I finished my Angel painting last night. So without further waiting, with permission by the owner, here is an image of my "Angel of the Storm." Acrylic on Masonite board, 26" x 16."

Further information: The Angel is an idealized portrait of the owner who commissioned it. The pink harp is a real harp which the owner plays. The painting contains areas done in iridescent metallic paint, such as the halo. All clouds and cloud formations are naturally occurring. Only free-range organic angels were modeled during the making of this painting. Prints will be available on request.

Posted at 9:17 pm | link

Enough of this arty stuff, let's get back to what is really important, that is, mathematics. I am going through the review chapter on functions and how they work. I never was completely sure about the whole thing but this chapter is a more complete and clearer re-working of the material. One thing that impresses me this time around is that functions and function notation represent a process, as calculus will, rather than simple one-time calculations as in arithmetic. One quantity is processed into another quantity: the input leads to output. x goes through function process f to become y,, hence the function notation y=f(x).

This notation is ambiguous if it points to any actual reality. Is y=f(x) a statement of causality? Does x cause y? When x changes, so does y, in a predictable way described by the function f. But is that predictable change a causal one? It looks that way, but it may not be. A function process may be abstracted from a bunch of data, so that it honestly looks like x causes the change in y. But it could very well be that the two changes are not dependent on each other but simply seem to be changing with respect to each other. The statement of a function f describes a relationship between those two quantities, but is this necessarily causal?

For instance, you could find some sort of causal relationship between unrelated phenomena which happen at the same time, and maybe even create a mathematical statement for it. You'd be right, but the causal reasoning would be wrong. Correlation is not causation, as many a teacher has told us. Mistaking correlation (occurring together) for causality (one thing making another happen) is a common form of bad thinking that may lead to everything from belief in paranormal phenomena and superstition, to what atheists consider religion to be: a mistaken perception of meaning and order in the world.

Or is it possible that there are no unrelated quantities in our world? Is there a function which defines the flutter of that now-famous butterfly's wing which causes the hurricane three thousand miles away? That's chaos theory, something my simple mathematical podging won't get to, perhaps ever. Mathematics on my level is about simplifying things, reductionism, and getting the relationship right, whether that relationship is real or not.

Posted at 3:09 am | link

Last July I wrote about painting the ocean, when I was doing my abstract picture "The Orange Sail." Now I am doing something more ambitious: I am painting lightning. I need to convey its brilliance in paint, including its purplish-pink color, which results from the ionization of nitrogen and oxygen in the air in its path. This takes quite a lot of painting as well as color strategy. I have to make sure that the lightning bolt will stand out from its background, which means that I have to plan the whole color scheme well ahead of time. Since acrylic painting is done in layers, I have to leave space for the lightning bolt in each layer I do. The lightning bolt is also done in layers: first a purplish one for the color, then white for the highlights.

There is more lightning elsewhere in the painting too, after all this is the "Angel of the Storm." White acrylic in its pure state is very, very bright because unlike white oil paint, the acrylic medium (the goo which holds the pigment together) is altogether colorless. With oil paint, the medium is a golden-colored oil of some kind, usually linseed, and that adds a warmth to all oil colors, even pure white. So if I were using oil paint to depict my lightning, I'd have to adjust it to be a bit bluer, and thus not as bright. I don't ever use oil paint, because it is smelly, toxic, messy, and a fire hazard. Many other artists these days avoid it all by working in digital media. I work with digital art and graphics, too, but when a private client orders an artwork, she doesn't want a CD plonked onto her desk. She wants a real live hand-done artwork that she can frame and put on her wall and show off to her friends. My digital stuff is done for commercial work.

