Music, Math and Models

I've said a few times that music is math. I've also said a few times that I'm a Chinese jet pilot and that Halle Berry wants to bear my children so it's probably hard to know when you should take me seriously and when you shouldn't. But let's go back to this "music is math" stuff. On that part I'm not kidding. At the end of the day, a lot of things can be math, including music and supermodels. A few months ago I did an article on how Phi, the famously named Golden Ratio, could even tell us who would be a supermodel. It contained excellent science, humor, Elle MacPherson, Carol Alt and Heidi Klum , yet still left some math questions unanswered. In that article I mentioned the golden ratio in music, namely that the octave, fifth, and major and minor sixths are ratios of consecutive numbers of the Fibonacci* sequence, making them the closest low integer ratios to the golden ratio. But that doesn't make a ton of sense until we get a little more basic, mostly because math doesn't exist in the real world, it isn't a hard science like physics. So we'll figure out how math is music but first we'll show how music is physics. And, in proper attention whore fashion, I can show off some of my guitars. Taylor 814CE. This and my Martin D28 are my go-to guitars. This has a cutaway so if I am playing up the neck I use it. As a stringed instrument the guitar shares common harmonics with all of the other stringed instruments. What makes the guitar different in sound from the others are shape, materials, the nature of the strings - oh, and being in the hands of Eric Johnson. Because a guitar string is elastic and fixed at both ends, it creates waves. It doesn't matter so much what waves are but if you want to know, a wave is the frequency times the length of the wave. v = f x λ Let's talk about the speed of that wave, v. That v is determined by string tension and linear mass density (mass/length) µ, measured in kg/m. Here's the concept you need to know to figure out how a string will make specific sounds: The wavelength of a standing wave on a guitar string is twice the distance between the bridge and the fret. Guitar strings are basically the same so you have to vary the tension and the size of the strings if you want cool sounds. You have to vary both because if you only varied the tension, for example, the high strings would be tight and the low strings would be loose. It's just better for playing to have all of the strings with the same tension (T ). Some mathematical magic: the strings are a perfect fourth apart in pitch ( except for the G and B, 4th and 5th strings counting from the top down ) so any monkey can calculate how much the mass density ( µ ) has to increase between strings for the tension ( T ) to remain constant. Even Al Gore can't get this one wrong. So here is the only math you need to know: v = square root of (T/µ) You then make individual notes by using the frets. The ratio of the widths of two frets is the 12th root of 2, about 1.059. The twelfth fret divides the string in two exact halves. Every twelve frets represents one octave. So that's how guitar makers know where to place the frets based on the size of the neck. Taylor 714. No pickguard, so it's only for fingerstyle. Pickguards are for sissies. Yes, I look like a dork. Try having someone take a picture of you while singing and see how you look. I guess that's enough gorey detail for Part I but for Part II we can talk about harmonics and the way they translate physics into the math in this whole 'music is math' concept. *Also what I named my favorite sexual position of 2002. Final gratuitous guitar girl shot. Because you've come to expect it.

