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Saturday, March 31, 2007

The Music of the Spheres

Continuing in the vein of art and mathematics, I encountered a jazz musician named Rudresh Mahanthappa who is employing his knowledge of crytography to his compositions. His recently released Codebook takes old standards and applies a kind of cypher to them to arrive at an original composition. The code is based on the Fibonacci sequence where each number is the sum of the two preceding numbers. 1,1,2,3,5,8,13,... Fibonacci, also known as Leonardo of Pisa, is said to have found the sequence while studying the breeding habits of rabbits, but the numbers have since popped up all over. From flower petals to seashells, the numbers continually crop up and they are intimately related to the golden ratio, the number mathematicians refer to as the Greek letter phi (Fibonacci also factored heavily into The DaVinci Code, for those of you who get your math from Dan Brown.)

It just goes to show how fruitful the marriage of music and mathematics can be.

Friday, March 30, 2007

Flatland: The Movie

I just found this trailer and it looks awesome. I don't know if anyone has tried to bring Edwin Abbott's classic geometric anti-utopia to life before, but this sounds like a must-see.

Refining the Fine Arts

Something special is happening today in Albany, New York. The annual Arts and Mathematics Conference is celebrating its 15th anniversary. The conference gives students who appreciate the inherent connection between the two subjects to unveil their work. Nat Friedman, founder of the Art and Mathematics Conference, says

"Art and mathematics are both about seeing relationships. Creativity is about seeing from a new viewpoint and this unifies art and mathematics."

Which got me thinking, why doesn't that intimate relationship manifest itself in our schools? I have several friends currently teaching fine arts in the public school system. More than most teachers, they have to worry about their funding being cut. It's hard for most pragmatic politicians to justify a marching band when science textbooks are out of date or missing entirely. Those art teachers will happily expound upon the documented correlations between art appreciation and IQ. They will point out that music education can actually raise a students performance on standardized tests. The problem is that they're only making half an argument, and they aren't backing it up with actions.

Why can music and art do all that? It isn't because the arts are so different from the sciences, but rather, that they are so similar, that makes them powerful. Music isn't like math; it is math. Yet many music teachers don't realize this. Study after study has shown that the mind of a composer and the mind of a mathematician look nearly identical, at least while practicing their crafts. Art is just applied mathematics. So why would we want to separate the two? At my high school, their was an entire building devoted to the arts. It was both a fortress and a prison to art education. Of the major fine art programs, only drama was housed in the main building, as a subset of the English department. (Of course, since my graduation, Drama has seceded and now resides within the fortress walls.) There is no logical explanation for this. Drama is literature, ans should be taught alongside novels and prose. In fact, all students should have to act out the plays the are "reading," not just the "creepy" theatre kids. Music theory should be taught in the Math department, and so on.

It isn't enough to say that there exists a connection between art and science, we have to show students what that connection is. Pleading that art education is imperative for our public schools isn't going to keep funding from being cut, we have to actually make it indispensable. This isn't going to happen as long as the art departments keep celebrating the difference between their courses and the core curriculum. They must become the core curriculum.

I would love to see math teachers invite composers to their classrooms, or music and art teachers to invite mathematicians to explain the sciences of sound and art. Only by truly understanding the patterns embedded deep within can students learn to appreciate the beauty on the surface.

Tuesday, March 27, 2007

What's in a Name?

This years Abel Prize, sort of a Nobel for math, has been awarded to an Indian mathematician by the name of Srinivasa. If the implications of this don't mean anything to you, let me give you the history. (Or you can find a quick reference to it in Good Will Hunting.) In the early years of last century, a British mathematician began receiving notebooks in the mail. They were filled with page after page of scribbles proofs. Many of them were unorthodox versions of known work, but some were intriguingly new. They turned out to be from a young Indian named Srinivasa Ramanujan. The boy had taught himself math using a primer he had found, and with nothing more than that was able to create entirely new lines of math. He is best known for his work with continued fractions, but perhaps his greatest legacy is the one that inspires young mathematicians the world over. It is possible to come from nothing, from the middle of nowhere, and yet solve puzzles that have confounded the great minds for centuries.