All this art talk is an introduction to yet another riff on science and scientists. I often read Cosmic Variance," which is one of the most successful of the new crop of physics blogs that has sprung up in the last couple of years. The group of scientists at Cosmic are all perky, young, and attractive, and they're all desperately trying to tell us that scientists are just like "real people" who have hobbies and gourmet dinners and vacations and go to jazz concerts. Well, they can say all they want, but I know it is only hopeful publicity. Scientists are not just like "real people." They are better than real people. Why? Well, they're smarter, more energetic, more dedicated, more determined and forceful, and simply stronger both physically and mentally. After all, they have spent at least 20 years getting to where they can be professional scientists, from elementary school science fairs to postdoc stints in worthy laboratory places. They have survived brutal competition that would weaken a Navy SEAL. In the descriptions of physicists' lives, we always are told that not only does Joe Physicist spend incredibly long hours at his classes and research, he somehow makes time to climb 14,000 foot mountains and go to Central Africa for a total solar eclipse. And he complains about how hard it is to have conference meeetings from Tokyo to Paris to New York in just a week. Uh huh. The rest of us are not doing these things. The rest of us are trying to get our laundry done and opening up cans of Campbell's Soup for dinner.

I believe the stereotypes about scientists because I have, in my few encounters with them, found the stereotypes to be truer than the blog propaganda. One of my favorite descriptions of Physics Life comes from a wonderful book about physics and chemistry published by Time-Life back in the ancient age of 1963. It was in the "Life Science Library" series and was titled simply "Matter." This book was a major inspiration to me when I was young, not only because it was full of excellent text and photos of physics being done, but because it had beautifully rendered photographs of every element in its native, pure state. It had the gleam of gold and the glow of argon, the shine of chromium and the mysterious metallic chips of "rare earths." They had glorious names like "Samarium" and "Praseodymium" and "Lutetium." Gases were represented by a sealed vial, assumed to be containing oxygen or nitrogen, though without the lightning glow. And there were pictures of physicists and chemists, usually with their lab equipment or in an academic setting with the inevitable blackboard.

The captions of two of those physicists' portraits sum up for me what Physics Life really is all about. I will excerpt from them (names of physicists are withheld since they are still alive somewhere on this planet).

"…Possessed of a puckish sense of humor and a brilliant mind preoccupied with physics nearly 24 hours a day, T. discusses his favorite subject…in his work a command of mathematics is vital, since "equations are the tools." And he is "at work" almost continually. "Research is a constant thing," he says. "You cannot count the hours—almost all the hours in the day.…A Nobel Prize winner at 34, he believes that youth is an actual advantage in scientific work. "As you get older, you get less daring…When you are younger you pursue new ideas immediately. Have I lost my daring? I often ask myself that question."

Gosh, I wonder whether I ever HAD any daring! Here I am dutifully reviewing mathematical functions in my book, hoping to actually get to something calculus-like before the next decade. Do I have that kind of dedication? I look at scientists as kind of like "techno-mages," possessed of amazing and un-shareable skills and knowledge, able to bend time and space with their theories, able to perceive galaxies thirteen billion light years away, able to re-create the primal sparks of the Big Bang in their vast accelerators. They don't paint pictures of lightning, they create it.

Now some folks feel the same mythic way about artists that I feel about scientists. In fact, the romantic movement of the nineteenth century made up a myth about artists that has haunted those who do art ever since. It was artists who were special, artists who were like some sort of magicians, who could create reality from simple paint or pencil, who saw deeper into the world. Now, in our post-modern age, dominated by photography and technology, artists have lost their magic. It is the scientists who command the lightning, not the artists. And thus the artist who loves science is haunted by the unbreachable gap of energy and brilliance between art and science, where paint cannot possibly equal plasma.

Posted at 3:55 am | link

I enjoyed the Pagan convention and even more, I made money. I didn't expect to make a cent, but I sold a good number of prints and made a surprising amount, even though there were fewer than a hundred people there. I also gave three talks, one on Zoroastrianism and two on my own art and how I design things. Each of these talks had a nice handful of people in the audience, and the group was small enough so that everyone had a chance to ask questions and participate in discussions.

