Electron Blue 2

Enthusiasm

2012-01-28T01:50:00.002-05:00

Having savored Freeman Dyson’s excellent science writing, I’m now reading a book by his fellow Englishman Ronald Knox. This isn’t about science, but about religion. “Enthusiasm” is Knox’s definitive study of what happens when religious people are convinced that God is talking to them personally and has a prophetic message to reveal. Many times in the history of Christianity, prophetic visionaries and ecstatic experiences have changed the course of the religion, and as many times, have given rise to schismatic sects and cults. How do you know the difference between visionary fervor and deluded craziness? Is there a difference? This is where the tradition of the longstanding Churches (such as Catholic or Eastern Orthodox) comes into play.

Ronald Knox is a fascinating figure I’d like to know more about. He flourished in the early to mid-20th century and was originally a well-known and prolific Anglican writer on Christian subjects. He was an Anglican priest who was a chaplain at Oxford. In 1917, he became a Roman Catholic, and a year later was ordained a Roman Catholic priest. He continued his writing career as well as his apologetic (promoting Roman Catholicism) work. He was a major character in what is known as the “Oxford Movement” in which many prominent Anglicans such as John Henry Newman (later a Cardinal) switched over to Roman Catholicism. Knox wrote in many different genres, from satire to history to criticism to personal memoir to spiritual inspiration. He also translated Jerome’s “Vulgate” Bible into English. Interestingly, he also wrote detective stories which sold well enough to make him a good living. Most of Knox’s books are still in print or easily found at online used-book sites.

I am only about 80 pages into this long book, which was written in 1950. It is in an elegant style (a bit flowery for our modern tastes) and incorporates many untranslated passages in French, quotes from earlier Church historians. There is plenty of material to interest an esoterically minded Christian, such as detailed descriptions of the early “charismatic” Montanists of the third century C.E., and the famous Cathars or Albigensians of medieval southern France. He will later write at length about the ultra-mystical movements of Jansenism and Quietism, controversies which changed how spirituality was cultivated in the Roman Catholic Church.

Here are some quotes from the beginning of Knox’s book, in which he lays out his definition of “enthusiasm.”

“For that is the real character of the enthusiast; he expects more evident results from the grace of God than we others...He will have no “almost-Christians,” no weaker brethren who plod and stumble...He has before his eyes a picture of the early Church, visibly penetrated with supernatural influences; and nothing less will serve him for a model....It involves a new approach to religion; hitherto this has been a matter of outward forms and ordinances, now it is an affair of the heart. Sacraments are not necessarily dispensed with; but the emphasis lies on a direct personal access to the Author of our salvation, with little of intellectual background or of liturgical expression....Especially, he decries the use of human reason as a guide to any sort of religious truth. A direct indication of the Divine will is communicated to him at every turn.”

You might recognize some of those themes in the current public religious scene here in the USA. There’s a lot of enthusiasm going around, and though Knox is always writing from a “Catholicism is the right way” perspective, he gives valuable background in this book about how devout, righteous people can go wrong even without political involvement.

My copy of Knox’s “Enthusiasm” is in poor shape, after almost thirty years in my library. At one point, I used this blocky book to prop up an air conditioner. I’m glad I saved it. It goes to show that in a library, every book should get its turn to be read. You also may be wondering why I am writing at length about a religious book on my science-oriented blog. Well, the phenomenon of “enthusiasm” and its related practices such as “channeling” or prophecy are now under the non-religious study of modern psychology, evolutionary psychology, sociology, and neuroscience, which will yield quite a different view than the one provided by priestly Ronald Knox.

Freeman Dyson as Rebel

2011-12-16T03:00:00.002-05:00

My science reading this month has been a collection of essays by Freeman Dyson, entitled "The Scientist as Rebel." This is published by the New York Review of Books, the highbrow publication that first featured these pieces. My friends gave me this book because they know I love to read not only about science but about scientists' lives, including the odd and rebellious types.

I've always liked and admired Freeman Dyson, and I also enjoy his writing, especially because his sentences are so clear and they don't run on. And he is mostly free of the arrogant attitude I find among many other scientist writers. He has been part of most of the great scientific enterprises of the twentieth century and knew just about every "famous scientist" in physics or astronomy.

I found his memoirs of the Manhattan Project and World War II to be some of the most interesting of the set of essays. Some rebel scientists, after the development and use of the atomic bomb, refused to work on any more government projects. But Dyson writes sympathetically of the ones who did, such as Robert Oppenheimer, and continued to do so after the war, such as Edward Teller. Dyson's review of the collected letters of Richard Feynman is even more sympathetic. Everyone who knows physics loves Feynman, because he was such a brilliant trickster and, as Dyson says, a "performer" who could play to the public. The world loves characters like that, although there are many scientists who do similarly great work but never become a Famous Figure.

Freeman Dyson is 88 years old as of this writing, and still active. At his age, he comes from a scientific and academic world that is gone, the imperial Anglo-American all-male system that produced the great particle accelerators and the laboratories of the 20th century. Nowadays being a physicist means working in a collaboration which resembles a huge corporation with thousands of diverse employees. I wonder whether it is now harder, or even impossible, to be a scientist rebel.

Randall to Graphic Feynman

2011-11-18T03:52:00.003-05:00

I finally finished reading Lisa Randall's WARPED PASSAGES. She and her fellow string and brane theorists can make up all the fantastic ideas they want, but I consider it all science fiction until some experiment confirms it. They're all hoping that the LHC at CERN delivers some world-shaking particle event, but so far no one is saying anything. Either the CERN machine has indeed cranked out something and they are keeping it a BIG SECRET, or the machine has not yet delivered a credible result. It would be hard to keep a really significant result secret, but not impossible, so they may be hiding something multi-dimensional until they can get confirmation and repeated proof events. Meanwhile we physics fans are still hoping for something...anything? Higgs? Extra dimensions? Kaluza-Klein particles? The LHC acronym, by the way, reminds me of a famous and shocking for its day effort by the great Dadaist Marcel Duchamp where he puts a mustache on a postcard of the Mona Lisa and adds the initials "L.H.O.O.Q" which when read in French give you the words "Elle a chaud au cul" which roughly translated into English means either, "She's got a hot ass" or more accurately, "She's hot for it. (horny)" This is not dignified Lisa Randall territory. It is more Richard Feynman territory which brings me to my next physics + graphics encounter.

Jim Ottaviani has been writing graphic novels about scientists for years now. I got an earlier one of his about Niels Bohr, "Suspended in Language," and enjoyed it. He can make an un-comic-book-like subject like theoretical physics work in a sequential art context, with no nude babes, explosions, bloodbaths, or monsters. When I saw the new Ottaviani book on Richard Feynman, I had to have it. The artist is Leland Myrick, who does the whole book in a conservative, three-level panel per page structure, with a bouncy, cartoonish but realistic clear-line style. Clear line means just what it says, no smudgy ink blots or action brushstrokes, just pen work colored with flat and rather modest colors. What a relief after decades of ugly, distorted and exaggerated manga-influenced comic art!

Feynman embodied the archetype of the "Trickster," and despite that, he managed to make world-changing physics discoveries as well as defense and engineering work, winning a Nobel Prize along the way. It's a journey through Feynman's life and career, with material from both Feynman's well-documented lectures on physics as well as his many autobiographical stories. You can tell that the artist did a load of research on everything from what Los Alamos Laboratories looked like when the Manhattan Project was going, to what physicists wore in class at MIT. (Men wore ties on many more occasions than they do today!) A graphic novel is also the perfect place to show the famous "Feynman Diagrams" which he invented to describe subatomic processes.

I liked this book so much that I parceled it out into chapters and read only one at a time so I could make it last longer. I don't think I would have gotten along with Feynman had I met him personally, as I am very un-Tricksterish and solemn, but being in the presence of the graphic Feynman brought back the challenge that I took on back in Year 2000. Namely, if physicists can do art and music, can an artist do physics? In the book, Feynman makes a deal with an artist friend. Feynman will teach the artist physics and the artist will teach F. to draw. The outcome was, that the artist learned no physics but Feynman did quite well at drawing. Hurrumph! This artist will learn physics. That means back to math, more math, and more more math. Back to calculus! I'm currently reviewing things with a math textbook I rescued from a recycling bin. Will I lose track again? Can I put aside even a few minutes for math work? We will see. The winter nights are long.

Frustrated Brane

2011-10-02T02:19:00.002-04:00

I'm still reading Lisa Randall's WARPED PASSAGES and I must say this is a job. It's a lot like work, but none of the work is really done by me. A select group of people, theoretical physicists, know what this book is really about and actually do work on it, while I read this account and ask questions I am not supposed to ask.

I'm reading patiently through this tale of strings and multiple dimensions and branes and braneworlds and broken symmetries and particle interactions. I encounter passages like this one from page 331:

"...This is another example of duality. In this case, an eleven-dimensional theory with two branes bounding the eleventh dimension (the tenth dimension of space) is dual to the ten-dimensional heterotic string. That is to say, when the interactions of the heterotic string are very strong, the theory is best described as an eleven-dimensional theory with two boundary branes and nine spatial dimensions. This is not unlike the duality between ten-dimensional superstring theory and eleven-dimensional supergravity that was discussed in the previous chapter."

