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 It is no longer being updated.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.
Fri, 31 Mar, 2006
Venn and Vesica
There's a lot of familiar mathematics at the beginning of my calculus book, including the aforementioned set theory. It is as I remembered it from my "new math" childhood, where for some incomprehensible reason, someone decided that seventh-graders should learn set theory. What I remember most are the Venn diagrams, named after the nineteenth century British mathematician John Venn who worked them out as diagrams illustrating sets and outcomes of logic problems. For an arty kid like me, anything that made a picture was more interesting than words or numbers, so that's what stayed in my mind. I've always thought that this was a failing of mine, because words and numbers are what really count in this world. Yet I am constantly told by both scientists and mathematicians that pictures and diagrams are immensely important in thinking about science. I still have the nagging feeling that they are somehow less macho and heroic than rigorous, abstract numbers and letters.
To get back to the Venn diagrams: They existed in many cultures long before John Venn's name got put on them. The intersecting circles are known in Hellenistic and Christian lore as the vesica piscis, the fish-shaped form created by the intersecting arcs of the circles. As the learned articles in Wikipedia convey, there is a wealth of non-Christian symbolism to it as well as the more familiar Christian "fish" symbol. The intersection, for Christians, symbolizes the character of Jesus Christ, who has both a divine and human nature, rather than just one or the other. Thus set theory supports theology.
Set theory leads in to inequalities, which I did a fairly long section on back in 2002 when I was re-learning algebra. These are all tricky, with their solutions switching negative and positive in many complex ways, as well as being either closed (including their terminal number) or open (up to but not including the cited number). I remember coloring in a lot of graphs back then, and I was pleased that I still remember how to solve algebraic equations, whether for equality or inequality.
I don't pretend to remember everything, or be able to solve everything as if I had just finished studying it. Back when I was re-learning algebra, I had a strict "no-mistake" rule. I also forced myself to solve every problem in the sets at the end of the chapter. If I couldn't solve it, I kept it until I could ask for help. I should be able to correctly solve anything the book figuratively threw at me. In fact, if I were really a "math whiz," I should be able to solve anything any problem set contained, right away without review, as long as it was something I had already learned. After all, if I were an aspiring high school student, any one of these could be on the upcoming test. And my marks on the upcoming tests, one after another, would help to determine whether I had any future as a scientist. Get too many wrong, and no high-powered, prestigious college or graduate school for me, and no career in science no matter how much I loved it.
But I'm not an aspiring high school student or potential graduate student, far from it. So does it matter whether I get the problems right the first time? For calculus, I've adopted a more lenient, and probably lazier, approach. It's also more pragmatic. I am not in formal school, and face-to-face contact with teachers is difficult and rare. Since I have the teacher's manual for this book, I have the resource to go back to in the absence of a live professor, even at 3 AM. My policy for calculus is to do as many problems as I can, and try to get them right. Then I will refer to the manual and figure out why I got them wrong. After I do a respectable number of them right, then I can move on. There will not be a test.
Posted at 8:38 pm | link
Thu, 30 Mar, 2006
Petals in the virtual wind
Plum blossoms fade,
Cherry trees bloom;
The mathematics of change written in petals.
A gust of spring wind, and a flurry of white petals flies from the plum trees, now shedding their blossoms after an unusually long flourishing. Just as the white flowers fragment into uncounted flying flakes, so the spams and the nametags fly to me in the postal mail and online. I have well over a thousand printed adhesive nametags now, and they keep coming. Yesterday's arrivals were adorned by drawings made by children with cancer, or lavishly colorful flowers of the season. Tomorrow, perhaps more kittens and puppies. If I were to use each one of these labels in the proper way, I'd have to send out more than a thousand pieces of paper mail. In other words, I would become a mass mailer myself.
On line, the hundreds and hundreds of spam e-mails don't stop either, nor the manufactured names which appear with them. The names are like those "virtual particles" which we are told are sizzling around us at every micro-moment, coming into being and disappearing so quickly that "existence" may not be the right word for them. Or they are like the multi-billions of neutrinos, each of them some form of individual existing entity, that nevertheless pass through us every second without a trace. Every spam-name neutrino is different for every recipient, produced by the endlessly inventive combinatorics of the name generators. I have heard from ordinary follks like Erma Mullen, Gilda Marino, Lesa Charles, and Alexander Howard. But I have also heard from fantastic characters like Reannon Cephus, Firdaus Cheeseman, Theodosius Stoker, Eustorgio Bingman, Lamprecht Hylton, Husam Reiff, and one of my favorites so far, Tutankhamon Barsh.