One of my art talks was about how I am trying to use scientific and mathematical themes and elements in my painting. I demonstrated on a piece of notebook paper how conic sections provide most of the curved lines I use in my art. I also use other mathematical curves such as exponential curves, switchbacks produced by numbers raised to the third power, and spirals. I showed my viewers the particle trails that appear in many of my physics-oriented paintings. I remember one Friendly Scientist quite a while ago explaining to me that those particle trails actually follow paths defined by conic sections! There is also the spiral (actually a helix, according to the Scientist) which is traced by a speeding electron under a strong magnetic field. Even simple conic section curves give me enough material for a whole gallery full of designs. When I mix these forms with Art Deco, then I have splendid design opportunities.

Since I was given the precious chance to talk about my art "live" to interested people, I went on a bit of a rant about what I felt was wrong with almost all the "scientific" art I see. This is really the subject of another Electron posting in the future, but I feel the need to react in my own work against what I consider an impersonal and often dull aesthetic as well as poor color choices. What works as a "false-color image" for scientists to study looks awful as an artwork, for instance. Even the famous images from the Hubble Space Telescope as well as other telescopes have been color-enhanced to make them more attractive. If I say too much about this, I will run into trouble with other scientific-minded artists, so I better stop now.

Towards the end of the talk I turned the table (so to speak) and asked my Pagan audience questions. What was the Pagan attitude towards Creationism and other perversions of science done by religious entities? Did they believe in a divine creation or the intervention of a divinity in the history of the material world? Did the Goddess have anything to say about evolution or genetic engineering or cloning?

Perhaps I asked too many questions too fast, but I didn't get any clear answers from them. The night before, I had a long and interesting discussion with the author guest of honor, a Wiccan priestess who has written many books on popular magic and what might be called "urban shamanism." I asked her whether the Neo-Pagan movement, which is by now more than fifty years old, had any trained philosophers or theologians, and whether they had any social and political programs. Yes to the second, she said; she was involved in many social causes which Pagans supported. But as to the first, Paganism had a serious deficiency.

There have been plenty of academic and intellectually "respectable" books written about Neo-Paganism and other "new religious movements," but few have been written from within the community aimed at providing Paganism with a coherent and logical body of belief and thought. The reason for this, according to the author, is that Neo-Pagans shy away from anything they fear might turn into "dogma" or "doctrine," which they equate with oppression and lack of freedom. This is understandable, given the dreadful problems that mainstream religions have had with the working out of doctrine. Neo-Pagans prefer to "work out their own truth" from their own experiences, which means that no Pagan will have quite the same set of ideas as another. In practice, this usually sorts out to some basic similarities, such as the veneration of female divinity and the sacredness of the Earth. But it also is so formless and non-structured that it's hard to make any coherent philosophical or theological statement that would answer questions such as I asked.

The author said that this formlessness and lack of intellectual structure was something she saw hindering the progress of Neo-Paganism. While it's comforting to know that you have escaped the spiked chains and iron bars of dogma, it also means that you do not compete in the hard public arena of ideas. This is why Neo-Pagans are still regarded at best as tree-hugging hippies lost in pretty dreams of a rainbow utopia, and at worst as Satan-worshippers. The author said she longed to write books that went into more depth and added more intellectualism to the Pagan movement, but her publishers weren't interested. They only wanted cute books on how to do kitchen spells.

Two thousand years ago and more, Paganism of the philosophical sort had a profound intellectual tradition. After all, both Pythagoras and Plato were "pagans." I mentioned to my audience that if I were to become a Neo-Pagan, I'd like to be a Pythagorean, meditating on the magic of numbers and entering into altered states of consciousness through the sides of a triangle. (Though I wouldn't want to be a strict vegetarian as they were.) In the early centuries of Christianity, "Pagan" philosophies such as Stoicism and Neo-Platonism flourished side-by-side with the Church Fathers and had a great influence on them. But somehow this ancient heritage hasn't become prevalent in modern Neo-Paganism. If the movement doesn't develop a stronger intellectual tradition, it will stay marginalized while other more rigorous, aggressive ideas prevail, both for good and no-good.

