Tuesday, 13 August 2013

Magic Square

A magic square is an array of integers divided into a square matrix such that the sum of the numbers in every row, every column and both diagonals always gives the same number; this integer is called the magic constant or magic constant or magic sum of the square. In mathematics, a square matrix is called a square matrix.
A magic square of order containing all the integers from 1 to n^2 is called perfect or normal. The magic constant of these squares is given by the formula:

 M (n) = \ frac1n \ sum_ {k = 1} ^ {n ^ 2} = k \ frac {1} {2} n (n ^ 2 + 1)
 The first 15 components of this sequence are: 1, 5, 15, 34, 65, 111, 175, 260, 369, 505, 671, 870, 1105, 1379, and 1695.

Tuesday, 5 March 2013

Squadrato magico

In recreational mathematics, a magic square is an arrangement of numbers in a square grid, where the numbers in each row, and in each column, and the numbers that run diagonally in both directions, all add up to the same number. A magic square has the same number of rows as it has columns, and in conventional math notation, "n" stands for the number of rows it has. Thus, a magic square always contains n2 numbers, and its size is described as being "of order n". A magic square that contains the integers from 1 to n2 is called a normal magic square.

Friday, 15 June 2007

anatomical burlesque

Our last circus, the one SweetCliffie directed, went pretty well. Unfortunately, the show was over-long, for SweetCliffie did not calculate the length of certain acts accurately, and also Swordswallower decided to go on forever! He not only did various fire-eating and fire-belching acts; he swallowed one, two, and then three swords; he did the bed-of-nails with four people standing on his chest thing... he just went on and on. He alone added about half an hour to the timing. But the black light acts went well, including our disco number -- we performed this once before, early in our circus careers, and it was nice to revive it with a more practiced, confident feel. The local news was there, filming, and apparently they intend to return next month and then put together a feature on us.

One thing I've learned from watching SweetCliffie direct is that I never want to do it myself. Good people, the circus folk, but not a group you want to be in the position of trying to organize.

We will be in one more circus before we leave for India. July's show has some special, out-of town guests, a married couple who perform extreme sideshow acts. Most of them are the sorts of things that one feels squeamish about watching, including suspensions, self-piercings, and variations on blockhead acts. The guy does this weird thing that involves twisting an oversized spring through his sinuses: it goes in his mouth and comes out his nostril. (Yes, it is really gross.) The acts for this particular month's circus will have a somewhat more adult content than usual; though this is not my favorite sort of show to do, our extreme shows often are very popular.

Since I don't have any self-mutilating acts in my repertoire (nor do I intend to develop any!), for this show I will do a somewhat tamer skit, but one that nevertheless is my absolute favorite piece: the anatomical burlesque. I've only performed it once before, so I'm looking forward to doing it again.Conceptually, the act is quite simple: I eroticize the act of stripping off layers of my body, rather than stripping off my clothes. The music is a classic sixties' bump-and-grind, and we also have a turntable on the stage. I come out wearing a robe, step onto the turntable, and then drop the clothing to reveal a "nude" colored unitard painted like a naked body. SweetCliffie slowly turns me like a statue. Then I descend, burlesque-dance a little for the audience, and SweetCliffie carefully peels off my "skin." Underneath is a red unitard painted to look like muscles. Dance, tease, spin to display the muscles properly -- then SweetCliffie strips them off to reveal a unitard painted with internal organs (at which, last time, somebody in the audience yelled out, "Yeah, show me your liver, baby!")... next comes the circulatory system... and finally, a complete skeletal system. The music is beautifully timed to the length needed for this act: at the last turn we end in a nice embrace.

This is our most "arty" piece, and the general response to it, from other performers as well as from strangers who've written about it, has been very positive. I wanted to play with the notion of laying onesself open, of making the body fully vulnerable to another's gaze, by taking a strip tease beyond the body's surface and into its interior. The act is supposed to make the audience think about the fetishizing of nudity, by fetishizing the body's other dimensions: the meat, the organs, the bones.

I painted all these unitards myself, and lemme tell you it was backbreaking work -- it took several days of crouching over the fabric, stuffed with pillows, trying to make everything reasonably accurate and symmetrical. (Actually, I've re-painted the internal organs since this photo was taken -- I wasn't happy with the lungs, and I changed the colors a little.) I do not normally consider myself to be particularly artistic, so I was very pleased with how well they came out. I cannot tell you how proud I am of the circulatory system one, in particular. I also want to note, for the record, that it is very uncomfortable to wear five unitards at once. Nor does it enhance one's hips.

In other news: SweetCliffie and I have just finished a major overhaul of our backyard, including turning a small structure into a steam hut. Lots of distracting work, taking me away from my writing, Ugh! But the formal opening party for our steam room will be this weekend, Yay!

