My weblog ELECTRON BLUE, which concentrated on science and mathematics, ran from 2004-2008. It is no longer being updated. My current blog, which is more art-related, is here.
Sat, 26 Mar, 2005
The Wrong Answer
I have not forgotten basic acceleration mechanics. I have not lost my mind. Not only was it backed up on disc, but I even found it. It turns out that I have been getting my problems right, not wrong. I agonized over one simple problem, wondering why my answer wasn't the one in the book. Finally in desperation I sent word to not one, but TWO of my Friendly Scientists, and they re-did the problems for me. My answers were right both times. And in the case of the one I was agonizing over, the book's answer was wrong. What an odd situation! This is not the first time I have been hung up over a wrong answer printed in my book. I trust the book, but it betrays me! It helps to have friends to check things for you, and I am hugely grateful to these helpful science guys. (They know who they are.)
I went to the bookstore anyway, and though they were out of the Schaum's series for classical physics, I bought another one specially for high school physics which is a collection of problems and their work-throughs. This should save wear and tear on my Friendly Scientists, whose time and attention are precious resources I cannot afford to waste or use frivolously.
One of my problems, as one of the Scientists has pointed out, is that I use so many different textbooks. This confuses me. Each one has a different order in which it presents its classical physics subjects. And many of them use different letters to designate the basic quantities that are to be worked with, like distance, acceleration, or velocity. Some of them use calculus, and thus I cannot yet work with them. Others are so simple that they don't have enough problems to work through.
I need books with lots of problems in them, because the only way I really learn anything is to work doggedly and determinedly on one after another after another after another. Most of the time I forget the problem as soon as I have solved it, so that in a week I can go back to it and solve it again as if I had never seen it before. But after a few repeats, problems get used up, so that I have to find new ones to work on. That's one reason I have so many books. The textbooks, unlike the review books, have that annoying feature of only showing the answers to the odd-numbered ones. I can't always check them myself. Where is that artificial intelligence when I need it?
Soon I'll be learning about circular motion, levers, wheels, cranks, tension, and torque. That will probably make me suitably cranky and tense, and probably torque me off. But I sure love solving them problems.
Posted at 3:13 am | link
Wed, 23 Mar, 2005
Physics Miseducation and Virtual Teacher
Before I get into the cranky part of this entry, I want to thank Sean Carroll, the intrepid cosmologist of "Preposterous Universe," for giving me a mention as "one of the cool kids" (even though I'm a lot older than he is). I am delighted to be part of the dark matter of the Blogosphere.
Now to the cranky part. I am reviewing straight-line motion and acceleration and distance yet again. This must be about the fifth time I have tried to learn this. I thought I learned it in 2002. I thought I had learned it in 2003. I thought I had surely learned it in 2004. (This assumes that in at least two of these years I even reviewed it twice.) But here in 2005, I am getting the wrong answers to the problems again. Why? How could I forget it so easily? I remember the formulas about acceleration and time and distance, but somehow when it comes to solving problems about these things, I lose out again and again. It's so frustrating.
One of the sources of my difficulty is that I am using not just one book to learn my classical mechanics, but a whole stack of them that reach from that dreary, heavy little tome from 1952 to a couple of current ones which are very lightweight, that is, figuratively so. I can't remember which one I used to teach me acceleration and motion the first time around. Each one takes a slightly different approach. Even the formulas are stated slightly differently. I want to re-trace my path to the one which first taught me, but which one was it? I am trying my own patience.
One of the most frustrating things about textbooks is that they only give answers to the odd-numbered problems. One of my Friendly Mathematicians once said that I should never even have the answers available to me. That might be right for a classroom, but if I am just struggling with it myself, how would I ever check my work? I cannot call up a Friendly Mathematician at 3 AM to ask why I didn't get the right answer. I have to go over it again and again and again. Sometimes it turns out that I mis-copied a number. Or added the wrong things; in other words, it was a failure of procedure. But if I really do misunderstand the process, I have no way of checking it other than to apply for time with a Friendly Mathematician/Physicist and wait till he can get back to me.
I'm often asked why I just don't take a course in this stuff and learn it that way. Well, the thought of sitting in a classroom to learn physics or math fills me with an unspeakable dread. It brings back every humiliating memory of my childhood, of being left behind further and further while the other kids went on learning. Would I be willing to do that again, this time outstripped by fresh young things thirty years my junior? I'd rather grub it out on the Internet and with my stack of learn-it-yourself books. Let me tell you, any textbook which is called "(Subject) Made Easy," isn't. They leave out too many steps in order to try to make it "easy." My best books, like the Schaum's Red Spine Book for trigonometry, put in every last little detail and give worked-out problems in pedantic, but satisfying multiple steps. I think there's a Red Spine book for classical physics. A few more bucks at Borders and it can join my tottering stack.
