An update, and some musings

I'm sitting in a café at the Mainz train station, studying for my two remaining exams. I am studying the material that I compared to a treadmill the last time I was writing here. And it still feels like that while studying. But studying for exams is also something I've gotten better at during the years. I feel like it's kind of like sketching - well, I've never really done much sketching, so maybe an actual artist can tell me if the comparison is good.

When the subject you want to review is small enough, you can go through every single detail. You can start in one corner and just move out from there, filling in all the bits you need. But if what you need to review is the equivalent of a mural, that's not the way to go. It's too overwhelming. So, you draw the biggest, least detailed sketch that you can. Then you fill in one more level of detail. Then one more, then one more.

That's what I'm doing now. That treadmill class met for an hour and a half twice per week for the last two semesters. And in two weeks, I have to answer questions about it. And next week, I have a different exam. So, splitting my head a bit to fit both things in - we'll see how it goes.

Like I said, I'm currently in a café. I have been wondering about café culture in the last few years. I know personally it has really been a positive thing. All through my college years, both in the States and in Germany, I have done a substantial amount of work in cafés - whether it be one at the train station here or the Mills College Tea Shop, or the one café in Berkeley where I always went when I had my German class at UC Berkeley (On a side note - that was the only café where I really was a regular. Only twice a week, but always those days at the same time when the same people were working. They started doing really creative designs in the foam of my cappuccinos - starting with friendly and lovely flowers, hearts, etc. - until one time, I swear they drew a pig in my cup. Not sure what they were trying to say with that one, but it made me smile.). There's less pressure than in a library, there's readily available caffeine, and there's not the pull of lounging around that you get at home. I feel this café culture has really increased in the last few years. But I wonder if that's also part of the function that "The Club" used to fill for men, back in the day. Maybe that was just smoking and talking, not so much working, but I've found it a useful place to collect my thoughts and get some work done.

When I don't get distracted by writing blog entries, that is.

I suppose I also have a soft spot for them because I used to work in a café, in the one café in my hometown and I did my best to make that one into a place where this kind of work could be done. So, I appreciate a good café. And a good pig drawn in the foam of my cappuccino.

Back to the algebraic treadmill.

Crossroads

All of a sudden, I'm in the second semester of the M.Sc. program here. The classes are getting harder, which is to be expected, and all around me, the folks I have been studying with are going in their own directions.

Here's what I mean. In the Bachelor's program, there's a core set of classes that everyone has to take - you have to prove you've mastered the basics of the three largest areas of mathematics. Here, we call them areas A, B, and C.

A is for Algebra, which includes abstract algebra (groups and rings and things I've explained a bit on this blog before), number theory (questions about finding prime numbers, for example, or figuring out how the primes are distributed ((they're all clumped together at the beginning, 3,5,7 for example - and even for larger numbers, you sometimes get some that are really far apart, but every now and then, some that are right close together, just two apart, like 137 and 139. Can we come up with a theorem about when this happens?), and topology (shapes, shapes, and more shapes. I think I've written about this before, too.).

B is for Analysis, which is what we tend to call calculus in the US. But it's not just integrating and differentiating. In analysis, you also encounter things like manifolds, you do differential geometry, things like that. Remember the post about Hausdorff dimension?

C is for Numerical Analysis and Stochastics (Probability Theory). The second half of this area, probability theory, is something that I have never warmed to. Partially it has to do with a lack of intuition and instinct in this area, and partly with the fact that I've never had close friends who really enjoyed it. Someone can explain to me several times what the probability is that you will pull three queens of different suits out of a deck of cards if you put them back in each time- and within an hour, I will have forgotten the explanation. Numerical Analysis, however, is something that I am starting to discover now. It's all about trying to simulate phenomena that can't necessarily be computed exactly, the way we'd like to in the rest of mathematics. There's many applications in physics, chemistry, biology and other fields.

Footnote: apparently mathematicians aren't good with the alphabet. No, those letters don't match up with the subject names in German, either. I feel it would be less confusing to use 1,2,3.

So, these are the three areas. You have to take introductory lectures in each of those during your Bachelor's - (three courses in A, three in B, and one in Numerical Analysis and one in Stochastics). Then, you have some more open credits where you can choose which fields you want to look into.