The Science of Orgasms

I read an article from Men's Health talking about how women get aroused during exercises. Specifically, hanging leg raises. "Coregasm" they called it, because some women can, apparently, have an orgasm while doing these exercises. Aside from the fact that it's a really cool term, I was a little jealous. Men need to do some real work to climax. Sure, we all know women have it easier in that regard, much like they have it easier than men in all aspects of life, but women can get off while exercising now? As if they need any more advantages. Anyway, I had never heard of it and I have dated some fit women, including a few for whom I am certain sex was just another way to "feel the burn." I never had one tell me she could could get off while lifting weights though. So I decided to do some investigating. As most of you are aware, I am something of an expert on female orgasms, and not just because my intellect and humor are the causes of more web-based rubouts than Brad Pitt and George Clooney combined. It's also because I do the research. You'll recall I wrote an article on whether the Theta waves in female orgasms would kill men and I even reverse engineered the female orgasm including how a calibrated vaginal stimulator works, for those of you unlucky enough to have never dated a scientist. So I am the perfect person to answer this question for you. It turns out there may be some science in this, though I think most female orgasms usually involve a combination of alcohol and magic. First, we have to know why some women don't get them to know why some do. A lack of orgasms during intercourse with non-scientists is quite common - around 50% of women don't have them that way. Most studies agree that orgasms correlate to the contraction strength of the pubbococcygeus, or PC muscle. Women who don't have orgasms tend to have weak PC muscles. The pubbococcygeus muscle is surrounded by four other pelvic muscles but they work as a system. A healthy PC muscle, the kind a woman who does a lot of ab exercises or hanging leg presses probably has, is very rigid while a weak one is not.* A strong PC muscle makes these orgasms much easier. That means a woman with a strong PC muscle can have an orgasm almost any time this muscle is stimulated. Abdominal exercises, friction from clothing, reading this article. But why would it be limited to just the gym? I thought. "Coregasms" are fine but truly fit women can do it anywhere. Watching An Inconvenient Truth, for example, might give them a "Gore-gasm." Standing outside Tiffany's? A "Store-gasm." Graham crackers, chocolate and marshmallows? A "Smore-gasm." Women have it so easy and I could go on all day. But you have other things to do and I need to go buy a trampoline with all of the money this research is going to make me. Miss Earth 2006 is enjoying her Goregasm even now. *Men, I would rather light a candle than curse your darkness - if you want to help her, the PC muscle is located about 2 inches within the vagina and runs circularly. Bonus: it contains most of the nerve endings in the vagina and is the primary source of sexual feeling, so even you can't mess this one up.

Queer As Fish: Estrogen in Pittsburgh rivers

There's a lot of "Can X make you gay?" articles being written these days. This fellow says soy is making you gay and even the New York Times wonders if you have a gay car. Now a study from the University of Pittsburgh says that fish from Pittsburgh rivers contain substances that act like estrogen. Estrogen. The female hormone. So you'll have to forgive me for the topical television reference, but when a show called Queer As Folk is set in Pittsburgh, 'fish' is going to jump in there rather naturally. We're supposed to make girls go fishing. Fishing is not supposed to make us into girls. Since fish are sentinels of the environment, say researchers at Pitt's Center for Environmental Oncology, and retain chemicals from their habitat within their bodies, their experiments show that feminizing chemicals are making their way into the region's waterways. Their study also says these chemicals caused increased growth of estrogen-sensitive breast cancer cells. Wow, you can become a woman and get breast cancer. Fishing in the 'Burgh sounds better and better. "We decided to look at pisciverous fish, those that eat other fish, for this project because we know that they bioaccumulate contaminants from water and their prey, which may include toxic metals, farm and industrial runoff and wastes from aging municipal sewer systems," said Conrad D. Volz, Dr.P.H., M.P.H., principal investigator, department of environmental and occupational health, University of Pittsburgh Graduate School of Public Health. "The goals of this project are to use fish as environmental sensors of chemicals in the water and the aquatic food chain, and to determine the origins of these chemical contaminants," said Dr. Volz. The study examined white bass and channel catfish caught in the Allegheny, Monongahela and Ohio Rivers. These fish are among those commonly caught as a food source by local anglers. The laboratory of Patricia K. Eagon, Ph.D., co-principal investigator of the study, found that extracts from the fish acted like estrogen, a female hormone, by binding to estrogen receptors – the proteins within cells that render the cells sensitive to estrogen.* "We know that there are hundreds, even thousands, of chemicals in the environment that can have estrogenic activity," said Dr. Eagon. "These chemicals usually come from industrial pollution, farm animals, farm chemicals and municipal water treatment plants. What surprised us most in this study was that these estrogenic materials are present in such easily detected levels in local fish." Mmmmmmm ... fish. Someone get that girl out of there. According to Volz, the next step in their research is to identify the sources of the estrogenic chemicals. "These findings have significant public health implications, since we drink water from the rivers where the fish were caught. Additionally, the consumption of river-caught fish, especially by semi-subsistence anglers, may increase the risk for endocrine-mediated health endpoints like some cancers and developmental problems." They drink from the river in Pittsburgh?? If they are doing that, they have a lot more to worry about than growing breasts. Source: University of Pittsburgh Schools of the Health Sciences.

