10 May, 2011

The Art of Not Running Away

I remember how back in our university, almost all the first year students that have the high-level math (the “laaja”) keep asking older students questions like “Was it worth it?”, “Did you learn anything?” and “Will it be hard?”. My answers to these would be yes, yes, and yes. But that’s not today’s point. More interesting would probably be asking “Why? especially related to the first two.

As background information, I didn’t come from a math-specialized high school. I felt confident about math and had some successes in high school, especially towards the end. I was invited to participate in the higher math at our University – as you might know, it’s not mandatory for automation students – so I got to choose if I wanted to do it or not. After some deliberation, I resolved to do it. Mainly, I was curious about how I’d do inside that peer group and how I’d feel about “proper math”. Secondly, I thought I could always switch back to normal math if I didn’t like the high-flying version.

To cut a long story short, it was a hard track. I remember sitting with friends and doing exercises late into the evening. I remember spending about 50% of my studying time just on math. It worked and my results were pretty good, although in no way top class. Solid 4s and a 5 Three courses were enough for me, as switching to Industrial Management meant I didn’t need the 4th course, so I dropped it as unnecessary.

Anyway, what was the learning experience? Honestly, I don’t think I remember half of the stuff we went through. The pace was fast, exercises were not always so plentiful – or understandable – and most of the stuff I haven’t needed since. Maybe it’s somewhere in the back of my mind, but I couldn’t recall it without some supporting material.

The most important thing for me was to learn not to run away. I remember staring at problems that seemed completely incomprehensible and thinking there’s no way in hell I’ll figure this out. But in most cases I finally got it. Actually, we got it. Since I was almost always solving the stuff with friends, and that was also a key ingredient to success. Four minds thinking along slightly different lines made for a better solving process, and naturally decreased erroneous calculations.

Anyway, if you think don’t run away is an obvious principle, you’re probably right. It’s not the principle that was hard for me, it was – and sometimes still is - applying it. The math courses were a valuable experience in the field of really confusing problems. Problems, which make you think “the solution must be really hard – how will I ever think of it?” Normal problems don’t do that. The confusion leads thoughts into a sort of meta-level, thinking that since you can’t see the outline of the solution right away, it must be something outside your current knowledge. This naturally induces a thought that if the solution is outside your knowledge, how on Earth can you come up with it in the first place? Needless to say, you start focusing more on freaking out about the problem than solving it, which is a terrible spiral to get into.

In retrospect, freaking out about a problem is very unnecessary – never mind useless. For every problem, there’s always a solution. The problem might not be solved by the end of the night, but slowly you’ll get there. Every step is a step towards the solution. Just keep taking those steps.

A practical application of the don’t run away principle are my German skills. Since high school, my German skills had started seriously deteriorating. In active vocabulary I’d already fallen down to the “Ich bin” level, meaning I couldn’t really have a decent conversation anymore. At some point, I realized the situation would only get worse with time. The vocabulary wasn’t going to magically pop back in my head. Improving my German would mean I’d need to, you know, actually try to learn it. It was time to face the issue and stop running. So I decided to plan an Erasmus year in Austria (to combine language with beautiful sights), which worked as a motivation pump to take some German courses in university before the Erasmus. Well, now I’m here in Graz with the year nearly behind me, and my German is better than ever. Problem solved.

These days, whenever I face a problem, I remind myself: don’t run away. If I feel imprisoned by the problem, I just think oh well, just have to start chipping away with this spoon. The wall will crumble eventually.

08 May, 2011

The career pyramid

The conventional way to think about one’s future career usually is to simulate the career as
1.       Learn basic skills
2.       Specialize
3.       Profit

This is a very intuitive way to think, as everyone agrees that advanced skills are based on more basic skills. Therefore, a career is like building a pyramid – you have to start from the foundations and gradually work your way up. So your career might look like this:

A common implicit derivation from this is that you have to commit to your chosen career in the early stages. After all, you can’t build a pyramid by chance – you have to know what you’re doing! This leads into the idea that the sooner you know what your thing is, the better you’ll be. This is a useful, yet a potentially very dangerous thought. How so?

To look at usefulness first, it is obvious that you need certain skills to succeed in a given profession. If you want to become a physicist, learning proper math skills is highly recommended. On the other hand, wanting to be a cook hardly requires any understanding in the subtleties of Laplace transformations. Building a large enough toolbox – yet one with enough punch per tool – is a necessary requirement for success. It doesn’t matter if you’re the brightest person in the field if you’re missing the necessary tools to solve the problems (although being smart admittedly makes it easier to learn stuff as you need it and make ad hoc solutions on the go). Still, often you simply don’t have the extra three months to learn a new methodology, but you must solve the problem with your hammer and screwdriver – even if a chainsaw was the perfect option. So, it is a rather good idea to think about the tools you’re going to need in the future.

The dangerousness of “the sooner the better” view is that it implicitly assumes that your interests cause the need for tools, and that the relationship never works the other way. This is, according to my experience, simply not true. There are two reasons for this: firstly, we humans have an uncanny ability to increase our interest in whatever we are focusing on. Personally, I’ve often only gotten really into something as I’ve started doing it. Keeping this blog would be a prime example of that effect. Secondly, sometimes you need to master a set of tools before you can even answer why you need them in the first place. Thinking about examples, I believe quantum mechanics would qualify for this (even though I’m not a physicist and possess hardly any knowledge in the quantum field).

In university everybody is taught the basic toolkit for a field. If we never recognize the existence of non-standard career paths most people are just going to aim for the standard track with the standard toolkit. Definitely a good way to suppress innovation! To exaggerate a bit: how are we ever going to think outside the box in other contexts, if we can't do it even in the context of our own career future?

As such, this issue is not really a hard problem. A lot could be done with simple cross-scientific socialization (to realize there are actual people outside one’s own field), mentoring (to exemplify out-of-the-box careers) and other methods that promote the existence of a non-standard toolkit.

So what is the grand realization, in reality? Depending on the person it could be anything from a simple “not every business student works in banking or a consulting” to a good understanding of possible problems outside the basic university skill set, finding them as interesting – or even more! Whatever the exact formulation, it could be characterized as an insight that not every career is like a pyramid. Nor should it be. To sum up graphically, your career pyramid might in the end instead look something like this:

Maybe the specialization helped you discover something even more important than before and you ended up doing something outside the standard track. With life, that’s actually quite likely to happen. I’m looking forward to it.