But here's an idea I've had for a long time. Our "virtual reality" technology is nearly able to create immersive, realistic "worlds." In fact, it is already there if you consider the elaborate scenes and characters from online games like the amazing "World of Warcraft," which a player friend showed me recently. What if there were online "worlds" for learning things rather than playing games? There, it would not matter how old you were or how fast or slowly you could learn. The online teaching area would be a safely maintained space, without harassment or pressure, where a virtual teacher existed only for you, or you and a few friends if you wanted. You could "order" the ideal teacher complete with a "personality" made to order: either a kindly gentle soul or a stern taskmaster or anything in between.
I got this idea from a famous book by Neal Stephenson, SNOW CRASH. In the course of the book, the hero, cleverly named "Hiro," enters a virtual library which is presided over by a virtual librarian, who does the research work on a hyper-wow search engine that covers the whole Earth. (This book was written in 1992, just before the beginning of the World Wide Web. Before Google. Like another century ago, man…) The hero meets the Librarian in this passage:
…"A man walks into the office. The Librarian daemon looks like a pleasant, fiftyish, silver-haired, bearded man with bright blue eyes, wearing a V-neck sweater over a work shirt, with a coarsely woven, tweedy-looking wool tie. The tie is loosened, the sleeves pushed up. Even though he's just a piece of software, he has reason to be cheerful; he can move through the nearly infinite stacks of information in the Library with the agility of a spider dancing across a vast web of cross-references….He is eager without being obnoxiously chipper; he clasps his hands behind his back, rocks forward…raises his eyebrows expectantly over his half-glasses.…
…"Hiro says, "You're a pretty decent piece of ware. Who wrote you, anyway?"
"For the most part, I write myself," the Librarian says. "That is, I have the innate ability to learn from experience.…" (Neal Stephenson, SNOW CRASH, pgs 107-109)
Now this Librarian from Stephenson, the way he looks and acts, could just as well be a Physicist. I am not talking about the little army of ugly animated cartoon Einsteins which you see at physics sites and elsewhere. This would be a realistic, lifelike piece of teaching software. It would never be too busy to help me, it would never be asleep or worried about tenure or grants, and never be away from its post. It would write printable equations on a virtual blackboard, and most of all, it would, like Stephenson's "Librarian," learn from how I try to learn (and from parameters I could input, as well) until it knew just how to explain things to me. And best of all, it would be software, not a real person, so I could not bore it, exhaust its patience, or insult it. It would work with me until I finally learned what I needed to know. Then it would suggest that it was time to do something new. And while we're at it, you could encode psychological insight and realistic dialogue potential into it, so that when I was feeling down because I couldn't manage to review simple acceleration again, he would encourage me. (Being the kind of person I am, I'd probably write an entire personal history for him, so that he'd be a real fictional character.)
Someday soon, things like this will exist. But for now, it's back to my growing stack of books, and yet another attempt to accelerate.
Posted at 3:32 am | link
Mon, 21 Mar, 2005
Sunday night is the worst time of the week. It's the smoldering stub of the week, the time that I realize that I have used up yet another seven days of my life. Even before I got the day job, I felt like this. It will not get any better as I get older, either. Even if I have a pleasant social engagement or some other nice thing on Sunday night, it still rolls around to the wee hours and the darkness and the sense that I am not achieving as much as I would like to. At the pace I am going, I will be sixty before I get to quantum mechanics, if I get there at all.
I am reviewing acceleration again. I have lost count of how many times I have gone through this material, but I have to do it again to get to new material in the book directly after it. It's not that I forget it; a quick review brings it back to me. But I still get that horrified feeling for a quick moment, looking at it, that I have never seen this before, that those numbers and square roots and symbols on the page are just incomprehensible squiggles. Then I remember what they are there for, and it's like a camera lens focusing in on something and bringing familiarity with it. Distance divided by time equals velocity (speed). The change in velocity divided by time elapsed equals acceleration. Find the distance covered, by multiplying…etc.
Today is the first day of spring, and in my area there was weird weather. There was a rush of dark clouds, and the first thunder and lightning of the year, followed by a rain of large, snowball-like hail. The projectiles were not hard pellets; they were wet skwushy chunks of ice and liquid water that went splorch on my car as I was driving. After a thick fall of splorches, the rain fell, and then the storm was gone, as quickly as it came. Let's see: a wet hail chunk falls out of a dark cloud at a specified height. How long does it take to arrive at your windshield with a chilly splat? And how long will it take for spring to really arrive?
After I make the accelerating raindrops make sense again, I am off to circular motion, and then into the next Newtonian room of forces, momentum, and orbits. After that, according to my Barron's physics book, I will once again enter clanking industrial workshops full of simple machines like pulleys and levers and gears.