Problems like P vs. NP, commonly epitomized by the Traveling Salesman Problem, may just take a really good idea from a fresh mind. That simple possibility is what keeps math new and exciting (for those of us who care enough anyway.)

Monday, March 26, 2007

A Kernel of Truth

Do you remember how every once in awhile, Bo and Luke Duke got into a bind and had to pour some of their moonshine into the General Lee's gas tank instead of regular unleaded? It seems like our President does? He's been sermonizing about ethanol like it's nature's miracle fuel. It sounds like a pretty good deal at first. You take a few bushels of freshly husked corn from America's heartland and convert it into a clean-burning liquid that can compete with all that evil foreign oil. It just makes you want to go out and hug the whole state of Iowa.

Only, like all things, there's a catch.

You see, the picture in your head is all wrong. The maize your think of doesn't exist much anymore. The corn plants that ethanol is made from were never intended for eating. Even the ones that aren't genetically engineered and patented by Monsanto have been bred for all sorts of traits that don't make any sense. They have been taught to stand up straight and grow so close together that you could hide entire leagues of baseball players so even Kevin Costner couldn't find them. These high yield varieties suck need a steady supply of nitrates to keep them big and strong. Only the don't get those nitrates from the natural world any longer.

Once upon a time, farmers rotated their crops, using legumes like soybeans to add nitrates back into the soil. Before the Great War, the only usable nitrogen in the ecosystem came from a special relationship between the roots of certain legumes and some helpful bacteria. Then a German chemist discovered a process whereby nitrates could be acquired via science- called nitrogen "fixing." It turns out that if you get some nitrogen, which is readily available in the atmosphere in an entirely stable and unusable condition, and put it together with some hydrogen, add the presence of a catalyst, and zap it with electricity, you can manufacture some black gold.

The process was originally intended for use in explosives. Those of you who remember that Uncle Sam grows terrorists as well as corn down on the farm might recall the Oklahoma City bombing. Nitrates go boom. After World War II, we ended up with surpluses of nitrates, and having of course discovered better ways to explode people, we needed something to do with them. We decided to sell it to our nation's farmers for fertilizer, and a new industry was born. Today's corn fields can't survive a season without a heavy dose of manufactured nitrates. Those nitrates (here's the best part) require petroleum to produce. That's right, oil. Remember the hydrogen in the "fixing" recipe? Well we get it from petroleum. Combine that with the natural gas in the fertilizer, the fossil fuels running the tractor and the turbine, and making the pesticides, and it takes between 1/4 and 1/3 of a barrel of oil to make a bushel of corn. Let me put it another way. It takes roughly 131,000 BTUs of energy to make a gallon of ethanol. A gallon of ethanol yields 77,000 BTU's of energy. Here's where the math comes into play. It's complicated, but it turns out that 131,000 is actually MORE than 77,000- by roughly 54,000.

Don't be fooled. The companies that control our corn commodities know this and so do the car companies and the oil companies. There is an alternate energy source out there somewhere. But this ain't it.

American Dream

My stepfather was born in England. He grew up drinking warm Guinness and watching cricket matches that lasted for days. Now he drinks cold Natural Light and watches Nascar. Quite a change.

He is a naturalized American citizen. I distinctly remember helping him study for his test, and let me tell you, he earned it. He had to learn everything that is taught in the average civics class and more. His final exam wasn't for a grade, it was for a new home. He loves America and he votes more regularly than my mother, who was of course born here. A little rain is enough to keep her from the polls. I have often wondered at the logic of this. The America I know means too much to be taken for granted. Yet that is what the majority of us do. We complain about politics, but don't vote. We complain about taxes, but don't have any idea where those taxes go. Most of us seem content to let a few privileged individuals run our country unmolested by the masses. That's not "of the people, by the people, for the people." That's not "liberty and justice for all." It's oligarchy, not democracy.

Recently, I wrote a post regarding the purpose of public education. In a democracy, teaching kids about their rights and roles as citizens ranks way up there, if not number one. Which is why I was impressed by an article about a 61-year old Scottish immigrant teaching in Tennessee, who believed so strongly in the lesson of civics that he arranged for his naturalization exam to be given in front of his students. I hope they learned what I did, when helping my step-dad study for his. He doesn't take his citizenship for granted, and neither will I.