And then I receive spam mails from those names made from dictionary words scrambled together, which can be a constant source of amusement. "Notably U. Worsens" has worriedly e-mailed me, as well as "Chimp J. Freaked" and the macho "Flexed U. Hairiest." "Arsenic R. Factorization" might have sent me a poison pen letter, while "Helsinki G. Bathed" sent a clean bill from Finland. "Dextrous U. Lozenge," as always, tries to sell me (fake) drugs, while "Equivocally D. Curlicue" offers me a low-cost mortgage. But the best one so far recently has been the ethnically relevant "Schmucks U. Birthplace." For me, that would be Boston, Massachusetts.
Their subject lines are cryptic and as always with virtual entities, on the edge of meaning but not quite there: "Trachea result arisen mel," reads one. "Peak formatting georgia accrual," offers another. "It tall rubbery," writes Ada Rutledge. What was tall and rubbery? Lately they have been more enthusiastic, adding punctuation: "At domain hades able?" "With denizen learn oh?" Walker Lacey writes: "Islamabad hey tributary at singular!" And Erin McFarland writes: "Confocal hey dibble in isotopic!" Hey dibble dibble, isotopes are so exciting! If I were schizophrenic, these would mean something. I'm almost there.
Electron readers may be tired by now of my posts about spam and junk mail. They are my seasonal refrains, all of them tied to myriad multiplication of individual entities, whether snowflakes or petals or neutrinos. Our world, as calculus and quantum mechanics tell us, is made not of any smooth continuous substance but a texture wrought of uncountable particles which shimmer and flow, to our macroscopic perspective, together as one surface. The whole living world, both virtual and physical, is built from these infinitesimals. The flying petals, the whispering digital voices, the flutter of a thousand blackbird wings in the trees, the pixels on the screen, the name-labels which plead and cajole, make up our world, where solidity is an illusion sustained only by our distance.
Posted at 3:39 am | link
Tue, 28 Mar, 2006
While transcribing ancient mystical sounds from the cassette tapes of Atlantis to shining rainbow crystal discs is entertaining, the reason I'm here is to learn physics and mathematics, and at this point, that means calculus. I was so frustrated by the little book of Sawyer that I have decided to put it away for now and pick up a much heavier book, a college calculus textbook given to me by a Friendly Mathematician. I hate to disappoint the other Friendly Mathematician who gave me the Sawyer book, but it just left out too much material and attempted to simplify things too much.
I am a step-by-step, pedantic sort of learner, and I need the more comprehensive approach. This next textbook will provide it, I hope. It is CALCULUS by Howard Anton, a well-worn text from 1980. There is an accompanying volume for teachers with all the answers to the problems in it. The Friendly Mathematician told me not to consult that last book, but since I am not in a course with other people and a teacher, I will need it. The book is big, thick, and heavy, though not as heavy as SoyMac the laptop. The cover features pictures of famous mathematicians in a postmodern design. Newton appears in a golden circle, while J. Carl Friedrich Gauss is being hit in the face by a rectangular solid with Descartes' picture on it.
The first few chapters offer a review of precalculus and set theory. I will pass through these hoping that I have not forgotten too much. I have not encountered set theory since my junior high school days, where it was foisted on us seventh-graders under the guise of "new math." That was, uh, quite some time ago for me and I wonder whether I will remember any of it. Looking at the simplest set definitions, it does sound vaguely familiar, though it brings back uneasy memories not of amusing pop tunes of the mid-60s, but of humiliation and failure in my math classes. Well, that was then, this is now, except for the soundtrack.
Posted at 2:48 am | link
Sun, 26 Mar, 2006
The Hiss of the Past
Now that my audio setup is complete, I have been digitizing my old tapes, preserving them for at least a few more years of posterity. Preserving what's left of them, that is. Many of these cassettes are twenty or more years old and I have not played them for at least ten of those years. They were commercially made, but not by any major labels; many of them were limited editions put out by a commune or a guru's followers or a small, private music producer, and never had a completely professional quality. So when I finally play them back, the sound has deteriorated considerably even from what I remember back in the twentieth century.