The Spring Equinox is also the Persian New Year. I wish all my Persian friends a very happy, prosperous, and light-filled New Year. And for all the musicians in my life, happy Bach's birthday.
Posted at 2:33 am | link
Wed, 16 Mar, 2005
I am finishing up my work with vectors in classical mechanics. The Agave Worm book has given me lots of problems finding vectors from triangles, using the sine and cosine formulas, which I remember well from my tedious 8 months of trigonometry. I can then find the resultants of the vectors, a process which is done with trigonometry. But tediousness is my talent. I am evolved to do dull, detail-oriented, non-risky, repetitive work, if you believe some evolutionary psychologists.
But the problems with vectors, force, weight, tension, and distances put me into a rough-hewn, industrial world full of heavy lifting, sliding blocks, cranes, brackets, bolts, metal frames, ropes, guy wires and towers, ships and planes and oil pipelines and the occasional artillery shell or missile. I feel as though I should be wearing a hard hat and work boots when I solve these problems. Some of the problems even have a kind of dark "gothic-industrial" feel, as with these two from my vintage 1952 text:
2-8. A horizontal boom 8 ft. long is hinged to a vertical wall at one end, and a 500-lb. body hangs from its outer end. The boom is supported by a guy wire from its outer end to a point on the wall directly above the boom….
2.18. A flexible chain of weight w hangs between two hooks at the same height…at each end the chain makes an angle theta with the horizontal….
It reminds me of the famous "Prisons" etchings by the eighteenth-century Italian artist Piranesi filled with ominous machinery, sooty furnaces, and shadowed massive archways. Here is the land of classical mechanics, grinding its way into the earth, weighted by Newtonian gravity and trigonometric tyranny.
Posted at 2:02 am | link
Fri, 11 Mar, 2005
Basic Technical Mathematics With Agave Worm
I've done a lot of vector problems, and will do a fair number more. But I think I've pretty much gotten the idea of it, deconstructing the different quantities and directions that describe force and velocity and other vectorized entities. When I've done enough problems so that it is almost automatic, then I will declare vectory and go on to something else. "Physics Made Easy" wants to teach me momentum, fluids and density, orbits, torque, pulleys, and work, though not in that order. One thing that mystifies me about classical mechanics is that it seems that it is composed of many different sectors of different sizes, each with its own set of problems. But these sectors don't follow one after another, like the chapters of a narrative. They all fit together under Newton's roof, but it seems that you can visit one room after another in any order you want. This confusion is probably because I am doing this on my own, rather than in a class where the schedule is what the teacher says it is.
The text I am using with the best section on vectors is a big thick old college text called BASIC TECHNICAL MATHEMATICS WITH CALCULUS, Fourth Edition, by Allyn J. Washington. (No text-writer's name can beat the co-author of my Geometry text, "Phares O'Daffer.") I found this book on the overloaded shelf of some friends of mine, a heavy, dust-collecting clunker left over from college days, and they were only too glad to give it to me. "Basic" covers the algebra I studied in years one and two, as well as much of the trigonometry I struggled with in year four. It is very useful for reviewing material. The calculus begins well into the book, on page 646.
The title of this book reminds me of some sort of food or drink combination, in which something simple has something extra added to it. Kind of like tomato juice with clam flavor added, or tortilla chips with chili and lime. Or, to continue the Southwestern theme, tequila with agave worm. I am not a tequila drinker, but I have seen plenty of ads for tequila which claim that there is a worm in the bottle. Here is the official word on the worm in the tequila bottle. You have to scroll down a bit to "Tequila Myth #1" to find the worm. In the case of "Basic Technical Mathematics," calculus is a big worm.
Posted at 3:17 am | link
Sun, 06 Mar, 2005
One of my Friendly Mathematicians has referred me to an article which appeared recently in the ECONOMIST Magazine. The article describes a rare form of synesthesia. Synesthesia is the perception of two usually unconnected sensory perceptions simultaneously, such as hearing colors or seeing notes. In the case cited in the article, a professional musician perceives notes as tastes. She also perceives notes as colors, but the association of musical notes with tastes is rarely observed.
Earlier in this Weblog, I described my own synaesthetic perceptions of numbers as colors. Interestingly, the more math that I do, the less this happens. Or perhaps I pay less attention to it. But I have never experienced a synesthesia of taste.
Fascinating, then, how musical notes can turn into flavors. But can it run the other way? Could every gourmet goodie at Trader Joe's translate into mathematics? That way I could have the algebra of salad mixes, the solid geometry of cheese, the trigonometry of triangular tortilla chips, and the calculus of chocolate!
Posted at 1:49 am | link
Sat, 05 Mar, 2005
I am doing vector problems. Lots of them. I find the vertical and horizontal components of one, or I find the resolution of two. If asked, I will resolve more than two together. This is why I learned all that trig last year. Whether force, velocity, or displacement, it is all vectorian.