This sounds like theology, not physics. Yes, I know it's physics of a sort. It is supposed to have some connection with the reality that is discovered in the particle accelerators, but so far nothing from string theory has had any experimental confirmation. The author herself admits it. But the string and brane theorists go on anyway, building more and more cycles and epicycles into their theories, hoping that maybe a pattern will emerge which somehow matches something that an experiment revealed. These people know what they're doing. But I don't. Is this science? Maybe it is really a fantastic art form.

I must admit I am frustrated, reading this book. This type of knowledge and mathematical inquiry is something I would like to be able to do, but I never will, any more than I will become an Olympic athlete. But at least Olympic athletes have understandable events and outcomes. String theory is celestial arcana that no one can win. But they can make whole careers out of it. I really admire people who can master something like this and who can share it with others, but after more than three hundred pages I am less and less able to appreciate what all this theorizing has to do with reality. I realize that this type of question is disrespectful to Ms. Randall and her colleagues but even more insulting is comparing it to theology. These are all good scientific atheists! There is no theology! But there is string theory and I would like to see any type of proof that this is not a big piece of vaporware floating in the eleven-dimensional sky.

Reading Randall

2011-08-18T17:24:00.002-04:00

It takes me a long time to read a book, especially one with such dense content as Lisa Randall's WARPED PASSAGES. This book describes itself, on a brilliant orange cover (always a plus for me) as "Unraveling the mysteries of the Universe's hidden dimensions." That way, it seems to belong to the same type of book as Brian Greene's THE ELEGANT UNIVERSE or THE FABRIC OF THE COSMOS. But Lisa Randall chooses to incorporate more than just string theory or trendy new stuff. After a chapter or two on what "dimensions" are, she switches into a heavy-hauling track of describing quantum physics as developed through the whole twentieth century. And then she works on quantum field theory, and a lot of stuff which she says we readers could skip over but you know that this reader won't be a wuss and wants to read the whole thing.

Basically all this high-end material from the 20th century is necessary for understanding string theory and the physics esoterica of the 21st century but it is, as I said, a heavy haul for about half of the entire book and this is why I have spent months reading it, one or two pages at a time, while I ponder things like "polarization in two directions" and "spontaneous symmetry breaking" and "fundamental fermionic particles." For Lisa Randall, this stuff is as familiar as her breakfast cereal (or croissant, or whatever she eats for breakfast) but as a physics fan and consumer of books, it is kind of difficult for me. But I hope that someday I'll be able to understand this material. Somehow. When I learn more time management and less pointless web surfing.

When I started my physics and mathematics quest in 2000-2001, now 10 years ago, I was hoping that I'd be working on quantum mechanics in the real way, that is mathematically, by now. Instead, I'm painting pictures of grapevines. Not that there's anything wrong with that, but do grapevines have anything to do with quantum physics? I haven't forgotten that I heard the call of the Beam there in Fermilab 11 years ago this September. And as Randall and all the physics book authors repeat, the LHC at CERN in Switzerland will give us answers to those supersymmetry and string questions, if it works, if we have enough patience, if we have enough billions of dollars, if we have enough energy. That's a big basket to put all your quantum eggs in. I hope it hatches something someday, if not soon.

Meanwhile I keep reading Lisa's book, page by page, and sooner or later she'll get to string theory, which for all I know resembles a grapevine in its multidimensional branching tendrils and leafy stems.

Quantum Life

2011-06-27T02:39:00.002-04:00

My favorite magazine, NEW SCIENTIST, never stops making fun of the New Age or pseudoscientific use of the word "quantum." Sure, the word has entered into pop culture and popular parlance in a false and unscientific way, which the righteous scientists are not going to be able to stop. But there is a way to use "quantum" that actually describes reality as we know it.

I am currently reading WARPED PASSAGES by the admirable Lisa Randall. Instead of making fun of us readers for our lack of true scientific knowledge and misuse of the word "quantum," she patiently explains to us exactly what and why physicists talk about quanta in their descriptions of subatomic phenomena. It was a revolution in ideas, as she says, when it was discovered that energy states are not continuous, but jump from one discrete level to another depending on their level of excitation. I haven't even gotten to the part about the uncertainty principle.

Quantum-ness reminds me of another current philosophical question which extends into physics. Is the world of "reality" made of discrete tiny bytes or pixels, like a computer screen, or is there a seamless, partless continuity behind it all that can't be divided into smaller segments? So far, the evidence, from atoms on down, is that the world is made of smaller pieces, which can still be called "things," which build up the edifice that we see and live in. Yet the scientists have not yet found the "things" or the divisions which make up time, space, and gravity, although the practitioners of the "loop quantum gravity" sect say they are on track to find them.

I am very lazy most of the time, unless I've consumed coffee, at which point I become amazingly diligent for about an hour or two. During most of my life I can only accomplish something if I break the task into bits, mini accomplishments. Wash one glass. Fold all the blue T-shirts. Pick up three books from the floor. Same with art, and with Lisa Randall's book. I can only do so much at one time, unlike those heroes of science, engineering, and industry working their 80-hour weeks. I cut a board to size tonight for a painting: that's one pixel of work. Or perhaps, a "quantum." My little life is composed of quanta of work. Coffee, like an incoming photon stream, can put me into a higher state of energy for a little while, but not for a long time, since hours later I have dropped back into my baseline state of being lazy and cranky. I can only read Randall's book for a few pages, because there are so many quanta of ideas on each page. Ideas and information are said to have their own energy, and I never give up hope that someday, energized by ideas and mathematics, I will attain a higher state of quantum consciousness, so that "New Scientist" or someone with an attitude like it can ridicule me.

Wake up, Electron

2011-06-07T01:20:00.002-04:00

Eight months ago, my inspiration for posting here sort of evaporated. There were a lot of reasons, most of which had to do with the time eaten up by my day job. I just couldn't maintain any level of mathematical or scientific activity when I was busy running the cash register and lettering signs at Trader Joe's. I'm still doing that day job but for the summer months my schedule has changed, I'm working fewer hours due to the usual seasonal lowering of business there. That means that I can respond to the inner voice that has been regularly reminding me to return to ELECTRON BLUE 2 and to math and science in some way.

I haven't been completely inactive. During the months of the hiatus I read NEW SCIENTIST enthusiastically, as I could read at the kitchen table and even take the magazine to restaurants. I also read books on cosmology. During the long dreary winter (even in Virginia, winter is dreary), I read two books by the excellent science writer Michael Lemonick, about cosmology and the information about the cosmic microwave background returned by two satellites, COBE (Cosmic Background Explorer) and WMAP (Wilkinson Microwave Anisotropy Probe). These satellites were decisive in the study of the cosmic microwave background radiation which is the remains of the original fireball of the "Big Bang." The first one, "The Light at the Edge of the Universe," (one of the best book titles ever, in my opinion) was about COBE and the first evidence of a pattern of temperature differences in this radiation over the whole area of the sky. The second one, a sequel as it were, is called "Echo of the Big Bang" and is about not only the WMAP satellite and measuring the background radiation, but the whole intense process of how scientists create a plan, a design, and a way to get that satellite into space. Their dedication is almost unbelievable from the standpoint of a hobbyist like me.

WMAP changed cosmology and now there are other satellites and projects working on new discoveries. The AMS (Alpha Magnetic Spectrometer) which the Endeavor astronauts installed just a month or so ago will look for antimatter from its place at the International Space Station. Meanwhile, the vast round behemoth of the LHC is churning out particle collisions, in the hope that something will reveal new physics or confirm strange old physics.

Having read Lemonick's books, I went on to start "Warped Passages" by Harvard theoretical physicist and stringmaster Lisa Randall. This is my current reading. In order for Randall to explain string theory and other esoteric modern physics, she has to take us readers through helpful though non-mathematical explanations of classical and relativistic physics. The section I am on right now deals with non-Euclidean geometry, in which familiar geometric axioms get twisted when the figures are inscribed on curved or convex surfaces.

OK, but the important thing is, when am I gonna get back to learning math, reading math books, and doing problems? This is the big one which I haven't solved yet. I have plenty of math books, but haven't had the, uh, initiative to open it up and calculate. I still must place making visual art ahead of working on math, because I haven't given up the (possibly forlorn) hope that I could return to making some money with my art. I am working on revising my portfolio for showing to publishers or art directors or galleries. I now have digital art skills I didn't have years ago when I halted my independent math study. I do lots of different kinds of artworks which fit into "lines" (strings?) of similar work. I make old-fashioned landscapes and architecture, fantasy and science fiction illustration, and lately, art done at wineries and on wine-related subject matter. But relevant to this Electron, I also have that geometric abstraction line which includes mathematical lines, curves, and motifs. To my amazement, these pictures are quite popular. I recently showed them to a renowned science fiction artist pro who said that with a few space, science fiction, or fantasy elements I could market them as a non-traditional illustration style. That's what I'm working on currently.