But I love this music as much as I did back in the late eighties, when I amassed my collection of New Age, obscure electronica, and world music cassettes. I played them over and over again back then, and they seem to come from a more innocent age, or perhaps a more innocent subculture. Maybe anything from the recent past seems to come from a more innocent age. Then as now, I was attracted to albums which would currently be thought of as cloying, sentimental, and simple-minded, full of tweeting birds, tinkling guitars, sparkling tiny bells, and rainbow pink graphics. Used as directed, such music transports me to a warm place where nature is kind and colors are soft and shimmery.
One of my favorite examples of this type of music was the "Golden Voyage" series by Robert Bearns and Ron Dexter. They released six of them and I have five of the set on cassette. These fulfill all the qualifications of the classic "New Age" genre: environmental sounds of birds and trickling water and rain and crickets accompanying short, quiet, slow pieces with simple melodies. In their day, these tapes were used as background music for massage, meditation, or other relaxing pursuits. They were so calming that I sometimes referred to them, and others of their kind, as "New Age Funeral Music."
I searched in vain for updated CD renderings of these albums, but if any had ever been made, they weren't available online. Some sites, either rare record marts or those promoting yoga or meditation, seemed to offer copies of them on vintage vinyl records or cassettes. I wasn't going to easily find them again. Therefore I went ahead and started digitizing the ones I had. Unfortunately, the Golden Voyage had long since passed its better days. Faded pieces of the Eighties met my twenty-first century digital clarity. I could not restore what was lost, but my software was at least able to reduce the hiss of the old audio tape.
I was back in the dreamworld of my old fantasy days, listening to the tinny sound of alien birds and the flow of a pristine stream that had never existed. It was as if I were a space colonist listening, as I have said before, to the sounds of a planet that I would never see again. But now they are with me on my computer, preserved like faded postcards of a vacation paradise.
This kind of music is still being produced. The excellent British commercial and TV composer Kevin Kendle has created a wide range of albums for relaxation and inspiration, with the same warm, nature-filled quality as Bearns and Dexter. And, to his credit, Kendle leaves out the metaphysical and pseudo-scientific themes which led Bearns and Dexter to give tracks names like "Quasars" and "Twilight's Fourth Dimension," as well as writing a text called "The Awakening Electromagnetic Spectrum." Kendle is more directly inspired by nature and the changing seasons. I'll be writing a whole entry about Kendle and his music later on.
As you recall, I searched for harpist Anne Williams and found her still active in Sedona, putting out good vibrations. What about Bearns and Dexter? Their output stops after the mid-80s. There is no information about them, that I can find, on the Great Net of Wisdom. The only thing I heard was a rumor, which may well be true. Bearns and Dexter were a gay couple, and in the mid-eighties, before the modern remedies had been devised, they both died of AIDS. And so ended the golden voyage. But I saved it on shining discs, etched with an awakening laser light.
Posted at 3:49 am | link
Thu, 23 Mar, 2006
Violets in Spring with Audio Cords
SoyMac is now wired for sound. It took a bit of doing. After installing "Toast," the Mac CD-burning program with its related sound recording software, "SpinDoctor," I then had to figure out how to connect my more than forty-year-old amplifier to the computer. I had to go to the Mac Store and get a gadget called an iMic which converts audio signals to whatever goes into a USB connection. Then I had to find the right adapters to connect the iMic from my amplifier to my computer, which is about ten feet away from the amplifier.
I have been using audio gadgets now for the same forty years as the amplifier's age. Along the way I have collected a variety of different cords and connections. I rummaged in my pile of grey and black spaghetti and came up with things that fitted together. The output of the amplifier (the headphone jack) fits a big steel phone plug which was used in the 50s and 60s. My phone plug adapter goes to a mini-stereo plug which served in the seventies and is still widely used today. That in turn leads to a twin-branched stereo fork which came with the iMic and ends in RCA plugs, which in turn fit into an RCA to mini-plug double cable. The mini-plug from this goes into the circular white iMic, which then, finally, plugs into SoyMac with the now-familiar small rectangular USB interface. This cable concoction has plenty of yardage, more than enough to go across my living room floor. It spans not only space but time, moving from the phone plug fifties to the RCA sixties to the mini-plug seventies, all the way up to the USB hardware of our own time. The next connection will not be a plug at all; it will be wireless.
