To Infinity and the Next Kind of Infinity

I can tell it's been a while since I've written because normally, when I type 'bl' into my navigation bar in my browser, I can immediately hit 'Enter' and I will be directed to Blogger, the automatic completion of 'bl'. However, when I typed 'bl'+'Enter' just now, I was directed  to another website, one having to do with the programming of linear algebra in Python - a website I have been frequenting more, well, frequently than this one in recent weeks!

I'm sitting with a mug of tea the size of my face in a toasty warm cafe right now. Tomorrow is officially the last day of classes before Christmas break, when I will be flying back home to the States. I have one more workshop tomorrow and then I'm done - no classes at all today, though I have some homework to finish.

All in all, it's been a good semester so far, and the last few weeks in particular. I have found people to work with in nearly every class and am starting to recognize more and more of the faces (and some of the names) in my classes, which is harder than I thought. I never quite realized when I was at Mills just how close-knit our community was. Even though I didn't necessarily like all of my classmates, I knew every single one of them, first name and last, and what year they were in, what major (I'm talking about math folks, for the most part here) -- here, I have no idea. But in some classes, that's getting better - people are getting to know me or at least recognize me in particular in my Fourier Series seminar, because I am the only girl and gave my presentation last week. I can't believe how little I thought about the friend-making process when I was a kid. It was just something you did (not that it was always easy!). But now that I've moved from place to place so frequently and had to go through this process so often, I take special note of it.

As everyone is about to start traveling to see family for the holidays, I want to throw some food for thought out there. Something to make your mind whizz while you pull off the highway because the snow is swirling too much to drive, or while you sit through your four-hour layover in London (which I will be doing), or just while you tune out at the dinner table when the age-old and much-repeated family conversations come up again.

I want to talk briefly about infinity. If you've ever been friends with a mathematician, or mathematician-in-training, or just someone who had a decent math teacher at some point in their life and paid attention at least some of the time -- you might already be aware that there are several types of infinity, or levels of infinite-ness. I'm bringing this up today because yesterday in Algebra, I learned something that I didn't know about infinity and it surprised me so much, I haven't been able to stop thinking about it since.

Okay. So, where do we start? First, one very basic but still (in my opinion) super-cool fact about infinite is as follows: if you have an infinite set of things (like grains of sand, for example) and you take any portion of that away -- so now you have two piles of grains of sand. At least one of those piles must be infinite. Either you took an infinite amount away and left a finite amount, or you took a finite amount away and the rest is infinite. Or both piles could be infinite. But you can't divide it into two finite piles. Because the sum of two finite piles of things would still be finite. Does this impress you? Or give you a new way to think about infinity? It certainly made my head spin when I first heard it.

Alright. Now let's get a little bit more mathematical. First of all, some terminology you probably haven't thought about since elementary school (I swear they teach us this there - I still remember the diagram). The Natural Numbers (abbreviated N) are the numbers {1,2,3,....}  -- the 'counting numbers' as they are sometimes called. (Depending on what context you are in, the Natural Numbers may also include 0, but not always). Then there's the Integers (abbreviated Z (from Zahl, the German for 'number') ), which is like the Natural Numbers but reflected across zero - i.e. you get the negative ones, too. Positive and negative whole numbers {...,-3,-2,-1,0,1,2,3,...},this time including zero for sure. Still no fractions allowed. The fractions are part of what we call the Rational Numbers (abbreviated  'Q' ((probably for 'quotient', but I'm not sure)). Rational Numbers by definition are all those numbers that can be written as "a/b" where both a and b are integers and b is not zero. You may have noticed that all of these sets of numbers that I've listed kind of fit neatly inside each other - the Natural Numbers are part of the Integers, who are part of the Rational Numbers -- who are in turn part of the Real Numbers (abbreviated 'R'), the last bunch I'm going to talk about here.

You've probably guessed who the Reals are by now - all the rest you're familiar with. Yes, fractions and integers but also strange decimals that go on and on and never terminate. Some of these decimals can actually be represented by a fraction, take .3 repeating for example which we know is 1/3. Others can't be. One really famous example of this is pi (which is actually particularly interesting for even more complex reasons). But it's not the only one.

So, clearly, the Rationals fit inside the Reals but there's a lot of Reals that aren't Rationals - so that inclusion only goes one way. In set-theory notation, we write this inclusion of sets like this:

So, I think we agree about this chain of inclusions up there. But now we have to notice - there are an infinite number of elements in each set in that chain. An infinite number of counting numbers, integers, rationals and reals. And yet, there's more integers than counting numbers, and more rationals than integers, and more reals than any of the rest. So, we do have a hierarchy of infinite-ness.

The way that Z is more infinite than N kind of makes sense - there's like, twice as many integers as counting numbers. The positive ones and then all their negatives. But what about Z and Q? Think about how many rational numbers there are just between 0 and 1. 1/2,1/3,1/4,...., 1/512,... -- a LOT. Like, really a lot. So, Q is way more infinite than Z. Then just think about R. Is your head hurting?

One way that mathematicians discuss or categorize infinity is by the idea of countability. This idea is not all that complicated - a set of things is countable if we can organize all the things in a line of some kind and give every item in the set a number denoting its place in line. So, finite sets are obviously countable - we know how many there are in total, so clearly we can count them. But infinite sets can also be countable. We might have to count for ever and ever, but we could count them, theoretically.

Think about the integers. If I want to set them up in a line, I can start at zero and arrange them like this: {0,1,-1,2,-2,3,-3,…} always alternating from the right side to the left side of zero, getting a number and its negative. If I arrange them like this, I can assign each one their place in the ‘line’ if you will. I know that when I count like this, I’m not missing any of them - I’ll find all of them with this method and all will get a number for their place in line. Thus, the integers are countable. 

But what if we tried this method with R, the real numbers? I can start at zero and then… what’s the next one to pick? Even if I just picked 0 and .1 — well, between 0 and .1 there’s .01, .001,.011,.0001 — all of these things! I can’t set them up in a line where I don’t miss any and where everyone has a place in line. The reals are not countable. So, we call them uncountably infinite. And that’s a bigger kind of infinite than the countable kind.

So, now, we’re finally set up for what blew my mind yesterday. Now, I must have been living under a mathematical rock because this is not a new discovery, but everything is new to us at the point when we first learn it, and this was new to me yesterday — the rationals are countable.

Not only that, but the proof is really easy. I’m linking to one version here because I think I’ve probably talked your ears off. Once you see the proof or just think hard about the rationals, it does actually make sense — or maybe it even seems obvious. But I had always assumed they were uncountably infinite. Pretty neat stuff.

Now, that fact about the rationals - specifically the relationship between the rationals and the reals, given that one is countable and one is not- leads to some interesting conclusions in Abstract Algebra, which is why we were talking about it yesterday in class. I might go into that some time - but not today. Now, it's time to go and turn in my algebra homework.

"Similarly Complicated", and other mathematical niceties, Part 2

But the first thing that made me want to write today happened much earlier, in one of my favorite classes – Algebra. I could talk about this subject all day. But I'm going to talk about one kind of proof in particular, of which we just happened to have an example today, and also about one of the funny comments made by my slightly crazy professor.

