Here, in honor of the hundredth anniversary of the General Theory of Relativity, is a very nice visualization:
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Archive for the 'Anniversaries' Category
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Fifty years ago today at 1:30 PM eastern standard time, a minor tragedy took the life of President John F. Kennedy. A little over an hour later, a major tragedy ensued, as Lyndon B. Johnson was sworn in to replace him.
If there is such a thing as evil, it lived in Lyndon Johnson, whose life was one long obsession with the accumulation and exercise of power. His biographer Robert Caro relates how, in college, Johnson engineered, by intimidation and deceit, a takeover of the Student Council partly so that he could, apparently for sport, force the removal of talented and hardworking students from the editorships of campus publications, replacing them with non-entities and reveling in the tragic aftermath as ousted incumbents (who had received small but urgently needed stipends for their work) were forced through financial hardship to drop out of school.
It was downhill from there. As President, Johnson presided over a misbegotten war in Southeast Asia — a whirlpool of destruction fed with lives and treasure — and an equally misbegotten “War on Poverty” that too often became a war on economic freedom, the only effective antidote to poverty the world has ever known.
The War on Poverty might have been more accurately termed a war to consolidate Johnson’s influence. Poor rural families got grants and loans to expand their farms — provided they stayed on the farms, where Johnson needed their votes. Job training, educational programs, small business loans — all were available as long as you lived your life in a way that suited Lyndon Johnson’s purposes.
Continue reading ‘This Day in History’
MathOverflow turns two years old this week — a milestone in the transformation of mathematical research into a massively collaborative endeavor. It’s happening on blogs, it’s happening on mailing lists, and it’s happening in a big way on MathOverlow, where mathematicians ask and answer the sorts of questions that might come up in the faculty lounge — if the faculty lounge were populated by hundreds of experts pooling their expertise.
If you’re interested in mathematics at the research level, MathOverflow is a place to learn something new and fascinating every single day. (If you are not doing mathematics at a research level, feel free to read but please don’t feel free to join the fray; questions at anything below about a second-year graduate level should be directed to MathStackExchange, another massively collaborative site aimed, roughly, at the college level — which reminds me that it’s not just mathematical research, but also mathematical education, that is being revolutionized before our eyes.)
Continue reading ‘Happy Birthday’
Bertrand Russell, that most rational of men, was nonetheless plagued by intermittent depression and the occasional nightmare. Including this one, as reported by Russell’s confidante, the mathematician G.H. Hardy:
[Russell] was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down books, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated….
Principia Mathematica, to which Russell had devoted ten years of his life, was his (and co-author Alfred North Whitehead‘s) audacious and ultimately futile attempt to reduce all of mathematics to pure logic. It is a failure that enabled some of the great successes of 20th century mathematics. And — the first volume having been published in December, 1910 — this is its 100th birthday.
Continue reading ‘Lord Russell’s Nightmare’
This weekend marked the 80th anniversary of the most significant event in the history of logic since the days of Aristotle. On October 23, 1930, the 24-year-old Kurt Godel presented his incompleteness theorems to the Vienna Academy of Sciences.
The first incompleteness theorem says this: No matter what axioms you start with, there will always be statements in arithmetic that you can neither prove nor disprove. (I am glossing over some technicalities here, but in this context they are not important.) Some of those statements take the form “Such-and-such an equation has (or does not have) any solutions”. You tell me your axioms, and I’ll produce an equation that you can neither prove solvable nor prove insolvable.
Continue reading ‘Eighty Years of Incompleteness’
1) I just had an extremely pleasant walk around the Beale Street area in Memphis, which strikes me, roughly, as Bourbon Street without the urine. (Also without the trash and the high general level of obnoxiousness — though also of course without the magnificent architecture, etc.) Yes, I realize it’s also a different musical genre (though in both cases it’s a sub-genre of “too loud”). But it’s astonishing to me how clean the streets are here, and how well-behaved the crowds, compared to what I’ve seen in Louisiana. If they can do that here, why can’t they do it there?
2) This weekend marks the anniversary of a world-changing event — an event that might be of particular interest to readers of The Big Questions, both the book and the blog. Who can tell me what event I have in mind? (Hint: It’s an anniversary ending in zero.) I’ll blog the answer on Monday.
3) The discussion of the Allais paradox rages on in comments on multiple posts. For the few of you who have not yet tuned this out, my latest comment is an attempt to cut through the fog and identify the locus of some commenters’ confusion, or disagreement, or both. I think it will very much help focus the discussion if the dissenters could tell us where they stand on these questions. (My answers are all “yes”.)
A month ago, I prematurely celebrated the 209th birthday of the great economic communicator Frederic Bastiat. Today (unless I’ve screwed up a second time) is actually his birthday. A good way to celebrate is to read (or reread!) Bastiat’s little masterpiece Economic Sophisms; you will never see the world the same way again. Here’s a taste:
At a time when everyone is trying to find a way of reducing the costs of transportation; when, in order to realize these economies, highways are being graded, rivers are being canalized, steamboats are being improved, and Paris is being connected with all our frontiers by a network of railroads and by atmospheric, hydraulic, pneumatic, electric, and other traction systems; when, in short, I believe that everyone is zealously and sincerely seeking the solution of the problem of reducing as much as possible the difference between the prices of commodities in the places where they are produced and their prices in the places where they are consumed; I should consider myself failing in my duty toward my country, toward my age, and toward myself, if I any longer kept secret the wonderful discovery I have just made.
Today is the ninety-ninth anniversary of the legendary fire at the Triangle Shirtwaist Factory, which reigned for ninety years as the worst workplace disaster in New York history. A hundred and forty six workers died that day, most of them young women. Escape routes were cut off by doors that were kept locked to prevent employee pilfering. The main exit from the factory floor was designed so that only one person at a time could pass through; departing workers had their handbags inspected by a night watchman. “It comes down to dollars and cents against human life, no matter how you look at it”, in the words of then-Fire Chief Edward Croker.
Well, yes, of course it comes down, at least in part, to dollars and cents against human life (where “dollars and cents” are, of course, stand-ins for “a whole lot of other things we care about”). The interesting question is whether the terms of trade were favorable. In other words: If the workers, in advance of the fire, had been fully informed of all the risks and all the potential consequences, would they have wanted those doors locked or open? Or more generally: When the New York state legislature responded to the fire with over two dozen new occupational health and safety laws, were they compounding the disaster?
Continue reading ‘Three Sides to the Story’
One hundred years ago today, Red Cloud, the last of the great Sioux warrior chiefs, died in peace on the Pine Ridge reservation at the age of 89. He was preceded in death by the way of life he fought so valiantly to preserve.
If there is such a thing as a just war, Red Cloud’s War of 1866 was more just than most. Black Kettle‘s village of peaceful Cheyenne had been recently and wantonly slaughtered by the Colorado militia under Colonel John Chivington at Sand Creek. (The survivors of this unhappy band would meet their deaths a few years later at Washita Creek, at the equally murderous hands of General George Armstrong Custer.) Against this background, the chiefs had been betrayed at Fort Laramie, where the government had summoned them to negotiate for the right to build roads through Indian territory. With the conference still in session and no agreement in sight, Colonel Henry Carrington and a force of 700 men arrived to build the Bozeman Trail.