Sunday, March 25, 2007

A Silver Lining

As much as I believe that the public education system, like any system, needs to be constantly assessed and improved, I have been very critical of NCLB. I do not believe that the plan was ever intended to improve our schools and have always felt that was meant as a purely superficial political maneuver. It has been underfunded and seriously lacking in logic from the get-go, and i have never heard of any positive results from it. Until now.

It seems that the testing industry is beginning to buckle under the strain of "accountability." The capitalist juggernaut that is the standardized testing business has made itself virtually indispensable for too long. I have never felt that these tests accurately predict anything other than one's ability to take that particular test, but I have never seen a way to weaken the beast. Yet it seems that we may be killing two birds with one stone on this one. NCLB cannot exist without constant testing, and the testing industry cannot survive NCLB. It's probably too much to ask that both would go the way of the dodo. Still, one can hope.

Friday, March 23, 2007

Attendance is Mandatory

There has been a lot of talk over the last few years about applying a business model to public education. You hear children described as though they are widgets on an assembly line, as some form of social capital gain. Many say the free market is the panacea for all of public education's woes. This isn't new, by any means. The business world has been sticking its nose into education for some time now. It makes sense from their perspective. Why worry about training workers on the job when you can get public education to churn out skilled workers? Maybe I'm being unfair to the private sector. Still, I think that as long as we're debating education, we need to revisit the question of what we actually want out of our schools.

My personal expectations are many fold, and I'm not in the mood to go into them all right now. I do want to make clear one thing about education and the free market. A key ingredient of a free market is consumer choice. This is the idea behind the voucher hub-bub. But the greatest choice of a consumer is whether or not to make use of a product in the first place, and this is the key reason why there is no free market in our public education system. Children must attend school. It's the law. Not even their parents have the right to opt out on their behalf.

How do we as a democratic nation justify this? Is it right for us to force anyone to become educated? It wasn't that long ago when it was perfectly acceptable to end one's formal schooling after the eighth grade. That's no longer the case. We almost take it for granted that there is no other way, but in other countries, there is. For instance, the UK is only recently considering compulsory attendance for all minors. There is much debate over it as well.

Look, I desperately believe in education. I am dying to become a teacher. But I don't think anyone should be in school if they really don't want to be. You can't force someone to learn. You just can't.

Thursday, March 22, 2007

Gaussian Madness in Kentucky

A school district in Kentucky, having already eliminated "D" as a passing grade, is now considering tossing out the "C" as well. When I read the headline, I got excited. Unfortunately, the article let me down. Although they claim to be seeing improvements since they made the switch, I am skeptical based on nothing more than mathematics. As long as you teach to a curve, meaning lumping kids together by age and expecting them all to perform at the same level on all subjects, you are going to get a range of grades. Those grades ought to fall along a bell shaped curve, though whether that curve is strictly Gaussian is up for debate. Regardless, there has to be a range of scores and I suspect that it will be large enough to guarantee plenty of kids will miss the "B" cut. I applaud the district for making changes in its grading policy, though I would suggest eradicating letter grades and grade levels entirely and begin using a more costly, yet more accurate, performance based assessment.

Tuesday, March 20, 2007

A Narrow Margin

It seems that the majority of school board members in Olympia, Washington agree with me. They voted 3-2 to begin using the new textbooks that emphasize math concepts over math skills. They also seem willing to fund the changes and ensure teachers are trained in the new methods. To me, the overarching problem is that many who teach math in the early years have no earthly idea what math is. They can perform basic computations and believe that they are doing math, when in fact, they are only succeeding in boring students into permanently hating all things numeric. Why is it that we do not require math teachers to have math degrees? Why do we expect high school teachers to understand more math than elementary school teachers, when they are arguably teaching the more complicated concepts? This is a big part of the problem as I see it. If teachers are content to be just one step ahead of their students, their students will never glimpse the mysterious mathematical world ahead. They will only know drudgery and apathy.