Math is all about proofs once you get done with the stuff they make you do in high school. Proofs are about, well, proving that something is true or not true, proving that a certain object has certain properties, proving that certain sets of objects all have something in common, or proving that various definitions or statements when combined lead to a much stronger statement. One fun type of theorem (that leads to a fun type of proof) has the following syntax:

Theorem (Name): Let X be a thing. Then the following statements are equivalent:

(i) X has property A.

(ii) X has property B.

(iii) X has property C.

(iv) X has property D.

“The statements are equivalent”– What does this mean? This means if you successfully prove something like this and you come across a beast (in the mathematical wilderness) with the quality of B, then you automatically know that it also certainly has the qualities A, C, and D. That’s the whole damn point. If I know that when bears (X) have blue fur (A), they also automatically are vegan (B), then if I see a blue bear I don’t have to ask it if it’s vegan or not. I already know, since A implies B.)

And how do you prove such a thing as this? Well, you start with whichever of the options A-D you are most comfortable with, say property A. Assume X has property A. Then you have to prove that if X has property A, it must also have property B. From there, show that if X has property B, then it must also have property D, and so on. At the end, you need to lead back to the property you started with — complete the circle. It doesn’t matter what order you go in as long as you can get from any one statement (A-D) to any other statement by the time you’ve finished.

If this is confusing, don’t worry. The whole point of this type of proof is this: Let’s say you come across a bear in the wild (yes, we’re back to the bear). You really want to know what blood type it has, but you are (understandably) hesitant about taking a blood sample. But because Blood Type = O Negative happened to be property D in the theorem you just proved, you know that since the bear has blue fur, it must have blood type O Negative. You saved yourself a lot of work (and maybe your life).

This style of theorem and proof has always fascinated me. Even though the real bulk of the proof might just be to find an easier way to show property D (like the example above), you still get to explore the other properties along the way, and maybe derive some neat consequences.

(If you are interested in these mathy things, please write to me - I can give examples that don’t involve bears, or more examples involving bears - or just talk about all these things. :) )

So, this is the type of proof we were tackling in Algebra at 8:00 this morning. Our professor rolled up his sleeves and wrote the whole theorem statement on the board, and then wrote those great letters: “Proof:” and we waited for what was to come next. “A implies B” he wrote. He turned to us. “This is a great proof,” he said. “Ready?” Collective, halfhearted nods from the crowd. Then he wrote “Obvious.”  on the board. And that was it.

After another one of the implications (say, C implies D) in the proof was also just “obvious” (or, another favorite word of mathematicians, “trivial”– oh, how this word sounds to math students. Can you see the self esteem shriveling into nothing?), we had to have a quick discussion about it. Here’s what he told us.

First of all, these statements “are only ‘obvious’ if you know which definitions or other theorems to apply and in which order”. But once you do, the answer is clear. Second of all, it’s not “supposed to be obvious to you today when you hear it in the lecture”. He continued: “The difficulties are hidden in the notation.” Quite clever and quite true, not only of mathematical things. 

 And finally, the real stuff:

“What I do here in the lecture is 10% of the work, of the material.” 

I think this is what a lot of people don’t realize about math courses and that is a reason that many don’t do well in them. Just the notes from the lecture, just passively writing them down isn’t enough. Even just mechanically doing the homework isn’t enough. There is much, much more work — hidden in the details. You have to work with it enough to understand it from the inside, not just from the outside.

And that is exactly why I need to stop writing this right now and go read over my notes from this morning. Oy vey!

"Similarly Complicated", and other mathematical niceties, Part 1

Today's a Monday, which for me means four lectures in a row, almost without break (there is generally a fifteen minute break between classes, but with going to the restroom, maybe going to another building or buying something to eat, this vanishes quickly). Each lecture is two hours long (roughly), so it's quite a long block of note-taking from 8 a.m. to 4 p.m. But today, each of my math professors have just been so...mathematician-y that I felt the need to use one of my fifteen minute breaks to write this.

One such hilarious (to me) moment today already made its appearance in the title of this post. In Analysis II (very abstract calculus, roughly explained) this morning, we worked our way at one point through a very tedious example. Lots of indices — let me say what I mean by indices. Indices (plural of index) are the subscripts we use to know which entry of a particular vector we are talking about. 

For example, the vector x:

The first entry in that vector is 5, the second 4, and the third -1. In math speak, we would write x₁=5, x₂=4, etc. This vector has three entries in it, so we say it has length 3 . Alright? Bear with me now, it’s going to get complicated. First, imagine you have a vector of length n. What’s n? Could be anything. Got that? Kinda? Good. Now imagine that you don’t have just one vector of length n but a whole series (or list) of them. So, now we might want to talk about the entry at index i  of the kth vector in that sequence…You get the idea. Subscripts of subscripts of indices. 

Most people in class were either pulling on bits of their hair as they tried to keep track of all the tiny k's and n's and x's, or they were just staring into space after having given up. (Let me note -these kinds of details are not, in my opinion, what makes math difficult. They are not abstract concepts that you need to wrap your head around. Rather, they are the tiny details (that are indeed very important) that we use to be incredibly precise about what it is we are calculating and though they are not in themselves difficult, these tedious indices and things like them certainly can, and do, make math problems discouraging). Finally, we finished the example in the lecture and the professor smiled at us and said we were about to do a different example now that was "ähnlich kompliziert", which means 'similarly complicated'. Also complicated, and in exactly the same way. Sometimes phrases just catch my eye (or ear) and I think they are worth noting in their perfect suitableness. 

Thoughts from the first week back in school.

Classes started this week. I’m finally officially matriculated and I can tell it’s going to be a full semester. I was going to try and write down here some of the classes that I’m taking - but in translation and explanation it seems to sound like I’m only taking things I’ve had before, but that’s not quite true. Some it’s more advanced versions of some things, review of some things, and since I’m switching academic systems there’s also just a bit here and there that I need to repeat just to satisfy the official requirements. Some courses I am only going to take and turn in the homework for but I don’t need to take the exam, since I already have a grade for it from Mills. And so on and so forth.

But the point is, I’m taking (in varying degrees of depth - i.e. lecture, homework, exams) four math courses and one computer science course. The very first class this week was one that I think will be quite difficult, but also probably one of my favorites. An Algebra course. Now, I’ve had some Algebra at both Mills and in Budapest, but I can tell from the first week that the pace in this course is quite different. We’re going to cover what I already know (or knew when I was in those other courses!) within the first few weeks, and then it will be all new after that. That lecture is at 8 a.m., twice a week. When I sat down in the first lecture on Monday, I had flashbacks of studying here three years ago.

I remember the enormous theater-style lecture halls, the multiple blackboards that slide up by twisting various knobs near the chalk tray at the bottom. I remember the professors actually carrying around huge sponges that they wet in the sink near the blackboards and use them to completely wipe the board clean, then use the enormous squeegee to get rid of the excess water. And I remember the pecking order of the rows in the hall. 