Thursday, 14 June 2007

nostalgia misgivings

Rambling thoughts: I wonder what my undergraduate institution is like now? It was such a perfect fit for me all those years ago, and yesterday, when they called to ask for money for the endowment fund, I gave it willingly. But I give, of course, based upon an image of the place that is quite out of date: I got my BA in the 80s.

There was a conversation moving around the blogosphere a couple of weeks back, concerning the impact of graduate school and contrasting the experience with one's undergraduate years. One distinctive thing about the education I received at my undergraduate institution is that I learned a skill one usually acquires only in graduate school: how to ask an interesting analytical question. During the whole of my undergraduate experience, I never once was assigned a textbook or a book of short, collected 1-2 page source extracts. We always read original sources in their entirety -- and not just in History classes -- and then analyzed them closely. We brainstormed together as a group in the classroom, throwing out ideas, responding to one another, and slowly building up interpretations (plural -- often several strands of analysis would be spun out in tandem). We learned critical thinking by challenging one another and being forced to look to the texts again and again. Often, the debates continued beyond the class hours: one thing I remember fondly about the place is the lack of a strong boundary between in-class and out-of-class conversations. Furthermore -- and this is key -- I very seldom was assigned a paper topic: we were required to come up with our own angle of analysis.

When I got to graduate school, there was quite a difference between myself and my new peers. I never had read a synthetic presentation of the Middle Ages, been asked to memorize facts, or taken an exam about the period. As a result, I knew next to nothing about Angevin Kingship, the Crusades, or the basic names-and-dates trajectory of the period. I did know a little about the Investiture Controversy, but that was the only Big Event I had in my repertoire at the time. On the other hand, I knew lots of texts: I was the only one who had read all of The Murder of Charles the Good, The Autobiography of Guibert of Nogent, The Little Flowers of Saint Francis of Assisi, lots of Icelandic Sagas, and nearly all of The History of the Franks, among other texts. Because I never had read a synthesis, I was used to setting my own research agenda. Graduate school, for me, was about learning facts and skills: languages, palaeography (largely self-taught), a body of historiography, and, lastly, the textbook-style synthesis that I lacked when I enrolled. I used to compare it to a trade school: I learned the ins and outs of manufacturing professional-grade essays about things that excited my curiosity. As an undergraduate, I learned how to pose questions; as a graduate student, I learned how to answer them.

My undergraduate SLAC was also an apt fit for me socially, with many slightly oddball types. Though, come to think of it, I may have been one of the odder ones around: once SweetCliffie and I met a former professor of ours at a big national conference, and he stated, affectionately, that we were "the flakiest man and the flakiest woman, making the flakiest couple, during [SLAC]'s flakiest years." Does this mean that it is no longer the freaky, yet intellectually-challenging place I remember so fondly?

It could well be. I did have occasion to spend some time with a recent graduate of the place a little while ago, and it was a rotten encounter. I came away with a negative impression of vapidity, narcissism, and entitlement. I know s/he's only one individual, and thus that his/her example is quite anecdotal. And of course not every graduate of an institution can be congenial: surely there were people there I did not like back in the years I was enrolled -- I simply avoided them and hence they do not form part of my lasting memories of SLAC. Nevertheless, if I'm honest I'll admit that s/he soured me a little on the place. It's funny how one event, one encounter, can color one's attidues so completely. I experienced nostalgia misgivings, a terrible thing!

Monday, 11 June 2007

the women we were raised to be

I just had a conversation with my mother that made me feel eager to get off the telephone as rapidly as possible. Why? Because I tried to discuss something having to do with work. I should know by now that such a move always is a recipe for irritation. So I am going to try, in this post, to turn that irritation into a larger reflection on mothers and daughters. More broadly, I want to reflect upon on the generational change in the scope of the feminine sphere that occurred in the 1970s; a shift that shapes much of my generation's relationships with parents. You may expect some personal venting, as well.

The problem with the communication between my mother and myself boils down to this, I think: she cannot fully “own” the ideas about female independence that she feels she should espouse. Rather, her default preoccupation in regard to women is marriage: whether someone is married, will stay married, is pathetically single, is single but has a good marriage prospect, and so forth. It took me a very long time to identify this discrepancy, in part because the preoccupation with marriage only manifested itself, in my own life, once I graduated from college. I think she probably is typical of her generation in her inability to consider an unmarried woman to be anything other than sad and desperate; and marriage to be the most important triumph of a woman's life, regardless of anything else she may achieve.

When I was a teenager, however, my mother mostly gave me positive messages about being smart, sassy, independent, and so forth. I say mostly, because I do remember her saying things like, “Boys won’t like you because you act too smart” -- but then she’d follow it up with advice that it was good to be smart, but that I should act dumb in front of eligible males. She taught me, “be a leader, not a follower,” that women could do anything men could, that I shouldn't be afraid to express and defend my opinions. She even told me to "play the field" - though she did not mean sexually (a subject about which she is quite uncomfortable), but rather, that I should have lots of boyfriends without being serious with, dependent upon, any particular one. (Since I was, in fact, an undesirable nerd in HS, there was no question of any of this actually happening.) She bought me any book I ever wanted, took me to museums and ballet. Moreover, she provided a role model: although she did not have a degree or work, she was at that time a woman of strong opinions, politically active in Democratic causes, going to anti-war rallies in Washington in the early 70s, confident, even brash and outspoken. She herself was always reading, and reading "good," literary books, not potboilers and romances. As a kid, I considered her to be clearly superior to my father in every way.