Monday, March 19, 2007

Define Irony

Had I known that the E8 announcement would come today, I would have entitled the last post differently. The 248 dimensional Lie group whose symmetries are at the heart of this proof was previously considered an unsolvable problem. Yet a team of mathematicians working together managed to crack it. This is what it's all about.

Sunday, March 18, 2007

Group Theory

One of my favorite things about mathematics is how cooperative it is. With few exceptions, math is done by teams of people, not by individuals. They work together, build off each other's strengths, and solve together what none could alone. Even the loners of math history like Newton, or Andrew Wiles more recently, have been standing on the shoulders of giants. So why then does most classroom math focus on keeping your eyes on your own paper, so to speak? Why the emphasis on individual work, when professional mathematicians don't work like that?

I have often thought that I would prefer to organize my class into several small groups. This will allow them to challenge one another, and uses their natural social structure to improve learning. It also effectively means that instead of teaching 30-40 separate students, I will be teaching 5-7 teams. I have recently read about creative math teachers using this approach with much success. I'm not saying that it's a revolutionary idea or anything, and I'm sure it's been done before. It is certainly the exception, rather than the rule. I would like to read some case studies on the subject. There are many variables that concern me. For example, I'm not sure yet whether I want to choose the groups myself or allow the students to do it themselves. The first way allows me to group quick-learners with struggling ones, but the second will better guarantee a positive group dynamic.

Regardless of the details, I am sure this will be a major element to my classroom structure. Whether its a few round tables or a bunch of desks shoved together, my students will be working in groups.

Saturday, March 17, 2007

Speaking My Greenpeace

I received an email from a close friend yesterday. The thrust of the message was that she is tired of certain members of the environmental movement turning climate science into a religion. There was an accompanying link to this video, which I am not posting directly to my blog due to its length, but suffice it to say that it is the anti-Inconvenient Truth. I recommend watching it, as I do all perspectives on an issue. The rest of this post is my response to the message. I think it falls under the "making the world a better place" clause of my mission statement.

"Quite frankly, I'm opposed to anything being turned into a religion. It's a sure-fire way to ruin what may have started as a great idea.

"In the case of "global warming," I will agree that media attention toward the issue tends to be extreme and politically polarizing. That's why it gets attention. This film is no different, it is merely crap rolling down a different hill. Unfortunately, as much as I love Google video, the quality of this particular download leaves much to my desire. I wish I could have watched it in a format where the graphs weren't so fuzzy and the sound dubbing synched up better. I was mostly watching for the alleged third-world impacts, which I felt were hastily added in the last five minutes and contained the least supporting data. I have also aggregated a few links for our little intellectual circle of articles pertaining to this film. They included, but are not limited to scientific rebuttals, accusations of deliberate distortion, and a letter from one of the interviewees stating that he was in fact "swindled" by the producers. In short, it's exactly what you would expect to come from one extreme after hearing the ideas of the other.

"Here are the most important issues as I see them. They are the same ones that apply to the economy, the environment, avian flu, political corruption, education and anything else that is worth being concerned about. All of these are chaotic systems. They all have more mitigating factors than there is time to list. They all show a sensitivity to initial conditions that makes modeling all but impossible. Even scientists with the best of intentions will disagree because of this. Ed has a favorite story about two economists arguing on the radio that illustrates the same principle. But here's the thing, and there's really know way of getting around it. Humans can be called a lot of things. We have shaped this planet in more ways than any of us know. We are responsible for unbelievable good and inescapable bad. But the one thing that we are NOT is content. We are a restless, and often, recklessly headstrong species. There is no way that we will ever be satisfied in waiting for all of the data to come in, especially concerning issues that so affect us.