There are at least twenty-five rows of seats, two aisles, in the steeply sloped hall. About 80 students in a lecture. No one sits in the first row. Are you crazy? You’d be like five feet from the lecturer. That makes no sense. Plus, when the blackboards are slid up to the top of their tracks so that folks in the back could see, you’d have to crane your neck to read. The second row? I hate to be so harsh, but I’m only reporting what I see (and this is often the case with American students as well). The second row is full of guys who happen to be paradoxically long-haired and balding at the same time, all while being in their early twenties. Some of them are using fountain pens and get the ink all over their hands, they have the homework done before it’s been assigned, etc. Oh, and there are also sometimes girls who wander into the lecture hall late, looking like they forgot they signed up for a math class, and then when all the other seats are taken, they end up sitting next to these characters. The third row is for people who want to pay attention but aren’t quite up to the level of nerdity necessitated by those second-row seats. After the third row, all bets are off. There, devoted students are mixed with those who are just fulfilling some distribution requirement to those who are taking this course for the third time after having failed it twice.*

As for me - what’s your guess?

On the second day of that particular lecture (Wednesday) I slid into an empty seat in the third row (did you guess right?) and hear some of the Row 2-ers talking in front of me about the homework (which at that point had only been posted online for about twelve hours). They were already done, discussing the subtleties of the last two proofs. I, meanwhile, had printed out the sheet, jotted down a few notes for each problem and had a solid plan for at least two, but hadn’t written any up in their entirety. So, I felt a little sheepish, worrying that I wasn't at the same level as the rest of the class. All of a sudden, from the row behind me, I heard the low voices of two guys, barely awake at this 8 a.m. class:

‘You here those two up there? Are they talking about the homework?”

—“Yeah, I think so. They’re already done.”

“What? Jeez… I haven’t even printed it yet.”

—“I know, me neither. God, they’re motivated.”

“I know. Horrible, right?”

I smiled to myself. I think I’m sitting in the right row.

——

After managing the first four days of the week (where all my classes are scheduled, though some homework is due on Friday) and finishing two of the first four homework assignments, I was feeling good, but exhausted. Thursday evening I went to babysit - not the two girls I’ve talked about before, but a young boy (5) and his younger sister (3.5). Both of them already are learning to speak both Russian and German because of their parents, and their knowledge of English is very limited (understandably!) . The boy has learn the words to some children’s songs, such as Head-Shoulders-Knees-and-Toes, The Itsy Bitsy Spider, etc. Neither one of them understands all the words to these songs, but they sing along anyway - the boy knowing fairly well how to pronounce everything but his sister just throws caution to the winds. When a kids version of ‘Yellow Submarine’ came on, the sister was singing loud enough for me to understand ‘sumbasine’ ‘tubmarine’ and even ‘subtartine’ during the course of the song.

The boy is a real mathematical mind - you can tell already. The way he builds with blocks, they fascinated way he stares at the rubics cube in their playroom, and - the one thing really on his level at the moment - when he plays cards. Right now, the card games we can manage together are Uno and War. I do believe we played about 30 games of Uno on Thursday. It started with him saying just the names of the numbers or the colors when he put his cards down, but then after playing for an hour and hearing me talk about the game, during the last hand when he kept getting a bunch of +4 cards from me (he can take it :) ) he finally exasperatedly held up his tiny hands full of the cards and said “Too many cards!!!”. Considering he didn’t know the word ‘card’ at the start of the game, I thought this was pretty successful. And after the week of classes and bureaucratic errands at the university, Uno was about as complicated a game as I could handle anyway, so we made a great team.

*If I haven’t mentioned it before, failing a class is something completely different here in Germany. Your grade in a course is determined entirely by your grade on the final exam. You are required to score a particular amount of points on the homework to be allowed to take the exam, but other than that, your homework doesn’t count for anything. Also, to make things more interesting, those who write the homework problems are traditionally TAs, the same ones who run the weekly workshops where that homework is due. But the person who writes the exam? The professor. Do you know how the professor likes to write problems before then? No. Also, are people paying exorbitant amounts of money to take these classes? No. So do they kick and scream and fuss (or do parents kick and scream and fuss) when students get grades below an A? No. You don’t need to study math to combine the above facts and come up with the result that failure is not an uncommon outcome in a course. Because of that, though, the attitude around failure is also quite different - you’re not expected to be perfect. Very few people (but some) get grades equivalent to 'A's in math. However, I’m coming into this system with my US-grade mindset, and thus I find the system frankly terrifying. 

A weekend of culture.

On Friday this week, I got to attend a ballet (modern-esque ballet) of one of my favorite children's books - Momo, a German novel by Michael Ende. While sitting here this afternoon, I have tried several times to come up with an adequate summary of Momo and I keep disappointing myself, so I won't really try. I'll just say that it's about a girl named Momo and a mysterious and dangerous group of beings called the Grey Gentlemen, who come into the world and try to convince all the people to "save time" by investing it in the Time Bank, but as most of us know, when you try to 'save time' you don't have a big pile of time waiting for you at the end of the day, or week, or month, or year. Most of the people in the world start to be driven mad by this constant rush, trying to be productive all the time and save as much time as they can - and Momo has to try and stop the Grey Gentlemen. I haven't been to a dance performance in years. After all my dancing in my youth, they always really affect me deeply, and this one was no exception. Plus, I think the experience of begin at a live performance of any kind can be so fascinating, from seeing the transformation of the performers in character (acting, dancing, singing, etc.) to them just being people when they take their bows, and when the house lights come up and you realize you are surrounded by strangers but you still just shared something with them by watching collectively. And dance. We should just dance more. I should dance more. Period.

  Click here if you want to see the preview of the ballet (try to guess which ones are the Grey Gentlemen :) ), and if you have a young child who you really like and who could use a new book for whatever reason, I really recommend Momo. (I have not read the English version, but I think it would be good, too. )

Then, on Saturday, I visited the Frankfurt Buchmesse, or Frankfurt Book Fair, which is the world's largest book trade fair (according to google). After being there during the day, being overwhelmed but enjoying ourselves, Claudia and I watched the news the next day and heard about the attendance for that very day we were there (somewhere in the 10s of thousands)--- no wonder it had felt so crowded!

There was everything at this fair. Some kind of comic book convention so that we saw at least three different Pikachus walking around in the train station on the way there, stands for self-publishers or those who hope to do so, stands with all kinds of subject-specific books from various publishers (for math, astrophysics, cooking, computer science), and rows and rows of stationary (!!!! If you know me at all, you'll know that this was one area I would not miss) and book binding companies, new education technology companies showing off their developments -- oh, and stands with ice cream and pretzels every now and then. :)

But during the day, we saw two rather spectacular things. One was a live cooking demonstration from an Indonesian chef, a charismatic woman who cooked three dishes and a dessert (I know for a fact that two were delicious, didn't get to try the other two)  the space of an hour and had drawn an enormous crowd of people from the enormous exhibition hall (there were eight such halls, with multiple levels. So many books!) and we were riveted for the hour! After that, we went and saw a 'Translation Slam' -- something I've never heard of before but Claudia was interested to see. It was three professional translators sitting on armchairs in front of the small crowd who had gathered and a screen behind them that showed various quotes (in English). Then, on the spot (alone and in collaboration with the others) the translators had to translate those lines into German. And they weren't easy things like, "Wow, the sky is blue today".

