The days are longer, but it's still the dead of winter. It's cold and snowy. I am still doing the most basic and elementary physics; I just did my end of chapter review about acceleration and vectors and gravity and orbits. I think my physics and math studies are orbits and not straight-line acceleration. I think sometimes I am just going around in circles. I never knew the formulas for acceleration going around in a circle before. I feel as though I have to apologize to my scientific readers. To them, this must look sort of like an illiterate over the age of 50 trying to learn how to read. When I read all this exciting stuff about dark energy and black holes and neutrinos and quarks and string theory, etc. I sometimes feel I should stop. I shouldn't tempt myself by wanting to learn about anything except the beginning material I have at hand. I must somehow earn my way to a real appreciation of string theory, dark matter, other universes, etc. by clawing myself up the wall of physics, bit by bit. Until then, I shouldn't look up, and maybe not even read anything more, at least for now, from those scientific weblogs. I have 23 problems about acceleration to do next.

I am just about to finish "Project 911" and when I do you will see it through the marvel of the Internet, which was made by people who managed to get beyond first semester physics. The question has arisen as to whether "Project 911" is SERIOUS art. It is possible that nothing I do could be legitimately called "serious" art, simply because I am the one doing it and I have an inadequate, or shallow, or commercialized conception of art. If that is true, then I will let you, the viewers, be the judges of whether 911 is "serious" art. There are a lot of artists who don't even concern themselves with "seriousness," but then, they may not be serious themselves.

At one point long ago, someone told me that I should only paint "recognizable" satellites, spacecraft, and cosmic subject matter when I was doing space art. I should paint pictures of The Orion Nebula, for instance, or other sky wonders shown to us by the Hubble Telescope. I am not sure why this person suggested that, other than a misguided desire to see me sell pictures or perhaps just a lack of imagination. I never took that advice, since in my opinion the Hubble photos speak for themselves and need no artistic imitation. Many years later I mentioned this to a Friendly Astrophysicist, who actually works with the Hubble telescope. Could I, uh, "make up" nebula or galaxy scenes which were not actually documented by Hubble or other telescopes? This seems a rather silly question in retrospect, but the Astrophysicist replied sincerely. The gist of the answer was: It's a big universe. There are countless nebulae and countless galaxies. Anything you could make up probably looks like something in some remote galaxy. We and our instruments will never see it, but we can assume that it is out there somewhere, orbiting in the black winter of distant space.

Posted at 2:14 am | link

Over my four years learning mathematics and physics on my own, I have often been asked whether I am going to go into it professionally, and be a "career-changer." America is full of people like this, who drop their high-powered careers as lawyers or doctors or architects or, yes, scientists, to do something completely different that they love to do. A lawyer goes back to school and becomes an elementary school music teacher. A doctor decides to leave medicine behind and run for political office. An architect becomes a restaurant owner. A physicist drops out of science and becomes a romance novelist. (All of these are real-life examples.) So why not change my career (puny and unprofitable as it was) and go into science or engineering professionally?

Anyone who suggests that has no grasp of the reality of careers in science. I have been spending quite a lot of time reading Weblogs written by professional scientists about their work and lives. After a year or so of this kind of reading, they have convinced me that even if I were young and just starting out, I should not choose this line of work. They have painted a rather miserable and unattractive picture of what professional science, at labs and industry but especially in academia, is like. First, competition is relentless, or whatever word is even more than relentless. Not only are you working those 80-hour weeks as a graduate and post-doc, you are under pressure constantly to publish, publish, and produce. As a professor, you are stuck with endless faculty and teaching duties which crowd out your time for your own research. You spend more tedious hours applying for grants. If you are working in industry or a laboratory, you are a cog or sprocket in a huge corporate entity of hundreds of people, and (unless you are the boss or some sort of higher-up) you will only experience the thrill of discovery and achievement in a collective sort of way. Some good and humble people don't mind that sort of team-based approach, but if you are an ambitious individualist, forget it. No Nobel Prize for you, sorry.