"So what are we supposed to do. Yes, it is true that the sources of global warming are complex, misunderstood, and mysterious. I don't see any climatologists on this recipient list, but any honest scientist ought to tell you that our predictive capabilities will never be close to absolute. Unfortunately, we have to make policy decisions in spite of that fact. The wait-and-see approach doesn't work well for us. Perhaps it is arrogant of us to think that we can affect the world so much. Or perhaps it isn't really the world we need be concerned with. Nothing we do is going to destroy this planet. Life on Earth will continue long after we're gone. Yet while it is true that the cockroach may one day be king, I would really prefer us to hang around for as long as we can. So I really don't see the harm in being on the safe side. Do I think we should keep the developing world from doing so? No, not really. Let them burn whatever fossil fuels they want. (And by the way, there is plenty of fuel mining going on in Africa. It's just that the first world can afford to outbid the indigenous populations and local warlords tend to embrace capitalism.) I don't think it's fair to deny others the prosperity that I often take for granted. But I can help balance things out. I can use energy efficient light bulbs and turn lights off when I'm not using them. I can recycle, even if some of the technology isn't at maximum efficiency. I can walk, ride my bike, or take the bus. I can do all these things because they are easy to do and I feel good doing them. I can lead by example. The marketing and propaganda, no matter how widespread, will only mobilize a fraction of the audience, who in turn, will only do a fraction of what they can.

"I will be one of the few and i will do as much as possible to make whatever insignificant dent I can.
And that is what the environmental movement means to me."

Friday, March 16, 2007

Don't Be Evil

Absolute power corrupts absolutely. At least, that's the conventional wisdom. Yet time and again, Larry Page and Sergei Brin prove that it is possible to have scruples, and still make obscene quantities of money. As they continue to drive the science of search, they're opportunities to cross to the Dark side abound, but still they refuse to compromise their simple mantra- Don't Be Evil. Each day, more and more information is aggregated inside the heart of the Googleplex. Year after year, additional services are unveiled. GMail, Google Video, and of course, Blogger. All free to the public. All that is required is that we put our faith and trust in their hands.

Thus far, they have proven worthy of that trust, and in the wake of numerous scandals brimming forth from our federal government, Google may be the only large organization that has. In fact, they have gone head-to-head with our government to protect our privacy and the very bedrock on which the Constitution is built. When the technology is present to track the click-stream of every user, the search giant is erring on the side of the 4th Amendment. They are placing a concrete limit of 18 to 24 months on the length of time they will hold personal information from their users in their data bank. They don't have to do this, mind you. There has been no government order mandating this policy change. In fact, our government would prefer they hold data indefinitely and clandestinely feed it directly to Homeland Security. The founders of Google continue to impress. One can only hope that the will find equally strong-willed successors, lest the power fall in to the wrong hands.

Thursday, March 15, 2007

Extracurricular Science

Many high schools have math teams, so their young math enthusiasts can experience the competition and teamwork of sports, while engaging in the subject they love. My own school had one, and I have friends that still attend and even proctor the national events. I'm sure the kids are having a lot of fun, and I don't mean to denigrate that in any way. But I was just reading about a 17 year old girl who has been awarded $1000,000 to build her own spectroscope, and well, that's pretty darn impressive. I have been reading about math and science my whole life, and I wouldn't have the first clue as to how to go about building one. This in turn, reminded me of an idea my friend Matt (aka Jebus to Appalachian Trail thru-hikers) told me about.

He was pointing out all the time and effort that goes into these math teams. What if all those hours went into doing actual math? I'm not talking about more book learning, I'm talking about research. If teenagers can build machines for sniffing out the chemical composition of molecules, then they can publish in peer reviewed math journals. I would think that would be more fun than winning trophies, and it would give them a head start on a career in math, while impressing the hell out of colleges.

Wednesday, March 14, 2007

The Full Monty

In the ongoing saga of American prudery, a Florida drama teacher has been given an ultimatum. Either he drops out of the local production of "The Full Monty," where he briefly bares cheek in the final scene, or he seeks employment elsewhere. I wasn't aware that an administration could threaten my job over something I do legally in my spare time. It's not like he's moonlighting as a male escort or entertaining at bachelorette parties. He's acting on stage in a Tony Award winning show. With all the support for the continuing education of teachers, I would think he would be applauded for further honing his craft. For the life of me, i can't figure out what this school is possible thinking. The either really love lawsuits or really fear the ass.