Practical Science Part I - Bugs Bunny and Beer

Anyone can tell you, the surest test of your science chops is your ability to make a kid understand it. Science, at its most fundamental, can be understood by anyone if explained properly. Science is, for the most part, conceptual. The math is relatively unimportant as long as you understand why things work the way they work. Bugs Bunny, I want my 4 hours of research back I bring that up because it's not always kids doing the learning. Most science questions I can answer pretty easily. I have a broad base of knowledge and one of those brains that recalls everything. In the age of Google that's relatively unimportant. Today, sub-literate sock monkeys who can barely spell their names can cite sources and keep a whole bookmark file full of facts in order to look smart. Luckily, most of them write about politics rather than science ( Huffington Report, RadioAmerica, I mean you ) so science is usually populated by people who know what they're talking about. That's not to say we can't be stumped. I had a recent question I couldn't answer without some significant research. I figure if I don't know the answer, maybe you don't either and we can all get a little smarter. So here it is: Why does the fat opera singer's head shrink when Bugs Bunny sprays Alum in his throat? This came up during the classic "Long-Haired Hare", after Bugs has had just about enough of Giovanni Jones breaking his banjo. Well, I wasn't sure. I never used Alum, I have no Alum in the house. I know they used to put Alum in water, 2500 years ago, and it would work pretty well today. Did the coagulating symbolize this head shrinking? I wrote a chemistry acquaintance but knew I wouldn't hear from him until morning. It doesn't help to have two smart people in the house. "Maybe Alum was the chemical used by Jivaro tribesmen to shrink heads in the Amazon," Lady Scientist offered. Actually, that made perfect sense. Bugs Bunny cartoons were always topical and almost every movie matinee serial had some tribesman or another as a villain, so shrinking heads using Alum may have been well known to kids and adults then. I did some research - I might as well have chewed some Ayahuasca. They apparently boil these 'heads' ( skin with the skull removed ) in Chinchipi juice and water. I spent an hour reading on the taxonomy of native plants in Ecuador but I couldn't find anything that said they had anything similar to Alum in them. Dead end. But I am not a total tease so here is the recipe to make your own shrunken head. I suggest you use a dog or something rather than attack your neighbors: 1. Slit the head at the back from the base of the neck to the crown. Peel the skin from the skull. Throw the skull/brains into the river as a sacrifice - to the spirit of the Anaconda. These people were vicious but they knew what they were doing so even if you're in upstate New York I suggest you fly to Ecuador and find a river. 2. Turn the face inside out and remove all fatty tissue. 3. Tie a rope to the top of the head through an incision. Lower the head into a pot of hot water and Chinchipi plant juice. Simmer for up to two hours, taking care not to leave it in too long or the hair will fall out. 4. Sew up the back of the neck and the eyelids with thread and seal the lips with three bamboo pegs. I suggest you go to Pier One and chop up some furniture in front of a sales associate to get these pegs. When you explain why you need it, they will let you alone and you pulled a great prank. 5. Insert hot pebbles into the neck cavity and whirl the head around by the hair to keep the stones from burning the flesh. Then do it with hot sand when it shrinks too much to use stones. It will take about 20 hours, over 3 - 7 days. 6. Polish your shrunken head up. It will be a little larger than an orange. Brag to your friends Congratulations! Your first shrunken head. Anyway, South American tribesmen were clearly a dead end. I went back to Chemistry. Alum has been around a long time so a lot of things get called Alum. Aluminum Sulfate is used in water but that seemed awfully obscure. Kids laughed when they saw the head shrink and I am betting they didn't know about Aluminum Sulfate. Deodorants, astringents, spices - this stuff is everywhere. Finally, I swallowed my pride, gave up on science, and cheated. I called my mother. Cash: "You remember in cartoons when they would use Alum and someone's head would shrink, right? It had to be common knowledge then but I can't figure out why they used that image to represent what Alum does." Science Matriarch: "You did it a hundred times when you were a kid. When we made dill pickles we put whole cucumbers in the jar with Alum and water and it makes them shrink. It's a pickling spice. Everyone did it back then but I don't think people make their own pickles any more." Cash: Oh. I should have known that. I didn't get this sweet eating dill pickles, though." Science Matriarch: "You also went to basic training. You don't think they still put saltpeter in the food? Alum kept your libido shrunk for 8 weeks too." Yikes. Satisfied that I had done hours of research for ... nothing ... well, not nothing but something that every 7-year old knew in 1949 ... I decided to grab a beer. I take a sip. It is cold. Really cold. It says "Miller Genuine Draft" and "unique cold-filtering process." "Wait. What's so great about cold-filtered beer?" I thought. And I found out. But this is already way too long so it has to wait until Part II.

