#final stuff

Monday (5/05/14)

Today started with cereal, then a conducting final review before our test. I got a pastry in the gap between classes and went to the classroom, where we had our last German lesson. After that, I got a döner at the newly opened Yufka's Kebap place, and ate it in the classroom before music history. We learned about aleatoric music and listened to a spooky example, before biking home all together. Hector's friend Ruben came by and stayed half the day, prompting a game night in which we all played cards and danced a little bit to the music we all played while cooking our dinners. 

Tuesday (5/06/14)

We took our German final today around noon - it was a challenge. For lunch afterward, Sam, Michelle and I went to a beautiful restaurant with an ugly name, Hackteufel. I got a meaty potato soup and garlic spread/olives for baguette slices, which was sooo tasty. We went souvenir shopping afterward, during which I got a deck of cards with Germany on the picture side. We returned home, where I eventually made dinner and danced to Hector playing the violin before I realized I had to study and write a paper -.- Studying and writing took up the rest of the evening.

Wednesday (5/07/14)

I finished and printed out my paper, after Michelle proof-read it (thanks Michelle!), and headed out to Raja Rani for possibly the last time. :( I got my usual and shook the hand of the guy behind the counter because he was there most often when I was, and he was extremely sweet. I am going to miss him!! I returned to the classroom and studied a lot for music history. I wrote between four and six pages in under two hours! We returned home and I decompressed and had dinner, as well as took a trip to Cafe Frisch with a couple housemates for pastries! Then I went to my 8pm voice lesson with Rinnat, who was visiting from Berlin! We said our goodbyes afterward, and I returned home to write thank you cards for my teachers. I delivered them personally to Rinnat and Zach, then went to bed.

Thursday (5/08/14)

I started off the day with another pastry from Cafe Frisch, then biked with housemates to the conducting classroom for our final. We got to use the room with the grand piano and a couch, so we were comfortable. I went third and felt alright about my conducting, then we all went to Raja Rani together for the final time now. Then Sam and I went to Yilliy for hot chocolate and a chat. We went souvenir shopping and crossed the Alte Brücke for the final time before heading back home to clean and begin packing. When everyone came home, we watched Signs. Then we had friends over for a little party, with games, flammkuchen, and superfrozen Coke! That was neat. Our game of Spoons got intense, and then Hector did pretty accurate imitations of everyone :P Then Judith gave us all farewell chocolate/cards, which was sooo sweet, and then we all retired for bed.

Friday (5/09/14)

Saturday (5/03/14)

I started off with a full night's sleep and got physically ready for our concert, then mentally ready when I went to practice with my voice teacher before finally heading over to the venue.  I was on the program first and sang Piangero la sorte mia and Ach, ich fühl's, then recorded Michelle and Sam after me. At intermission, we went downstairs for a delicious reception spread put out by Andrea and mingled with the audience. We went back and listened to Sara, Jonathan, and finally Hector perform their pieces before the concert ended and we all went up for applause/roses/pictures. It was a fun time. The concert dispersed around and we headed to the Mensa (Heidelberg Universität cafeteria) around 10pm for social interaction with a good-sized group of peers (11 people total). We went back home around 11:30 for bedtime.

Sunday (5/04/14)

Today started out with a bike ride to church, and after the service, we stayed for a potluck downstairs! It was pleasant, with pasta, desserts, and friends for a good 45 minutes. We returned to the house after that because it was time for a party! Sort of. We were "booked" to sing some hymns for our landlady's son's first Communion party! We sang Amazing Grace, Beautiful Things, How Great Thou Art, and It is Well (we made the audience cry, aww).  They shared the party with us afterward and we quite enjoyed it. Because this Sunday afternoon was so sunny, someone suggested we take a bike trip up the mountain to Thingstätte, an arena above Philosopher's Way. I don't regret going, but I never want to go again! It was horribly steep and we worked our way up, with bikes, for at least 45 minutes if not more. But the view was great, and I got to sing a little bit on the stage :P