Tuesday, March 13, 2007

Experiment #1

I have begun thinking about how I want to structure my class. I know that I haven't even begun teaching yet, in fact, I am still several years away from certification. Still, I don't think it's too early to begin. So when I have an idea, I am going to post it as an "experiment." Generally, that means I'm not sure how the idea would affect a classroom full of kids, and I am interested in feedback from current teachers. Here is the first of those ideas.

I don't like how the cumulative grading system works. Students who fail early on are forced to carry those grades with them. No matter how hard they work, even if their grades improve, they may be too far in the hole. I know teachers have a little leeway, and could easily weight later grades if the situation mandated, but that still leaves it up to discretion and if I were a student, I would rather have a system with that kind of forgiveness built in. I am thinking about treating classroom tests similarly to the SATs, in at least one respect. Just as a student can retake the SATs as often as is required to improve their score, so shall they be able to retake portions of my tests. Each test will be broken up into skill sets and students will be able to replace grades in each skill as they desire. Students who want to improve, will thus be given the opportunity to do so without being penalized for earlier failure. I realize this will mean a lot of work on my part, since new problems will have to be administered each time. that is a time commitment i am willing to make.

I do wonder how administrations would feel about this. Also, how will students who ace the test in one shot feel? Will they cheer their peers on, or feel resentment toward them? I just don't know, but I'd like to find out.

Positive Feedback

A while back, one of my co-workers caught me reading a popular physics book on my lunch break. She asked me if I would be willing to tutor her son in Physics. Evidently, he was failing miserably and she hadn't been able to find a tutor anywhere. I was a bit reluctant, since despite being embroiled in a physics related book, it has been some time since I had to actually solve kinematic equations. I figured it would all come back to me, but I felt unsure of committing myself. She convinced me that I couldn't possibly do any harm, so I decided to give it a try.

The back story on the situation is a good example of how inept administrations can really mess with a kid's education. Her son was allowed to enroll in Honors Physics as a Freshman. He is concurrently taking Algebra I. If that sounds odd to you, it should. He is missing approximately two years of math background required to understand basic physics. He has never encountered rates of change. He has not even studied trigonometry. It's no wonder he was failing! This is inexcusable.

Just before I began meeting with him, he had downgraded to CP Physics, meaning he switched classrooms and teachers. Unfortunately, this did not have an immediate effect on his grade. He had just received a 40% on the most recent test. Enter me. As i got to know him, I quickly realized that he wasn't terribly excited about the subject matter, yet he was determined to improve. Even when I pointed out that he may be in such a large hole, all of his best efforts may prove fruitless, he still insisted on pushing forward. So we went to work. I started by walking him through some problems, and then let him take over. I saw improvement quickly, and was able to give him some tips for better problem solving strategies. A lot of his problem lied in some bad habits he had picked up. These habits would have been broken with more math experience, but he wasn't given that chance. Anyway, a week later, there was another test. He earned a solid "C." I was extremely pleased, as were his parents. More tutoring, more tests, more improvement. On his most recent test he made an 89% and just got back a 95% on a quiz.

I'm not trying to prove causality here. He has a new teacher, and is in a class moving at a slower pace. He has parents that care enough to have gone to all the trouble to get help. He has been working hard, and deserves much recognition. But I have to feel like there's at least some correlation here. I must have something to do with it. At least, that's the way I feel. It makes me think I have chosen the right path for myself.

Monday, March 12, 2007

Open-Source Education

Apparently, the prestigious technical school MIT is going to be the first institution of higher learning to make all of its courses available free online. You won't be able to get college credit, but you can audit classes with some of the most respected instructors in the country. Any student, anybody with web access, can learn anything from quantum mechanics to chaos theory and everything in between for free. It turns out Will Hunting was wrong. You can now get a college education for much less than "a dollar fifty in late charges at the public library."

Sunday, March 11, 2007

Spring Forward

Thankfully, I had the day off today. I didn't have to worry about losing a precious hour of sleep. In fact, I didn't stumble out of bed until ten. I was one of the lucky ones. Millions of other working men and women had to pry their eyes open with crowbars and slap their circadian rhythms into shape, because of a wonderfully silly mandate we like to call Daylight Savings Time. DST, originally conceived by Benjamin Franklin, is designed to provide more usable hours of sunlight during the summer months. It is alleged to conserve energy as well, since artificial light is used for less time each day. Congress even decided to make the switch earlier this year to save more energy.