If you think you are going to make any money with a PhD in physics, these writers disillusion you. The jobs aren't there. Unless you are a computer genius, your chances of making bucks with your professional qualifications are low. Not only that, there is always someone from India or China who will do your job for less and work 100-hour weeks to top your 80-hour weeks. If you aspire to be a theoretical physicist, for instance a string theorist, your chances of actually becoming a professional in that field are equivalent to a sandlot player getting into the big leagues. Many physicists have written, basically, that physics is closed. The field is full, no new people need apply (unless they are from China).

It's a big difference from the picture of science that is offered to layfolk. I have dozens of books that romanticize the practice of science and have scientists (usually now deceased) talking about how much they love their work and how they make discoveries, do exciting things like visit observatories in remote places, or stand in wonder before some glorious phenomenon. Television programs such as one I recently saw about the Mars Rovers show roomfuls of clean-cut, youngish science types repeatedly cheering as their machines landed safely, sent back the first pictures, got unstuck, and wandered off into the ruddy desert of Mars. (They're still going, after more than a year!) But again, your chance of being one of those cheering scientists is about as much as a street ball player getting into the NBA.

Even so, I wonder whether if I had my life to live over, and I could start young again, would I choose to be some kind of scientist rather than an artist? In my own life, this was so not an option that I never even thought about it. Now, as I plug at my little increments of classical mechanics and beginning calculus, the notion of going into a scientific career has floated by me. But there is just too much reality to consider. I can dream about the romantic image of science and scientists, but I know it is, like most romantic images, an illusion.

Also, I know my weakness. I am not good in competition, and I'm petrified of difficult, high-pressure tests. I have never been able to hold my own in aggressive intellectual confrontation, and would not be able to win those science contests that show off the talents of teen scientists. I am too lazy, not to mention too old, to work 80-hour weeks. I like my low-key bohemian lifestyle. And, well, I like doing art too much. If I went into a science career, that is, graduate school and postdoc work, etc., I wouldn't have any time to do art any more. Now I am well aware that the wide world would not be diminished if I never painted another picture, but my local circle of friends and collectors probably would be disappointed. I cannot claim to have had a "brilliant career" doing art, and I may have a dim future as an artist, but it is something I keep coming back to and I don't get bored with it, though I may be confused as to what I would like to paint.

Some of my wiser friends have suggested that I will end up doing something on the outskirts of science, such as art on scientific (physics or astronomical) themes, or science writing. This is much more plausible for me, though it isn't as hard-edge macho as being a "real" scientist. Then why do I keep wanting to do mathematics and physics on a mathematical level, rather than just getting inspired by non-mathematical books to make pretty abstract pictures? What is all that studying and problem-solving for? I regularly ask myself that question. If I'm not going into it professionally, why bother? Do I have to keep coming up with reasonable reasons for doing this?

I will let someone much more eloquent than I, say it for me. This is from John F. Kennedy's speech in September of 1962, when he announced that the USA would put a man on the moon before the decade was ended. JFK, who was so romantically portrayed in his day, had this to say:

"….We choose to go to the moon. We choose to go to the moon in this decade and do the other things, not because they are easy, but because they are hard, because that goal will serve to organize and measure the best of our energies and skills, because that challenge is one that we are willing to accept, one we are unwilling to postpone, and one which we intend to win, and the others, too."

Just substitute "study mathematics and physics" for going to the moon, substitute "my" for "our," and "learn" for "win." Perhaps I should apologize for being pretentious and "above myself" here. Reality is always ready to correct me.

Posted at 3:59 am | link

The latest news from the Huygens probe says that the terribly cold landscape of Saturn's moon Titan has rivers, lakes, and even rain made not of water, but of liquid methane gas. As the scientists put it, Titan has a landscape which is strangely similar to Earth's, but the processes which form it are done with very different materials. This successful voyage to Titan is one of the things which keeps me from falling into total despair about the human world.

