Saturday, November 25, 2006
I was walking past the Visitors' Center on the Tremont St side of the park, and happened to glance up at the sculptures that border the little circle in front of the Visitors' Center building. I was face-to-face with the one entitled Industry. And what do you suppose the man in the sculpture was working on? A dodecahedron!!! [Not sure what a dodecahedron looks like? Click here for a good picture and description.]
Who would have thought I would find such a fabulous polyhedron just hanging out in a sculpture in the middle of the city of Boston?
I suppose, however, that I should give a brief explanation of phi and it's link to the dodecahedron. I recently finished reading The Golden Ratio: the Story of Phi, the World's Most Astonishing Number, by Mario Livio, so the explanation is quite fresh in my mind. [And it's actually quite a simple relationship, without a lot of bells and whistles. The amazing properties of the number phi make the number infinitely cooler than it may sound here. Look it up, it's fabulous!]
The diagonals of a regular pentagon (all sides of the same length, all angles equal to 108 degrees) cut each other in what Euclid defined as an "extreme and mean ratio" (which later became known as the Golden Ratio or the number phi, equal to 1.61803399...). Thus, you would use phi in the geometric construction of a regular pentagon. The dodecahedron is a twelve-sided object whose twelve faces are all regular pentagons. The number phi is literally bursting out of the dodecahedron from every side!
And I suddenly feel quite a different connection with the Common because of this find. The Common is suddenly connected much more to my world of mathematical images and patterns and structures. I love seeing geometrical structures in architecture as I wander the streets of Boston and Cambridge. I pick out patterns in just about anything that can be formed into a pattern (including random patterns in asphalt, brick, cobblestones, etc.). And I love bumping into shapes and 3D geometrical objects in unexpected places when it's obvious someone explicitly put them there (in other words, not by natural causes - there was a plan for the placement of said shape or object).
I find it fascinating that a familiar place can change so drastically depending on the perspective with which I'm looking at it. Day vs. night, time of year, other people dwelling there, personal circumstances and moods. All of these affect one's view of a place. And it changes its appearance, feel, scent, sound, mood with these different perspectives. But, with all of that, a place can take on a whole new meaning to me with one little discovery. Truly amazing...
P.S. - Some of my favorite properties of this fabulous number phi are:
- [phi]^2=[phi]+1 (phi squared equals phi plus one)
- 1/[phi]=[phi]-1 (one over phi equals phi minus one)
- the Fibonacci numbers are intricately related to phi
- phi is found in the pattern of placement for a rose's petals, a sunflower's seeds, a fern's leaves, and a nautilus's chambers on it's shell
- other places that phi pops up: the pentagon, the pentagram (a regular star: the diagonals of a pentagon), the icosahedron (pretty much the "opposite" geometrical object of the dodecahedron), Penrose tilings, quasi-crystals...the list can go on and on...
Seriously. Look it up. It's a truly remarkable number!
Sunday, November 19, 2006
What is Thanksgiving anyway? And why is it such a big deal?
It just seems to me that the holiday has become massive amounts of food (almost a competition for who can have more at their table and who can eat more of it at the table), and family politics, and huge amounts of food prep time, and sore bellies after the gorge-fest of dinner.
And of course, just like any other holiday in America, I we have to go through all the motions and hubbub and hoopla because it's a holiday and that's what people do. On New Year's we party all night and look for someone to kiss. On Halloween, we dress up and go door-to-door in our neighborhoods hoping to fill a bucket with candy and sweets and things. On St. Patrick's Day, we get roaring drunk on green beer, hopefully at Irish pubs (especially if you're in Boston). On Easter we search for baskets and dye eggs. On Christmas we give presents and sing carols and all that jazz. [I should, of course, make a shout out to holidays associated with other religions, but seeing as I don't know the customs of those holidays, I won't dig myself a hole by trying to inadequately describe "expected behaviors" of those holidays. I speak merely from my own experience, and I apologize for leaving out things I don't know enough about to include in my list.]
My beef, of course, is with Thanksgiving, so I will focus on this holiday in particular. But be sure that I do feel that question should apply to all of the major holidays of the year. (At least, in America, I can't speak for cultures in other countries since I don't belong to those societies.)
Thanksgiving. What are we supposed to do on Thanksgiving? Eat. And eat some more. And eat some more. We must have a huge turkey. And that turkey has to be roasted all day so that the whole house/apartment smells like turkey. We have to have lots and lots of side dishes to go along with this turkey, too. Obviously every family may have their own idiosyncratic additions to the side dish menu, but the required list includes stuffing (i.e. Stove Top, as my family used to say - kinda like "Kleenex" is used as the official term for a tissue with which one blows one's nose), mashed potatoes (in huge heaping mountains), sweet potatoes/yams with brown sugar and marshmallows on top, corn, green beans (perhaps the variation of green bean casserole substituted for plain old stand-alone green beans), gravy made from turkey giblets, cranberry sauce, and pumpkin pie. And we have to all fit at an enormous table set with the good dishes and the nice wine glasses (red and white wine must be served) - well, all except for the children, who are to sit at the smaller kids table (most often a card table) either next to the main table or nearby but in the next room.
And then, we must eat. We are required to take seconds; thirds are optional but highly encouraged after letting the firsts and seconds sit for a bit to digest a little.
Now, you may read this and think I'm batty for having a "beef" with Thanksgiving. After all, who should complain about having wonderful food made for you to eat and eat to your heart's content? Certainly I must be crazy for disliking this holiday.
But you haven't finished reading, or given me a chance to explain what I mean by having a beef with this holiday. I was merely setting the scene so we're all at the same place. Let me continue...
