The distribution of prime numbers is related to the values at which a certain function ("Riemann's zeta function") evaluates to zero. Long story, but it's a big deal to mathematicians.
From The Penguin Dictionary of Curious and Interesting Numbers:
Riemann conjectured that, considered as a complex function with complex roots, [the zeta function's] roots all had real part equal to 1/2. So important is this possibility that many mathematical proofs have been published that assume that Riemann's hypothesis is true.Suggesting that 1½ billion instances constitute a small‑numbered trend: humor possibly lost on one Christopher Hirst, who called that book "a volume which none but propeller‑heads will find either curious or interesting". (Mr. Hirst is "an award-winning food writer".)
A proof of the Riemann conjecture would apply to an infinite number of roots, dwarfing the 1½ billion examples (and no known counterexamples) verified so far. This looks like a chance to segue back to Pascal's wager. 1,500,000,000 versus ∞: the number of seconds in an earthly lifetime versus eternity. (I've passed the 1½ billion second mark, although Pascal and Riemann each only made it to about 1¼ billion.)
In section 233 of Pensées where Pascal describes his wager, he also speaks of the incomprehensibility of the infinite:
We know then the existence and nature of the finite, because we are also finite and have extension. We know the existence of the infinite, and are ignorant of its nature, because it has extension like us, but not limits like us. But we know neither the existence nor the nature of God, because He has neither extension nor limits.Thanks to Cantor, we are no longer ignorant of the nature of the infinite.
A girl in my brother's AP Calculus class named her cat Riemann. A couple days after my recent posting on Pascal's wager, the NY Times ran a column by Professor Gary Gutting that describes a variant:
I propose to reformulate Pascal's wager as urging those who doubt God's existence to embrace a doubt of desire rather than a doubt of indifference. This means, first, that they should hope—and therefore desire—that they might find a higher meaning and value to their existence by making contact with a beneficent power beyond the natural world. There's no need to further specify the nature of this power in terms, say, of the teachings of a particular religion.Well. I might really like there to be a fountain of youth, but that doesn't mean I should go all Ponce de León. And if, in an ordinary spring, I found what I believed was a fountain of youth, I'd be living in fantasy at the cost of overlooking how fine spring water is for its own sake.
Professor Gutting proposes a doubt of desire rather than a doubt of indifference. To the extent he means desire for a particular seductive result, I can't accept his proposal. I'm with Bertrand Russell:
Why not admit that metaphysics, like science, is justified by intellectual curiosity and ought to be guided by intellectual curiosity alone? The desire to find comfort in metaphysics has, we must all admit, produced a great deal of fallacious reasoning and intellectual dishonesty.
The tower I get cell phone service from (19000' away).
And yeah, a rainbow.
The code of the spy has always been, "Never celebrate your successes or explain your failures."I'd rather have dinner with a spy than a politician, and not just because they'd have more interesting stories to tell. I'd be interested to see what kind of person has the austere discipline it takes to work in the shadows. Spies are highly trained; politicians not necessarily. Missteps in espionage can kill you or worse; missteps in politics need not be any impediment to advancement. Pascal's wager, in fifteen words: you can't prove whether God exists but you should believe because the stakes are infinite.
The argument is criticized—deservedly—on logical grounds, but it also should be called out for being an appeal to fear: think what might happen, for eternity mind you, if you don't believe.
Ben Carson gave Pascal's wager as his closing words in a debate on science and faith. Carson is second in some polls of GOP voters, second only to a buffoon whose signature tactic is appealing to fear of immigrants. It seems like an eternity since we had a President who said the only thing we have to fear is fear itself. Happy equinox, everyone, at 01:21 PDT this morning (0821Z). One medicine I take requires fine tuning of dosage. My doctor told me it's important to stick with one manufacturer, as there's potential variation between what are supposed to be equivalent formulations. The pharmacy in town stocks the drug in a range of dosages, all from the same manufacturer: Mylan. Out of curiosity, I read up on the company.
From Wikipedia, I learned that Mylan hired a private eye back in the 1980s to check out FDA officials who seemed to be delaying its drug approval requests. Their concerns were well‑founded; several of Mylan's competitors were bribing the FDA. Mylan seemed like one of the good guys.
Then I read about an episode where Mylan had cornered the market on raw ingredients for a few popular generic drugs, allowing them to raise the price through the roof. Not the good guys there. Mylan settled with the government for $147 million without admitting any wrongdoing.
A smaller drug company, Turing Pharmaceuticals, was in the news this month for raising the price of a decades‑old drug from $13.50 a tablet to $750. Turing's CEO, Martin Shkreli, said "the drug was unprofitable at the former price." A tablet sells for $0.66 in the UK and for $0.10 or less in India. Asked how he sleeps at night, Shkreli said, "You know, Ambien."
Alfred Hitchcock said that his father asked the police to lock him up for five minutes after he'd misbehaved as a kid. Frank Zappa was arrested in a dopey sting operation when he was 24. Both went on to distrust police and to explore the theme of injustice in their art.
Some are quick to say it's horrible that 14‑year‑old Ahmed Mohamed had to endure harsh treatment; others say it's awesome that he's now been invited to the White House. Me, I'm reminded of a parable I quoted a few years ago. From an early transcript of this evening's debate:
Hugh Hewitt: ... Governor Kasich, you've been on my show a lot. You refused to attack Hillary Clinton, ... .Hewitt said "you bring her up sua sponte." Your first guess as to what subject he's a professor of will likely be correct.
I remember the ten stamps the USPS issued in 1991 showing the planets (and the moon) along with spacecraft that had photographed them. People had their favorites: one friend liked Neptune for its serene blueness, another was partial to the Pluto stamp for its text: not yet explored. The former was an artist; the latter, an engineer. Neither lived to see the pics we're now getting of Pluto.
Pluto has far exceeded my expectations. It looks amazing. "It's half the size of an adult, so it's more manageable and would fit in a lot of homes." Just the thing for an Amazon wish list.
Today's topic is Google's new sans-serif logo.
The double-loop g is a highlight of most serif (and some sans) fonts. I wish there were a g in Tommyjournal to grace the top of this page. Google had a proper g, but now they are yet another company to have boiled the taste out of their logo to make it legible on tiny screens.
Google trots out another rationale: the new logo is concisely expressible in SVG, saving bandwidth. Well, music played with sine waves and no vibrato can be encoded concisely too.