Our nation was founded on a bedrock principle that we are all created equal. The project of each generation is to bridge the meaning of those founding words with the realities of changing times -- a never-ending quest to ensure those words ring true for every single American.

Progress on this journey often comes in small increments. Sometimes two steps forward, one step back, compelled by the persistent effort of dedicated citizens. And then sometimes there are days like this, when that slow, steady effort is rewarded with justice that arrives like a thunderbolt.

This decision will end the patchwork system we currently have. It will end the uncertainty hundreds of thousands of same-sex couples face from not knowing whether their marriage, legitimate in the eyes of one state, will remain if they decide to move or even visit another.

This ruling will strengthen all of our communities by offering to all loving same-sex couples the dignity of marriage across this great land.

We are people who believe every child is entitled to life and liberty and the pursuit of happiness. There is so much more work to be done to extend the full promise of America to every American. But today, we can say in no uncertain terms that we’ve made our union a little more perfect. (...)

The right to marry whoever one wishes is an elementary human right compared to which "the right to attend an integrated school, the right to sit where one pleases on a bus, the right to go into any hotel or recreation area or place of amusement, regardless of one’s skin or color or race" are minor indeed. Even

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I love the place I'm working this summer. (A smallish proprietary trading firm in lower Manhattan.) It has one of the most vibrantly intellectual atmospheres I've seen anywhere, and the problems that we're working on really are interesting, often novel, and eminently practical. For a place that aims to compete in international financial markets by hiring the best mathematical talent that (1) cool math problems and (2) money can buy, it's...just about exactly what you might expect.

In particular, I'm in love with my current research project, which is easily the coolest thing I've been asked to do yet. (I also interned for all of last summer there.) What exactly it is is proprietary (sorry), but it has me mixing machine-learning and stochastic calculus in some really cool ways that have me alternating between coding furiously and filling up whiteboard upon whiteboard with math. Also, I recently got yelled at for taking up too much computing power on the shared intern server, so I got upgraded to supercomputing-cluster access.

The day I got my project (and after I had spent the entire morning figuring out just what it was), I was pretty insufferable. Most of the interns had just gotten our projects, but I was ready to explain mine to anyone who would listen, and would consistently get animated and excited about just how darn cool it was.

On my way out of the office, I ran into one of my mentors from last summer, who asked me what I was working on now, and I launched right into---

---nothing, as the elevator stopped on another floor, someone else got in, and my ready explanation of this tremendously

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Today (a few days ago) from the NYT's Upshot column: When Family-Friendly Policies Backfire.

In Chile, a law requires employers to provide working mothers with child care. One result? Women are paid less.

In Spain, a policy to give parents of young children the right to work part-time has led to a decline in full-time, stable jobs available to all women -- even those who are not mothers.

Elsewhere in Europe, generous maternity leaves have meant that women are much less likely than men to become managers or achieve other high-powered positions at work.

Family-friendly policies can help parents balance jobs and responsibilities at home, and go a long way toward making it possible for women with children to remain in the work force. But these policies often have unintended consequences.

They can end up discouraging employers from hiring women in the first place, because they fear women will leave for long periods or use expensive benefits. "For employers, it becomes much easier to justify discrimination," said Sarah Jane Glynn, director of women's economic policy at the Center for American Progress.

It goes on to rattle off some supporting statistics: In the wake of strong maternity-leave protections, women are more likely to remain employed after having a child, but less likely to be hired or promoted (even if not planning on having

Well, okay, somehow the fact that his life inspired a Hollywood film made it into the obit before the fact that he won the 1994 Nobel Prize in Economics. (Note: "Nash called the film an 'artistic' interpretation based on his life of how mental illness could evolve -- one that did not 'describe accurately' the nature of his delusions or treatment.") But in actuality, it's enormously difficult to describe the impact that this man had on the field of Game Theory, which now underlies much of economics, politics, and has even been applied to describe the strategy of penalty shootouts in soccer (where it closely predicts the strategies that top players actually use).