Life, as we all know is a vastly underrated experience. The saying goes ‘you don’t know what you have until it’s gone’ and nothing could be truer now. Reading through the musician’s nightmare I too felt the sting of grievance at the idea that music could be so structures. The thought that a child  being unable to touch, let alone play, an instrument when it is a fundamental part of life just sounds odd. “It would be ludicrous to expect a child to sing a song or play an instrument without having a throughout grounding in music notation and theory” is the equivalent of reading that a child can’t run until they learn the physicality of that action. Knowing how the joints work with the muscles and how the brain sends a signal to the legs to move is all unrelated with the action it takes place. When a kid wants to run, they will run whether they understand how it works or not. For an artist, who is the ideal of self expression, being trapped in a box of rules is suffocating.

Yet the connection is made clear, the running theme in both nightmares is that these two art forms are being treated in the exact same way that math is. Math is taught in these rigid forms, first we learn to count, then add, subtract, divide and multiply. Little by little we eventually end up repeating what is being told to us and practicing what that by working through the same problems with different numbers.

To stifle the creative processes of an individual thought these nightmarish rules would keep anyone from picking up a crayon or humming a sung at all. I know if it was me and I lived in a world like this I’d never would have done either. The argument is that math is just as creative and expressive as any other art form, because it is, at the core, art.

I agree that institutionalized math education falls under this category of ‘no fun all work’. When I was learning class I followed the same boring steps any other student did. I hated it. It was only when shapes and toys would be brought out that I would begin to work a little harder. Learning math was the same as learning what happens in a history book. Nothing ever changes, the rules are always the same and ironically enough repeating patterns is one of the things that’s always bashed into our heads. Math always has a repeating pattern, math always has rules. Honestly who cares?

It wasn’t until taking this course that I began to see things differently. It was a tough and tedious process and often times I felt like I was bashing away at a wall with a picket ax. I was slowly breaking down what I believed to be math; a very long and annoying requirement to graduate. I never expected to leave the classroom with any newfound knowledge or love for the subject. Hopefully a passing grade and the relief that I was finally done with math and I’d never ever have to step into another classroom again. But I did learn and I evolved and through this class I began to look at other things in a new light.

Going back to my pattern theory, mathematics is all made up of patterns. Formulas fit under puzzles and one formula will lead to another (something I learned extremely well in connecting circles, which are rounded shapes, to it’s more straight lines counterparts). In general I love finding patterns in things. Once a pattern is found I can predict how something will occur and continue on for as long as I want. It is argued that a math formula is discovered, like a new planet outside the solar system, or created from the imagination like the statues of the Greek Gods in museums. Yet, both things imitate life so well and that is the fundamental connection.

While studying a sphere it was hard not to imagine it was the earth on the stand. How the circumference taken wasn’t the equator we were looking at. Whether it is with differentiated ratios of shapes (which was ridiculously long and annoying to do) a pattern was right there all along. When I imagine a triangle within a rectangle I imagine something that isn’t there. I make it up, and what I make up is often  the ideal rectangle and the ideal triangle. It is, without a doubt, the most perfect shape I can come up with. If I were to put it on paper, it stops being perfect. Like all things in life perfection is unreachable. All we can do as humanity is use our imaginations and find the patterns to make our lives a little easier.

Like I was saying before, the imaginary triangle inside the mind of a mathematician is exactly what he or she wants it to be. The one on paper has already lost that “perfection” that they had created. It curves just a little, the points don’t meet in the exact same way. The lines take up a space within the drawing so do we measure from the outer edge of the lines or the middle? How precise will out answered truly be?

What makes it imaginary is that you can’t touch it or feel it. Math isn’t a concept that can be accurately portrayed on a canvas and displayed. Like an art piece of a bouquet of flowers, it can’t ever mimic the smell of those flowers or the feel of the petals against the skin. A piece of music that’s supposed to invoke the feeling of red is not the shade, and then what shade is it supposed to be? These concepts can’t be studied like World War II or experimented on like what happens when you put a Mentos in a bottle of Coca-Cola. They are just that; concepts, beliefs, and aspirations we hope are as accurate as possible.

