Wednesday, February 02, 2005

SNPs of Music

I've been attending a meeting on obesity and diabetes this week (which explains the paucity of entries). A whimsical thought came to my mind as I listened to one of the many talks related to gene expression - the number of unique human beings is finite. Our genome is about 3 billion base pairs long. However, individuals differ in something like 3 million of these bases in what are called Single Nucleotide Polymorphisms (SNPs). Thus there are at most 4 to the power of 3 million unique individuals! Since two of every three SNPs, involves replacing cytosine (C) with thymine (T), this number is reduced somewhat. This is a very big number but it is still finite.

A much smaller number is the number of different pop songs. In most cases, pop songs consist of no more than 4 or 5 melodic phrases of 5 to 10 notes. George Harrison was sued for plagarizing his song "My Sweet Lord" for repeating 8 notes of the song "He's So Fine". Usually a song is identified by its ``hook'', which is a single melodic phrase such as "We All Live in a Yellow Submarine" or "My Sweet Lord ". Almost all pop songs are based on a diatonic scale in a minor or major key which consists of 7 notes. Pop songs are almost always in 4/4 time. In order to be singable, notes cannot differ too much in time or range. So let's say each note can be either a whole note, half note, quarter note or eighth note and in one octave. That gives 28 possibilities per note. For a 10 note phrase this is 28^10 different hooks, not an astronomically large number. However, a hook is usually identified by fewer than 10 notes and the timing of the notes can vary by a certain degree and still seem the same to most people. The rules of harmony also restrict transitions to a smaller set of notes. So maybe there are just 10 possibilities per note and since absolute key and tempo doesn't matter the first note is fixed. For a five note hook, there may only be 10^4 different combinations. In other words, there are only about ten thousand different possible pop songs! No wonder they are starting to sound the same to me.

5 comments:

Anonymous said...

"That which is done is that which shall be done."

I happened to stumble through here while doing a search on Wigner, and this particular post made me think...

The American-turned-Canadian SF author Spider Robinson (http://www.spiderrobinson.com/index.html) is an excellent writer. Back in 1983, he won science fiction's Hugo for the short story "Melancholy Elephants" (and deservedly so). This story is available for reading (and legally so, to boot [Baen Books has a policy of posting selected works {excerpts in some cases, complete works in others} on their web site to help encourage sales {and evidently successfully}. This story is one one of several from one of Mr. Robinson's collections that are included]!) at http://www.baen.com/chapters/W200011/0671319744.htm?blurb.

In this work, the finite number of musical compositions is explicitly referenced, as well as other other issues of the finiteness of the creativity of human output.

Since this story was written, the copyright situation has gotten worse, not better.

As for the possible number of genetically-distinct humans, since mutations may occur in those portions of the genome which otherwise do NOT vary (not to mention such things as added/deleted/merged chromosomes, transpositions, etc.), the number is potentially much larger (albeit still finite). The question would then become, "How much variation in the human genome could be allowed and still have a human (i.e., homo sapiens sapiens)?" The empirical definition of species is probably the only one that could be used.

Thanks!

Grant C. McCormick
gmccormick@win.net

Carson Chow said...

Hi Grant,

Thanks for dropping by the blog. Your point on genetically distinct humans is completely true. I was considering adding a caveat but thought it is sometimes better to be wrong and provocative than correct and boring.

best,
Carson

Anonymous said...

http://www.nytimes.com/2005/02/06/books/review/06REEDL.html?incamp=article_popular_1&pagewanted=all&position=

'French Women Don't Get Fat': Like Champagne for Chocolate
By JULIA REED

FRENCH WOMEN DON'T GET FAT
By Mireille Guiliano

When I was 15, I studied in France, at the University of Strasbourg, for six weeks. On weekdays, my fellow American students and I ate lunch in the school cafeteria and discovered the wonders of braised rabbit and coq au vin, followed always by an apricot tart or napoleon (my first ever!) at the nearby patisserie. On weekends we toured the country by train, fortified by bread and (real!) cheese, along with copious amounts of cheap red wine. Already weight-obsessed, I was sure I'd put on at least 10 pounds. But when I stepped off the plane, the jaws of my waiting parents and my best friend literally dropped. It turns out I'd lost 10 pounds -- I'm not sure I've looked as good since.

Mireille Guiliano had quite a different teenage experience abroad. As an 18-year-old from a small town in eastern France, she spent a year as an exchange student in the well-to-do Boston suburb of Weston, Mass., where she discovered the distinctly American joys of bagels, brownies and chocolate chip cookies and gained 20 pounds. When her own parents met her ocean liner in Le Havre, they were as stunned as mine were, but for a different reason -- her father told her she looked like a sack of potatoes. ''I could not have imagined anything more hurtful,'' she writes. ''And to this day the sting has not been topped.''