Those who follow space art, hearing about Titan, will easily recall the view of the planet Saturn from Titan as painted by the greatest American space artist of all time, Chesley Bonestell, one of my art heroes. When Bonestell painted that famous picture in 1944, no one knew what the surface of Titan was like or whether the sky was clear or cloudy. Nowadays we know that an observer on that moon would not be able to see Saturn due to the clouds which cover the whole sphere. And yet the Bonestell picture shows deposits of snow which need not be water, but some other frozen organic compound, just as it might be on the planet. And there may indeed be craggy mountains somewhere on Titan, since the probe could only show us a small area. The rest of Titan will remain unknown, at least for now, a world of perpetual winter, where January never ends.

Posted at 3:26 am | link

The very injudicious remarks of Lawrence Summers, the president of Harvard, about the "innate differences" of men and women in regards to science and math have made national news and are all over the "blogosphere," the network of Weblogs. You can read a summary of Summers at this location, if you are interested. The event and the little storm of controversy it has unleashed brings me again to a subject which is constantly on my mind as I pursue my own math and physics quest. Namely, that of gender. I cannot achieve the kind of righteous indignation that some of the women scientists in the discussion have. What I feel is more like depression, because despite all their protestations, I still suspect that what Summers said has some truth in it.

I haven't talked about gender too much on this Weblog, not because I don't have anything to say, but because it would enrage and alienate some of my readers. And I don't have that many readers anyway so I don't want to lose them. I have noticed in my discourse with scientists that as soon as I bring up the gender issue, they either stop talking to me, or they ignore me, or they deny there is such a problem. (This is true even with the female scientists I've talked to!) Not all my scientist contacts are like that of course, and one or two of them (you know who you are) have been courageous, or patient enough to rationally discuss it with me. But most of the time, it's better for me not to bring it up because I want to be diplomatic and learn physics.

Therefore I won't go off on a long personal diatribe on my unhappy personal history with mathematics and science and how it relates to being female. I can provide you with my rant in private correspondence, if you are truly interested in such a thing. But as I pursue the path I was called to back in 2000, I know that I am at a disadvantage, because I did not get the background I needed when I was young. And if Summers and those who support his views are right, I was born with a disadvantage due to my gender. And even more, not only don't I have the mental watts to light up the physics bulb, I'm far too old to have the mental athletic ability needed to leap those mathematical hurdles and do the Olympic gymnastics that spring through space and time. I'm just beginning to study math and physics at an age where (according to what I've read) most mathematicians and physicists have finished doing their best and most creative work.

It doesn't help that I obsessively read the personal web pages of physicists (of both genders) and find out how active and energetic and young and brilliant they are. They travel the world the way I travel my local neighborhood. Seems like not only do they smash atoms or spin string theory in their working days, on their off-days they hike in the wilderness, climb craggy mountains, run marathons, ski deep powder snow, play the saxophone in hip jazz clubs, or do other super things. Jeez, I can barely get out of bed most days, especially in winter.

So when I do even a modest bit of mathematics or physics, like vectors (which I am now reviewing) it's a major victory for me. It comes down to a matter of scale, at least right now. And I do have some basic and important advantages, as a friend pointed out to me. Not only do I have the underlying (and rare!) advantage of being able to function as an independent female in a technologically advanced society, I am not faced with the pressures of school or family. And I have something which can overcome any disadvantage, even far more than the ones I have quoted. I have determination. That alone is going to take me a long way.

Posted at 2:49 am | link

I am currently reviewing scientific notation with my Barron's text. I am very pleased so far with this text because it is explaining some totally fundamental things to me that I never learned. I should have started physics directly with this text rather than going to other, more cursory introductory texts. For instance, it has explained to me that some labels of measurements are considered fundamental, like meters and kilograms and seconds, and other measurements are made of ratios of these quantities, like meters per second, square meters, or kilogram per cubic meter. When I first encountered these composite quantities, I was mystified as to why two disparate measurements were being "mixed" together.