Well, that's enough for now. The Electron is active again, but due to the Uncertainty Principle, one cannot know for sure when I will post or what length the posting will be. I will be interested if anyone, in this universe or any other, will read this, or whether they will return data comments from space that acknowledge that blog particles have been detected.

Desperately Decluttering

2010-09-22T01:51:00.002-04:00

I need to remove stuff from my apartment. I am overwhelmed by clutter and stuff, which has over the 18 years I've lived here, packed every corner of this dwelling. I tell myself I'm not a hoarder, because I do remove stuff and I keep only good, useful or pretty, sometimes valuable stuff. But maybe I am a bit of a hoarder regarding books. I buy many more than I can read or use. You may have also experienced this. Well right now I just have to thin the collection out. And that includes science and math books.

Some of these I bought, others were given to me by helpful mathy friends. Some are vintage textbooks from the mid-twentieth century. Most of them were physics books with enticing titles that I bought from catalogues during my most enthusiastic time. They were monuments to my ambition, aspirational texts that I hoped I would read and easily understand once I was the equivalent of a physics graduate student.

Well, wrong-o. My aspirational texts only gathered dust for years. I am de-accessioning "Constructing Quarks" by Andrew Pickering (published 1984), and "Waves and Grains" by Mark Silverman (published 1998). Both books are filled with heavily technical language and higher mathematics that goes far beyond my modest knowledge. I really thought that I would understand them by now, but it didn't happen. So I am passing them along via the "donation" bin at the local library. Maybe some physics graduate student will happen across them at a charity book sale. Or they might, for all I know, be recycled into cardboard boxes for frozen vegetables.

I am also giving away "The Emperor's New Mind" by Roger Penrose. I paid nothing for this one, because I found it in a stack of books that some other declutterer was giving away. He had placed them near (but not in) the paper recycling bin. The title of this, and the reviewer's description, was exciting, but the text was again full of difficult technical and mathematical language. Will there ever be a time when I will be able to read these books and get something out of it? I am now back in the deplorable condition that physicists lament: a reader who only wants a book if there are none of those pesky equations in them. But in fact I still want the equations; it's the books I have to get rid of.

Ten Years from Fermilab

2010-09-09T01:23:00.006-04:00

September 7th marks a ten-year anniversary for me. It was on September 7, 2000, that I visited Fermilab and started my quest to learn mathematics and physics. Throughout those ten years I have told the story a thousand times, so I don't need to tell it again. Here's the Twitter-size sound bite, the current form of 21st century communication. "I took a guided tour of the Tevatron at Fermilab, and when I emerged I was overcome with a desire to learn mathematics and physics."

So I went and did that, all on my own with no formal teaching, just from books. I started at the beginning, with children's arithmetic. (2000-2001.) Then I went through pre-algebra and first year algebra. (2001-2002.) I spent most of a year doing geometry. (2003) That was as far as I ever got in high school, and I didn't do well in it back then. My learning process involved just reading the chapter and doing EVERY PROBLEM in the set. I struggled with algebra word problems. I struggled even more with trigonometry and logarithms. (2004).

In 2005 I decided to take the same approach with classical Galilean/Newtonian physics. I spent the year hacking through problems about gravity pulling on objects in various contraptions. Lots of moving and falling things too, and a few projectiles. Then back to bricks tied with cables, sliding across tabletops with a coefficient of friction.

By 2006 I deemed myself worthy of studying introductory calculus, and so I learned the very first concepts of limits and derivatives. But by 2007, for various reasons, my rate of learning, my acceleration as it were, slowed to almost nothing. And there it stays, alas, to my great shame.

I thought, in my early enthusiasm, that by 2010 I would already be working in physics on a graduate level. I'd be doing problems about relativity and quantum mechanics. I'd know how to get subatomic particles to manifest themselves.

This did not happen. Instead I am running the cash register at a grocery store. There is some math involved with this, but the register does it for me unless the customer tries to even out his tally by offering a few pennies, at which I get confused. I am not among the hard-edged, competitive, tireless scientific elite whom I idolized after reading books about modern physics.

I keep wanting to pick up my math and physics and continue, but I am constantly hampered by the notion that I have forgotten everything of the mathematical basics I need to continue. In other words, I have to have mastered all the math that supports the new material before I can go on. That means I have to go back and review it, again and again and again, because I keep forgetting it. Right now I couldn't pass a trigonometry test, let alone a classical physics test. Go back to all those pulleys and sliding blocks! Review the formula for an ellipse and a hyperbola! It's in the book, after all.

It's a question of space-time, but not Einsteinian space-time. It's a matter of what I

can allocate to my scientific and mathematical learning, faced with a day job as well as

my other ambition, to build a digital art portfolio and resume my work as a

professional illustrator. What, you say...other people do it! Right, they do, so why can't I find the time and the space to do more math? It's a problem. Problems are made to be solved. Let's find a way to put me, the Electron artist, back on the path to quantum reality. I want to be true to the ambition I found ten years ago, in the presence of the great Proton Beam and the roar of the klystron engines, the jets of smashed quarks and the trajectories of spinning particles. And we all wait for the outcome of the Large Hadron Collider.

Mathematical Squirrel

2010-07-25T02:22:00.003-04:00

Mama Squirrel appeared on my terrace railing the other day, reminding me that I haven't done any math in MONTHS. That's true, ma'am. I haven't posted, and I have been either busy or distracted. I am also still parked in the garage of reviewing and not being confident enough to move forward on calculus. A big portion of the Humongous Book is not calculus, but reviewing basic math skills so you can do calculus. Remember that poor guy with the rock, whose job was to push it to the top of the hill, but it always fell back down as soon as he got it there? Sisyphus was his name, and I have felt like him for ages. I feel like I can't go ahead unless I have everything that goes before mastered or at least familiar. That would mean, in this case, conic sections. I have looked at the same ellipse problem for months, when I had the time to look at it, and thought, You can do this. OK. I haven't done it.

It's summer, which is my altogether favorite time of year. The heat has been intense, even for me. It is coming up to, believe it or not, the tenth anniversary of my epiphany at Fermilab. Have I done the Great Proton Beam justice? I really hoped that, by 2010, I'd be doing advanced math and physics. Instead, I have not even left high school. It is true that in 2000, I didn't know that I would get a day job which takes up a lot of my time. Nor did I know that I would lose my momentum and career as an artist. I managed to do a lot of math, even with the day job, but now I have decided to take up my art career again and be a digital fantasy/science fiction illustrator. So what time is not spent at the day job is spent at Photoshop.

Recently I have finally made some progress organizing my various pursuits, so it is possible that I will finally work through that ellipse problem and move on to...hyperbolas or something. Things will be posted here, though not at the level and frequency of my epic "Electron Blue I." And we're all still waiting for the Large Hadron Collider to show us something that will change the world.

Digital or Paint?

2010-06-06T02:15:00.002-04:00

If anyone is reading this, they may have wondered where I was and why I hadn't posted in a while. The reason is that I had to prepare for and then exhibit at Balticon, a science fiction convention in the Baltimore area. I showed 9 pictures on my panel among the other artists at the show, and I'm pleased to say that I sold 6 out of the 9. They were all space images or spacey geometric abstractions, and three of them were prints. Of these, two were prints of digital compositions which had never had an existence on paper or board, while one of them was a photoprint of a painting that I had done from a digital sketch.

This proves that someone will buy a print of a digitally made image if they like the image enough. The disadvantage, though, is that they will not pay very much. I asked potential buyers and my friends at the convention whether they wanted me to drop "conventional" painting entirely, as many artists have already done. I was surprised to find that most of them still wanted to collect a hand-done image in real paint, even if they couldn't afford it.

My geometric space compositions are far easier to make in a digital medium than in paint on a board. Drawing the image is not the hard part. In fact, my geometric abstractions are done using an algorithm (a step by step "recipe") which anyone with a little technical drawing skill can use. I did a workshop at the convention in which I demonstrated this algorithm, and related algorithmic art generators, using a ruler and a bendable curve and drawing with a white pencil on a black background. In a future posting here, I will show you the art algorithms that make up my Spacey Geometrics.

The composition might take only about 15 minutes, whether done with pencil or Adobe Illustrator. The difference in time comes when you have to paint it. Acrylic, despite being a fast medium, does take a few hours to dry, and it's hard to get a smooth blend. I want to keep all those hard edge lines neat, so I have to use a small brush to get it even. But if I import the "wire-frame" drawing into Photoshop, I can just click away, use my "edge-finder" tool, and create a blend in a minute which would take me half an hour to do in acrylic paint.