So now I had the connection, and it was time to try the music. What would I choose to record first? I have a lot of tapes, and some of them are out-of-print rarities, beloved only by myself. One of my favorites, which I got when I was working at a New Age bookstore in Cambridge, Mass. in 1987, was VIOLETS IN SPRING by harpist Anne Williams. This 1985 album was produced by Williams and a bevy of other acoustic players and chanters, answerable to "Earthsong Productions" in (where else?) Sedona, Arizona. The liner notes read: "Judgement represents the return of Gaia, the Mother of Life, to Earth…the feminine ray coming back into manifestation…a return in consciousness to the presence of the Mother…" Some of the pieces are: "Goddess Star," "Amethyst Pool," "Crystals Dancing," and the title track, "Violets in Spring." I just love this tape. It's totally sweet and relaxing.
I put the Mother of Life into my nineties-vintage tape player and ran the Feminine Ray through the iMic into my milky Macintosh. My first attempt to register Earthsong's tinkling harp resulted in distortion and noise, because I had the recording level too high. The second attempt was much better. I ended up putting each side onto a separate CD, out of caution in case I lost some of the music, and then re-assembled the transcribed product onto one CD. I won't have to do that again, I can do them now in one session. Thus I saved the return of Gaia from media obsolescence, at least for a few years more. Now I can move on to even more unknown audio recordings, including, I hope, reel-to-reel tapes on which I recorded the sounds of my youth.
By the way, Anne Williams is still around, which is nice to see. She goes by "Ani Williams" now, and she's still coming into manifestation, harp and all. And she still lives in Sedona, a place I hope to visit someday. You can see her website at Songaia Sound Productions.
Celestial harps are much on my mind these days because I am painting a picture of an Angel with a Harp, flying among the towering clouds. This may sound heavenly, except for the lightning bolts and the tornado. Severe weather is predicted for that return in consciousness.
Posted at 3:21 am | link
Sun, 19 Mar, 2006
The Japanese plum blossoms are blooming, and color is coming back to our urban world. I am doing my part at Starbucks and with fashion statements. As you know, I decorate coffee signs at three or four of my local Starbucks. Usually I use art nouveau or deco design elements which I find in my many sample books. But this time I am experimenting with design more in tune with current tastes. Design in this era is frenetic, driving, busy, fast-moving and confrontative. It's not made for languid Art Nouveau ladies but for caffeine-pounding go-getters whose lives move at the bang-bang-bang pace of video games or action movies. Therefore I referred to another design source entirely: Japanese children's game comics. Most of you who are over 15 have never heard of these games and cartoons. I picked a very popular one called "Yu-Gi-Oh" which is played by young folk all over the world. "Yu-Gi-Oh" also comes in comic book form in which characters play the card game in panels jam-packed with action and special effects. Since I have no interest in playing the game or even reading the comic, but only in the Japanese pictorial elements, I turned the comic book upside down and used only the designs with no reference to any character images or cards. Add a lot of coffee to the mix and here is what I came up with for one of my spring Starbucks signs.
Am I finally getting fashionable, by immersing myself in everything Japanese? Will I replace my big-eyed Byzantine icons with even bigger-eyed Japanese animation characters? Will I drop calculus and study Japanese instead? Perhaps I might abandon my Euro-centric fantasy world and re-cast everyone as sword-wielding Japanese? Well, I drive a Japanese car and enjoy sushi, that's a start. In fact, now not only can I drive my Honda, I can wear Honda shoes as well. On one of my many Websurfing journeys looking for colorful fashion accessories, I found that Honda had, at one point, sponsored a collector's item line of sneakers. Some of you know that I am a sneaker collector (very trendy) and that I specialize in orange, with some in blue as well. I was thrilled to find these Honda kicks in ELECTRON BLUE…made to match my car, whose color gave this Weblog its name! What was even nicer, since the Honda sneakers had been discontinued, their price was way low, less than fifteen dollars! Here is the splendid display, on the tailgate of the Electron Car. The difference is that while the car has four-wheel drive, I only have two.
Posted at 2:40 am | link
Fri, 17 Mar, 2006
The Innocent Laptop
And what would its name be? Its milky technological whiteness suggested "SoyMac." It sits in my studio, on but currently "asleep." An eerie, slowly pulsating little cool light on the edge shows its dormant status. The rhythm of that pulsation is uncannily like that of breathing while asleep. The Mac designers doubtless had this in mind when they put that feature in. As I learn the Mac user interface, I see that some "humanizing" or perhaps just "creature-izing" touches remain from the earlier days. Someone wants us users to think that we are working with a living thing rather than a machine.