Some time ago, a Friendly Scientist told me that the more physics you do, the more your view of the world changes. You see physics all around you. Even with my so-far limited encounter, I can see that happening. When I am driving in the Electron Car, I am vectoring. When other cars come near me, they are also vectoring, and hopefully not intersecting my own vector. My butt sitting in the computer chair is a vector, and so is the computer chair's "elastic recoil." The world is full of interacting objects: it is a vector world.
How much can my world-view change? When I am in artist or fantasy mode, the world is not full of abstract vectors, forces, and counterforces. It is full of stories and colors and mythology and symbolism and theologies and stacked universes of holy, unholy, alien or angelic beings. I used to live exclusively in that world, with only brief and necessary visits to the world of ordinary reality to pay the rent. Now I find myself commuting between the abstract, mathematical world of physics and the world of fictional or religious imagination.
Some people don't have this dual citizenship. Some live in a world of religiously described reality in which miracles happen in the "real" world and the stories in the holy texts are literally true. Others, including many (perhaps most?) scientists live in a non-theistic, non-fantastic world where there is only one criterion for "true" reality, namely experimental proof and mathematical description. Most other folks live somewhere in between, with less logical rigor.
What if there were metaphysical vectors? Vectors that gave us the vertical and horizontal components of our beliefs? Vectors that gave us the direction and speed of our journeys between different world-views? Or even moral vectors? When I was doing my research in Zoroastrianism (see my main webpage for more on this fascinating ancient philosophical religion) one of my teachers was the noble and learned Parsi Zoroastrian Kaikhosrov D. Irani, who was at that time a professor of philosophy at City College of New York. Dr. Irani had studied chemistry and physics, and his specialty was philosophy of science. He used to explain the difficult problem of moral and ethical dualism in the Zoroastrian religion by the metaphor of vectors. Zoroastrianism teaches that the forces of good and evil are always in conflict as long as this world exists, though at the end of time good will triumph over evil. But where are these forces of good and evil? Are they in the material world, corrupting not only humans but non-human things, or are they only in the world of human psychology and behavior? Dr. Irani said that "good" and "evil" existed not as personified, conflicting entities, but as vectors, directions and magnitudes of forces that had the potential to exist, but did not actually exist until something went that way. And perhaps in that way you could resolve the ambiguous moral world into components: an x of evil and a y of good.
Posted at 3:12 am | link
Tue, 01 Mar, 2005
Early on in my ambitious project, one of my Friendly Mathematicians gave me a set of college physics books from his own earlier days. At that time, I lacked most of what I needed to work with the books. But now that I have studied intermediate algebra, trigonometry and a little bit of calculus, I can apply my knowledge and work with these books. The one I am using now is a tome from 1952 (before I was born) called COLLEGE PHYSICS: Mechanics, Heat, and Sound, by Francis Weston Sears and Mark W. Zemansky. This was the second edition. The seventh edition was published in 1991 and is available for the whopping price of about $144.
Classical mechanics, which is what I am learning, hasn't changed since 1952, so I don't have to worry about the updated edition. This antique physics book is certainly good enough for what I need. I am working through the chapter on vectors, which is more complete than the Barron's book. It contains exciting (at least to me) problems involving not just two vectors, but three or four, which are resolved by finding their vertical and horizontal components and their resultants, and then re-vectoring those. In the Real World multiple vector situations occur all the time, including those inclined plane problems which I have been dealing with. There are some of them in this book.
Sears and Zemansky 1952 does not have the same undertone of Cold War paranoia that my 1958 college algebra textbook did. You'd think that it would, since 1952 was at the height of the McCarthy era and the early proliferation of nuclear weapons. But this physics text is as dry as it gets, colorless, compact, and grey, with purely abstract physics illustrated by purely abstract texts. This is the stereotype of science I grew up with: the impersonal, objective man thinking impersonal, abstract thoughts. There is one moment of zany humor, though, slipped into a problem set about gravity and acceleration on page 63:
"4-13. A student determined to test the law of gravity for himself walks off a skyscraper 900 ft. high, stop-watch in hand, and starts his free fall (zero initial velocity). Five seconds later, Superman arrives at the scene and dives off the roof to save the student…."
The problem assumes that Superman is subject to the same forces that a normal object with mass would encounter. But comic book fans (I am one, despite my inappropriate age) are still debating whether he is at all subject to the law of gravity when he flies, or whether he can stop and hover in mid-air. And what enables him to fly in the first place? Now whoever finds that out, will have done some world-shaking physics.
Meanwhile, a correction to my entry of February 27. I wrote that the sine of the angle of incidence would give the "normal" force perpendicular to the incline. That should be the cosine of the angle of incidence. The sine will give you the magnitude of the force parallel to the inclined plane. Please excuse, this is new material for me.
Posted at 3:29 am | link