Therefore I am tempted to switch all my spacey geometric art to digital, as I'm doing with most of my fantasy art as well. But will I sell it? Unfortunately, I am not an "inspired" artist doing "art for art's sake" and I need to sell my work once I have made it. I am still undecided whether I want to put a lot of effort into making conventionally painted geometric abstractions. They have had some success in the limited market I've experienced so far, but I don't enjoy the tedium of painting it all in when Photoshop beckons me to the screen with its seductive blue light.

Cold Dark Matter

2010-05-17T02:44:00.004-04:00

Back in the '90s (back? so long ago?) astronomers knew that the Universe was full of something they called "dark matter," something which had enough mass and gravitational pull to change the orbits of galaxies and alter the expansion of the universe. But they had no idea what the "dark matter" might be. The problem is still unsolved today although there are some leads toward an answer and "dark matter" has been documented in observations.

In those premillennial days, they thought that perhaps dark matter was something as prosaic as a vast amount of space rocks and debris, too dark or small to reflect light that telescopes could see. That was what I depicted in this painting. I imagined a universe filled with crunchy floating rocks, every star surrounded by a rubble field. There must be plenty of this stuff really out there, countless asteroid fields with anything from planet-sized down to clouds of gravel. But the scientists decided that this was not enough to be dark matter, and they're still looking now.

"Cold Dark Matter" is acrylic on illustration board, 16" x 20", January 1991.

This entry is also posted on "Art By-Products."

Bizmac, Mathematical Mid-Century

2010-05-14T02:54:00.002-04:00

Hello, reader(s)! I'm back from Massachusetts and back in the studio struggling with Photoshop CS4. I seem to have bent it to my will enough to show you my latest digital effort. This is "Bizmac," named after an RCA computer which was made in 1956. I wanted to get some "mid-century modern" references in there because this design is like the chic art of the 1950s and 1960s. The kind of art you would put on your wall next to your free-form furniture and your spaceship-designed TV and your boxy, white stucco, big window California house. I grew up with Mid-Century Modern and have waited 40 years for it to come back into fashion.

But this picture also has plenty of mathematics, justifying its place on ELECTRON BLUE 2. There is a parabola, drawn with white lines on the spacey background, right in the middle of the composition. There are also exponential curves, circle arcs, and some plain old straight lines. There is also Hidden Calculus. It comes from a tool that I use in CS4 called an "edge-finder." This traces edges of areas using strings of points, and it divides the line into smaller and smaller segments, in order to calculate the edge's place in the pixel plane of the picture. The concept of dividing the line into smaller and smaller segments in order to find its slope is classic calculus. So even though I haven't been number-and-letter crunching recently, I have been recognizing how my BizMacintosh uses calculus concepts to refine its lines.

"Bizmac" is made on Photoshop and Adobe Illustrator CS4, designed to be printed at 14" x 11".

An ellipsis

2010-04-24T01:55:00.002-04:00

I got through circles a while ago, but then other projects have intervened to keep me from doing mathematics. A terrible earthquake happened in an imaginary city of mine, and I am reporting from the "media feed" from people either on the scene or telepathically linked to those at the scene. If psychic communications were real and controllable the way radio communications are, the news media would be quite different! I always have a storyline or two unfolding in my head, whether I write it down or not. This has been considered a mental disorder called "fantasy-prone" syndrome. Well I'm sure I have a number of syndromes, such as "delayed sleep-phase syndrome" (staying up all night and sleeping most of the day) and even some level of "autism spectrum syndrome" or why I like math in my older years.

So for now I am in an ellipsis, or a "..." state of mind, and since I have to leave for more than a week for family birthday duties, I won't orbit through ellipses for more than a week at least. I won't have time or space to take Humongous with me on the road. I'd need an 18-wheeler to take "Humongous" with me anyway. If I have a thought, maybe I'll communicate it from my WiFi outpost, but I doubt that I will have any thoughts worth sharing, especially in Massachusetts.

Circling About

2010-04-09T03:39:00.003-04:00

I have progressed in my millimeter-at-a-time review to Circles. I have circled around this whole subject at least four times in my math self-education, hoping that I would not forget everything I learned each time I went around it. This time, with the help of Humongous' idiot-proof scribbles, I actually understand how to get a proper circle equation out of the little parade of x^2s and y^2s and their subordinates, that colorful "standard form" which equates itself, clownishly, to zero. Seven years ago, many circles ago, I stood in stupid silence before the lineup: x^2 + y^2 +5x - 7y + 6 = 0 or some other such mathematical conga line. Now I know that they are challenging me to complete the square twice. Don't forget to add those virtual quantities to both sides of the equation! Then they throw a necklace of shiny plastic number beads at me.

I actually got one of these problems right, without missing a plus or minus sign. By far in my algebraic life, this is the mistake that causes me the most mayhem. And once I've failed a problem due to a minus sign where a plus should have been or vice versa, I need to wait a while before I try it again. That allows for the circle of forgetting to do its work.

From the circus of circles to the mind of God: "What does the observable universe tell us about God?" The answer: God likes round things. This is the circle that is unbroken, which is mystically inscribed inside the completed square.

Comets and Parabolas

2010-04-01T01:32:00.004-04:00

While I'm still on the subject of parabolas (parabolae?) I will reminisce about comets. When I was in middle school I made up stories about a character called the "Comet Prince," who lived in a kind of nineteenth-century swashbuckling world and had a helmet with a comet-like tassel at the top. Later on, in 1970, I saw a real comet, "Comet Bennett," which was bright in the sky and easily sketchable. I went to the library and read up on comets and looked at lots of pictures of them, learning that they were quite variable in appearance. Like most things I got interested in, comets were almost living things for me, with personalities and unpredictable behavior. For instance, I learned about Comet Morehouse, which appeared in 1908, and whose tail flickered and fragmented like a candle flame in a cosmic breeze. Later on I viewed the disappointing re-appearance of Comet Halley in 1986, and the excellent Hale-Bopp in 1997.

Now much more is known about comets than in 1908, and probes have been sent to photograph them up close and to blow craters in their icy nuclei. They aren't portents of disasters to come, they are just building debris left over from the construction of the solar system. I try to think like a scientist and not personify anything nor give in to the entertaining delusions of fantasy.

And what about the parabolas? Comets have elongated orbits, which bring them in from the outer depths of the solar system for a quick and precipitous descent toward the sun. This trajectory is a parabola, with the sun at its focus. Some comets get so close to the sun they are known as "sun-grazers." Their parabola is narrow and their turnaround time is short as they whip through this curve. Within a few months, they are out of our sight and headed back towards the black edge from which they came.

But are these parabolic travelers really orbiting? A parabola opens up into infinity, and there is only one closed side to it. Some comets really follow a parabolic orbit and never come back to the sun. Other comets, periodic comets like Halley, may appear to be making a parabolic turn around the sun, but their orbits are really very long ellipses. This antique website, from the Hale-Bopp era, explains it quite well. Some comets even look like parabolas. My drawing of Comet Bennett from 1970 shows a shaded parabolic shape with a bright nucleus about where the focus would be. Purely coincidental, probably, though some case might be made for the shapes created by the pressure of gases as the comet melts in the heat of the sun. By the way, the word "parable," a tale of comparisons, comes from the word "parabola," which is originally Greek and meant "comparison," or literally a "throwing beside." So this has been a story about comets, a parabolic parable.

Parabola Reflections

2010-03-27T03:11:00.002-04:00

I found my math book. It was under a lot of papers. When I was not sorting out papers or doing laundry, I returned to my review of parabolas. When I first studied these shapes and their formulas, many years ago, I never quite understood what made them go. I knew that there was a point at the center of the tip of a parabola called the "focus," and a line just ahead of its tip called, in a somewhat fetishistic term, the "directrix." The line that describes the parabola is made of points that are equidistant between the focus and the directrix. I have seen this done as an animation.

"Humongous" takes me through the creation of parabola equations in proper form, that is, y = a(x-h)^2 + k. (h,k) is the vertex (tip point) of the parabola and after you've sorted and worked your equation into the formula, you will find not only the vertex but the focus and directrix as well. You just need to know a bit more machinery to get the focus and directrix.

What I find interesting is that for parabolas on their side, the ones with the x = y^2 format, the formula reverses itself. h and k switch places and the focus and directrix also are found by switching h and k and their positive/negative signs as well. This means something. There is a basic principle of mirror reflection that I should learn. Given that the problems in Humongous are teaching problems, they are offered to me before the explanation of how to do them is given. If I had more experience with this mirroring principle, I'd be able to apply it to a parabola turned on its side and come up with the formulas myself. Maybe someday I'll be able to do this. Meanwhile, my mathematical imagination looks ahead to a more exotic parabola: one whose axis of symmetry is not vertical or horizontal, but at an angle. The formula is out there, waiting for me to get clever enough to figure it out.

Meeting Ray Solomonoff

2010-03-19T02:35:00.004-04:00

I have been desperately shuffling things around my art studio trying to make some kind of order. I hate disorder and clutter and that's what I have right now. My math book and worksheets are buried under random papers. I worked on "Neutron Starlight" and then I had to mount and mat fourteen prints for a dealer who wants to sell them at Persian gatherings this weekend. This Saturday is the long-awaited first day of spring, which is also NoRuz, the Persian New Year. Happy NoRuz, if anyone Persian is reading this.