The theme of computer as living, conscious being has been with us from the very start of their development. There are so many cartoons and movies about it (The Demon Seed, for instance, let alone the most famous one, 2001: A Space Odyssey) that many of us, even the most hard-headed and techno-tough physicists, have a kind of underlying feeling that a computer is alive and conscious. And, at times, not only conscious but angry. It's hard to resist thinking of the machine you use every day for work and play as more than just a piece of hardware, but a companion. Not perhaps human, maybe, but somewhat like a working dog or a clever-tongued parrot, whom you come to depend on. Didn't the folk of earlier centuries name their ships and paint eyes on their bows?
Its pristine simplicity and soft contours feel almost like some kind of health and beauty kit rather than a working computer, as if it could disperse moisturizer or aromatherapeutic vapors. But that smooth whiteness also suggests innocence and purity, rather than the black and silver sportscar design of Dell's gamer models or the prosaic greyish white of office desktops. Then there were those other Macs with the shiny candy colors on them, which I would have been ashamed to use. A computer should not look like a toy.
SoyMac is still barely touched. The only change I have made to its out-of-box state is that I have loaded my favorite pictures into it: erupting volcanoes, glorious blooming flowers, world architecture, astronomical wonders, and cloudscapes. I haven't added any programs into it, although I will do so very soon. Its original state tells me about the culture I live in and what the makers expect the users to want. It came loaded with iTunes which brings me an interesting array of musical possibilities, but hardly any (free) classical music. It was also equipped with an introduction to the online or DVD edition of "World Book" encyclopedia, which I last remember as a hefty series of books which was my favorite bathroom reading in my youth. It was still aimed at kids, though I don't know whether they should take their expensive Mac iBooks into the bathroom with them.
So there it sits, the innocent white laptop, a tabula rasa eagerly awaiting my creative input. In the past, Macintoshes used to smile when they were welcoming you and frown when they failed. Fortunately, (I hope) these logos have disappeared, though their "Finder" still has an abstract smiling face design on its icon. One of the reasons, believe it or not, that I have chosen to use PC's is that they are impersonal and easy to treat as mere hardware. I try to resist the almost biological temptation to consider these things as living beings. But then I see my two other machines, well-used and experienced veterans in my service. There is my truck-like Dell desktop, on which literally thousands of graphic designs, as well as most of my writing, have been done. And there is my sleek silver Dell laptop, named after a Persian angel, now re-assigned to educational duties. Do they regard the pale newcomer as an interloper? Are they jealous? Will I have to mediate between computers of different sects? What will happen when I must end SoyMac's innocence and put it (her) to work?
Posted at 3:30 am | link
Wed, 15 Mar, 2006
Some good things have finally happened to me over the last couple of weeks. One which is provisionally good, and one which is astonishingly good. The first one, the provisional one, is that I seem to have found at least a temporary remedy for the debilitating menopause symptoms which I have been suffering from for the last year or so. The remedy is surprisingly simple and available at any supermarket, and of course at Trader Joe's. To alleviate symptoms, I drink two to three cups of enriched soymilk a day. I happen to like soymilk a lot, so this isn't too much of a chore. Within a week of starting the soymilk regimen, the hot flashes diminished and have almost disappeared, and those I still get are not too bad.
I have tried soy remedies before, but in pill form. The pills were too strong and I got side effects that were just as unpleasant as what they were supposed to help. With the liquid, I can regulate just how much I get per day, rather than having the fixed amount of a pill. The problem, though, is that in my experience, my body gets used to whatever substance I try, so that it is very possible that my 2 or 3 cups of potion will lose their effect. However, it had an effect last year and is still effective this year, so it is possible either to maintain it long-term or go off it and let my resistance wear off. But so far, so good. Enriched soymilk is not fat-free and does contain a few calories, so I must watch myself lest I gain weight on it. But spring and walking season is almost here, so I should be able to work it off. In its "original" form soymilk tastes like liquid plaster. But I can put various flavorings in it and I can also put it in my coffee. A little soymilk in the espresso makes what the Italians, and Starbucks, call a "macchiato," or "spotted" espresso, only slightly adulterated.
The second good thing to happen to me was the astonishing one. I was sitting around with some friends a week or so ago, wondering whether I could learn to use a Macintosh computer even though for the last 15 years or so I have used only PC's. Most graphic designers have "historically" used Macintosh equipment and Photoshop. I have been one of a minority of designers who use CorelDraw and its associated programs. CorelDraw and Corel PhotoPaint are often scorned by designers, and in the past, you couldn't even present a project to a printer in CorelDraw format because their system wouldn't carry or print CorelDraw files. This is no longer true, but Mac and Photoshop are still the tools of choice for professional graphic designers and digital artists.