In your master's, you are required to take at least six credits (a normal lecture + workshop) in every one of these areas, but that's the only distribution requirement. You also pick an area in which to do your "Vertiefung", or the area on which you wish to focus. This will be a sub-area in A, B, or C. And that's why in the Master's, people are drifting apart. They pick a direction and go and soon, it's hard to understand what they're doing if they have picked a direction different to yours. The basics that you had to take in your Bachelor's help you have a rough understanding of what the others are doing, but the specifics get pretty mysterious.

So, that's a changing dynamic. Another other dynamic? Well, these classes are getting hard. That might seem silly to say as we are talking about a master's program in mathematics, but still. I've noticed a big jump from  last semester to this one. In the meantime, you (as a student) also have a minor in which you take classes and in your Master's, you might very well take classes that are technically for Master's students in that field - even though you only have it as a minor. You notice the gaps in your knowledge.

That's one great thing that mathematics teaches. You know, and I mean know, when you have understood something and when you haven't. Three-dimensional understanding. Inside and out, can explain it and cannot forget it. That's understanding.  It's a beautiful feeling. You want it all the time. And you know there's not enough time to have it in everything you do, especially in your minor.

Don't get me wrong - we have a few people here who really can and do have that level of understanding in every class. It's partly because they put in more time and partly because, frankly, some of them are brilliant. It's easier to detect the brilliant ones later in your studies. At the beginning, when someone seems like they are brilliant, they could just be an asshole pretending.

I'm not one of those folks. I don't mean it in a "poor me" sort of way. I know I am smart and I know I have worked hard to understand what I understand. But I know who those people are and I know I am not one of them. And this semester, I can feel the speed being cranked up in the lectures I attend. In some of them, I can increase my pace and keep going but in some, it's a chore. It's like running on the treadmill at a speed just above the pace you can comfortably keep up. It's not that I'm about to fall off, nor that any one particular moment is unbearable - but it's hard to keep going at this pace. And this semester, I also have a lot of extracurricular things on my plate that are filling my time - and I don't just mean those silly luxuries of food, sleep, and exercise.

And just to sprinkle some spice on the top of this situation, I can feel my interests shifting. At this moment, I'm rather enamored with some classes in area C. Area C! Good grief, what has happened to me? I have been an A-girl since I first stumbled into a Linear Algebra class seven years ago. I feel like I'm having an affair. But I'm sitting in rapt attention in a class on computational fluid dynamics and that is exciting and scary. Because, of course, the next big question after all of these classes and credits are done is: what will your thesis be?

At the moment, I'm torn. I guess we'll just have to see what happens next.

Words, Words, Words

A few months ago (I know it's been ages since I've written), I was sitting in the cafeteria with some new acquaintances. These were folks I had met in the course of a math class and who might be becoming friends but it was too early to tell. We were in the loud, cavernous cafeteria room with clattering trays and cutlery and happened to see a pile of pamphlets on the table about local campus elections. These were from the different student government groups, explaining changes they wanted to make on the campus.

There were mostly groups only between the far left and the center. One in particular caught my eye because it was discussing gentrification in the neighborhood in which I live - gentrification that I have seen over the course of the years I have been here. I have many a time wondered how much of a role I play in it myself. I mentioned this to the rest of the group - and I got blank stares.

Soon, I was asked to define gentrification. Now, gentrification is a hard subject to discuss even with close friends and even when everyone has a basic understanding of the concept. Introducing it to people who were, as privileged, white, oblivious individuals, very similar to myself at the beginning of my college career - well, let's say they were resistant to the idea, as I was for a very long time. I failed miserably at explaining exactly what gentrification is and why they should care.

And I thought about other similar situations - situations in which someone has used a term that is harmful, racist, sexist, classist - and about how sometimes, I do what I wish I did all the time and confront them (kindly) about their choice of language. But sometimes I don't. If I am the only girl in the group, I usually shy away. If I am younger than everyone in the group, I usually shy away. If I am a new member in the group, I usually shy away. I wish I didn't. I'm working on it.

But part of working on it is having a bunch of explanations ready and at hand, so that at least under the pressure of being younger/new/the only girl, I don't have to come up with anything new. And then I stumbled upon this video today, which I think will help me in that respect. Maybe it'll help you, too. Because we should never shy away from that conversation.

