Yes, It’s Right

Phil Bowermaster is wondering if there’s something dodgy about the math here.

No, this is in fact a standard technique for determining the sum of an infinite series, which is in fact what 0.999… is (it could be expressed as the sum, from n=0 to infinity, of the expression 9 times 10 to the minus n). Perhaps, as one commenter notes, it’s the word “precisely” that’s hanging people up, but certainly that number is equal to one, whatever modifier you want to put on it or leave off.

[Update in the afternoon]

I’m not sure I follow the commenter’s objection. He claims that no matter what you start out with as “a” you get a=1. I don’t see that.

Try it with two, as suggested.

a = 2
10a = 20
10a – a = 20 – 2
9a = 18

Ergo, a = 2.

In fact, do it with 1.999…

a=1.999…
10a = 19.999…
9a = 18
a = 2

As I said, it’s a standard technique for expressing repitends as whole numbers or fractions.

Yes, It’s Right

Phil Bowermaster is wondering if there’s something dodgy about the math here.

No, this is in fact a standard technique for determining the sum of an infinite series, which is in fact what 0.999… is (it could be expressed as the sum, from n=0 to infinity, of the expression 9 times 10 to the minus n). Perhaps, as one commenter notes, it’s the word “precisely” that’s hanging people up, but certainly that number is equal to one, whatever modifier you want to put on it or leave off.

[Update in the afternoon]

I’m not sure I follow the commenter’s objection. He claims that no matter what you start out with as “a” you get a=1. I don’t see that.

Try it with two, as suggested.

a = 2
10a = 20
10a – a = 20 – 2
9a = 18

Ergo, a = 2.

In fact, do it with 1.999…

a=1.999…
10a = 19.999…
9a = 18
a = 2

As I said, it’s a standard technique for expressing repitends as whole numbers or fractions.

Man Bites Dog

The leftist/Arabist myth that Israel and the plight of the “Palestinians” is the cause of all ills in the Middle East is a lie and a nonsense, and stories and editorials pointing it out aren’t new. What is new is that even Time magazine seems to have figured it out:

Yes, it was a great disturbance in the Arab world in the 1940s when a Jewish state was born through a U.N. vote and a war that made refugees of many Palestinians. Then the 1967 war left Israel in control of the West Bank and Gaza Strip, and thus the Palestinians who lived there. But the pan-Arabism that once made the Palestinian cause the region’s cause is long dead, and the Arab countries have their own worries aplenty. In a decade of reporting in the region, I found it rarely took more than the arching of an eyebrow to get the most candid of Arab thinkers to acknowledge that the tears shed for the Palestinians today outside the West Bank and Gaza are of the crocodile variety. Palestinians know this best of all.

To promote the canard that the troubles of the Arab world are rooted in the Palestinians’ misfortune does great harm. It encourages the Arabs to continue to avoid addressing their colossal societal and political ills by hiding behind their Great Excuse: it’s all Israel’s fault. Certainly, Israel has at times been an obnoxious neighbor, but God help the Arab leaders, propagandists and apologists if a day ever comes when the Arab-Israeli mess is unraveled. One wonders how they would then explain why in Egypt 4 of every 10 people are illiterate; Saudi Arabian Shi’ites (not to mention women) are second-class citizens; 11% of Syrians live below subsistence level; and Jordan’s King can unilaterally dissolve Parliament, as he did in 2001. Or why no Middle Eastern government but Israel’s and to some extent Lebanon’s tolerates freedom of assembly or speech, or democratic institutions like a robust press or civic organizations with independence and clout–let alone unfettered competitive elections.

Setback

Some history, and advice for the future, from Charles Krauthammer:

So we have this half decade of American assertion. And it was an astonishing demonstration. In the mood of despair and disorientation of today, we forget what happened less than half a decade ago. The astonishingly swift and decisive success in Afghanistan, with a few hundred soldiers, some of them riding horses, directing lasers, organizing a campaign with indigenous Afghans, and defeating a regime in about a month and a half in a place that others had said was impossible to conquer; that the British and the Russians and others had left in defeat and despair in the past. It was an event so remarkable that the aforementioned Paul Kennedy now wrote an article, “The Eagle has Landed” (Financial Times, Feb. 2, 2002) in which he simply expressed his astonishment at the primacy, the power, and the unrivalled strength of the United States as demonstrated in the Afghan campaign.

After that, of course, was the swift initial victory in Iraq, in which the capital fell within three weeks. After that was a ripple effect in the region. Libya, seeing what we had done in Iraq, gave up its nuclear capacity; then the remarkable revolution in Lebanon in which Syria was essentially expelled. And that demarks the date that I spoke of. March 14 is the name of the movement in Lebanon of those who rose up against the Syrians and essentially created a new democracy

Wacky Headline Contest

Let’s have a vote. Which is more surreal:

Wisconsin Man Runs Over, Eats Seven-Legged Transgendered Deer,” or “World’s Tallest Man Saves Plastic Eating Dolphins“?

Boy, the copy editors must have had a blast with those.

That last one is kind of ambiguous. I think that “plastic eating” should be hyphenated. As written, one could interpret it as the man was saving plastic while it was eating dolphins, or that he was saving plastic while he was eating dolphins. Neither of which is the actual story.

I used to have an hilarious book of journalism bloopers, including miswritten headlines. The book’s title was “Milk Drinkers Turn To Powder.” It included the classic from the Jimmy Carter era, on one of his speeches: “More Mush From The Wimp.”

Break Out The Ice Cream

This could be huge. I’d like to see it replicated as soon as possible. Some researchers may have come up with a cure for diabetes. And it’s an unconventional one, out of left field:

Dr. Dosch had concluded in a 1999 paper that there were surprising similarities between diabetes and multiple sclerosis, a central nervous system disease. His interest was also piqued by the presence around the insulin-producing islets of an “enormous” number of nerves, pain neurons primarily used to signal the brain that tissue has been damaged.

Suspecting a link between the nerves and diabetes, he and Dr. Salter used an old experimental trick — injecting capsaicin, the active ingredient in hot chili peppers, to kill the pancreatic sensory nerves in mice that had an equivalent of Type 1 diabetes.

“Then we had the biggest shock of our lives,” Dr. Dosch said. Almost immediately, the islets began producing insulin normally “It was a shock ? really out of left field, because nothing in the literature was saying anything about this.”

The only problem I see is that this is worse than stem cells from a human sacrifice standpoint. How many people will a small band like the Hot Chili Peppers be able to cure? Just how much capsaicin can they produce, and how fast?

Springtime On Mars

This won’t put an end to the humans versus robots debate, but it should.

Via emailer Jon Bossard, who notes:

The argument that robotic missions are far cheaper and more effective than human missions is belied by the fact that, even with more than half a dozen robotic missions to Mars, we still don

Biting Commentary about Infinity…and Beyond!