My friends are all Mac users and allowed me to poke around on one of their Macintosh laptops to see whether the system was really that alien to me. I found that it wasn't at all like the cranky and bewildering older Macs I've used as a "guest." So I finally had some positive things to say about Macintosh. I decided that it would be a good thing to learn Photoshop as well as my familiar CorelDraw and PhotoPaint, for the purpose of compatibility with the larger digital design "community." Perhaps I'd scrape some pennies together someday and buy a Mac, so that I could, uh, "swing both ways."
I thought no more about it for a couple of weeks until just a few days ago. Then my same friends visited me at my workplace in the evening. They led me out to their car, while I wondered what was going on. Did they have a new cat or something? They opened the trunk and there was a Macintosh iBook G4 laptop in a pristine box. "It's for you," they said. HUH? I was stunned. They were giving me a Mac computer! This was not a re-conditioned used one, nor was it a castoff from a high-tech office somewhere. It was brand new, fresh and untouched.
Why would they do such a generous thing? I just couldn't figure out why they would outright give me one…I know how expensive these things are. Did they want some major artwork in exchange? No, all they wanted was for me to use the machine and learn on it and do good work. These are also collectors who own four of my most important pieces (at least so far.).
There wasn't anything I could say other than incoherent thanks. Within a few hours, after I got home, the machine was up and running. Equipped with wireless access, it immediately glommed onto my home network and updated its software. Then I put it to work delivering internet "radio" music. I don't have drawing, painting, and sound processing software for it yet; that will come later. The Mac has taken the space in my art studio occupied by my other laptop, a Dell PC. That, in turn, has been moved into my computer studio where it will help teach me digital art and physics, and I will continue to use it at work for Trader Joe's graphics. I hope it is not jealous of the newcomer.
I have not found a catchy, clever, erudite name for the new computer yet, but I'm sure that one will emerge. The new machine, like soymilk, is a pure, opaque white.
Posted at 3:49 am | link
Sat, 11 Mar, 2006
Accelerating the slug
I worked out the annoying problem in the calculus book, with the help of a Friendly Scientist as well as my own physics textbooks. The screaming yellow "Solved Physics Problems" book helped me out here, though in previous encounters it had not been helpful at all. Besides, it was there at 4 AM when people would not be. This is one of the good things about a modern literate civilization. Books, or nowadays websites, stand in for people. I don't have to wait for the village wise man to hear my question. And I'm not sure whether the village wise man would know formal physics and mathematics anyway.
The problem was actually somewhat complex for my low level of understanding. Not only did it involve weights tied together which pull against each other in two directions, but it was in the "English system" of ounces, feet, and pounds, which is only prevalent in the USA and in some other English-speaking countries. In this system, mass is not measured in pounds, while force is. Mass is measured in a unit called the "slug," which only a couple of my physics books talked about. From reference sites, the kilogram per square meter appears to be about 1.35 times the mass of a slug per square foot, though I'm not sure how this comparison is worked out. The "slug" unit of mass appeals to me because I have a somewhat perverse fondness for these slow, stupid, slimy molluscs, possibly because they remind me of myself in my math and physics journey.
Once I had found the amount of sluggishness, by dividing the weight by 32 (feet per second2), then I was able, with the help of the physics book, to re-calculate the force = mass x acceleration for the problem's components, and figure out the acceleration for the system, which is what the whole thing was about in the first place. The idea is that the velocity increases, or accelerates, as the system moves, and calculus is going to help me find out just what the velocity is at any given instant while it is changing.
I remember doing problems similar to this back in 2002 when I was doing algebra exclusively. I did problems out of my old 1958 college algebra book which required me to find a number of different values which fit into a parabolic curve. Although my 1958 fellow-students had only slide rules, I had a calculator which made things much easier as I plotted my points. There would be one apex point which could be approached by finer and finer approximations, easy enough for the gadget to do. This was before I learned the art of apex finding and curve fitting for parabolas and other algebraic curves. I suspect I will have to review these processes sometime soon.