Look, I'm all for saving energy, but I sincerely wish DST would go the way of the dodo. It is ridiculously inconvenient and stupendously counterproductive. Any energy saved at night is surely lost each morning, when (Surprise!) early-risers have to turn on the lights to get ready. Our biological clocks have been built into us by evolution. There's not much we can do about the fact that the earth rotates about the sun on a pivoting axis and sometimes it's light and sometimes isn't. The 24 hour day is a function of life on this planet.

Which brings me to an interesting point. How will we measure time when we finally get off this rock? Will space-travelers remain harnessed to earth seconds or will they develop a new unit with which to sub-divide the day? What will happen if and when we encounter alien life? The odds of their planet rotating on its axis in the same period as hours isn't terribly good. Will the universe have to agree on a Greenwich Mean Time for the cosmos?

I think Poor Richard was a genius and by all accounts a snazzy dresser. I love his almanac, his high-flying kite, and his public libraries. But this Daylight Savings Time needs to go.

Worshipping Algorithms

I found this video entitled Math Education: An Inconvenient Truth, which quickly and accurately demonstrates the popular misconceptions of math held my many in our culture. In the clip, a meteorologist, a scientist that must use math on a daily basis and ought to know better, launches a public campaign against a series of grade school math texts being used in local curricula. She is essentially complaining about new-fangled ideas that are different from the ones she learned when she was a kid, and blames the crazy liberal hippies that wrote the books for dumbing-down our kids by not drilling the standard algorithms into students' heads. She is particularly married to that word, and seems to think that her ability to define algorithm gives her the right to shepherd her viewing flock away from these radical ideas.

And would you like to know what these wacky ideas are? They are this: math is not about algorithms. Nor is it about numbers, though they are often used. Math is about patterns. It is critical thinking at its finest. As many times as the author utters the word, one would think that she truly understands what an algorithm is. She does not. It is a tool. You can't hold it in your hand, but it is a tool nonetheless. The standard algorithms that she demonstrates are the ones whose combination of speed, efficiency, practicality, accuracy, and fashion have allowed them to survive natural selection. It is this combination of factors, but no one alone. For example, only when paper technology became affordable were these methods even possible, and even then, skilled abacus operators could beat them for speed. But once paper was readily accessible, written methods won the day. Well guess what, the digital age has brought us a new tool. Its affordable, lightning fast, and never gets bored- the calculator.

I'm not suggesting that we discontinue learning arithmetic. What I am suggesting is that this woman has overlooked the intentions of the textbooks she is critiquing. These books are teaching how to think mathematically. In order to solve the examples she gives, students must master concepts like the distributive and associative properties. They must understand place value. They must think for themselves. Yes, I believe the standard algorithms should be taught, but as a companion to these other ideas. There is no need to memorize times tables or perform speed tests. Proficiency will come with time, but not unless it is accompanied by reason, rationality, and not a small amount of enthusiasm.

I would much rather students understand why they are doing something, to appreciate what the question is really asking, and to think mathematically. This woman clearly misses the point.

Thursday, March 8, 2007

V is for Vagina

It seems that our nation's Puritanical heritage just can't be legislated away. On the same day that the Senate passes a much needed bill mandating medically accurate sex education in public schools, three high school juniors are suspended in New York for uttering the word "vagina" as part of a play reading in a school forum. The popular play "The Vagina Monologues" necessarily requires mention of that part of the female anatomy, but the girls were forbidden by the administration to say it. Instead they were to abbreviate it as simply "V." The school is claiming that the punishment is not about censorship, but insubordination.

First of all, how are we going to provide comprehensive sex ed if we can't say "vagina?" I can think of myriad other terms for that organ that are rightfully considered offensive. (I won't mention them, don't worry.) Secondly, school administrations need to accept that minors are still US citizens. They are still protected by the Bill of Rights. The Supreme Court has been a little wishy-washy on this issue. Certain things, like hate speech, that are protected in society, are restricted in schools. Even me, civil libertarian that I am, understand some of this. Children are different from adults, and we ought to be sensitive to this. But in this particular situation, the school went way too far and the girls were right to make an issue of it. You cannot restrict a person's freedom to speak the name of a part of their own body.