The Case of the Missing Files

I have recently started a new job. One of my duties involves updating files that are located on a server. With the right simple software, this isn't too complicated and barely takes any time to learn. I copy the files over onto my computer, work on them, upload them again – just like using Dropbox or even getting an email attachment. The cool part is that these are the background files of a website so when I change something and want to see if it has worked, I just upload the files I changed and reload the website to see if the changes took.

This worked just fine when I started this job last January. I'm working for a small math magazine that gets distributed to some local schools. Students work on the problems in the magazine, send in solutions and accumulate points for the problems they do correctly. I'm the one who keeps the website for the magazine up and running, so people can check when the next issue is coming out, who has collected how many points during the current year, etc.

All of a sudden, just a few weeks ago, a lot of my files went missing. The biggest file, the one with the list of students from all the schools with their points on the last three issues – gone! At least, it would not show up in my program that shows me what is saved on the server. Imagine looking in a directory on your own computer where you thought a file was saved, but now the file is gone. However, the file couldn't just be gone – because when I went to the website and loaded the page, lo and behold, there was the list of students with all of their points, exactly how I had last updated it.

But I needed to update that list again. How to do it? I didn't have the file and didn't want to write it from scratch again. So, I figured out – with a bit of help from the Internet – that the GoogleChrome browser has a tool that lets you view the source code from a page. I tried it out, and – hey, presto! – there was my beautiful php code, just as I had left it, displayed in a browser tab. I copied it and created a new document, edited it, saved it under the original name, and dragged it over to the server. Here's the other weird thing: usually, my program alerts me when I put a new version of a file on the server; it asks me, as you might expect, if I would like to overwrite the old one, etc. But that time, it didn't ask me. Not only that, but when the file transfer was done, the new file still wasn't listed. I had transferred it, the transfer had been successful, and then it had been swallowed up into the ether. Except it hadn’t been. My changes showed up on the website.

This happened to several files on the server, files that I had downloaded and worked on and uploaded without a problem when I started working there. Some files were still there. I could see them on the server; some I couldn't.

This was vexing. 

I'm not very well versed in this area, so I eventually went to see our department's technical support person. This gentleman I had met only once before when I introduced myself as the new member of the magazine team. I explained my problem and he stared at me. I stared back. It is a weird problem to try to explain. 

Slowly, he rolled his swivel chair over to face his two desktop screens. On one, he opened a program similar to mine that let him look at the files on the server. I placed my laptop on his desk, displaying my version of the program that lets me transfer files to and from the server. He used one monitor to open the command line: that place where once upon a time – in an ancient pre-mouse era – we typed 'pwd' to print our working directory, 'cd' to change the directory, and other commands to run things on a computer. It is still used, and sometimes, there is nothing better.

For the first fifteen minutes, I didn't say a thing. He looked, tested, copied, uploaded, scratched his head, squinted at the screen. Nothing worked. On his computer, it said there were 193 files on the server. My computer registered only 177. Sixteen files were missing. Files that had nothing to do with each other.

He made a copy of certain files, changed the server settings, re-uploaded everything. I restarted my program and looked again. Still 177. He changed the basic settings of my program. 177. We looked at every single preference setting that could be changed in the program. 177.

About forty-five minutes had now passed. I had put my backpack at my feet and was admiring his patience but I wasn't thinking we would get to the bottom of this.

All of a sudden, he spun his chair around and began to type in the command line. Lines of code popped up, he entered new commands, looking into the settings of the server. Then he looked at me. 

"When did you start working with the magazine?" -"January." 

"And you could access all of the files at the start?" - "Yes."

"When you uploaded them, they were still there and you could then download them to edit?" -"Yes."

"So it just changed at some point recently? Recently the files just started not showing up?" -"Yes, exactly."

He smiled. "Every file that is missing was uploaded to the server in March," he said.

I stared blankly.

What followed were five minutes of typing during which I felt very silly, not understanding this breakthrough. After those five minutes, he refreshed my program once again and… all the files appeared. 193.

What was this miracle cure?