Never fear -- Guiliano's story has a happy ending. After a few miserable months during which she gains more weight, cries herself to sleep and hurries past mirrors clothed in shapeless flannel shifts, her mother brings in the family doctor, a k a ''Dr. Miracle.'' He detoxes her with leek broth for a weekend, teaches her to become a master of both her ''willpower'' and her ''pleasures,'' and supplies her with recipes, including one for apple tart without the dough. She learns to love walking, finds her ''equilibrium'' and goes on to become C.E.O. of Clicquot Inc. and a director of Champagne Veuve Clicquot. Most remarkably, despite the fact that she dines out 300 times a year and enjoys two- and three-course meals for lunch and dinner every day -- always accompanied by a glass of Champagne -- she has remained thin.

Guiliano recommends Dr. Miracle's plan as the French way, but it is not unlike the advice that American nutritionists on Web sites and at spas and clinics across the country dispense every day. It is exactly the advice I got last year at Dallas's Cooper Clinic during my annual physical: if you want a glass of wine with dinner, don't eat the bread or skip the baked potato. Do some aerobic exercise; if you're over 40, lift weights. Keep a food diary and cut out the processed junk. Slowly changing your eating habits is far more effective than any crash diet. You don't have to deprive yourself if you learn to make trade-offs. And on and on....

Anne

Anonymous said...

http://www.nytimes.com/2005/02/06/books/chapters/0206-1st-guili.html

'French Women Don't Get Fat'
By MIREILLE GUILIANO

VIVE L'AMÉRIQUE:

THE BEGINNING ... I AM OVERWEIGHT

I love my adopted homeland. But first, as an exchange student in Massachusetts, I learned to love chocolate-chip cookies and brownies. And I gained twenty pounds.

My love affair with America had begun with my love of the English language; we met at the lycée (junior high and high school) when I turned eleven. English was my favorite class after French literature, and I simply adored my English teacher. He had never been abroad but spoke English without a French accent or even a British one. He had learned it during World War II, when he found himself in a POW camp with a high school teacher from Weston, Massachusetts (I suspect they had long hours to practice). Without knowing whether they'd make it out alive, they decided that if they did, they would start an exchange program for high school seniors. Each year, one student from the United States would come to our town and one of us would go to Weston. The exchange continues to this day, and the competition is keen.

During my last year at the lycée, I had good enough grades to apply, but I wasn't interested. With dreams of becoming an English teacher or professor, I was eager to start undergraduate studies at the local university. And at eighteen, naturally I had also convinced myself I was madly in love with a boy in my town. He was the handsomest though admittedly not the brightest boy around, the coqueluche (the darling) of all the girls. I couldn't dream of parting from him, so I didn't even think of applying for Weston. But in the schoolyard, between classes, there was hardly another topic of conversation. Among my friends, the odds-on favorite to go was Monique; she wanted it so badly, and besides, she was the best in our class, a fact not lost on the selection committee, which was chaired by my English teacher and included among its distinguished ranks PTA members, other teachers, the mayor, and the local Catholic priest, balanced by the Protestant minister. But on the Monday morning when the announcement was expected, the only thing announced was that no decision had been made.

At home that Thursday morning (those days, there was no school on Thursdays but half days on Saturday), my English teacher appeared at the door. He had come to see my mother, which seemed rather strange, considering my good grades. As soon as he left, with a big, satisfied smile but not a word to me except hello, my mother called me. Something was très important.

Anne

Anonymous said...

http://www.nytimes.com/2005/02/09/dining/09lady.html?adxnnl=1&adxnnlx=1108075602-ut8ngb8Rvw8wPL0qKWoSVw&pagewanted=all&position=

Something to Chew On: Frenchwomen Eat Smart
By ELAINE SCIOLINO

Paris

THE CROISSANT looked golden-brown and flaky, but one bite was enough.

Mireille Guiliano declared it "disgusting."

The waiter apologized. The regular croissant vendor wasn't baking. But Ms. Guiliano, the author of the best seller "French Women Don't Get Fat: The Secret of Eating for Pleasure" (Alfred A. Knopf, 2005), was not about to waste all those calories on a second-rate bread product.

"Life is too short to drink bad wine and to eat bad food," she said. "This is all about fooling yourself."

Self-deception and sensuality are the secrets of how to eat well and stay slim, according to Ms. Guiliano's bonbon of a book.

In her world, Frenchwomen instinctively understand the centrality of food as a tool of seduction. And seduction, she writes, "figures prominently in the Frenchwoman's sense of herself."

To that end, Frenchwomen eat small portions. They eat whatever they want - even chocolate - but certainly not every day. They use ultrafresh ingredients and avoid processed foods. They drink a lot of water, but never take wine without food.

Frenchwomen are never too busy to go food shopping several times a week or to make their own yogurt from scratch. They are never too cash-strapped to buy farm-fresh items from open-air markets. They never eat in front of the television or standing up. They eat slowly, savor every bite and make dining a ritual - using all five senses and enjoying multicourse meals on separate plates....

Anne