I'm certain that the very officials who were so queasy over the "vagina" will claim to be against teen pregnancy. Well you're not going to keep young girls from becoming young mothers if you force them to speak in code.

Update: Eve Ensler, the author of "Monologues" has agreed to appear on the girls behalf, calling the suspension "a throwback to the Dark Ages."

Monday, March 5, 2007

Scientific Semantics

Being a skeptic, it often troubles me how many Americans reject such carefully tested theories as evolution through natural selection or the Big Bang. There is so much data to verify these theories that it is mind-boggling to me that someone would choose to ignore them. Until recently, I have blamed this phenomenon on ignorance and confusion. I heard people say evolution was "just a theory" as though it were merely a hunch or a guess, no better or worse than any other. This, of course, is not at all what scientists mean by the word "theory." They mean a clear, usually simple, explanation for gathered observations that is both predictive and falsifiable. The general public simply doesn't grasp this.

Recently, however, it occurs to me that certain chunks of the scientific community are not practicing what they preach. Consider the present predicament in physics. There have been no major advancements in the understanding of physics in thirty years, except for possibly the discovery that neutrinos have mass. Instead, the vast majority of the theoretical community are plugging away at string theory or M theory or some other background-dependent scheme that as beautiful and elegant as it may be, has not been supported by any experiment thus far, nor likely to be in the future. Instead, the theories (because there are something like 10^1500 of them) hide just out of reach. That's not the way it is supposed to be. Either it agrees with experiment or it doesn't, and if it doesn't, we throw it out. The music of the spheres theory of planetary orbits was elegant as well. Beauty doesn't keep something from being wrong.

So we can't expect the general public to understand what constitutes a theory if our own scientific priesthood is breaking the rules to suit their own needs. It's just bad science.

Sunday, March 4, 2007

The Hawkman Cometh

Beware of Link, It is Rated R

CAPE CANAVERAL, Florida (AP) -- Renowned theoretical physicist Stephen Hawking, who wrote the best-selling book, "A Brief History of Time," soon will experience a brief history with weightlessness.

Hawking, who uses a wheelchair and is almost completely paralyzed by amyotrophic lateral sclerosis, or Lou Gehrig's disease, plans to go on a weightless flight on April 26, officials at the flight operator said Thursday.

The flight, operated by Zero Gravity Corp., a Fort Lauderdale, Florida-based space tourism and entertainment company, will take off and return to a landing strip at the Kennedy Space Center.

"As someone who has studied gravity and black holes all of my life, I am excited to experience firsthand weightlessness and a zero-gravity environment," Hawking said in a statement.

The modified Boeing 727 generally soars to 32,000 feet at a sharp angle and then plunges 8,000 feet so passengers can experience 25-second snippets of zero gravity during the descent. As the plane climbs, passengers experience 25 seconds of being pushed down hard, as they feel 1.8 times the normal pull of the Earth.

Zero Gravity CEO Peter Diamandis said assistants will be onboard to help Hawking.

"The key thing here is that weightless and personal spaceflight is something available to everyone, even someone like Professor Hawking," Diamandis told The Associated Press. "This something that almost everyone can now experience."

Zero Gravity will pick up the bill, which normally is $3,750. The company also plans to have two seats on the flight auctioned off by two charities.

The company began offering the flights in 2004.
Virgin Galactic promises Hawking space flight

Last year, Hawking publicly spoke of his desire to go into space and made an appeal to Sir Richard Branson, whose company, Virgin Galactic, is building a suborbital spaceship that could be flying passengers as early as 2009.

Branson has decided he will personally finance Hawking's ticket into space -- a flight that would normally cost $200,000.

"He's one of the greatest physicists of all time," Virgin Galactic president Will Whitehorn told AP earlier this year.

Copyright 2007 The Associated Press. All rights reserved.This material may not be published, broadcast, rewritten, or redistributed.