I have sheafs of old newspapers in the studio which I use as background to spraying paint. I was attempting to lay down some matte black backgrounds yesterday, which was the first decent sunny day in weeks. I pulled out the New York Times from January 13, 2010 and found an obituary for Ray Solomonoff. He had died in December 2009 at the age of 83.

This brought back some vivid memories from my life in Cambridge. Ray Solomonoff was a pioneer in the theory and development of artificial intelligence, or how machines can solve mathematical and other problems. I lived in Cambridge, Massachusetts for many years. The first two of those years, from 1976-78, were spent being a graduate student in classics at Harvard. I didn't do well in academia and those years were miserable. But I also moved in science fiction fan circles and met a lot of interesting people who were not just fans, but real scientists and space travel promoters. Ray was part of that community. One night in winter 1977, I went to dinner at the dwelling of Ray and his wife Grace, who was a writer and poet.

They lived in one of the strangest hideaways I've ever visited. Tucked away behind retail buildings right in the center of Harvard Square were ramshackle apartments, some of them windowless and probably illegal. Their rents were low and living in them was not too different from "squatting." Ray and Grace lived in one of these. I thought it was amazing. They were the archetypal old hippies, except that Ray was a world-renowned scientist. Their hidden rabbit hole was book-lined, cluttered and filled with odd artifacts, just like my digs, but without the art studio. This was 1977, the last years of the Old World before the Internet. Ray knew that the NetWorld was coming. I had no clue. What did I know back then, struggling with Greek grammar and Late Roman rhetoric? Math was hostile alien territory to me. So even though I dined at his house, I had no idea what Ray Solomonoff was really an expert in. I had heard the words "artificial intelligence" but that was about it. It would take me another 23 years to discover mathematics for myself.

I brought my sketchbook to that dinner, and drew portraits of both Ray and Grace. Here's my rendition of Ray, along with some kitchen utensils and a mug from the dinner table. Rest in peace, Ray, there at the Infinity Point you envisioned.

Neutron Star Surface as Fantasy Landscape

2010-03-12T03:46:00.005-05:00

I'm still thinking about neutron stars. This time, it's the astronomically unthinkable idea of what the surface of a neutron star might look like. According to my sources, a neutron star is a round thing about 12 miles in diameter, with a solid crust and a soft center filled with incredibly dense Swiss chocolate. Oops, wrong blog. The neutron star is, according to the sources I've read, more like a planet than a star, except it's made of "degenerate matter" so dense that all the atomic nuclei have been crushed together by incredible gravity. Not only that, it spins really fast, even a hundred or more rotations a second. Even if you could solve the gravity problem, this is not something you could ever land on. The whole thing is one of those astronomical phenomena which cannot be visualized.

This does not stop science fiction and fantasy writers and artists from trying. One s.f. book I read, of which I really wish I could remember the title and author, fantasized that in the distant starfaring future, humans and aliens had some technology that could neutralize gravity, so they could visit supergravitated places, like neutron stars. The author described the surface of a neutron star as being so smooth as to be a perfect mirror, since its gravity would prevent anything from rising even a millimeter from the surface.

Later authors have speculated that neutron star surfaces might have at least some texture. And observations of these stars have given evidence that "starquakes" occur on neutron stars, where the crust shakes, breaks, spews unspeakable radioactive ichor, and then reforms, altering the rotation slightly. There actually is a science fiction treatment of neutron stars by author Robert Forward, which I ought to read before continuing to yammer about them.

As for visual arts, I would imagine that a "realistic" treatment of the surface of a neutron star would show nothing, or just a bright gaseous blur of stuff swirled by mega-gravity. Other pictures I've seen show something that looks like a ball of fiery goo with some crust over it, surrounded by a purple whirlpool. But what if you could stand on this surface? What would you see? My imagination tells me that you wouldn't see individual stars, just their trails in a blur of light as the thing rotates so fast. And as for the surface, it's not totally mirror-like but broken with fissures through which the glowing substance below gleams with an ominous radiance, and fountains of ultraheavy transuranian elements spatter like a psychedelic volcanic field at the edge of the universe. Here's my visualization of it. Photoshoppe speedpaint, 10" x 7".

Neutron Starlight, the painting

2010-03-09T01:51:00.003-05:00

Here we are in the realm of warped space! I have finished my Neutron Star astronomical fantasy and here it is. (Click on the image for a slightly larger view.) This is not an "accurate" astronomical depiction but rather a fantasy about what it is like to orbit the core of a supernova. The title of the piece is "Frame Dragging," which is how a rapidly rotating super-gravity object like a neutron star warps and pulls space around it. This is symbolized by the twisted grids I included in the picture. Someday I hope to learn the mathematics which describes how grids can twist. A jet of charged particles emerges from the center of the disk.

This piece is a commission from a composer friend of mine. He has commissioned other artwork from other artists he knows and he plans to write a musical piece to go with each painting. I will be interested in what he writes for my neutron star.

"Frame Dragging" is acrylic on masonite board, 16" x 20", February-March 2010.

Neutron Starlight

2010-03-07T02:48:00.004-05:00

I'm working on a painting which is an astronomical fantasy involving a neutron star, or to be more precise, a neutron star which has an accretion disk of gas and dust whirling about it at high speeds. I will show you this picture when I'm done, but it's not done yet so please have patience.

Neutron stars are some of the most extreme phenomena in the universe, at least in our universe. They arise when a large star, much larger than our sun, uses up its fuel and collapses into itself, at which point it then explodes into a supernova. This huge blast blows away most of the star, leaving a super-heavy core which collapses further under mega gravity into a ball of skwushed-together neutrons and other subatomic particles. This core picks up rotational speed as it gets more and more compact, so by the time it reaches super-ball density, it is spinning at super-fast speed, many times a second at least.

It is made out of atoms and "degenerate" atoms, all crushed together in a material of which a teaspoon would weigh more than a whole city. Its gravity is so strong that it bends light around it. Some neutron stars emit a beam of high-energy radiation, which can be seen by astronomers in a regular pattern, as the starcore rotates and shines like a lighthouse. That's called a "pulsar."

I only know this because I did some research, namely I asked someone who knew about it. Here's an excellent weblog which describes all of this better and more accurately than I can. So having chosen to spend my time with a neutron star, naturally the first thing I ask as an artist is, "what does it look like?" Does it glow in the dark? Is it green like Kryptonite? I go straight to the superficiality of the matter. If you could possibly stand on the surface of a neutron star, what would you see? (Some science fiction writers have tried to imagine this.)

It turns out that a neutron star by itself isn't very bright, at most glowing like a dull ember in a fireplace. But if it has attracted a disc of gas about it, then you would get a bright whirlpool of glowing gases, spinning wildly with the neutron star hidden at the center. And from the center of the glowing disc, a beam of energized particles blows out perpendicular to the plane of the disc.

OK! With that design layout, I'm in business. I've got my charged particle airbrush, and my heavy metal elemental paints. Titanium White, Cadmium Red, Cobalt Blue, all come from elements formed in supernovas (as do you and I). And I have my super-compacted black iron gravitational coating, which artists call "Mars Black." With the power of imagination I can go stand on the surface of that neutron star as the flame winds swirl around me. I can hop to another neutron star where the stars of its "sky" are just a blur. And I can put a teaspoon of neutron star material into my cosmic coffee, which now weighs more than Washington, DC.

Iconic Conics

2010-02-27T02:31:00.006-05:00

The buzzword of the last few years has been "iconic." This word, like an invasive weed, has infested English-language journalism to the point that you cannot read an article about just about anything without finding something described as "iconic." Anything that used to be "famous" or "memorable" or even just "well-known" is now iconic. If you are a reader of current media, check it out: how far can you read into an article in "Time" magazine or even the "New York Times" without finding the i-word? Usually, it's about a few paragraphs, and then bzzzt! there it is.

Is there a right use of the word outside an Eastern Orthodox church? Well, if anything is "iconic," it is the time-honored, millennia-old diagram representing the sections of a double cone. This is the conic section diagram, thus it is an iconic conic. You see it here to the left: two cones, joined only at their apexes, out of which sections or slices are taken. The sections of the cone include circles, ellipses, parabolas, hyperbolas, and straight lines, all of which are the graphed outcomes of the high school algebra equations that I have been re-visiting with my Humongous Book of Problems.

I'm currently working on parabola problems. I find the parabola one of the most beautiful shapes in mathematics. I originally knew it by the basic formula y = x^2, which gives you an archetypal parabola sitting with its vertex on the origin of the graph. And I also know it by various simple quadratic expressions of the ax^2 + bx + c variety. But Humongous is more specific, and provides me with a parabola formula which I have not worked with before, the more precise y = a(x-h)^2 + k, where h and k tack down the vertex of the curve. You can work your equations over from the previous form to fit the more precise form. You can even reverse x and y so you get a parabola resting on its side. Although if your parabola is on its side, some of the numbers could spill out, and you'd lose some of the iconic from your conic.