Posted at 3:17 am | link

While physicists dash off to romantic Italian islands or cosmopolitan European cities or exotic Asian locales to talk about their particles and cosmology, I am going to Baltimore, Maryland for a conference this weekend. The conference is Ecumenicon 2006 and I will be doing art presentations there. This conference, as advertised, has been going on in one form or another for twenty years, and I have an Ecumenicon T-shirt that is about 15 years old. (I'm not sure I still fit into it, though.) I have been going to these events for quite a while, selling art and giving talks.

Ecumenicon is somewhat mis-named, because the "ecumenical" quality of the conference extends mostly to different types of neo-paganism or other esoteric spiritualities. At times, Christians, Jews, or Buddhists have shown up, but few of them are "mainstream" representatives of their faiths. In this way it doesn't resemble a physics conference at all, except perhaps one on string theory. However, I expect to talk about science and mathematics when I'm there, and hope to be on a panel discussion about science, fundamentalism, and neo-paganism.

I'm not a Neo-Pagan, but I know a large number of them and have learned about this multivariant "new religious movement" over the years. One thing which interests me is that as far as I know, Neo-Paganism has no complaints about evolution and embraces a scientific world-view along with its fondness for Goddesses and Celtic mythology. In fact, I even know some Pagan scientists. They seem to resolve the contradictions of belief and research by acknowledging that different forms of knowledge and experience take place on different levels of reality. This multi-level reality is a world-view that I also share, and I'll be talking about it in the future. I don't think that the physicists at those high-energy conferences worry about that. Their "multiple worlds" are in theory only, and will never be directly experienced. Nor does Neo-Paganism ever cross those busy physicist minds. In a way, the atheist scientists have it easier; they don't have to concern themselves with any other reality than the material one we all seem to inhabit. I hope to ask the Pagans some questions.

Posted at 3:00 am | link

It sounds like I've been doing a bit of spring skiing, but you know I don't ski. The slopes I am referring to are the slopes of lines on graphs. As I work through Dr. Anton's calculus book's first chapters, I'm reviewing things I learned years ago. It seems amazing to me that I have already been at my math and physics learning program for more than five years. So, "back in 2002," which also sounds surreal to someone born in the mid-twentieth century, I studied graphs and linear equations and that basic high school algebra I suffered over when I was young.

What is new this time around is that in reference to calculus, it is pointed out to me that the slope of a line is also the tangent of the angle formed by that line and the X- axis of the graph. This is something I wondered about, believe it or not, when I was first re-learning graphs and linear equations. That is, I figured that the angle of the line had something to do with the math that put it there. But I didn't study trigonometry till "back in 2004," and the linear connection somehow wasn't made in all those books that I struggled with then.

But now the simple truth about the tangent is revealed to me. It's the ratio of rise over run, of y over or against x. In the right triangle formed by the line and the x-axis, it is the ratio of the triangle's sides that are opposite and adjacent to the angle made by the slope. It was something I should have seen as totally obvious, but the book had to point it out. And what's more, the relationship between the tangents of two sloping and intersecting lines is expressed in a trigonometric identity. These mind-numbing identities were what I was attempting to learn when I first started this Electron Weblog. I cannot claim that I am bright enough to remember any of them outright, but as soon as I was presented with one, I recognized it. That meant that I could go to my trigonometry book (the excellent Schaum's Outline) and review it. So finally, I encounter a use for at least one of those trigonometric formulas. I'm sure there will be plenty more.

Posted at 3:02 am | link

My "Angel of the Storm" painting is meteorologically correct. That is, the cloud formations and phenomena depicted therein are all well-documented atmospheric features. I have at least three types of storm clouds: the Cumulus congestus big pile of clouds over a growing storm, the incus anvil-shaped thundercloud, and the rounded bulbs of Cumulonimbus mammatus clouds which appear during severe thunderstorms. I depict cloud-to-cloud and cloud-to-ground lightning. And at the bottom, there is a tornado, probably an F2 or F3 strength twister. The colors I use for my various storm elements are also realistically depicted results of light refraction and filtering through clouds of different thicknesses. I also have suggestions of both hail and rain.