And if you're anything like me, you'll find his 1950 dissertation a refreshing respite from page after page of obituary:

Non-Cooperative Games (typewriter facsimile)

Introduction

Von Neumann and Morgenstern have developed a very fruitful theory of two-person zero-sum games in their book Theory of Games and Economic Behavior. This book also contains a theory of n-person games of a type which we would call cooperative. This theory is based on an analysis of the interrelationships of the various coalitions which can be formed by the players of the game.

Our theory, in contradistinction, is based on the absence of coalitions in that it is assumed that each participant acts independently, without collaboration or communication with any of the others.

The notion of an equilibrium

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A few number-theoretic \(\pi\) facts:

• \(\pi\) is provably transcendental, thus also irrational.
• \(\pi\) is suspected, but not known, to be normal, a generalization of transcendence.
• \(\pi\), provably, has Liouville-Roth constant (or irrationality coefficient) no greater than \(7.6063\), and is suspected to have constant no greater than \(2.5\). (As a consequence of its irrationality, its L-R constant is \(\geq2\).)

Note, though, that each of these things is also true of literally 100% of numbers. And before you scoff at my use of the figurative 'literally', no no -- measure-theoretically, the non-(normal, transcendental, irrational, irrationality-coefficient-less-than-8) numbers make up exactly, mathematically 0% of the number line.

For the record: irrational algebraics like \(\sqrt2\) are also nonterminating and nonrepeating, and it's not clear what features of the stringwise-local decimal expansion (which seems to be the only thing \(\pi\) enthusiasts focus on, rather than the much-more-informative continued fraction representation...) distinguish transcendentals from irrational algebraics -- and yet \(\sqrt2\) seems to mystify no one, despite also plausibly encoding all possible variations of Hamlet, going on forever, holding all the universe's secrets, &c.

For more, the ever-wonderful Vi Hart:

Right so. Scott Aaronson has a recently-published essay titled "Why isn’t it more mysterious?", in response to the prompt "Q: Is there something mysterious about mathematics?":

Granted, not all mathematical mysteries have the character of "rigorously proving what common sense would predict." In 1978, John McKay noticed that the number 196,883 showed up in two completely

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Ecuador, attempting to prove that it's indistinguishable from Costa Rica, tricks a tour group thinking they've gone to Costa Rica into believing that they were going to Costa Rica when in fact, they were taken to a part of Ecuador that was, apparently, indistinguishable from Costa Rica.

I'm really not kidding:

As Ecuador residents arrived, not in Costa Rica but another Ecuador airport, Tena, where they were given fake stamps in their passports as they went through a staged passport control. No attention to detail was spared as huge posters were placed over the welcome billboards at the airport. Adverts depicting Imperial beer and 'Esencial Costa Rica,' Costa Rica's national brand, were displayed in the airport to throw the group off the scent.

Even fictitious immigration documents and car licence plates were created to make the group think they were in Golfito, a port town in Costa Rica. On top of all that organisers used mobile phone and GPS blockers to keep passengers from using technology to discover the hoax. (...)

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In more serious airline news, the Congressional Research Service, a policy-analysis agency within the Library of Congress, released a 20-page report titled Terrorist Databases and the No Fly List: Procedural Due Process and Hurdles to Litigation. Footnote 41 (of 201!) reads:

Prior to 9/11, aviation security was handled by the Federal Aviation Administration (FAA). The FAA ordered air carriers not to board certain individuals who were deemed a threat to aviation safety. On 9/11, this "no fly" list contained 12 names.

Somehow, I guess I assumed that there were more than twelve people on the no-fly before 2001. But then again, in hindsight,

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False-flag tactics in social advocacy are selfish, since they (1) erode a public expectation of frankness in favor of monotonous cynicism, and (2) prime people's minds with the most-polarizing views of conversational participants, instead of framing them in ways that induce exchange of ideas. The right reason to critique the satirists here is for their anti-conversational tactics -- not their demonstrated anti-anti-racism -- since we shouldn't be okay with the same tactics