No, we are talking about elements from music with tricky wordplay:

"But in the end, the love you take is equal to the love you make."- The Beatles 

Positively crazy and fantastic sentences like:

"The sun shone, having no alternative, on nothing new." - Samuel Beckett

"You used to be much more...muchier. You've lost your muchness." - Lewis Carroll, Alice in Wonderland

And, to our positive delight, the best chunk of the Monty Python 'Dead Parrot' Sketch. You know it, but I'll put it here anyway:

" 'E's not pinin'! 'E's passed on! This parrot is no more! He has ceased to be! 'E's expired and gone to meet 'is maker! 'E's a stiff! Bereft of life, 'e rests in peace! If you hadn't nailed 'im to the perch 'e'd be pushing up the daisies! 'Is metabolic processes are now 'istory! 'E's off the twig! 'E's kicked the bucket, 'e's shuffled off 'is mortal coil, run down the curtain and joined the bleedin' choir invisible!! THIS IS AN EX-PARROT!!"

And to wrap it all up, there were a series of Shakespeare quotes that the professionals had to translate but in a particular style drawn from a hat - including the beloved 'that which we call a rose' quote in the style of today's young people's German slang, and 'If music be the food of love, play on' in the style of a children's book. Quite a fantastic and impressive presentation!

Autumn

Abby, at home in Meadville. I miss that one quite a lot.

The leaves are turning.

I think they all fell on the ground at the same time. Or, at least the first wave has. The trees aren't bare yet, but all of a sudden the ones that have come down cover my shoes while I wait at the bus stop.

I'm still negotiating the transition from one academic system to another but I think the end is in sight. One more exam and if/when I pass that, I can start math again. I feel like it's been forever. My friends encourage me that I'll jump right back in and it will be okay, but the nervousness I have is the kind that doesn't go away until you actually prove it false, as nice as encouragement can be.

I got to go hang out with the girls I mentioned in the last post again this week. This time, to learn more English (specifically to practice some writing and reading) we had a very fun game. Each person wrote down the name of an animal in English (this took a considerable amount of time, especially since the youngest one doesn't even know the full alphabet yet, even with the German names for the letters, let alone the English ones). I coached the four year old, who frequently had the right idea for how a letter was shaped but didn't trust herself to get it right, so she would "write" it in the air with her hand first and run that by me before committing it to paper. After making all these flashcards, we would hold one up at a time (not looking at which one it was) and whoever was "it" had to read the word on the card and pretend to be that animal so that we could guess which one it was.

Pretending to be animals seemed to work as a good motivator for some language learning. The 7-year-old, however, is too clever and has too broad of a vocabulary for her own good - or at least for mine. She made me have to act like a snail. If anyone knows how to do that convincingly, please do tell me.

Somewhere Between Monday and Tuesday

One of life's modern pleasures, quite different from the almost immediate gratification of the internet and other entertainment forms we currently have, is waiting for the delivery of furniture to your home. I am supposed to be getting a desk in the mail -- and according to the tracking information, it should arrive "between Monday and Tuesday". Well, it's Wednesday. Someone has to be home to sign for it when it arrives, so here I am.

And as I opened the window to let some of the morning air in, even though it feels like it will be quite a warm day outside, there was that definite crispness in the air, a scent that -- well, can something smell 'cold'? I feel like that makes no sense, but it smells like cold and autumn. I suppose I'm back in a place with real seasons. I can't wait!

And yesterday, I had quite the interesting experience. I've been looking for some part-time work here in Mainz and though I have been looking primarily for math tutoring (one of my favorite things) I've also found quite a few families who would like to have English-speaking babysitters for their children. I haven't babysat (if you don't count living with the youngsters this summer or with my ((second? Once removed?)) cousins the summer before) in years, but I thought I'd give it a try. So, last night, I met two adorable youngsters - one 4, one 7 - daughters of two nice German parents in a suburb of Mainz. But here's the interesting part. I was asked not to let the children know that I spoke any German. The parents told them I would only understand English (which they have already started to learn, to various extents) -- and let me tell you, it was an interesting experience.

First of all, I watched the older girl do something pretty neat for a person new to a language. She really believed I spoke absolutely no German and knew that her sister couldn't help her if she couldn't come up with a word in English, so she had to explain what she meant when she didn't know exactly what something was called. For example, at one point, her sister was looking around desperately for (what turned out to be) her stuffed rabbit, but when the youngest one was running around and saying the words for exactly that in German, I asked the older one what she was looking for and she stood the, puzzled, and then finally said "Her going to bed teddy bear rabbit", which is a fairly fantastic description. I have a lot of respect for this particular kind of speaking, as it's something that I also have to deal with.  I was having a discussion about this recently with C. The thing is, as a native English speaker, I can be incredibly, incredibly lazy. Well, I could have been so lazy as to never have learned a second language at all, but even though I have gone to the lengths to learn German, I still get to be lazy in ways people with a different first language can never be -- i.e. when I come across a word in the German sentence I want to say that I don't know how to say, I can just casually say the English word instead and most of the time, I will be understood.

I do this less than I used to (because my German has gotten better) but it still happens. In my own defense, I don't do it necessarily out of laziness -- more because I don't want to interrupt the flow of the conversation by saying 'huh' or something equally eloquent. Anyways. It's a hard thing to do and a very interesting thing to do from a learning standpoint - to be able to describe something even if you don't know how to say it exactly, and this seven-year-old was pretty damn good at it.

And the other hard part for me yesterday was when the youngest had trouble falling asleep and wanted to know when her mother would be home, and I had to speak to her in English even though I know she couldn't understand everything I said. She got a lot of it, though, and eventually, did fall asleep. But it was very hard to not just switch to German, which I am sure would have been more comforting to her.

Well, still no desk. I guess I'll keep waiting.

Just a little bit more.

These were the signs that marked the WHW - after every junction and maybe every few miles along the path, we would find them.

An astounding amount of water in Scotland. This was the day after a heavy rain.

And quite striking plants. The spirals on this kind really intrigued me.

Another fantastic aspect of the trail was the abundance of blackberry bushes. In the strangest places and (as the week went on) in the prime ripe season, we would find these bushes. After miles and miles and weary feet, nothing like some freshly picked blackberries washed by the rain or dew to make you feel like you could keep on walking. :)

Fort William, at the end of the Way.

Intrepid travelers. 

The West Highland Way, Abridged

On a train from Fort William to Glasgow at the moment, with what's come to be familiar Scottish highland scenery sliding past the windows.

We started what feels like ages ago at the smallish town of Milngavie (pronounced Mull-guy), but already by the morning of the second day, a cold that had been threatening me the last week in California took hold and then after trying to push through it until day four, I had a mild fever, a cough, and there was simply no way we could walk the last two days.

Let me recap briefly. The whole West Highland Way (hereafter referred to as the WHW) is around 96 miles in its entirety, from Milngavie to Fort William. There are various towns and villages spaced out along the way that allow for places to stay at night or places to get some lunch, so you don't have to carry everything on your back. We decided to book our nights along the WHW with a company that suggested you walk the way in a minimum of 5 days, and the maximum that they offered was 9 days. Due to financial reasons, we went with the 6 day plan - this means every day was on average about 14 miles of walking, with two outlier days (19 and 21 miles). Some days have convenient halfway points  along the way, and maybe buses that could take you to the next stop if need be (which we eventually did need) but not every part of the way has a convenient alternative to walking.