He explained to me that buried deep in the server, the files edited in March had not been saved with some numerical date, as I had expected – 03/05/2016, for example – but with the actual month written out. So, on this German server: 'März': the only month with an umlaut in it (those little ¨ dots). And my poor American computer couldn't read them. Couldn’t read the dots, and thus, couldn’t read the date – and did not display them. This explained why there had been no problem with those exact files when I had edited them in January and February, and why they then disappeared so mysteriously after months of being fine.

We smiled at each other. "Wow," I said. "Thank you so much! I never would have thought of that." He grinned, and it was like, together, we had vanquished an invisible foe.

Then, since we really don't know each other at all, I gathered my things and exited rather awkwardly. But still – we now share that victory.

Here's to all the computer detectives out there. Cheers!

Groundhog Day at the Pittsburgh Airport

I'm at the Pittsburgh airport, Concourse D. I’ve gotten to know it quite well over the last 24 hours. Yesterday, I arrived at the aiport around noon, waited in the security line, took the train to the departures terminal and found my gate a good hour and a half before take-off – like a responsible traveler. Gate D80. Our departure time came and went while we were being provided with updates from our gate agent roughly once every ten minutes. I wandered. I found a Starbucks as well as some nice tables with comfortable chairs, and stood in line behind a besuited businessman who sheepishly asks for a lattice of extra caramel on his iced latte and turns to me and says this caramel is the highlight of this day. Back to D80. Our last update was just to tell us when our next update will be. It is now three hours past the original departure time. The problem is not in Pittsburgh; the problem is in New York City. Weather. I’m not even trying to go to NYC, simply through it to Frankfurt. But in NYC, nothing is going in or out. Eventually, our flight was cancelled. I was rebooked for an early afternoon flight the next day to catch the exact same flight from JFK 24 hours later. 

Now, seasoned travelers will know that this type of cancellation entitles the travelers to practically nothing. (When there is a mechanical malfunction, some maintenance problem that even just delays a flight, you might be eligible for compensation as those are technically the airline’s fault. That's what happened to C and myself a few months ago, during our saga of a return from California.) This means that this time, even though I needed to find accommodation for the night, the airline could offer me at best a „distressed rate“ at one particular hotel (which may even have been full, considering the number of passengers who were delayed until the next day) – and that’s all. Even that distressed rate would have been a blow. But luckily, serendipitously, my mother – who had dropped me off at the airport a mere 6.5 hours previously – was still in the general area doing work, and she could simply pick me up again.

We had a lovely evening and a relaxed morning together, and here I am again – but now I know the terminal. I go to the faster alternative security checkpoint, which I didn’t do yesterday. I don’t fight with the water fountain that insists on pouring water horizontally, at an angle that doesn’t agree with the neck of my reusable water bottle. Instead, I head to the water-bottle refilling station that I found late in the afternoon yesterday. I go back to the same Starbucks to get a cup of tea – the gentleman behind the counter looks at me. I look at him. „Were you here yesterday?“ – „Yes. Were you?“ He was kind yesterday and is kind again today, giving me an extra tea bag in case my journey today gets delayed again and tells me I can just come back and they’ll give me a cup of hot water for that teabag. I won’t tell him that my backpack is stuffed with Peets coffee.

For now, I’m enjoying my tea and then I’ll it's back to – believe it or not – D80, where I sincerely hope, pleasant as this has been, that it does not all begin again.

On a slightly lighter note...

I have my first oral math exam this coming Saturday and it happens to be in Topology, one of (I think) the most playful and fun branches of math - and one that math-lay-people can get their heads wrapped around, at least a little. So, if you feel like thinking about some of this, check out these links:

First off, two very cool topological spaces, Bing's House (or the House with Two Rooms) and the Infinite Earring. Let me know what you think!

And now, a video - of a lay-person's proof of a very cool theorem in Topology (no lectures needed!)
 about how under certain, simple assumptions, you can show that two spots on the earth have exactly the same weather...


Alright - I'll get back to the technical details of these spaces - they are less fun than the articles I've posted here, but I suppose, as a mathematician-in-training, I have to accept that they are important.