Similarly, with scientific notation, though I was already familiar with the concept and had worked with it before, I had wondered how one does addition and subtraction with numbers in this form. When I asked a Friendly Mathematician how this was done, he replied that you "normalize" the numbers and make their exponents of 10 the same. I had no idea how to do this, until the book explained it to me. The decimal point moves back and forth, and you can increase or decrease the ten exponent by moving the decimal point on your number. My mnemonic is one of contrary motion. If the decimal point moves one point to the left, the exponent increases in volume by one. If the decimal point moves to the right, the exponent decreases in volume. If it's a negative exponent, you have to remember that an increase in volume means that the "number" goes down, as in -3 going down to -2. And vice versa. That's how you normalize.

Books are patient, books are kind. They stay up with you all night and never complain that you are taking up too much of their time. They are never too busy to help you. They don't complain about being insulted and they rarely (if they are well-written and helpful books, that is) make you feel belittled or stupid. A book will not condescend or laugh at me because I am doing the most basic things over again. And you can work with a book at your own pace. My own pace, in physics, has been exceedingly slow. I also have a very narrow point of attention; big spreads of information intimidate and frighten me. I once said to a Live Physicist that I am learning physics one electron at a time. He replied that this would mean that the time-span of my learning physics would exceed the projected life-span of the entire universe. Well, it may indeed take me that long to get to any kind of advanced physics. But I might as well start where I am, and keep going.

Posted at 1:40 am | link

I catalogue my artworks by number, and have done so for almost thirty years. I assign numbers not to individual artworks, but to art projects which result in one or more artworks. There are often many different pieces in a series under one number. The actual artworks in a given series receive a main number and a letter that designates the order in which I did them. Larger or "stand-alone" works of art simply receive a number.

I started with number 1 in the fall of 1976. Interestingly, I met the owner of Number One after 28 years of no contact, at the World Science Fiction Convention in Boston last year. He said that he remembers it but the original artwork, which was no bigger than a business envelope, has long since disappeared due to the many moves and unceasing domestic clutter of his life. I remember it too; it was a little watercolor depicting "Elric," the albino knight of the Michael Moorcock series. (None of the art on that site is by me, unfortunately; it is by artists Michael Whelan and Robert Gould, among others.) Back in 1976, I was very fond of the Elric fantasy series. I haven't read an Elric book or done an Elric picture in about 10 years.

Back to the catalogue. In the old days, when I did lots of tiny pictures, numbers went quickly and I went through the first five "centuries" or so in a few years. But as I did larger works, or larger series with more sub-headings, the count went slower. As of January 2005, more than twenty-eight years after starting my catalog, I am now in the 900s.

I wonder if all this methodical and numeric art cataloguing means that even when I was an ignorant math-incompetent artist, I had the nucleus of a mathematician and scientist within my color-ridden mind.

I tend to mark "significant" numbers with "significant" pictures. Thus the artworks which get assigned "century" numbers are important to me. Number 600 accompanied one of my first published articles, in a long-gone and much-missed magazine about Western esotericism called GNOSIS. Number 700 was a major project I did in 1992, the "CorelDraw Tarot," in which I used my primitive computer graphic resources to do a more than slightly ironic Tarot Major Arcana. This art still exists, though in a degraded state due to its translation through subsequent versions of CorelDraw, up to CorelDraw 11. Number 800 was a big commission, CITY OF LIGHT, painted in 1995, which can be seen at my main Website's art gallery. And number 900, painted in 2003, was an architectural/religious fantasy, mixed with science fiction, called "The Cosmic Cloister."

By the year dates, you can see that it took me eight years to get from number 800 to number 900. As of January 2005, I am working in the second "decade" of the 900s. Last fall, I came to number 911, which was made only too significant by the events of 2001. So I decided to dedicate project number 911 to a commemoration of the cataclysm, in whatever way I thought best.

