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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

So, I've been pretty delinquent about these, but at least I've had the decency to keep stashing things I found worth reading at Reading Feed, with backlogs at Reading Feed (March 2015) and Reading Feed (February 2015).

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WSJ | China to Start Keeping a List of Badly Behaved Tourists sounded pretty scary -- until I read the article and realized that the measures are directed at Chinese citizens abroad, not visitors to China. And then it all sorta made sense, conditioned on China being, 'yknow, China.

Said Chinese president Xi Jinping:

Don't throw water bottles everywhere, don't destroy people's coral reefs and eat fewer instant noodles and more local seafood. (...)

On the topic of environmentalism, I'm on the record opining that pressuring the Harvard Management Corporation to divest from fossil fuels is a red herring, but that doesn't mean that digging up all of the of the known deposits of fossil fuels and burning them would be exactly as horrible as you'd expect: (all numbers Fahrenheit)

The next set of fossil fuels in line is referred to as resources, rather than reserves. The difference is that they are recoverable with today’s technology, but not at current prices. There is 3.1 degrees’ worth of warming if the oil and natural gas in this category are utilized, which would lead to a total increase in global temperatures of 7.6 degrees.

This warming does not even consider our coal resources. A middle-of-the-road estimate of the coal that qualifies as resources indicates that its use would lead

I'm in the Harvard Political Review today, with a guest piece responding to Eric Posner's anti-effective-altruism opinion in Slate:

Posner...is convinced that this tendency toward scrupulosity is enough of an issue that we should abandon the concept of effectiveness in altruism entirely. His critique, though, is not a new one—several effective altruists are also concerned about scrupulosity, and many of them have shared stories from their own lives about balancing giving effectively against more personal cares. For me, these stories are important because they demonstrate that caring about effective opportunities to do good is not mutually exclusive with making the world better in other ways you choose. (...)

Much-deserved thank-yous go to Advik Shreekumar, Ben Kuhn, and Leah Libresco for helping with edits. Meanwhile, here's the original version with footnotes (the HPR doesn't do footnotes).

Man, writing for real publications is so stressful. Word limits, even if they're only suggestions, suck.

A few things that didn't make it into the HPR version (besides those glorious, glorious footnotes):

Scott Alexander defends a definition of "doing effective good" that's keyed to a 10% donation, rather than a [maximum]% one:

If you want to feel anxiety and self-loathing for not giving 100% of your income, minus living expenses, to charity, then no one can stop you.

I, on the other hand, would prefer to call that "not being perfect". I would prefer to say that if you feel like you will live in anxiety and self-loathing until you have given a certain amount of money to charity, you should make that certain amount ten percent.

Why ten percent?

It's ten percent because that is the standard decreed

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Stanford's in the news today for: Stanford just made tuition free for families earning less than $125,000 per year. The news is usually accompanied by pictures of smiling students and balloons:

...and it usually takes the article in question a few paragraphs to get around to noting that:

The announcement is an expansion of Stanford's old financial aid policy, which previously applied to students from families making less than $100,000 per year. (...)

...which raises the question: Just how many students at Stanford come from families with incomes greater than $100k and less than $125k? ...and just how desperately did those families need to have their tuition costs reduced from \(\leq\)$13.5k^[1] to $5k^[2]?

(EDIT | A bird in my ear mentions that $100k/yr puts you in the 80%tile of American families, which seems at least approximately-correct.)

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About a year ago, Ken Griffin donated $125 million in support of Harvard's financial aid program, funding 539 full scholarships to Harvard. Kim Soffen, writing in the Harvard Political Review, wrote:

An important first note is that the recipients of this new pool of money will not be the poorest students at Harvard; even before this donation, Harvard already guaranteed full scholarships to any family making under $65,000 per year, and that families making up to $150,000 would not have to pay more than ten percent of their income. Consequently, these additional scholarships would be going towards students from families who are already safely

"The Gender Gap in Math" presented by the Harvard Undergraduate Mathematics Association

Panel: Gigliola Staffilani (Professor, MIT Math), Rediet Adebe '13 (PhD, Harvard SEAS), Hilary Finucane '09 (PhD, MIT), Alison Miller '08 (Postdoc, Harvard Math)
Moderator: Sarah Richardson (Professor, Harvard Social Studies)

HUMS: Some Numbers

The Harvard Undergraduate Math Survey (May 2014) was organized by Meena Boppana, Kate Donahue, Domniki Georgopoulou, and Caitlin Stanton, with contributions by Rahul Dalal, Ellen Robo, and Isabel Vogt, and advised by Prof. Benedict Gross. It had 130 responses, 55 from math concentrators (1/3 of math undergrads); here are a few of the findings.

Are you made uncomfortable by the gender gap in math?

• 3% of male responents
• 54% of female respondents

How many professors do you believe you can ask for a letter of recommendation?

• Female respondents: 1.0
• Male respondents: 1.6

Did you compete in math competitions in high school?

• 80% of male respondents
• 75% of female respondents

Are you planning on writing a thesis in pure mathematics?

• 25% of female respondents
• 50% of male respondents

Are you planning on grad school in mathematics?

• 65% of male respondents
• 25% of female respondents

Panel Discussion

Moderated by: Professor Sarah Richardson, Professor of popular gen-ed "Gender and Science: From Marie Curie to Gamergate"

Richardson: Let's get a