So far, so good. But I also have an angel in the picture. Why would I put an angel in the picture? Angels don't exist, according to scientists. They say there can be no conscious living being without a physical body to support consciousness. References in sacred texts and mythology are not evidence at all, merely the illusory beliefs of people who are following evolutionary adaptations that have ceased to be any value in an age of technology and scientific inquiry. Why would I spoil a well-rendered and accurate picture of stormy weather with a religious figure? Am I endorsing Creationism by implying that storms happen not because of atmospheric temperature differences and lots of airborne moisture, but because an angel makes it so?

The Scientists continue: Suppose for some absurd minute, that angel really existed. How would it get airborne? Is it lighter than air? If it is not made of gas but is rather a kind of flying mammal, where is the structure that could support such large wings? It is also playing a harp. If the angel is lighter than air in order to float, how could it carry with it a heavy object such as a wood and metal harp? The angel appears humanoid, but we know well that there have never been any humans with wings, unless they are costumed performers, who would definitely not be able to fly, let alone fly into a thunderstorm. Perhaps this "angel" is a performer who is doing a stunt in front of a video screen? Or perhaps it is a cleverly contrived computer-generated animation? No, this is an acrylic painting on a simple panel. It is a cultural object.

Nevertheless, cultural objects are not free from the rigors of scientific investigation. Let us consider what message is being conveyed by a painting of an angel playing its (her?) colorful harp in the midst of a raging storm. The artist must believe in some form of religion which she wishes to promote. We scientists know that religion of all kinds is a sad and mind-destroying meme which we desperately hope humanity will eventually outgrow. How much destruction and atrocity has been done by people who believe in angels! Religion is far more destructive than tornadoes and hurricanes! We can only hope that the artist will see the error of her ways and purge her art of all but properly documented, peer-reviewed, experimentally verifiable image material which can serve to enlighten people about the value of science rather than delude them with the beauty of angels.

Posted at 3:07 am | link

Just before a heavy thunderstorm, the sky sometimes turns an ominous and unmistakable shade of green. In areas prone to tornadoes, this color is the signal to take cover and if possible get into the basement, because a twister could strike at any moment. I have seen this color a few times during storms here in my urban Mid-Atlantic area but fortunately no tornado emerged. The green storm sky phenomenon isn't quite understood, but it seems to be the result of light refracting through many miles of thick clouds in just the right way. The reason I'm talking about the green sky is that I'm trying to replicate the color in my current painting, "Angel of the Storm." I'm also trying to reproduce other unusual colors you only see during thunderstorms, such as the pink and bluish-purple light of lightning reflections.

In my area we are moving into what I call "crossover weather," where the chilly, stable weather of winter changes to the tumultuous, humid summer atmosphere. By May I hope to experience many exciting thunderstorms. I have been admiring and sketching clouds for years, and now I finally get to use my visual observations in a painting. Unlike my usual rich colors against black, this one is full of pale greys and greens and pinks, which change to darker greys and blues and finally black as you get to the bottom of the painting. In the upper center is the Angel, a portrait of the client holding her wild pink harp.

This picture isn't a formal, static, reverent icon like the other ones I've done over the years. Since my client has been in the rock music broadcasting business for many years, I can allow myself to be inspired by a different and possibly more dynamic aesthetic. That will not be to everyone's taste, because I know that some of my viewers will only be satisfied with formal, high-toned art purged of references to what they consider the vulgar barbarism of popular culture. Fortunately, the "Angel of the Storm" is already bought, and it only has to please two people: me and the client. If other people like it, that's fine too. I am about two weeks from finishing it, and when I do, you'll see an image of it here. If all goes well, the client will receive the painting on April 28. I may borrow it back from her for an upcoming show later this year.

Because of this time-consuming project, I can only do a small amount of mathematics each day. I am patiently reading through the review of pre-calculus in the big Anton book, hoping that I remember my algebra and conic sections. There are thunderstorms predicted for later today.

Posted at 2:51 am | link