A mind for numbers

Article written for Visionen 2015/3.

When was the last time you felt stupid? For me, it happens practically every day. Sometimes it involves dealing with scientific papers, sometimes with a colleague who is explaining something and the concept simply cannot penetrate my thick skull, sometimes when I get a question from a student at a course I am teaching and I do not know the answer, and sometimes when I am doing basic calculus and it takes too long.

Indeed, at a prestigious university such as ETH, it is very difficult not to feel stupid. (If you are one of those wizards with a GPA closely approaching 6.0, this text is probably not for you.) Those of us that are not from Switzerland came to ETH from our home universities, convinced of our own brilliance compared to the mere mortals that used to surround us. But then we were surrounded with people that were just as smart or (ghasp!) smarter than us. It is no easier for the natives: they beat the competition to pulp at the Basisprüfung, and suddenly found themselves, not only with equally difficult course material, but also colleagues that have just as good of a grasp on the subject matter.

But I am convinced that feeling stupid is indeed what pushes me to progress. The motivation of conquering a difficult topic will push me out of my comfort zone and force me to progress. Think about it in the context of the topic of this Visionen, “active”: for example, when you are exercising, you are not training your muscles with the 0.2 kg dumbbells that you could pick up with your pinky; you push yourself, each time more. Still, I think that it is not only working hard—which is a non-trivial prerequisite—but it is also working smart what is needed. What are some of the techniques we can use to improve our performance, for example at exams that are closely approaching?

In my quest for working smarter, I stumbled upon a wonderful book called “A Mind For Numbers.” The title, and in particular the subtitle, might sound condescending for students at a technical university, but I would urge you to take a look at the book. I now have a bit of experience with giving examinations to students, both written and oral, and I often have the impression that they would have benefited from appreciating the main points in the book. In particular in oral examinations, it feels that some students have a false sense of security in the amount of knowledge they have, because the sense of security is based on wrong repetition techniques; when asked to explain or reproduce what they have learned, they find themselves incoherently trying to paste some buzz words together in their answer.

I think that even the most successful students will benefit from reading this book; they might have reached some learning principles on their own, but it is always beneficial to have a clear understanding of why a particular method works. Listed below are few of the techniques that help me in trying to work smarter that are dealt with more deeply in the book “A Mind For Numbers.”


You have some spare time between the lectures, so you sat down at your computer to write the homework that is due soon, but you just want to check Facebook, as you are waiting for some friends to respond to your invitation for a your party next week. Then check Twitter, Instagram, Tumblr, and Youtube, the last one to make sure there was nothing critical in the 300 hours of video that are uploaded every minute. Next thing you know, an hour has passed and you have to leave for the next lecture. Feeling guilty, you decide there is still enough time to write the homework in the next couple of days. A couple of Youtube videos later, you end up writing up the homework in the late hours, the day before it is due. You swear to yourself this will never happen again. Until it happens next time.

Procrastination is an ever-present demon. Unfortunately, for handling a complex topic, which involves practically everything in your syllabus, you need time for the concepts to settle in your mind and you are able to remember the course material in the stressful exam situation. If you have read my article in the last Visionen, I might sound like a broken record, but it bares repeating: procrastinating until the last moment is probably the worst habit, and the one that is likely to have the largest positive impact on your study success if you manage to break it.

If you are struggling with procrastination, you can take a look at the productivity techniques I covered in the previous Visionen edition; I think the pomodoro principle works particularly well.

Studying with your colleagues

I see groups of students studying together all the time at ETH, and I do think this a very valuable practice: your colleagues provide you with a sanity check, they can correct your faulty thinking, and you can cement your knowledge on a topic by explaining it to someone else. Still, in the group interaction, it is important not to be only a sponge, absorbing, but not contributing, as this passive state does not allow you to exploit the full potential of group work: it is not fair to your colleagues if you are only taking, and, more importantly, you will remember the topics better if you come to the conclusion (or the homework solution) yourself, rather than when copying someone else’s solution.

Visualizing to help memory

Occasionally, we need to learn things by heart, and there is nothing reasonable in what we need to commit to our memory. To take a random example, consider genders of German nouns. Why is a knife neutral, a spoon male, and a fork female? Or the genders of animals: why a cat is female, a dog male, and a horse neutral, I will never understand. But I recently found a very handy trick to remember genders of German nouns: in his book “Fluent Forever,” the author Gabriel Wyner suggests to visualize all the male nouns exploding, all the female nouns catching fire, and all the neutral nouns shattering like glass or ice. The more visual the image, more likely you are to remember it. Such tricks can be, with a little imagination, easily applied to lists of things that we need to learn, committing them to memory with visualization. In particular, techniques such as the memory palace sound promising in helping us remember more. As a gentle—and very interesting—introduction to the topic, I can recommend Joshua Foer’s book Moonwalking with Einstein.

We cannot (yet?) do it like Neo

Wouldn’t it be wonderful if we could learn in the same way that Neo learned kung fu and Trinity learned to drive a helicopter in the Matrix? My mind is buzzing with all the potential for advancement in science, art, and technology, if only we would have so many skills and so much knowledge so easily and readily available. Well, with the rapid digitalization of knowledge and ever-improving search algorithms, I guess we are not too bad off as it is. In the meantime, last words of encouragement: get back to your studying.