This is probably an insincere way of making art. I was as horrified and saddened as most Americans when it happened, but I didn't lose anyone I knew and had no personal connection to it. My feelings about 9/11 and how our world has changed since then are confused, if I have feelings at all about it. I don't have anything "important" to say. Really, I am just doing a 9/11 picture because my catalog got to number 911.

I decided to take it seriously, though, and set out to do a geometric abstraction which would be a meditation on the architectural forms which were destroyed or damaged in the attacks. I am doing a lot of geometric work these days, along the lines of the blue and orange picture ("Earth-X") which is at the header of this Weblog. Project 911, a single picture, is a network of straight lines and circles, with a central roundel in which the two rectangular blocks of the lost World Trade Center towers are inscribed. A pentagon intersects another circle nearby. The predominant colors of this picture are somber greys, dark blues, and mid-blues, with one bright accent of red in a central place. It is acrylic on a black-surfaced illustration board, 20 inches by 16 inches. The title will be, "The Geometry of Remembrance."

Due to time constraints, I can't paint very much on it at any one session, but it is getting done and I will show it to you all when it is finished. I've been through eight centuries since 1976, and it's a long way from Elric.

Posted at 2:13 am | link

This is the one hundredth posting of mine here at ELECTRON BLUE, and it also happens to be at the beginning of a new year. So I am taking this time to review what I have done in the last four years and where I hope to go. Before I start, I wish all my Electron Readers, the entire handful, a very happy and serene New Year.

It has been more than four years since I visited Fermilab and resolved to learn what I had never learned. I began my math studies in early 2001, starting literally from the beginning. I started with kiddie math from elementary school, including long division, which was where I remember losing any ability to do math back in third grade. Once I had re-acquainted myself with arithmetic, I moved on to first year algebra, which had tormented me in high school. I finally redeemed my high school agony by learning to factor quadratic equations and solve them with the quadratic formula. By late 2001, I was toiling my way through endless stacks of polynomials and doing high school senior year algebra.

In 2002, I "graduated" to first-year college algebra, using a vintage textbook from 1958. I worked through systems of equations in two and three variables along with determinants, systems of quadratic equations, inequalities, imaginary numbers, and much more. I also introduced myself to sequences and progressions, which I did since they were in the book. I solved endless series of problems, including the dreadful Word Problems which were the bane of my youth and many other folks' youth as well. Regarding physics, in 2002 I was introduced to some basic classical mechanics, including Newton's laws, how to mathematically describe straight-line acceleration, and determine the distance traveled while accelerating.

By autumn of 2002 it was time for something else, so I acquired a geometry book and worked my way completely through it in just less than a year. Geometry was the only mathematical thing I was good at in high school, so it was less challenging for me to pick it up again after the decades since my last exposure to it. I did hundreds and hundreds of proofs, with thousands of congruent or similar triangles. They proliferate, as if they were living things.

Having come to the end of my book of geometry, I then proceeded, in the autumn of 2003, into trigonometry. Of all the mathematical studies I have done so far, I found trigonometry the hardest and the most tedious. When it came to solving triangles with their sines, cosines, tangents, and so forth, I was adequate; after all, this has to do with geometric space, in which I was now at home. But I found trigonometric identities oppressive. Their endless, complex equivalencies multiplied and multiplied, and it seemed I would never get free of them. Nor could I figure out what purpose these trigonometric identities had in the "real world" of physics or any other science.

Trigonometry dragged me into 2004. When I began this Electron Blog back in February of 2004, I was still doing those blasted trigonometric identities. I did them all through the winter and into the spring and early summer, when I finally decided to give up on trigonometry, more out of exhaustion than any other reason. From trigonometry I moved into Logarithms, another tedious discipline without any visible purpose. Using the 1958 book and the tables in its back pages, I learned to find the logarithms of numbers without using either calculator or slide rule. This was a rather pointless achievement, given that I had both calculator and slide rule at hand.