Logarithmic Encounter

2010-02-19T03:09:00.003-05:00

I have just finished walking through Humongous' chapter on logarithms and logarithmic equations. This chapter contained math that I had never seen before. But because it follows orderly patterns, I was able to handle it fairly well. I have encountered logarithms before, as I said in a previous post, but I never knew how to add them, subtract them, or exponentiate them. The author's explanatory frames were, as usual, very helpful. But I do have just one little question, which is....what the fook are these things for, anyway? Pardon me for being dense, but usually, in my experience, math is about something. It describes an existing phenomenon, which is how science is done. Without math, no science. But without science, still plenty of math!

I am told by well-meaning websites that logarithms, especially the "natural" kind which use the very irrational number "e" as their base, are about how things grow, whether it's your investment (in this case, it shrinks) or how numbers increase by folding and unfolding increments. But I can't figure out what a logarithm with a base 5 would be doing, nor what something with a whole polynomial for an exponent would describe. I don't want to be rude to numbers, but I can solve these things (after instruction) without any idea of what they mean. I'm still too much of a humanities type I guess, I wonder what things mean. But as is attributed to Saint Feynman, I should just "shut up and calculate." Mathematics turns the wheels of the world, and as a mere amateur student I should not concern myself for why they turn or where these wheels go.

The Old Papers

2010-02-16T03:05:00.002-05:00

I've been going through more of my old papers from the 1990s. The idea that something from the 1990s is now OLD is the first depressing thing about this particular project of mine. But it's old. It is B.F. by at least five years. "B.F." stands for "Before Fermilab," the major turning point in my life in 2000 when I visited the Tevatron and swore to study mathematics and physics. How'm I doing? The past makes me depressed.

In those days I did not have a day job. I did freelance illustration work for luxury home builders (it was the era of the "McMansions" which now stand empty all over America) and for magazines and an occasional book cover. Sometimes I lectured on Zoroastrianism, which was my previous intellectual adventure before mathematics. It was a science fiction convention which took me out to the Chicago area where I visited the atomic cathedral.

Another thing that makes me depressed about these old papers is that I was doing a lot of fantasy and science fiction art then, but not now. I don't do much of this any more, for a couple of reasons. One reason is that I can't sell it. The convention market has almost disappeared, and collectors now are too old and too impoverished to buy it. As for book and magazine illustration, there's plenty of it but it is all done in digital media which I am now struggling to learn. Another reason is that I don't consider fantasy and science fiction art "serious." It may be fun and entertaining, but it is not something that a "grown-up" artist does. The "serious" art is those geometric abstractions that you see on my main page at pyracantha.com. I've done a lot of these and have sold a few to discerning collectors, but I just don't have as much fun doing them as when I did magic cities and electrical angels, which was my output in the '90s.

I traveled a lot in the USA (and once to Canada) during that decade. I was much more mobile, since I was not tied down to a day job. I went to Kansas, to California for the World Science Fiction Convention in Anaheim, to Toronto to give a talk to the Zoroastrian community there, and many times to Tennessee to go to conventions and visit friends.

Where have all these people gone, and what happened to my fan friends? I hesitate to find out. Some of them, thankfully, are still around. I suspect that others are no longer alive. Are there still science fiction conventions? I go to a couple each year, but they are sorry affairs lacking the excitement of times past. I have kept every program book from every convention I ever went to. My art show paperwork from the conventions is in the boxes. 1995, 1996, 1997. 1998 and 1999 are buried so deep in a closet that I risk being crushed if I try to retrieve them.

I didn't expect to be so depressed by going through my old papers. I figured that After Fermilab, that world of fantasy and magic and esoteric religion would be dead to me. I would walk into the mathematical light purified of silly myths, idiotic diversions, and unscientific superstitions, meeting the chaotic, irrational world with my empowered scientific rationalism. Instead, I find myself missing the old world, the smelly fantasy fan world full of Ascended Masters and half-elven game characters and fantastic cities on rivers of stars.

Raise and Root

2010-02-09T01:22:00.003-05:00

As I prepare to be confined in my quarters again for another round of blizzardry, I work my way through Humongous' chapter on Logarithms. The last time I blogged about Logarithms, it was 2004, in the original Electron Blue, let us say Electron Blue 1. I cannot use "Blogarithms" as a title, because of course other math folk more clever than I have taken it, including this endearing blog I just discovered tonight, written by a devoted Christian mathematician.

Logarithms totally mystified me in 2004, mainly because I was studying them from an antiquated college algebra textbook from 1958. They didn't have calculators then, and a lot of my log work was spent interpolating logarithms from in between given values in printed log tables. I spent hours sweating through calculations that never quite worked out and which can now be performed by a fifteen-dollar calculator in less than a second. I eventually gave it up as a bad job and forgot everything I had tried to learn.

Now that I am reviewing this, I find enlightenment in my Humongous text. Logarithms are numbers. I didn't know this. They are about transforming one number (alchemically called the "base") into another by the dual process of raising it to a power and then getting the root of it. I'm talking square roots, cube roots, and any number of times you can do them to the base number. The process of raising and rooting is expressed in a ratio in which the root part is the denominator and the raise part is the numerator. Most of the time this ratio runs out to the misty Beyond in a long irrational decimal, which my 1958 book preserves to four or five digits in poorly printed yellowing tables.

Humongous moves right along to manipulating and using these logarithmic numbers. Their original purpose, to help multiply large numbers, has long since been superseded by gadgetry, but logarithms are still useful in calculus (I have not been illuminated in that regard yet) and in the modeling of growth, both biological and financial. This excellent math education website, which didn't exist in 2004, has been very helpful in explaining why I should pay attention to logarithms. And Humongous has taught me in just a chapter, what I failed to learn in weeks struggling with the 1958 text. Raise me to a higher power, modern world! And then root me in the ancient ground of mathematics, so I may turn toward the light in logarithmic growth.

The Untouchable Dotted Line of the Asymptote

2010-02-03T03:00:00.002-05:00

Well I re-learned something about blogging I should have remembered, which is that you never know who is reading what you write. I just figured that no one but three of my friends read this. And then I got comments from the author of a book I reviewed, about my remark about sexism in the introduction. Yikes! I apologize! All I can say is that I have lived through decades of sexism which I am only now allowing myself to realize, and I tend to see it everywhere.

I am reminded of a similar incident many, many years ago, when I panned a new recording by Irish pop star Enya, and got angry responses from Enya fans around the globe, from places I didn't even know were places, let alone Internet connected.

So here's another try at re-connecting with one of my blogfails. (I just coined that word, but I'm sure someone else was there before me.) I used to link to a wonderful blog, still in existence, called "Asymptotia." This slice of an exotic life is written by a theoretical physicist and string theorist in southern California. He has incredible energy, and he has a full academic schedule, appears on TV, does outreach to young people, gardens, cooks, travels, hikes and camps in the wilderness, builds things, and in general lives a fascinating life. For various reasons I annoyed the Asymptotia author, and I decided for my own good to drop off his radar. But I couldn't stop being fascinated with physics and math, I had to go back to it no matter what, so I apologize to him, and wish I was back in touch, and I promise to be good.

Asymptotia brings me to the current chapter in "Humongous," where I am contemplating how a graph of a function shoots out toward a line, either one of the axes of the graph or a limit, or even a slanted line, that it never touches. The line that it never touches is the asymptote. It's just math, but since math is a story too, there is a mood and meaning to an asymptote. You can see it, you feel its draw, you can keep multiplying and running out your function, but you will never reach the goal. If you touch the asymptote (or that limit) you are dividing by zero and you lose the game. You fail, fall into the black hole and are vaporized into atomic waste. Play again?

And yet you keep going toward it, knowing you'll never reach it. You keep playing the game, knowing that you can't win, you can only get closer. Your achievements grow ever more immeasurable, and you still will never get there. In my case, the asymptote is far off. Any bit of mathematics I do is still a major change in my personal graph. As I trudge through midwinter, the asymptote is covered with snow and the graph, for a moment, is clean and untracked.

Minutiae of the past

2010-01-30T22:55:00.003-05:00

The chapter of "Humongous" I'm working through now is about functions, which I mostly know about but this set makes it much clearer to me. This includes what might be called "flipping" functions, or finding the inverse. Meanwhile outside it continues to snow, relentlessly winterizing our urban landscape again.

I am opening up my old boxes of archived papers from years past, in the hope of freeing up a little more space in my packed dwelling. I keep what has personal significance, or the receipts for stuff I still have, art business records, or important financial and tax documents. But is it really necessary for me to keep documentation of my grocery buys or my coffee sips? If I were more obsessive than I already am, I could possibly document and recreate my actions during any chosen day in 2002, or 1987, simply by the time-stamped receipts I saved and the journal entry I made for that date. I could do it, but should I do it? No one is auditing me or prosecuting me. No one is interested in what I did 8 or 23 years ago. (23 years!! Yikes!). So why should I keep these minutiae and receipts? Let them be recycled.