When you are staying in B&Bs in towns practically designed and maintained for people walking the WHW, eating dinners in pubs surrounded by other walkers (it's actually quite a fun type of community- you see some folks setting out with you at breakfast, lose track of them because everyone walks at different speeds during the day, but if you end up staying at the same town for the next night, you find those folks at dinner again) - - it's hard not to bury yourself in disappointment if you cannot walk.

Let me tell you, the disappointment hurts. Presently, we are sitting on the train two rows behind several groups of people who just completed the WHW in Fort William and who have been talking non-stop for the last two hours (I kid you not) about the beautiful last day of the hike. But I can't blame them. If we'd finished, we'd be talking about it, too.

So, bad timing of sickness really took a toll on the trip, but we did end up walking a little more than 40 miles, so it's not to say we didn't do it! And we talked to lots of other walkers and didn't run into any other people who were attempting the walk in six days -- always a minimum of eight. Lessons learned for the next time!

But still, this has been an amazing, amazing trip. I have always wanted to walk from one town to another -- it's crazy that I live in a time where we do that for a "fun, exciting vacation" instead of out of necessity - and the first four days of walking were truly, truly beautiful.

Forty miles on foot. Mountains, lochs, sheep, cows, fields, and that beautiful silence you find only in nature. Rainbows and sunsets and a  newfound love of 'walking holidays'. This one won't be the last.

Funny Turnaround

Well, as luck and cooncidence would have it, I was not met by C in the airport when I arrived in Germany three days go. Due to family matters, she couldn't be in Mainz that day and instead, I was met by a dear friend and had a lovely brunch with her that both nourished my stomach after airport food and also kept me engaged as I battled the inevitable jetlag sleep all that first day. 

But C wasn't there, and it was odd to be in that apartment- except it still feels a lot like home, too. The complication really came with the trip to Scotland that we had planned. I'm not sure if I've told everyone about this, but C and I planned a trip to Scotland almost immediately (approx. 27 hours) after I arrived in Germany as my dearest friend Erin has been living in Edinburgh for the last year and will be returning to the States tomorrow. Rather than be on opposite continents again, we decided to use the opportunity. And after she departs, C and I will embark on the West Highland Way - a long distance walking path into the Highlands.

But the point is, C couldn't be with me to travel to Scotland. But she did manage to find a flight from her current location and now, flipping the planned circumstances, I am on my way to meet her in the Edinburgh airport as she arrives from Germany. :)

Also, the following photo is from my road trip with my mom up the coast of California. I hadn't had the chance to post it yet, but I wanted to. 

Southern California Mini Adventure

So, there is no more work. It's all done. This is a bit weird to me- especially today, as it's Monday and I'm hanging out at my aunt's house and my uncle is about to come home after a day of work and normally if I were to be here on a work day, I would be riding home with him right now. Odd.

But, like any normal person, to respond to the end of an internship at a satellite company, I went snorkeling to see sharks this weekend.

Let me give a bit of backstory. Just a few miles South of here is a town called La Jolla (pronounced 'la ho-ha' -- and coincidentally was one of the areas that I was researching as a high housing appreciation area for Primarq last summer) that has some lovely shoreline that is home to many sea lions (or seals? Haven't found out which yet), snorkelers, and sunburned tourists. I went with a few other interns (I always seem to be going on these weekend trips with only boys - one of the occupational hazards of doing a tech internship, I suppose. I hope this changes soon.) ((Not that boys aren't nice. Just a 1:1 ratio would be groovy.)) and we went to a beach that is also known for hosting many, many leopard sharks.

Now, these sharks are bottom feeders (I realized the necessity to use this term after I told my girlfriend "It's fine, they only eat little things near the bottom" to which she responded "but what if you're kinda little and near the bottom?!") - shrimp, fish eggs, clams, etc. So, here's what happens. You squeeze your face into the borrowed snorkeling equipment (the water where the sharks are is fairly shallow, so none of us used fins) which is mostly just a face mask over your eyes and nose as well as the snorkel and then you star tot march down the beach, feeling silly until you get into the water. But, you are also informed that this area is known for it's plethora of sting rays (wikipedia says "the injury is very painful, but seldom life threatening..." -usually stings occur from when unsuspecting beachgoers step right on top of these critters that are chilling in the sand). So, the experts say, you just have to "shuffle" as you walk into the water to scare them away. This means scrunching and shuffling your feet on the sandy floor so that you make a ruckus down there - I did a combination stomp-shuffle to ensure that no sting rays hung out by my feet - and always keep at least part of your feet on the ground as you move forward, never just pick up a foot and plop it down on the sand.

So, even though I was doing exactly what I was supposed to be doing, I was convinced that every tiny bit of seaweed that brushed my toes was going to send me to the hospital and was very shaky as I went into the water.  I took my feet of the floor and began to swim in earnest as soon as that was possible - so, in about 2.5 feet of water. Imagine how silly this looks.

Anyways, then we were in the water and it looks as it normally does in the Pacific Ocean. No clear blue water, no clear blue skies, even - it was an overcast day. The water is dark, the waves are big but we are out past where the waves break so you just gently float over them as they come. And as everyone swam way in their different directions, you feel very alone - until you put your face under the water and realize that a school of fish is around you!

I had fun with the schools of fish. I paddled gently around with my face in the water and they swam with me, most of them about the size of my hand, and then all of a sudden I would see a dark shadow ripple along the floor underneath me -- and I realized it was one of these sharks! The ones I saw (about five in total) were between four and five feet in length and they move just like you'd think they would after watching so many nature documentaries. They glide. They swoop their tail across the xy plane (as I see it - if you consider their fins to be on the z axis) and are incredibly serene. The fish flit in comparison. Though I did, at one point, also see a sting ray and let me tell you, I was distinctly un-calm for the five minutes that followed.

All in all, a fun experience - and all you need is the mask and people to convince you to jump in.

There went twelve weeks.

I'm sitting in the very comfortable armchair in my room at my host family's house, the house I'll only be staying in for two more nights. Yesterday I said all my goodbyes to friends, coworkers, and bosses at ViaSat. I had high hopes for that internship - that it would be fun, that I might learn a thing or two. It exceeded all of my expectations. I learned "material" things if you will (new programming languages -- though I'm not great at them, I had to write at least a little bit of code in 4 different languages by the end of my project, also new software in general) but also intangible things lil learning to interact in a more corporate environment, finding out what work I like and what work I don't, etc.

Even when I worked at Primarq last summer, it wasn't this kind of work experience - though I remember thinking then what I thought this week. Namely, that work is apparently 8 hours a day, but it's really more than that. You don't actually have 8 hours for you, 8 hours for sleep, 8 hours for you each day. No, because you take lunch at work and that isn't really your time, plus the time it takes you to get to and from work - just like even if you lie down at 10 to sleep and technically have until 6, it doesn't mean you are immediately asleep at 10. These things are tricky.

And now, again, it's time to pack up and leave. I mean, I don't leave for a few days, but coming and going seems to be one of my main activities these last few years. When I say this, I don't mean to sound ungrateful for the opportunities I've had to live in all of these amazing places -- San Francisco, Berkeley, Oakland, Budapest, Santa Cruz, Carlsbad -- but all of those have been in the last year. I'm very familiar with my big red suitcase. And in a few weeks, that suitcase will be pushed into the belly of a plane and come with me to Frankfurt, where it will get dragged onto a train in the airport, then down an escalator a few stops later and pulled down the street in Mainz, and finally hauled up six flights (12 half-flights) of stairs on Pankratiusstr. And when it gets there, I really hope it stays there, unused and empty, for a long time. Say, longer than six months. At least.