Yet at the same time, it was openly understood in my family that only my brother really “needed” to go to a competitive college, for only he would someday have to support a family. But after both my older siblings dropped out of their respective colleges (Sis later went back), I became the last, best hope of my upwardly-mobile-striving family to get that first college degree. I was encouraged to apply to elite colleges and was desperate to get into one, for I detested my substandard, clique-ish high school (despite having three school-age children, my parents moved to their community because it had low school taxes -- and therefore, terrible schools).

When I was accepted into an exclusive, and expensive, private SLAC, my mother went back to work as a secretary for the first time in over 25 years in order to help pay for it. It was a bargain she made with my father, who deeply resented paying the bill for this school for a girl. It must have been pretty terrifying for her, but she sucked it up and did it for my sake. Around this time she even, as a mark of independence within her own marriage, went back to using her "maiden name" most of the time. Yet, despite this sacrifice and support, she increasingly began to make clear that what she really was hoping for, in sending me to college, was an “MRS degree.” As I became an adult, her earlier rhetoric of female independence and self-sufficiency fell by the wayside and was replaced by an obsession with my marriage prospects. She expected SweetCliffie and myself to wed as soon as we graduated. When, instead, we lived together for many years while pursuing our PhDs, she began a stream of anxious complaints: “He’s not really committed to you if you're not legal.” “When are you gonna get a great big rock on your finger?” and my personal favorite (as well as one of hers), “Why should he buy the cow when he's getting the milk for free?” Over... and over... and over... in every conversation, for years.

The change of tone had crept up slowly, but it confused me, nonetheless. It was not the standard of achievement I had been raised to strive for, and I kept on relating to her in the old way even as things changed. When I did get married, I imagine she fully expected me to drop out of my PhD program; she must have assumed I was finishing only because I was funded through grants. I’ll never forget the day I called her, elated, after my final dissertation defense. I explained that I had finished my final requirement, and that even though graduation was not for a couple of months, by convention I could now be called “Doctor.”

“Good!” she replied, chirpily. “You've proven whatever it was you had to prove. Now you can let SweetCliffie go to work as a professor, and if you really still want to work, you can get a job as a secretary!”

It’s one of the only times in my life I literally have been speechless. I think the secretary reference is significant, but I still am completely flummoxed by the memory of this.

I am who I am because of the mother who raised me, but that woman somehow vanished once the raising was done. Indeed, as she grew older, she moved farther and farther from the person I remember in the 1970s. In her mid-50s, though physically healthy, she became consumed by irrational fears. The confidence I recall evaporated as she became agoraphobic, terrified of airplanes as well as of long car rides, a hypocondriac, prone to constant panic attacks. Some of this attenuated and she now is more active, but she is... diminished. She no longer reads, she no longer is politically active, she stopped using her own name, and she certainly no longer is outspoken or opinionated. I suspect that this is the person she was raised to be – and probably was throughout her life except during that one decade of her forties. Then, she somehow felt different, forceful; she was swept up in cultural and social change. And that decade coincided with my formative years.

What happened to women of her generation? How did the woman she was raised to be, raise the woman I was raised to be? Did all of them do this -- be shining with strength for a while, then slowly fade... and vanish away? I sound harsh, but what I feel is mournful. I miss the person she was.

Friday, 8 June 2007

creative access

Inconsistency is a beautiful thing. So, as a follow-up to my post on gatekeeping and standards, I have a confession to make: My circus has no standards.

Let me explain. When I say we have no standards, I don’t mean that we suck. We’re actually quite good. But the circus has a peculiar ethos (derived from the Burning Man community) that rejects the idea that one must attain mastery in order to have the right to be creative. As a philosophical stance, the circus folk believe that everyone can perform, anyone can entertain, we all can make art. Not that everyone can be Jackson Pollock, mind you, but that it is a normal part of human nature -- a human right, even -- to be creative and to wish to explore and express it. And, therefore, that everyone ought to have creative access without having to worry about standards and gatekeeping.

Furthermore, the circus folk believe that watching others be creative is inherently entertaining, whatever the person's level of skill. And you know what? This is acutely, brilliantly true. There's nothing more fun, in fact, than watching people be creative: it’s why I loved the circus from the first. It's why we're so much more fun than mass-media entertainments, which seldom are truly creative because they must appeal to lowest-common-denominator tastes.

One of the most fruitful juxtapositions in my life is the fact that I work within a very stringent professional discipline, and play with a no-rules, no-standards performance group.