Thoughts from Brussels

Two Germans, two Americans, a half-English, half-Canadian girl from France, and a half-Bulgarian half-Dutch girl from Germany get onto a bus in Brussels on their way to a restaurant. There they meet up with another three Americans as well as a mostly Dutch, somewhat American man. They eat Eritrean food for dinner, drink Belgian beer, eat French bread for breakfast and speak in a glorious mishmash of languages, including folks attempting to mix and compare Flemish with the German dialect of East Frisia, depending on who is sitting next to whom at what time (and how many beers have been drunk).  They are musicians, interpreters, students, and EU Commission employees – and they are all Unitarian Universalists, which is how they all happened to meet.

I have to say, it was a pretty cool weekend. I didn’t really expect that I would start going to a UU church again at my current age. I did grow up as part of a UU congregation but I started to feel rather anti-church (even anti-UU church) during my teen years and a bit after – so when I found myself on the train and going to a service of my own volition in January 2015, I was pretty surprised. But I’ve been thrilled with the community I’ve found there – it’s really quite something.

I could say a lot about how it feels to be going to this church or about UUism in general – and maybe I will in another entry – but this one I wanted to use to talk about something else that hit me while I was on that bus in Brussels.

I was standing next to Claudia who was talking to a very good friend of ours (the half-Bulgarian, half-Dutch girl from Germany). As Claudia is from East Frisia, an area of Germany that is quite close to the Dutch border, she grew up hearing a little bit of “ostfriesisch Platt”, or the East Frisian version of the Low German dialect. Now, you have to understand, East Frisians think that the Platt that is spoken in the town 10 kilometers away is not real Platt, so this is a dialect that can be spoken many ways! One of the fun about East Frisia is its proximity to the border – because that means that there’s a little melding of languages (also, the language was there before the border, after all!). So, she and our friend were trading phrases back and forth in Dutch and Platt, figuring out which ones were similar and which ones weren’t, which words existed in both languages with the same meaning or in both languages with quite different meanings. I was listening and chuckling, but I can’t understand very much Dutch at all and very little Platt (I have a decent passive understanding of phrases like 'Does anyone want another cup of tea?' and 'Oh, what a shame, it’s raining again!' since those are the things I hear around the tea table at birthday parties in Claudia’s hometown – but that’s about the extent of it!).

So, these two were talking and everywhere around me on the bus, there were other languages I couldn’t understand. There were a few Italian men chatting a few steps away, teenagers having conversations in Dutch and Flemish, and the bus announcing its stops French announcements. I have a teensy bit of French in my repertoire (haha) but only as much as three college semesters and virtually no time spent in a French-speaking place will get you. I am of course fluent in English and damn near fluent in German, but that didn’t really matter, surrounded by bilingual Flemish and French street signs. I felt pretty helpless.

I’m not saying ‘Poor me, I only know two languages’. I realize that the company I keep really over-represents bi-, tri- and even quadrilingual people. But that time on the bus nevertheless made me think about the powerlessness you feel when you worry that you might not be able to communicate, might not be understood in a strange place. And I thought about how harshly we judge people who do not speak our own language – even ones who speak it well grammatically, but have an accent that is hard to understand. Mangled pronunciation, searching for words, the inability to form sentences the way a native speaker would: What do we think when we hear such things? We assume, even if it’s only for an instant, that the speaker is stupid.

This is, of course, ridiculous. We know, I know, in every rational part of my brain that a person's foreign language skills have practically nothing to do with their intelligence.  I have also spent a good deal of time abroad and have met people from all kinds of places – and yet I do this, too. It is cruelly common, this reaction.

So, while feeling like I had one of my senses cut off in that bus in Brussels, I appreciated for a fraction of a second what it must feel like to constantly worry about your inability to communicate or about being judged prematurely by strangers because of it. In addition to that I had this experience in Brussels, a few kilometers from the European Commission, where all kinds of decisions are being made about the flood of refugees coming into Europe. I thought about all the upset and unrest in Germany in reaction to the influx of refugees and about this internal bias. A bias which is so very unfair, and which makes it easier to classify strangers as somehow profoundly 'other' and 'less than'.

I hope to be able to remind myself of that feeling I had on that bus in Brussels every time I feel myself falling prey to this kind of bias. We need to realize that we're all strangers most places we go, and that it is a privilege to be able to live in a place where we understand people and are understood.