And yet I feel sad getting rid of these trivial papers, even though I wasn't particularly happy when they were getting made and saved. I am erasing the past, irrevocably. Good or bad thing? I remember what life was like for me back in Cambridge, Mass. at that time. Winter ruled, except for two short hot months of summer. In 1987 I was working at "Sky Light Books," a New Age bookstore just outside of Harvard Square. I would look up at the sky and see the snow coming down, and walk in the slush on the streets, and I would wonder, "Why does anyone live here?" and, then, "Why do I live here?" So I went to what I thought would be a warmer climate and a better job.

There I was, in Harvard's shadow, and I never visited the math or physics department! My math and physics journey wasn't even a gleam in my eye back then, though I did want to know more about computers. ("Windows is the future!") Fast forward through the dusty papers to 2002. I find the same little receipt slips, for the same things: groceries, coffee, photocopies, art materials. The vendors have changed, but that isn't the only thing that changed. On the back of many of these receipts from '02, I find algebra workings and notes, and graphs and, uh, functions. I scribbled them on the scraps at odd moments, solving problems here and there and using the receipts as the only paper immediately available. I save these from the recycle bin. That past is now.

The Humongous Book

2010-01-27T02:03:00.004-05:00

I depend on books for my math education. I don't have a professor or a tutor and I'm not in a class, for various personal reasons. And I often do my math work at hours when any normal human being, even a mathematician, is dead asleep. I have shelves of math books that I've collected over the years. As with any other created thing, math books vary in quality and helpfulness.

I have had to trade away some math books which looked promising but turned out to be frustrating and ill-fitting. When a book advertises that it makes math (or physics) "easy," I have learned that the authors leave out important stages of learning or problem solving to make matters shorter and more compact. That isn't good for someone who doesn't have a teacher to explain what goes between the written steps.

Every so often I find a math book that is just right for a slow, stepwise mind like mine. In my early days of mathfulness, back in 2001, I enjoyed Lynette Long's "Painless Algebra," published by Barron's. Later on, I was both entertained and educated in very basic physics by Gonick and Huffman's "Cartoon Guide to Physics." Now that I am back into calculus, I am finding an excellent guide in Michael Kelley's "The Humongous Book of Calculus Problems." Its cover says that it is "translated for people who don't speak math!!" I speak math all right now, but the explanations are welcome to someone who doesn't have a teacher to do the translating. Each problem is worked out in detail. In the name of mathematical honor, I give myself the task of trying to work the problem out myself before I turn to the answer. Since the answer and its process is printed on the same page as the problem, I mask it from my sight with a piece of thick paper, until I'm ready to look at it and reveal either my cleverness or more often, my cluelessness.

I will warn you that I was put off by a sexist remark in the author's introduction (quote on request), about his own daughters, no less. It only reminds me of how difficult it is for a woman of any age to make her way in mathematics, physics, or other "hard" disciplines. But I am willing to put this aside because the book is so well-written and useful for me.

The first chapters are review chapters in high school algebra, such as graphing, trigonometry, things which you need to know enough of to do calculus. (If I am a glutton for punishment, there are "Humongous" books of algebra and trigonometry problems too.) Interestingly, "Humongous'" explanations elucidate many math questions that I had asked all along with no clear answer. The chapter I am currently working through is about how transformations work on the graph of a function: what algebraic operation turns your graphed pattern upside down, or backwards, or what squishes it or elongates it. These are the same transformations I often do in Illustrator or Photoshop. It's interesting to see how the magic power of a computer can work graphic transformations on a whole picture rather than just a line on a graph.

As in all math books, the problems in a section increase in difficulty and complexity as the chapter progresses. This progression of difficulty is mitigated, in "Humongous," by the comforting thought that these problems are here to teach me something, not to test my knowledge and skills. These problems are my friends. They are not going to destroy my chances of getting into MIT.

I put "Humongous" on my table next to my "WinterBright 2001" lamp which I wrote about in the previous post, and use the light to work on math. But now I have my brilliant BlueMax task light as well, and my studio looks like a road construction site by night, lit with industrial spotlights. I love it. All those photons, just for me.

Lack of Light

2010-01-22T02:00:00.003-05:00

A day without solving a math problem is like a day without sunlight, to paraphrase a famous fruit juice slogan. But in the dead of winter, dark January, it's hard to see my math, even though it glows with intellectual light. My studio is a little island of greyish-orange light in a cold sea of darkness. But I have one bright light, and I've set it next to my math books. This is the "WinterBright 2001," a fluorescent fixture designed to combat "seasonal affective disorder."

Seasonal affective disorder is not something recently made up by conniving psychologists. It is an authentic feeling of melancholy and lethargy caused by winter's lack of light. I have always had this, especially when I lived in my homeland of New England, a place where winter never seems to end. I hoped to be more mellow in the Mid-Atlantic area, where the climate is a bit milder, but it wasn't much of a difference. So in about 1999 I bought this optimistically dated light.

Turn it on, and I can see my math. I'm huddling close to it while I pore through yet another review of functions. The union of f(x) and g(x) is f o g, which doesn't spell "fog," (though that would be appropriate) but stands for "Run function G through function F." F "operates" on G. You can treat a process as if it were a single thing. The light from my WinterBright 2001, though, doesn't reach very far.

For years I have held on to an ad I tore from a gadget catalogue. It says, "Turn any room in your home into a sunroom." My old standing studio light, an overheated obstacle that I never failed to bump into, finally fizzled out late last year. I called the catalogue people at the number on the ad and found that the company had gone out of business and been sold to another similar company. I reached a real person on the phone and asked for illumination. In a short while I had bought an expensive new lamp hoping for more light.

It arrived this week and I heaved it up the stairs. Who knew that light was so heavy? It is still in its box, but will soon be deployed. It is waiting, the "BlueMax Lighting High Definition Patented Dimmable Task Lamp and Light Therapy Unit." If this works, my studio with both art and math will be a friendly sunroom and not a campfire in an industrial cave. But what I need to know is, will this mathematical light make me brighter?

Pennies and Probability

2010-01-15T22:01:00.004-05:00

I find at least one penny (coin) on the street almost every day. I drop them into my "charity coin" jar with other change, so they are eventually returned into the economy as contributions to some worthy cause, usually animal rescue and welfare. My most recent penny find was crushed and corroded, but it was still a penny and I saved it.

All these fortunate little finds have caused me to wonder, though. Is someone dropping pennies just so I can find them? No, I don't think so. I know that people drop pennies and don't bother to pick them up because they are too low in value, but they don't drop them thinking that I will find them. Or: are the streets, parking lots, and sidewalks covered with an equal distribution of pennies, and I only find the ones that are where I walk? Maybe, but that seems like that would show up as a drain on the U.S. economy. It is most likely that the pennies are distributed irregularly on the pavements. I conjecture that pennies are more likely to be found in well-traveled areas, where there are plenty of people to drop them.

If that is so, why do I find so many of them? Do other people find them too? If I find more than other people, is it because I somehow pick paths which are more penny-rich? Or is it that I am more observant, and am able to pick the circular shape of a small coin out from the background of gravel or pavement? Perhaps it's my bad posture, walking with my head down, which aims my view at the penny-strewn ground rather than the goal ahead of me.

I don't know much about probability. It is an aspect of mathematics which I have not yet studied. Would probability theory explain why I find so many pennies on the ground? There is probably a distribution pattern of pennies on parking lots or sidewalks which, if graphed and analyzed, would reveal to planners how people use the space. I often find the coins around parking spaces, near the lines between where cars park, possibly because they fall out of people's purses or wallets or pockets there as they get into their cars.

For some reason my apartment's parking lot is richer in penny drops than other parking lots I have perused. In fact, I have sometimes found nickels, dimes, or even quarters on the pavement there. This now becomes more than just a probability problem; it is a socio-economic question. Why would people who are not at all rich throw away small change? Or is it their children, who don't know any better, throwing the coins onto the ground? For me, the question is, how much money can I collect, and could I collect more if mathematics and sociology could tell me where these cast-off coins were likely to appear? It is not a matter of "pennies from Heaven," it is pennies from probability. I have not even begun to consider whether these are found heads-up or tails.

Walking the Limits

2010-01-11T02:00:00.003-05:00

Calculus limits are supposed to be an answer to the famous "Zeno's Paradox," in which the ancient philosopher proposed that you could never reach a destination because you would be continually traveling smaller and smaller divisions of space but never arrive there. When I first encountered calculus limits and their problems, they were in graph form and I was able to see for myself where the limit was. Very soon, given my visualizing nature, I could place myself into a virtual space where the graph was my terrain and I was walking through a three-dimensional environment.