I don't know when I started to love my hometown.

But I really do now.

On this trip, I was there for about three days in between flights, and this time everything - the tiny roads with fields on the sides, running into ten people you know while out to breakfast, the Saturday morning market, the animals from my old home, the tornado siren and thunder lulling me to sleep. And I got to see my grandmother, my mother, and my dear, dear sister.

What a fantastic trip.

One more.

More classic Calvinball, for good measure. Here.

All of a sudden, 23.

It was a very mellow day in lots of ways. I slept in (for me, so, 7:30 or so) and had a swim in the morning, talked to my host family and my skyped with lots of my actual family. I had a few presents to unwrap in the morning and then my aunt picked me up for lunch with her and the boys, Calder and Powell. We went and had Pho (and the squiggle over the o is one of the marks I don't know how to make on a keyboard - I know ö and ø and ó but not that one...) and it was delicious, and then (silly as it might sound) I went back to their place and had a positively blissful nap.

I think I was and still am quite tired - this week not only did I work on Saturday to compensate for my absence this coming Friday, but also from Thursday to Friday this week was the intern Hackathon, a hacking competition - except 'hack' in the sense of something you throw together, not breaking into someone's computer. So, this 24 hour ridiculous competition where we stayed at work (I came home for about five hours of sleep, I'm a wimp) and got to know each other as you only can at 1:30 in the morning when you've given up on your idea, right before you get your second wind.  So, I was wiped out from that.

And so the nap was blissful. If my affection for sleep continues as it has so far, then by the time I hit forty-five or so, all I will want to do is sleep!


But then I woke up and had a lovely afternoon with my aunt, drinking tea, looking at pictures, watching a movie. And then we had an incredible dinner - grilled Maui onions and eggplant(who knows if they're really from Maui, but damn, are they delicious), grilled steak, roasted cauliflower and corn on the cob. Of course, courtesy of my uncle Sam, we also had a lovely bottle of wine. He opened it and told me it was from 2007 and that I should think back to 2007, who I was then, what I had done since then, how different I am now. He said that was one of his favorite things about wine - that you can think of when it was made and how long it aged, and every time you sip or inhale it's aroma, you can think back to that time. It really made drinking that glass of wine a particularly lovely experience.

Of course, there was also cake. :)

And then, after cake and laughter and smiles, I came back to my host family.  We hung out in the kitchen and talked about our days and then my two youngest host sisters and I engaged in what I can only call some form of Calvinball -- for those of you who have never heard of Calvinball, I've attached a comic for your edification. Basically, we each guard one of the doorways in the entry hall - there's one to the music room, one to the dining room, and one to my bedroom - the first two are at least eight feet across, whereas mine is a normal door size. So, getting the inflatable ball through another doorway is one point each for the first two goals, two points if it goes in mine. But then again, I'm at least twice as big as these two girls, so things were slightly skewed in my favor. Still, I lost. Also, you can use hands or feet. And sometimes pick up the ball and walk directly up to the goalie past whom you are trying to shoot the ball. Everything is fare game. Hence, Calvinball.

And now, I'm going to go to bed. Only three weeks left of this internship-- crazy. And a very lovely Birthday.

A Southern California Day

So, I woke up this morning at around 7:30 -- the latest I've slept in a while. I'm one of those folks who keeps waking up at 6 out of habit even on the weekends. But I got to sleep in and I went out into the kitchen to make my coffee and toast and joke with my two host sisters - as some of my Facebook friends know, we had a fun night of face painting the other night which ended with me somehow getting a really bushy painted mustache -- pitch black, obviously, as befits my complexion.

After breakfast, I changed into more suitable clothes and was picked up by a fellow intern to go and play soccer at a local park. Now, even the "just for fun" teams around here are incredibly serious about soccer - everyone has cleats, they even have proper referees running around, as well as matching jerseys. This bunch of misfits that I was with is nothing like that. Our skill levels range from the two people who play actively while they are at college to the rest of us, who "played in middle school" - which basically means we know which end of the field to aim at.

Also, these non-professional serious teams always take up the soccer fields, so we play in a baseball outfield with goals that are made of two water bottles precariously balanced on the grass -- today at least both goals were the same size, but I don't think they were really totally aligned on the different sides of the field. We didn't care.  We were 12 people today, six on six, and the teams were quite well matched. As a result, of course, in spite of the generous amount of sunscreen I put on my nearly translucent skin, I still managed to end up rather pink in the face but I think I can just blame it on the sweat that made the sun screen run away. Still, we had a blast and though I have yet to score a goal in one of these games (I've been on the winning team all the times we've played ((twice)) and have played on basically the same team) today I had a few good moments of defense (where I play by default, though I enjoy forward as well) and one assist.  Who knows if any of us will care about soccer in three months - or even on Monday when the World Cup is over- but it doesn't matter! It's a great way to spend a Saturday morning.

After that, we headed to another intern's house to barbecue and watch the professionals in the Brazil-Netherlands game. This house was classic California - a ping pong table on the open porch, beautiful open design, and a plum, a peach, a nectarine, and a lemon tree. Plus cherry tomatoes in the garden. I don't know how these people ever go to work in the morning. Especially because this little one is wandering around.

Her name is Ivy.

Alright. Now I have a bit of work to do - I was asked to join another project this week which is exciting, but first, as a good friend of mine says, I need to "put an upper bound on my ignorance". This project/problem involves so many things I've never worked with before that I really have quite a lot of catching up to do. Still, I like learning. Here I come, Information Theory, Data Compression, and C++!

Sometimes, I do actually stop to smell the flowers.

This week will be the 6th in this 12-week internship, and I feel like things have just barely started. The last intern on my "team" or "project" arrived this Monday - the arrivals of all interns were staggered depending on when that particular intern's college started summer break. I started particularly early since I wasn't bound to any college, and I don't think any other project has such a wide spread of starting dates - but it has worked out well for us. I got the chance to immerse myself in the kind of data that I now am actually starting to analyze, before it started flying at me with the speed and volume of -- do elephants run quickly? If so, a herd of elephants. Maybe a few seconds in between, then I hear of another dataset where, if we process it in such a way, will end up being an Excel spreadsheet with 1.3 million rows - I almost wish I were kidding, but I'm not.

Don't worry, I don't have to tackle sets like that multiple times a day. They're usually followed by an email from the third intern, a programmer, who says "whoops, forgot to import them in columns, that'll be a ***** to organize - sorry about that! I'll have a better version in a moment."It's only his third day in, so he's not only doing what the rest of our team has been waiting for him to do (talk to this enormous database in the internet and get it to give us the information we want in a form we can process) but also has to understand all of the acronyms the rest of the team uses when we talk to each other, and then do all those first-week things -- get the stupid desk phone working, manage all of the passwords, find your way to the bathroom and lunch without managing to somehow go the least efficient way.

