags.
There is no need to do so in the general case. Let community moderation take its course. Once the question gets 5 close votes, it will be closed.
The only exception for me personally is when I stumble upon something which most definitely needs to be closed, but where attention for the particular question seems to be non-existent. In such a case I do occasionally flag for moderator attention, explaining that I think it should be closed, casting my close vote at the same time so it does not appear to be a unilateral decision from a moderator.
Normally no as the question will appear in the close voters queue and other users can vote to close it as well.
However there are a few cases where I think you should
You don't need to flag a question for close. When a user with more than 3K reputation flag any question for close, it automatically converts in to vote-to close.


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Box Score | Game Notes
GRAND RAPIDS, Mich. (February 24, 2013) -- The San Antonio Rampage (24-25-1-4) finished the Rodeo Road Trip with a winning record, but were unable to wrap up the road trip with a weekend sweep, as the Silver and Black fell to the Grand Rapids Griffins (30-18-2-2), 7-3, Sunday afternoon at Van Andel Arena.
San Antonio finished the Rodeo Road Trip with a 5-3-1-0 record. The team also wraps up the month of February with a 6-3-1-0 record, their best record in an individual month this season.
Jon Rheault scored the third penalty shot in Rampage franchise history while defenseman Zach Miskovic tallied his first goal in the Silver & Black. But a hat trick by Chad Billins and strong goaltending from AHL All-Star Petr Mrazek propelled the Midwest division-leading Griffins to a victory.
Rampage netminder Dov Grumet-Morris once again faced 40-plus shots against the Griffins and turned aside 39 of the 46 shots he faced on the night. In the two games against the Griffins this weekend, Grumet-Morris faced a combined 89 shots.
Miskovic struck first for San Antonio at 5:59 of the first period while on the power play. His shot from the point deflected off the crossbar and into the net to make it 1-0. The goal was Miskovic's first as a member of the Rampage, while Brendon Nash's assist was his fifth point in his last five games.
Rheault would give the Rampage a 2-0 lead when he drew a penalty shot at 12:03 of the first period. Rheault walked in on Mrazek and sent a backhand shot high to open the two-goal lead. The penalty shot was the first successful attempt this season in two tries and was the third successful attempt in team history. The goal was Rheault's 17th of the season, which marks a career high for the winger.
The Griffins would gain some momentum at the end of the period when Brett Skinner scored at 18:38 of the frame. That momentum would carry into the second frame as Grand Rapids came back in the second period courtesy of three straight power-play goals off five Rampage penalties.
Francis Pare scored the first goal of the middle frame at 11:33 when Gustav Nyquist found him open on the left wing side. Chad Billins struck next, on the power play, at 14:26 of the second period when he collected a rebound and sent it high on Grumet-Morris.
Billins would add his second of the period in the closing moments when he fired a shot from the point after a faceoff win at 19:23 to give the Griffins a 4-2 lead at the second intermission.
The Griffins would pull away in the third period, scoring three times. Nyquist made the score 5-2 at 9:52 of the third period while on the power play. Mitch Callahan would pot the sixth unanswered Griffins goal at 16:17 of the third period.
Eric Selleck answered for the Rampage at 18:24 of the third period when he buried a rebound off Garrett Wilson's hard drive to the net to make it 6-3.
Despite the late tally, the Griffins would strike one more time, as Billins completed the hat trick with just over a minute remaining in regulation.
The Griffins finished the game 4-for-7 on the power play, marking the most goals the Rampage had surrendered on the penalty kill this season. The Silver and Black went 1-for-4 on the man advantage to finish the Rodeo Road Trip 8-for-40 on the power play.
The Rampage will return to the AT&T Center for the first time in a month as they faceoff against the Chicago Wolves on Military Appreciation Night on Saturday, March 2nd at 7:00 p.m. Individual and season tickets can be purchased at the AT&T Center Southeast Box Office, by calling a Rampage representative at 210-444-5554 or online at sarampage.com


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The Orioles will host LUNGevity Foundation's Breathe Deep Baltimore, a walk to raise funds and awareness for lung cancer in memory of Orioles' late Public Relations Director, Monica Pence Barlow. All proceeds of the walk will benefit LUNGevity Foundation, a non-profit firmly committed to making an immediate impact on increasing quality-of-life and survivorship of people with lung cancer by accelerating research into early detection and more effective treatments, as well as providing community, support and education for all those affected by the disease.
Monica Pence Barlow was the Orioles Public Relations Director and a member of the organization for 14 years. Barlow passed away in 2014 after a four and a half year battle with non-small cell lung cancer. Barlow was very active with LUNGevity Foundation, raising funds and awareness through interviews and walks.
Walk Begins: 9 a.m. ET and concludes on the field
Registration Begins: 7 a.m. ET
Entry Fee: $25 for adults, $15 for students and seniors, and $10 for youth. There is no race fee for lung cancer survivors and children four and under.
All current registrations have been automatically rolled over to the new date.
Fee Includes: T-shirt and refreshments.


