2024/10/28

TALES OF THE CITY and the Fight to Save PBS

Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan

 Math Is Still Catching Up to the Mysterious Genius of Srinivasa Ramanujan

Consider an integer such as the number 4. It can be broken up into parts in a finite number of ways: You can write it as 4, as 3 + 1, as 2 + 2, as 2 + 1 + 1 or as 1 + 1 + 1 + 1. Mathematicians say that the number 4 has five “partitions.” Bigger numbers have far more partitions: The number 200, for instance, has nearly 4 trillion. Partitions are so basic that “people have thought about them as long as people have thought about mathematics,” said Andrew Sills(opens a new tab) of Georgia Southern University.

The first mathematician to study partitions systematically was Leonhard Euler in the 18th century. He proved the very first partition identity: that for any integer (say, 4), the number of partitions whose parts are all odd (two partitions in this case: 3 + 1 and 1 + 1 + 1 + 1) is equal to the number of partitions whose parts are all distinct, meaning there are no repetitions among them (4 and 3 + 1).

MacMahon saw that the two Rogers-Ramanujan identities could be interpreted in a similar way. (The German mathematician Issai Schur, isolated due to World War I, independently discovered the identities and came to the same conclusion.) The sum side of the first Rogers-Ramanujan identity counts the number of partitions of a given integer that don’t have any duplicated or consecutive parts. (For the number 4, there are two: 4 and 3 + 1.) The product side counts the number of partitions whose parts all leave a remainder of 1 or 4 when divided by 5 (4 and 1 + 1 + 1 + 1). For any integer, the number of partitions satisfying each condition will always be equal.



This is a very weird fact. It’s mysterious,” said Shashank Kanade(opens a new tab) of the University of Denver. “I mean, where did the 5 come from?”

For much of the 20th century, mathematicians would delight in thinking about the strange hidden phenomena that Ramanujan had unearthed. During World War II, for instance, the physicist Freeman Dyson wrote that he “kept sane by wandering in Ramanujan’s garden.”

Linguist Answers Word Origin Questions | Tech Support | WIRED

Todays Thought

The President is merely the most important among a large number of public servants. He should be supported or opposed exactly to the degree which is warranted by his good conduct or bad conduct, his efficiency or inefficiency in rendering loyal, able, and disinterested service to the Nation as a whole. Therefore it is absolutely necessary that there should be full liberty to tell the truth about his acts, and this means that it is exactly necessary to blame him when he does wrong as to praise him when he does right. Any other attitude in an American citizen is both base and servile. To announce that there must be no criticism of the President, or that we are to stand by the President, right or wrong, is not only unpatriotic and servile, but is morally treasonable to the American public. Nothing but the truth should be spoken about him or any one else. But it is even more important to tell the truth, pleasant or unpleasant, about him than about any one else. 

-Theodore Roosevelt, 26th US President (1858-1919)

2024/10/25

Rye Bread | The French Chef Season 8 | Julia Child


Side note: about the 23 minute mark you will see Peak French - baker wrestling dough with a cig hanging on his lips. 

Todays Thought

Those who compare the age in which their lot has fallen with a golden age which exists only in imagination, may talk of degeneracy and decay; but no man who is correctly informed as to the past, will be disposed to take a morose or desponding view of the present. 

-Thomas Babington Macaulay, author and statesman (25 Oct 1800-1859)

2024/10/23

Todays Thought

 Remember, we all stumble, every one of us. That's why it's a comfort to go hand in hand. 

-Emily Kimbrough, author and broadcaster (23 Oct 1899-1989)

2024/10/15

Todays Thought

One will rarely err if extreme actions be ascribed to vanity, ordinary actions to habit, and mean actions to fear

-Friedrich Nietzsche, philosopher (15 Oct 1844-1900)

2024/10/14

Todays Thought

To be nobody but myself -- in a world which is doing its best, night and day, to make you everybody else -- means to fight the hardest battle which any human being can fight, and never stop fighting. 

-E.E. Cummings, poet (14 Oct 1894-1962)

2024/10/08

Todays Thought

When Alexander the Great visited Diogenes and asked whether he could do anything for the famed teacher, Diogenes replied: 

"Only stand out of my light." 

Perhaps some day we shall know how to heighten creativity. Until then, one of the best things we can do for creative men and women is to stand out of their light. 

-John W. Gardner, author and educator (8 Oct 1912-2002)

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Todays Thought

A strong nation, like a strong person, can afford to be gentle, firm, thoughtful, and restrained. It can afford to extend a helping hand to others. It is a weak nation, like a weak person, that must behave with bluster and boasting and rashness and other signs of insecurity. 

-Jimmy Carter, 39th US President, Nobel laureate (b. 1 Oct 1924)