But since Monday, I swear, it's like we were building a rocket in the weeks leading up to this but I never saw the whole blueprint - I carried bits to the construction site, I hammered and sawed and welded just a bit (learning those things as I went) and then there was something on this launch pad but it was too big to see the top and it really wasn't perfectly finished yet. And then our last intern comes, and it's like there's sparks underneath the thing now - someone handed over the blueprint and not only that, but told us our destination --- and if I can continue with this preposterously dramatic analogy for just one second longer - I feel like it's my job to determine the flight path. One intern finishes the proper construction of our ship and makes sure the launch sequence operates properly, in the air and atmosphere it's my job to direct it, and the final intern makes sure that when we get to where we're going, we're in the right shape to land and report on our flight.

And given that I work for a company with such stringent security measures, I fear that's all I should say in this public form!

But quite a few things have happened this week.

1. I've learned what it feels like to try and fail, try and fail, try a much more complex approach and still fail and then have someone tell you that there's a better tool for what you want to do -- I didn't even feel silly or stupid when this happened. Rather, I felt relieved, because I had known there must be a way to do what I wanted. That being said, I don't know how to use that other tool yet (it's the statistical programming language R, with the ruthless and infamous learning curve), but I know it's there.

2. I was asked to be on a panel for a program that ViaSat hosted for schoolgirls going into 8th grade about women in mathematics and technology. When I got the email asking me, I almost jumped out of my chair, and I had a fantastic time talking to them. I can't believe I'm one of the people who gets to be on the stage at an event like that.

3. I've learned that there is so much data out in the world, in the cloud, in the whatever you want to call it right now. And I've learned that it is far, far easier to create data and store it in the cloud than to actually harness what you want and use it.

4. And, unfortunately, I hurt my hand during boxing. At least, I think it was in boxing. It's not the normal injury one would expect from a beginning person in a boxing class (I won't say boxer- I haven't hit anything except a bag yet, well, except for one other intern, but we were practicing various blocks so he knew exactly where I was going to hit him, so that doesn't count) - I haven't hurt my wrist or anything. I seem to have pulled a muscle right in the fleshy part of the hand, in the area between the thumb and middle finger (encompassing where the pointer finger meets the palm as well). It's an unfortunately pervasive injury - I can't do push-ups or downward-facing-dog because the pressing down of my hand on the ground causes it pain (and I could push through it, it's not excruciating, but I feel like it might get better if I don't piss it off more) -- but apparently, things that I never expected exert exactly that kind of pressure and tension in that hand. And it's my right hand. So, things like holding my phone in one hand to text, holding a carton of milk to pour it, twisting a key in a stiff lock, or wringing out a damn sponge! Ugh! It's been quite a few days and it hasn't gotten better - I'll have to figure something out.

And finally, tomorrow is the traditional (apparently) Carlsbad ViaSat Interns Beach Bonfire- in which much fun will be had, I am assured, and I (along with whichever other interns were silly enough to sign the waiver) will have a surfing lesson. I'll be sure to let you know how it goes.

A visualization of the week.

Chasing the sunset.

A beautiful surprise just above 10,000 ft outside Seattle.

“Good evening, ladies and gentlemen. Our flying time tonight will be a quick 5 hours and 45 minutes. “ Yeah, right.

Once again, I found myself in a long line of travelers – heads down, feet shuffling, moving like chained inmates in the cinema, we all hold our elbows in and misjudge the depth of our backpacks as we trundle down the airplane aisle. Trundle. I cannot think of a better word for that reluctant and simultaneously impatient gait. Some of us have been rather rudely parted from our carry-ons planeside, which we only brought as carry-ons to avoid the baggage fee which is moot at this point anyway, but the knowledge that our extra t-shirts and socks are under our feet rather than above our heads still rankles.

I’ve done a lot of flying this week with a lot of different airlines. (Now, I have to also say at this point before I launch into a bit of a ramble about ports and planes that I also had a positively splendid time with family in DC, family which I wasn’t expecting to get to see for a long time – a completely coincidental meeting and it was just lovely. I am so grateful that it happened!)

Back to what I was saying. Traveling in this world is an interesting beast. You have to give a lot up. Yes, on the one hand, we are miles and lightyears ahead of what used to be the case for this kind of travel – scurvy and occasionally being lost at sea, then broken wagon wheels and dying of rattlesnake bites in the middle of the desert (Oregon Trail, anyone?). But today’s traveling comes with its own idiosyncrasies.

Thing 1: We submit ourselves to a world completely controlled by capitalism when we travel. Sometimes, it comes right down to what I call “minor injustices” in my head (okay, a bit dramatic, but you’ll see) when we’re trapped in the traveling world. For example, to log on to the “free” wifi at several airports, you need to watch an add on your device in order to do so. If you mute the video, you cannot log on. Now, you can still let it play and look the other direction, but this forced entry into capitalism and materialism can hurt. (NOTE: Being without wifi is not cruel or inhumane. I do not mind being unconnected to wifi. I do think that whoever decided the forced consumption of an advertisement was a fair exchange for internet in an airport is a creepy and twisted individual.)

Another instance of this happened on one of my early flights when something was happening with the air circulation system on the plane and when I asked, I was informed that blankets were only available for purchase. Now, part of this is because the airlines as a whole are not doing well – but still. I imagine you could come up with a story if you had a shivering child and get a blanket without charge, but we shouldn’t have to stoop to that.

These are just some examples of the way in which one is trapped when one travels. In the world of the airport and airlines, you have to give in unless you are incredibly, incredibly prepared. I refer mainly here to airport food. The options are the only ones left to you. I felt like I was in a horror film these past few days, reading ingredient lists on things like pretzels and trail mix and feeling myself quake in my shoes at the partially-hydrogenated-corn-solids that are somehow necessary in RAISINS, not to mention what goes into yogurt or bread. Finding vegetables that are not iceberg lettuce is – well, let’s just say that I spent a lot of time in airports this week and I did not always succeed.

Sensory bombardment – whether it is billboards, posters, PA announcements or the blaring TVs in every terminal, we are assaulted while we travel with noise and agendas. It’s never been so obvious to me as it has been this week, since I have spent so much time in these places.

And interactions with people – you can tell my thoughts are all over the place this week. I’ve had a lot of time in my own head. My longest conversations have been while checking in to hotels. But strangers – we are so far apart fom our fellow human beings these days. So very, very far away. Hours and hours of sitting next to each other, and not a word. An awkward glance when someone has to go to the restroom and the rest have to stand up to let them go. And bad moods can spread like wildfire when there is rudeness (which there frequently is – because these are strangers, we’ll never see them again, why does it matter if we are rude to them?) – we simmer and grumble but never communicate.

Okay, humanity isn’t doomed and neither is the travel industry. It’s just the demand for service on the part of the consumer and the demand for profit on the part of the providers seems to be leading to more and more uncomfortable circumstances and interactions. I caught myself thinking yesterday “Imagine how many more people could fit in a plane if we made them stand? All the room those legs take up while sitting could be done away with…”

But then again, it has to be said that flight is one very cool thing that we have managed to do as humans. Last night when I got on that “short” five-and-a-bit hour flight from Washington, DC back to California, we boarded in the evening and I had a sudden flashback to the first flight that I ever remember consciously taking as a kid. It was a similar flight – from the East coast to the West, leaving in the evening. And I remember thinking then that we were “chasing the sunset”—which you do. The sun is setting in the west and you fly towards it, extending that beautiful red sky for longer than you ever normally get to see it. We’re still not fast enough, of course, and time passes as you fly so eventually the sun does set, but that visual and the words describing it stayed in my head all of these years.