An Equation About Easter Miracles - Should Captain Carrot Quit Smoking?

I got some questions from a writer named Captain Carrot, i.e. a stranger, who deduced that, because I write this column for free, I must also be available for free science consultation and/or general life and relationship advice. Here is a sample: I am 27. Should I try to stop smoking, or will I regret it later in life? Most of you know me well enough by now to realize that, unless you provide webcam proof you are a supermodel, I am unlikely to even bother learning to spell your name. Yet something in his plea struck me. Maybe because it's Easter Weekend and I feel bad that Jesus died so most of you could tell George Bush how much smarter you are than he is, or maybe it's because I feel a twinge of guilt at Photoshopping a picture of myself in a picture as a half-Crusader/half-Crusaded warrior of the 12th century, or maybe it's because I am saddened that this poor monkey can't even decide for himself whether or not he should ingest carcinogens that we've spent trillions of dollars telling him he should not ingest. It doesn't matter. I felt his pain so I answered his call. However, I am a busy man - if I am to have an orgy of unprotected sex with supermodels this weekend to celebrate the Resurrection of the Messiah, I need to make a coke run. And don't let me forget to buy a grape for them to share when they have the munchies. One of my pals is Garth Sundem author of Geek Logik: 50 Foolproof Equations For Everyday Life. Garth is a good guy and he loves to do this kind of stuff - for my kid's Christmas he even made him a custom equation ,"How many homeruns will you blast in high school even though your father chased the breaking stuff way too often" - but I am sure he has a life and doesn't want to do this. I even looked in his book and, surprisingly, he never covered this subject. So in his stead, I will do it. I don't know how to do LaTeX input here so I am forced to do this in crappy HTML text and it won't look all pretty and nice. But for free, you can't complain. Because this question has more than one variable, you can't really solve it, you can only converge on a perfect answer. Nonetheless, I can at least tell the Captain how to decide if he should commence with the DTs: Should Captain Carrot Shake That Demon Weed? Q = H/D + F(S-8)/(C x 0.2) Where Q is Quitting, namely whether or not you should. H is for Halitosis, namely how much quitting would improve your breath on a 1-10 scale. 1 being "it always smells great anyway" and 10 being "peanut butter and onions would be a nice way to describe my breath" D is for Difficulty, namely how much fortitude you have with 10 being Job ( staying in our Biblical theme ) is impressed by how much aggravation you can withstand. F is for Family, namely the number of Family members who reminded you to quit smoking last week. S is for your marital Status. 5 for happy and 10 if you are married. C is for Cigarettes, namely how many you smoke per day. From there, it is simple. If Q >1, you should quit. And what the heck, since it is the season for sacrifice I will also answer your question on whether or not it is possible to insure through genetic manipulation that your child is exceptional at science : It is possible. Namely, by having me impregnate your wife.

Happy Easter

Be sure to enjoy a wholesome Crusade. I know I will: Even if you don't admire my Photoshop skills, you have to admit I don't look as silly as a British guy who signs up to be crucified and then claims God told him at the last minute not to do it. Maybe I'm crazy but I bet God didn't have as much to do with it as watching nine Filipinos before him get whipped and nailed to crosses. That would make me get down on my knees and have a religious epiphany too. How did the crowd react? They boo'ed him, of course. If I go all that way to see radical Catholics re-enact the Crucifixion you can bet nothing would make me happier than seeing some smarmy British journalists take some spikes to the hands.