Later in 2004, I returned to sequences and progressions, which I find much more interesting than trig or logs. In the autumn of 2004 I reached a milestone, when I finally declared myself ready to approach calculus. I am well-stocked with books on the subject, and as 2004 ended I stood at the outskirts of Newtonville (not the one in Massachusetts) or perhaps Leibnizburg.

I must admit that if I were to be given a sudden test in any of these subjects, other than geometry or elementary algebra, I would not pass it. I would have to review and study hard to pass a test in intermediate algebra, progressions, trigonometry or logarithms. I am glad that I am not in a formal school program. The anxiety about the tests would just be too much for me.

I now have some mathematical background suitable for physics: familiarity with algebra, and with one basic concept of calculus, that is, change in velocity divided by change in time. I am now, finally, addressing physics directly, working from a few basic texts designed for people who want to teach themselves physics or review physics for tests. I have reviewed Newton's Laws, though I still have trouble wrapping my mind around the Third Law: equal and opposite forces? I have to remember that force is proportional to mass. I am finally learning about momentum and potential energy and kinetic energy. I am learning what is conserved and what is transformed. It's likely I'll be doing classical mechanics for a long time to come. I wonder whether I will ever get beyond it, let alone into the higher reaches of relativity, particle physics or the much-ballyhooed string theory. Well, the "landscape" may be mountainous, with my path only in the lower valleys, but all I can do is keep walking and hope that I get somewhere.

I have a book, from the notorious Barron's series of high school review texts, called PHYSICS THE EASY WAY. Fortunately, this book does not have fantasy characters in it. But it will be anything but easy, at least for me. I don't believe anything is worth doing if it is easy, except perhaps sauteing onions. This book is full of problems. I'll solve as many of them as I can, for as long as I need. I like to solve problems. It's one of the few things that makes me feel good. I don't care if they're pointless, unreal problems that don't help humanity. Just let me solve them.

I still feel a great force of resistance and inertia, coming from my peculiar circumstances. Very few people, as far as I can see, attempt to learn physics after their high school years. I've heard from one or two, but lately they seem to have given up or gone away. It seems you are either a whiz at it, gifted with undeniable talent, in which case you are already bound for a scientific career at age 10, building your own computers out of spare electronic parts, or you are a hopeless case who will never go beyond rolling balls down inclined planes. And it still seems very much a boys' world to me, including boys who are in their thirties and forties. Physics seems to me like a strenuous sport, where you cannot hope to do anything with it if you start when you are middle-aged. Imagine an out-of-shape middle-aged lady trying to learn skateboarding or mountain-biking or surfing, having never done it before. Very inappropriate for someone like me. You can get hurt doing these things! Watch out, I could hurt myself accelerating too fast and not conserving my momentum!

So here I am at the beginning of 2005, poking my way through beginning physics that I should have learned in junior high school. In fact, I remember not learning it in Mr. Cinkosky's seventh grade science class. He was a sweet old guy, a World War II veteran, who tried to teach us about falling objects, friction, and "mechanical advantage," how simple machines like levers and pulleys worked, and other beginning physics stuff. The demonstrations stayed with me, but the math certainly didn't. I didn't build anything electronic in my youth, (though I certainly worked with enough electronic music gadgets) and it was clear that I would never do anything scientific; coming from a family of artists, I was destined to be something artistic.

Yet something came over me four years ago, an infusion of mathematical grace from the atheistic world of science, that somehow transformed me into someone who looks forward to studying calculus. Back in junior high I could imagine that I would be doing art or writing fantasy in my later years. That seemed natural. But math and physics? Perhaps some burst of exotic particles re-arranged an area of neurons in my math-disadvantaged brain. Why I am doing this, and why I have stuck with it for four years when most people assumed it was just another of my whims? Never underestimate the power of Inappropriate Desire.

Posted at 2:36 am | link