Graph lines became landmarks and even trees and buildings. Some had a reassuring solidity and others were unbalanced and shaky. Each equation that I graphed, mostly on a graphing calculator, revealed another landscape. A very simplified scape, but one which was walkable by my virtual mathematical self.

Then came limits. If a limit was some specific number, up against which I could press, that was OK. But then there were those other limits in which there was no end, no reassuring specific number, just positive infinity or negative infinity, a track extending into an endless horizon, a kite string going up into the sky, or a sounding cord down into the sea, forever. Others were the graphs of rational functions, where there was a gap where the denominator would be zero, which is not defined and thus not existing.

I looked down or up the zero hole with a feeling of dread. This is where reality breaks down in my virtual world. There's a hole there that, if you step into it, you will disappear, never to return. You've perhaps heard the saying, "Black holes are where God divides by zero." There they are in Limitsville. How do I get by it? If I attempt to step over it, will its pressure suck me in? How do you get by the limit? Why do you reach the destination that Zeno said you could never attain? One of my Friendly Mathematicians mysteriously told me that you could cover an infinite amount of distance in a finite amount of time. I guess it depends on which infinity you're considering.

Math Problem as Narrative

2010-01-08T03:33:00.002-05:00

I'm currently doing limit problems, which get plotted onto number lines. You find the limits and then the area on the graph in which the inequality is true. Before that I was re-acquainting myself with polynomials and algebra problems which were solved by going through a number of steps. It brought back an observation of mine which I remember from the first Electron Blog and my encounter with multi-step problems. Which is that if you look at an algebra problem, at least at the modest level I was working with, it resembles a story. A math problem has a beginning, middle, and, if you're lucky, a reasonable ending.

It's more like a mystery or detective story than other types of fiction. Something is missing. Or someone is dead. That's the X-quantity. You, the reader, need to solve this mystery by going through the procedures. You have the other constants as evidence, and the structure of a quadratic or trigonometric or whatever equation to guide you. There are pursuits and reversals (shifting quantities across the equals sign, for instance). Something that was positive and friendly turns out to be negative and unfriendly, or vice versa. Then you perform a forceful operation and get to the (square) root of the matter. And there is your culprit, morally ambiguous perhaps with his or her "plus/minus" of rootedness. But X is now identified, and you can turn the page.

There are other genres of problems which probably resemble romances or war stories or other genres. But it is harder to find math problems which resemble modern mainstream fiction, because modern fiction often lacks conventional plot and any kind of rational structure. But there will always be more advanced math problems, the kind I may never get to, which are so far away from the math of ordinary life that they resemble the fiction that got me where I am today, namely science fiction.

Saved by the Net

2010-01-04T03:03:00.003-05:00

My polynomial panic didn't last very long. I reverently attended the Church of Google and within minutes my prayers were answered (Does Google out-perform God??) as my search for "algebra problems" and similar phrases was rewarded. I found a number of sites which offered just what I was looking for: worked-out problems with detailed procedures and helpful hints. I now see that instead of blundering about trying to unify all the terms on one side, I can reduce them to linear sense on each side of the Equals Bridge, before I have to add them all up. I tackle the number and letter crunching one bit at a time. Then I can carefully sort out whether something is negative or positive.

When I was first learning this in 2001-2002, which is now a scary 8 years ago, there was plenty of internet math, but somehow I didn't find sites as helpful as the ones I just found. I think they may not have existed. Desperate high school students have driven the need for such sites to exist, and I'm glad they do (not the students, the sites). I am also warmed by the fact that these sites are always available, even at 3 in the morning. There is nobody to bother, no one to call with splutters of frustration. The site is always serenely willing to help you. All you need do is go to a place like "AnalyzeMath.com" (which was started in 2003) and you will find what you need, at least mathematically.

The Internet is a math-send (math=God) for people like me, independent students who hate classrooms and don't have the resources to get tutors. It's one of the few genuinely benign qualities of this technology. I learn in my own private space, at my own private pace, and no one needs to know, except that I just told you.

Polynomials

2010-01-03T01:58:00.002-05:00

As I practice my math skills before re-entering the world of calculus, I am re-visisting polynomials and basic algebra. I have been doing algebra since 2001 anyway. Doing problems with polynomials brings back my memories (and also my failures) in algebra.

Polynomials are agglutinations of letters and numbers which depict things that are multiplied together, added, subtracted, and squared, cubed, or otherwise exponented. They come in single clusters, such as 3x^2 (this means three times x squared), or double clusters known as "binomials," such as (2x + 9), or "trinomials" with three working parts, such as x^2 + 4x + 4, or even more-nomials. Equations are made from these, some of them in a single line, others with fractions such as (4x - 3)/(x - 5). My job is to review my polynomials, and re-gain what skill I had when I first learned them in 2002.

I am OK with the simpler manipulations, and multiplying and dividing them. But when it gets into problems using longer strings or higher stacks of these expressions, I am the same as I was 7 years ago. When it comes to trying to solve equations, whether linear or quadratic (with x-squared variables), I miss every single problem. And I did back then, too. Why? It comes down to one thing which I make a mistake in every time: negative or positive quantities. I simply cannot seem to figure out whether something comes out minus or plus. In algebraic manipulation (number play, in a way), negative and positive quantities often switch back and forth, depending on what side of the equal sign they are on, or what they are multiplied by. I will get the whole string correct, and yet lose the problem (game?) on one wrong sign, negative instead of positive or vice versa.

I keep doing problem after problem, trying to get it right, and again and again I fail. I try to keep track of the switching but it doesn't happen. Just as before, when I was stuck trying to learn something, I try and try to get it right, consuming dozens of problems. And still there is one minus or plus out of place. Or I have copied it wrong, or even missed some simple multiplication. I want to get it right at least once before I move on to review something else. If I were in school, I'd be failing all my tests. So I keep on trying. It is an old familiar feeling, trying to solve the endless riddles at the mathematical thresholds.

ELECTRON BLUE is back!

2010-01-01T02:19:00.001-05:00

Greetings brave and perhaps imaginary readers! This is the revived version of my older Blog, ELECTRON BLUE, which ran from 2004-2008. I was inspired to write it by my years-long project of learning mathematics and physics. Let me re-tell the story in a condensed form.

I was always interested in science, especially physics and astronomy, and I grew up in a family and culture that had a high respect for science and scientists. But I didn't do well in math or science in school. In fact, I was wretched in math and barely passed. So I lived for decades in fear of mathematics, although I yearned for it. I am a systems-oriented type of personality. I love to gather things and put them in order, and I love solving problems.

My yearning to learn something challenging and systematic was ignited when I visited Fermilab in September 2000. I was in the Chicago area for the World Science Fiction Convention and knew someone at Fermilab who had bought a print of one of my paintings. I got myself invited to the laboratory for a guided tour. It was an awesome and life-changing experience. Once I had finished touring, I told my host: "I want to study physics! I want more physics!" He said there were books I could read which had few or no equations and would explain modern physics for the layperson. But I resolved to learn physics the way an aspiring physicist would: with the math and the equations.

Math....I would have to learn math. So in 2001, that's what I started to do. I began with elementary and middle school arithmetic, then proceeded to "pre-algebra" and finally the real algebra that defeated me in high school. I spent 2001 and 2002 pushing numbers and letters around. In about 2003, I took a geometry book and just ran through it chapter by chapter, doing all the problems and proofs. In 2004, I struggled with trigonometry. Trig is still my poorest math skill, especially the mind-numbing trigonometric identities. I also spent time on sequences, progressions, and logarithms in '04, all of which I will have to review seriously if I need to revisit them. I was tangled up in trigonometry when I started the first ELECTRON BLUE in February of 2004.

In 2005, the International Year of Physics, I spent most of the year learning first year physics, the kind you learn in high school with Newton's laws, gravity, vectors, spring tensions, torque, pulling sliding blocks with friction, going around in circles, and other everyday occurrences. I will have to review all of this before I go on to anything else.

In 2006 I achieved a long-term goal by starting calculus. I approached first year calculus, as I approached all of my studies, by working from books, with lots of help from people I call "Friendly Mathematicians" and "Friendly Scientists." I do not like classrooms; I have perceptual difficulties which probably slowed me down in the past and made classrooms a place of humiliation and pain for me. But one-on-one I am fine. I worked my way up through limits to derivatives, and that's where I had to stop, along with the first Electron Blog. I stopped calculus not because I failed to understand and work with it, but because I ran out of time and energy, given my day job and all the other art and graphics I do in my home studio.

But I never forgot my self-challenging task. After almost two years of hard day job work and other distractions, I have gone back to the math. I have a big book of pre-calculus and calculus problems on my table, plus the calculus text I used in my previous sessions. I have high school physics texts too. I don't know how far I will go. At the beginning of my project I thought perhaps in ten years I would be working with quantum mechanics. This didn't happen, not at all. But I have not given up hoping.

I still have my contacts with some of my Friendly Scientists and Mathematicians; others have faded away. I would like to build up a following for ELECTRON BLUE 2. You are invited to follow the path of the Electron in this virtual particle accelerator.