Posted at 3:15 am | link
Wed, 08 Mar, 2006
Perplexity in the wee hours
It seems that I get into math difficulties after midnight. And by three or four AM, when every other rational, normal, hard-working human being should be fast asleep, I am sitting at my studio table staring at my book, wondering why I am stumped by a totally simple problem I should be able to solve. Now the obvious answer is, if I had been asleep at that time so I could study at some decent hour, I wouldn't have that problem. But I still would have the perplexity.
At this point I would love to ask one of my Friendly Scientists or Mathematicians, "Sorry to bother you, but, uh, what is this all about?" But they, being human beings with real lives, are asleep. I will have to leave my problem at their virtual doorstep, like a newspaper, until they are ready to pick it up and help me with it. But then, this is Internet World. I have co-workers and friends whose lives are so entwined with the Internet that they see nothing unusual in having a circle of friends all over the world. They have intimates in Australia they have never met face to face; they trustingly sell to and buy from people thousands of miles away. If I had a Friendly Scientist who was, say, in Europe, I could e-mail him at 3 AM here and find him perky and fresh with morning energy, reading (and answering) his e-mail before or during breakfast. But I don't. Nor has the Virtual Artificial Intelligence Physicist I described in an entry last year been invented.
I encountered yet another one of those sliding block problems in Sawyer's text. In itself it is rather irrelevant, used as an "aside" to illustrate an introduction to accelerated motion. But it brought back all that work I did on the sliding blocks, with the normal force and the static friction and the kinetic friction and the weights on the pulleys. I hesitate to quote it because there is something really simple about this I have missed. Newton's second law is implicated somewhere, but in the gloom of the pre-dawn hours I do not have his enlightenment.
Posted at 2:55 am | link
Sun, 05 Mar, 2006
Warm Fuzzy Volcano
My friend Sally Byers, also known as "Threadwitch," has created some fantastic cloth and fiber pieces for me over the years, including the "Cartesian Solar Cross" quilt which I exhibited last year. This winter, she knitted me a lava flow. Sally and I are both big volcano fans, and I have given her hundreds of volcano pictures for inspiration. This knitted piece, called the "Lava Shawl," is made of exotic black frizzy-textured yarn as well as appropriately colored chenilles, smooth yarn, and multi-colored yarn. All of the fibers are acrylic, as I am somewhat sensitive to wool. The shawl is in a roughly triangular shape and has a heavy, draped, very soft texture. Its fluffy weave traps a lot of air, making it very warm. It's just right for winter nights, which are not over yet, and for all year round in New England.
Here's the shawl, draped over my office chair:
And here's a view of the shawl compared with real lava.
Posted at 10:18 pm | link
Thu, 02 Mar, 2006
A new month has begun, and my orbit has finally returned to a "point of opportunity" I have passed by more than once. This time I'm taking that trajectory and have started studying calculus for real. This means that I've put away my physics book for now and have opened my calculus primer. I mentioned this a year or so ago, but was more interested in getting some first-year physics done so I put it off.
My Friendly Mathematicians, if they still remember me, are wondering what took me so long. They encouraged me to start calculus back in 2004 but I was too nervous to do it. After all, just about everyone I've met who gave up math said that calculus was the reason. They said to me, "I was great in algebra and geometry, but when I took calculus, it was like hitting a wall and I couldn't get it at all." So the possibility exists that I, too, will hit the proverbial wall and find out that I can't learn calculus. However, in doing even the simplest of physics, I am told that I have already done some elementary calculus. So maybe I'll just climb up the wall and go over it.
Back in 2004 a Friendly Mathematician gave me his favorite introductory book on Calculus. This is WHAT IS CALCULUS ABOUT? by W. W. Sawyer. I looked into it before but found some of its very first graphs confusing. Now I have moved past those graphs and am going on to the next chapter. This book is just a simple introduction, as the author says in his preface, but it does have problem sets to do and will lead into a more formal study later on. Another Friendly Mathematician gave me his textbooks from old courses he had taught, including one massive tome (and its answer book companion) which weighs many kilograms. I expect to heft that set and open it for business later on this year. For now, I have not only Sawyer but another introductory text by Eli S. Pine, optimistically called HOW TO ENJOY CALCULUS. I'll be working with both these books as 2006 progresses.
I am studying calculus not just because it is a worthy challenge but because I need it to proceed any further in physics. Calculus is the next step on the journey I began back in 2000 when I beheld the particle accelerator at Fermilab. Some folks, at my age, get fast cars to jazz up their lives. I don't have a fast car, but I will get the mathematics that describes its velocity and movement.
Posted at 3:08 am | link