One of the problems we worked on during class that still sort of bugs me when I think of was way back in the first half where we had two exact looking triangles with smaller triangles inside that on the large had the same area. However when the area of the smaller triangles were taken and added the numbers weren’t the same. They weren’t off by much (about a few decimals) but the idea stuck with me. How can two similar looking things be off to begin with? It goes back to the imaginary, how two mathematicians can see the same thing but get different answers. I think that mathematicians might be interested in these kind of problems because it creates a challenge. Those in math are curious, challenge-driven individuals and so it makes sense that they would find these sort of things engaging.

The beauty that Lockhart describes is imagination. His excitement is contagious even, full of vivid details and exclamations. He created a simple shape within a shape in his mind and realized that the shape takes exactly one half. That goes into the area formula of a triangle which is ½ base times height. It can also be described as half length times width which is the area formula of a square. This is just one way math finds patterns and adapts it to other things. It is beautiful and when thought about in “art terms” instead of “math terms” it’s relatively simple.

Lockhart doesn’t argue about the facts of a problem. We know that:

A= ½ b h

What he says is the problem that by giving the students the answer and question at the same time, we are inadvertently ruining mathematics for them. All they learn is to repeat and repeat the same thing without ever thinking of why it is we do what we do. It can be frustrating for anyone to do and it is no surprise why students tend to learn to hate mathematics but love art. Math isn’t fact, math is ideas formulated and played with to create those facts. Math isn’t ‘what is it?’ but ‘why is it?’ why does it do what it does and how can we explain it the same way a painting might make you go ‘huh?’ and never give you an answer.

In his example he explains and calculates that the triangle takes half the space of a square when a line is put through it from one point to the middle of the adjacent line. Math isn’t just the formula, but the explanation behind it, which is what he wants students to leave the classroom remembering. In class we do the same thing, taking apart a shape, putting it together, and forcing ourselves to explain what it is we’ve done in words instead of just numbers. We’ve used it throughout the sessions and no one problem differs.

During the course of the section I wasn't sure what to think Sure, pi seemed to be an important number but besides free pies on March fourteen every year I never really bothered. Whatever I learned about pi I learned in classes where the teacher regurgitated information and we, as happy students, repeated it back. In a way it feels easier to learn math this way, mindless droning year after year, but what have I really learned?

This course had proven that we very rarely learn from just listening and repeating. Before this session, I didn't know why pi was used in finding the area of a circle I just knew it was. I didn't know why pi was an infinite number but slowly I began to fit these pieces together. Does it matter? Some would argue that it does and some that it doesn't. To be quite honest, I'm right in the middle. The information is good to have, it makes it easier to understand how other shapes work (who knew that the area formulas for a triangle and a circle were so similar!), but in the long run will I ever use it?

Taking a look back on my notes I realized my answers to questions 25 through 27 are sarcastic but hopeful. I went in with the idea that the new section was going to be hard and it was. It felt tedious and has made me dislike the number very much.

No amount of free pie can make up for the headaches this section has cause.

That was probably the most surprising aspect of all, how even though I expected the difficulties they still hit me like a pile of bricks. Yet, through it all, I came out a well informed individual and learned problem solving skills that I would not have learned had I gone the traditional route.

“Does the number pi make more or less sense?” is a double edge sword of a question. On the one part, I understand it more now than I did before. I learned where it comes from, why it’s used and how through that number we learn that universe as a whole is one giant neverending always expanding sphere and no line we draw will ever be 100% straight. That is unnerving for someone who has a hard time thinking about deep space and deep sea exploration without shivering. I’m not a curious person by nature, so this whole section was the equivalence of me putting on a suit and diving into the deepest blackest abyss of the ocean.