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Play classroom games as simple as A-B-C
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Raymond Hernandez
Recent and archived news articles by Raymond Hernandez of The New York Times.
Booker to End Association With Start-Up He Founded
His association with the Internet firm Waywire had become an embarrassment for Mayor Cory A. Booker of Newark even as he seemed poised to capture a Senate seat in a special election.
September 7, 2013, Saturday
Group Financed by Business Leaders Has Put Nearly $7 Million Into Council Races
As Mayor Michael R. Bloomberg departs, Jobs for New York, a political action committee, is throwing its support behind allies who are pro-development.
September 6, 2013, Friday
Questions on the Dual Role of a Clinton Aide Persist
The State Department says it allowed Huma Abedin, former Representative Anthony D. Weiner's wife, to consult for private clients because she had "irreplaceable" expertise.
August 19, 2013, Monday
Booker Coasts in Primary; 'Make Me Your Senator,' He Tells New Jersey
The victory, after an abbreviated and contentious contest with some of the state's best-known Democrats, makes Mr. Booker a heavy favorite to win the October general election.
August 14, 2013, Wednesday
In New Jersey, Short Senate Primary Race Ends With Final Appeals to Voters
Much of the attention has focused on Cory A. Booker, the mayor of Newark, who has built a national reputation as a rising star in the Democratic Party.
August 13, 2013, Tuesday
Booker's Web Company, Struggling, Sought Buyer as Senate Drive Began
Mayor Cory A. Booker's Internet start-up stalled, and it feared that his election to the Senate this fall would deprive it of its main asset: him.
August 10, 2013, Saturday
Tech Magnates Bet on Booker and His Future
Silicon Valley moguls provided the brainpower and financing for a company that could make Cory A. Booker, the Newark mayor and United States Senate candidate, very rich.
August 7, 2013, Wednesday
Coming to an Old Friend's Aid, With an Eye on the Clinton Image
Clinton loyalists have rushed to assist Huma Abedin, herself a top Clinton aide and Anthony D. Weiner's wife.
August 2, 2013, Friday
Peter King Seeks to Fuel Talk of Presidential Bid
Representative Peter King of New York is helping to generate buzz around the idea of a 2016 presidential campaign, recently sending a fund-raising solicitation to supporters saying that he is considering a run.
July 19, 2013, Friday
Young, Rich and Relocating Yet Again in Hunt for Political Office
Sean Eldridge and his husband, the Facebook co-founder Chris Hughes, bought two multimillion-dollar homes in New York State that were seen as launching pads for a Congressional run.
July 11, 2013, Thursday
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(Edit: I've realized that there was an error in my reasoning when I was convincing myself that these two formulations are equivalent. Hailong has given a beautiful affirmative answer to my first question in the case of finite type modules over a noetherian commutative ring. Mariano has given a slick negative answer to the question for non-finite-type modules. Greg has given a beautiful negative answer to my "alternative formulation" even in the finite type case over a noetherian commutative ring. I'm accepting Hailong's answer since that's the one I imagine people will be most immediately interested in if they find this question in the future.)
Suppose we're working the category of modules over some ring $R$. Suppose a module $E$ is an extension of $M$ by $N$ in two different ways. In other words, I have two short exact sequences
\begin{array}{ccccccccc} 0&\to &N&\xrightarrow{i_1}&E&\xrightarrow{p_1}&M&\to &0\\ & & \wr\downarrow ?& & \wr\downarrow ?& & \wr\downarrow ?\\ 0&\to &N&\xrightarrow{i_2}&E&\xrightarrow{p_2}&M&\to &0 \end{array}
Must there be an isomorphism between these two short exact sequences?
Alternative formulation
$Ext^1(M,N)$ parameterizes extensions of $M$ by $N$ modulo isomorphims of extensions. Suppose I'm interested in parameterizing extensions of $M$ by $N$ modulo abstract isomorphisms (which don't have to respect the submodule $N$ or the quotient $M$). One obvious thing to note is that there is a left action of $Aut(M)$ on $Ext^1(M,N)$, and that any two extensions related by this action are abstractly isomorphic. Similarly, there is a right action of $Aut(N)$ so that any two extensions related by the action are abstractly isomorphic.
Does the quotient set $Aut(M)\backslash Ext^1(M,N)/Aut(N)$ parameterize extensions of $M$ by $N$ modulo abstract isomorphism?
Note: I'm not asking whether all abstract isomorphisms are generated by $Aut(M)$ and $Aut(N)$. They certainly aren't. I'm asking whether for every pair of abstractly isomorphic extensions there exists some isomorphism between them which is generated by $Aut(M)$ and $Aut(N)$.