Practice Rooms and Planes

So, this afternoon, I went with my Aunt to an event at a local music center - where children and adults alike can go for individual lessons, to play in ensembles, and sometimes to perform! Today was an event where the local jazz group played while a local painter got the chance to display some of his work around the music center. We were mostly there in an organizational and helping capacity, but I did get to wander around the center just a bit.

I kept being reminded of the music building at Mills - without a doubt, one of the prettiest buildings on an already stunning campus. But that building was the kind of pretty that comes with elegance, some grandeur - a big auditorium with paintings all around, curvy railings and beautiful seats, and the entryway had a vaulted ceiling and beautiful stone floors. An elegant building. One semester, I had a class there, which in addition to the coursework meant that I got the chance to walk through that building.

In addition to the grand auditorium, this building has hallways and hallways snaking around filled with small practice rooms. I remember practice rooms from way back to my days in Meadville, at the Allegheny College Music Festival - back when I played the saxophone. And the idea of practice rooms has always made me -- well, happy. A room whose only purpose is to provide a space just for you- a place designed for you to go and work to get better at something. Where it's okay to sound terrible, because if you didn't, you wouldn't need to practice. You can go in there alone, no need for a lesson, and just play, or sing, or compose. It's the office of the musician, I suppose. And for some reason, even though everyone tells us it's okay not to be good at things when you first try them, it seems like music is one situation when practicing is simply an obvious (and important) thing to do. Maybe it's because when we talk about other fields like math or theater, we don't say 'practice' - we say 'homework' or 'rehearsal'. I don't know if this idea of it being okay to need practice means anything to anyone else, but to me, it always has been important and practice rooms are a representation of it, and I think they are fantastic because of that.

In addition, as I was watching a timid flute player attempt a solo during the jazz performance tonight, I remembered my own forays into improvisational solos back in high school and I remember when it was time to play that I was overcome with such nervousness --- and you know what I was nervous about? That if I played, I might be heard. I was PLAYING AN INSTRUMENT and worried I was going to be heard. I still frequently feel that way when I sing. How does that make any sense???

Oh, well. We're all a little crazy, aren't we?

Speaking of crazy, I will be flying again this week. To several states around the country. I have tests to run on the wifi while I'm on my planes and work to do for my internship once those tests are over - and in between, I get to travel. Traveling by myself - travel for business, as they say, except where the business is when you are on the plane, not when you get there. It'll be an experience, for sure.

That day got a mind of it's own.

I just got back from my first time of flying-somewhere-on-company-funds-just-so-I-can-run-tests-on-the-wifi. Tonight it was from Long Beach to San Francisco and back - yes, on the same plane. So I was in San Francisco for about twenty-five minutes. And now I'm back in Carlsbad. And I didn't know I would be doing all of that until eleven this morning.

I'm exhausted but happy and the main thought that keeps coming to my mind is that there's just something about walking down from a plane on steps or an outdoor ramp instead of a jetway that just makes one feel so damn important. I like it.

Goodnight.

Oh deary, deary me.

All of a sudden, it's about to be Wednesday in my second week of my internship. And my head is buzzing with thoughts but unfortunately not with the kind of thoughts that usually flow so easily into blog entries, but I'll do my best.

I presented some of my work to my supervisor today and I was told I was doing a great job! I'm not sure whether today I can call myself any kind of a data analyst, but I think at the end of the summer, I will be able to say a bit of that, which is very, very exciting!

And other things are going well, too. I spent the long weekend hanging out with my cousins here while my aunt and uncle went to a wedding. It was a weekend of meals out, naps in between (for me), and many, many X-Men films (we had to watch a bunch of the old ones to be ready for the new one, you see ((which I thought was good!)) and then when we came home from the theater, one of the ones we hadn't watched was on TV...). I also got to hang out with the little Watson, their (if I remember correctly) Pomeranian-Chihuahua mix. I will never own a dog so small, but I have to say, he's growing on me a little.

And today I did possibly the craziest thing yet - I went to a boxing class at the gym by my work. It was a great class - but I honestly - HONESTLY am having trouble convincing the muscles in my fingers to type this right now. I had no idea my hands could be so tired.

So, I close my eyes and see spreadsheets right now and my hands ache from being balled up inside huge gloves, but I'm excited to get back to my office tomorrow. And that's just a great thing.

At the same time, though, I watch the news at night and I feel like the world there can't possibly be the same one that I am going to work in, the one where I go grocery shopping and walk around the neighborhood. I think the events that are happening (Santa Barbara is foremost in my mind, but the rest of the globe as well) are only about as tragic and frequent as they always are, but when you pay attention, it rattles you inside.

"Of things beyond my ken."

So I had my first day today - and it began with hours and hours of orientation. Security briefing, HR orientation, IT orientation, badges here, scan passport there, this that and the other, don't carry secure documents down the hall unless they are covered by a folder - and then finally, I had my little badge with my name and employee number that gets me into all buildings, had an account on the company intranet, and - well, I met my team.

When I write this out here, it's different than when I explain my day in person. When I was on the phone with friends earlier, I explained in a bit more detail. The interesting thing is that I'm not actually sure just how much I'm allowed to tell. We got these huge and tedious security briefings because the company itself does provide services for the Department of Defense, and most of the security protocols only apply to you if you happen to be working with documents or equipment relating to that, which I will not be during my internship. But still, you're in the building, you have the badge - it feels a bit different than any other work I've had before.

But once I shook off the strange feeling the security stuff left with me, I met my people. I'm working on the very young but exciting project of airplane wifi (look it up! "Exede In The Air"). Not something completely new (we've all seen GoGo in Flight advertised on planes before... competition!), but this company (ViaSat, if I haven't mentioned the name before) has some new ideas for how to do it right.

So, I met the people working on this project and within five minutes, I had a fairly great realization about why I think they hired me. Not necessarily because I can do calculus and linear algebra - but rather that studying math has given my brain certain skills and patterns of thinking, abstract and problem solving abilities - and that's what they want. That brain with those skills on this project. And I'd rather be hired for that than for my ability to solve differential equations. :) Not only that, but they are already telling me to be creative, to "follow my nose", if you will. And the company is very laid back and very productive at the same time -- that may seem like a contradiction, but it really boils down to this: "Do whatever you need to do in order to do your best work." So, how does this look? Employees going surfing during their lunch break or out to the beach volleyball courts next to the work buildings. Some people come in at 4 a.m. and leave at noon, some don't show up until 11 a.m. and stay as long as they can. Some men wear shorts and t-shirts, some where suits (okay, that also varies by department) and everyone is on a first-name basis, but not in an awkward way.

Basically, a good first day. I'm excited to go back tomorrow and not spend the whole day fighting my way into the computer system (so much administrative stuff yesterday!). And - I'm excited to meet these people and work more.

I'm the first intern on my project. Next week another will come, and a month after that, another. But for now, just me. That's kind of fun. :)