The requirements for this holiday do not stop with the food and the table arrangements and the number of helpings one takes at dinner. With every Thanksgiving, there must be politics. Family politics. If a couple just got married, whose parents to they have Thanksgiving with? If there are children involved and the couple is a bit older, then perhaps the family will come to their house...both sets of parents, and aunts and uncles and nieces and nephews will probably also come along for the ride. But then not everyone likes everyone else. Everyone is polite and friendly at first, of course, because after all - what a lovely dinner was made for all to enjoy. But bellies get full and people get grouchy as their discomfort of having too much food inside their bellies gets the better of them. Old arguments flare up. New arguments begin. Bickering over minor nothings is a rule, and taking sides according to family lines is a given.
People leave feeling heavy and too full to think they'll ever be comfortable again. Family social structure has yet again been ruffled. And lots of dishes lie in the kitchen waiting ever so patiently to be cleaned.
And then, after all that, you have turkey for a million years afterward. Turkey everything - to the point where you don't want to think the word any more, let alone eat another bite of it. You only regain your taste for turkey again after about a year, right in time for the next Thanksgiving, then you start the cycle all over again.
But wait, here's the best (or worst, depending on how you define your terms) part of the whole affair. What if you are missing one or more of those requirements? This is what kills me about this holiday. You feel GUILTY!!!
You feel bad that you aren't flying home to be with your family (if you're single) or you feel bad that you're not visiting either set of parents if you're a couple not able to travel.
...Or you feel sad that you don't know how to cook a turkey and feel inadequate for needing to order one pre-made.
...Or you feel embarrassed that your table is so bare if you can't afford to buy everything "necessary" to make a fabulous Thanksgiving dinner - or that your table doesn't have the exact required elements in the recipe for the "successful" Thanksgiving dinner.
It's the guilt factor that kills me about this holiday. You feel bad about yourself if you aren't stuffing yourself full of food or if you can't afford to travel to see family or if you simply make the choice not to travel for Thanksgiving in favor of traveling for Christmas instead.
[Alright, you caught me. I have quite the personal bias against this holiday. And I could go into the whys and wherefores and stories from Thanksgivings of old, but I feel I'd be getting off-track with my original train of thought. Not that that's never happened before in any of my posts...if you read my blog for long enough, you'll notice that I can have a tendency to run off-track and end on a point (or not a point, for that matter) completely different from where I started in the beginning of the post. But, I digress...]
Here's the thing:
We all know what we're supposed to do on Thanksgiving (and on all of the big holidays, I'm sure). But why? And do we actually know what we're celebrating anymore?
Thanksgiving is supposed to be a time to give thanks for what we have. And I believe that people in general think that they are doing just that. But that's not the main thought on their minds, poor things. They want the food. The goal of Thanksgiving has become the food.
Thanksgiving stories of old talk of pilgrims and Native Americans sharing what they have to create a nice feast that they can eat together in peace. All of my elementary school pictures to color during November are of peaceful meetings between these two groups of people. But that's a lie. They weren't peaceful. A simple lesson in U.S. History will tell you that things were not very much at all like what my old color pages would have my little 5th grade self believe.
Thanksgiving should not include guilt. "Giving thanks for what you have" is not a phrase that one expects guilt to play in to. So what if you don't have as big a table set out as Mr. and Mrs. Joe-Schmoe next door or Mr. and Mrs. Snooty down the street? What's it to them? And why should you feel like less of a person for it? It's not a competition. This holiday is not designed as a status indicator. The point is to give thanks for what you have, not pine over what you don't have.
Perhaps that's where a lot of my beef comes from. When did Thanksgiving stop being content with what you've earned, created, and accomplished and start being about what you wish you could have?
I don't believe that people take the time to sit back and remember what this holiday is supposedly founded upon. Or what they should be truly thankful for. Instead, it's become the Gorge-Fest. And I can't help but wonder why...
Now that I've written this incredibly long and bitter rant about Thanksgiving and all of it's ill-use in today's society, you all think I'm still so completely messed up for thinking this is a bad holiday. You all still think that I've somehow missed the point. And perhaps I have. Perhaps I don't really truly understand this holiday as much as I think I do. I must admit that as a possibility. But, in the interest of ending with a positive spin, since I tend to think smiling is a much better use of one's time than frowning or thinking bad thoughts, I will share with you my list of things for which I am thankful.
I'm having a small Thanksgiving with 2 good friends of mine, here in Boston. I don't go home for Thanksgiving. Our meal will not include anything near enough food with which to gorge ourselves. I (nor they, for that matter) see no point in it.
And I am truly thankful for these 2 friends to share a day with me that would otherwise turn into something lonely simply because I don't attach myself to the customs of this holiday like everyone else. I am thankful for my own family: my mom, my brother, my grandparents, my dad. I'm thankful for the incredible friends I know through swing dancing all over the country, but most especially in New England. I'm thankful for sunny days and blue skies. I'm thankful for the view of Boston over the Longfellow Bridge, and the fact that my walking commute to and from work allows me to see this - my favorite view of Boston - each day. I'm thankful for bad pop music that sounds so good, and for cheesy family movies and ridiculous "chick flicks" and exciting edge-of-your-seat action films. I'm thankful for the beauty of mathematics all around me, and for my ability to understand and truly appreciate the intricacies of that beauty. I'm thankful for old friends who know me better than I know myself. I'm thankful for cold days and fall foliage and serene winter nights. I'm thankful for my new apartment in my lovely new neighborhood, and for my fabulous new job that keeps me in a low-stress and happy-with-work-each-day state of being.
And for a million other little things that don't pop into my mind at this moment...
And for those little helicopter seeds. The ones that you can watch a hundred times in a row with a gleeful grin as they spin out of your hand to the ground below or whirl their way on a gust of wind to find new adventures away from the place on which they originally rested.