Mathematics of the mob


Excellent inaugural lecture by my mentor, Pierre Degond. It is interesting and entertaining! This is precisely the framework in which my research takes place:


Learning by doing


How many traps we put on our own way towards learning! (and how many we put to other people too).

Learning is a process, it is a struggle. It is not a result. Results may fix our path towards learning, may guide us in the correct direction, but they are not part of the process of learning. However, we are constantly focused on results.

As Aristotle said, there are habilities that are by nature and habilities that are not by nature. In the things that are by nature first we exhibit the capacity and afterwards the activity (think for example on the eyes; first they are formed with the capacity of sight and only afterwards, when the baby is born, they are actually used). On the contrary, things that are not by nature, it happens the other way round; first we need to actively practice a quality or skill, to develop it through a process of learning until, finally, we are capacitated with that quality or skill (Aristotle call this `virtue’).

Basically, Aristotle is saying that if you want to learn something, it does not make any sense to start by the final result you are aiming to. For example, say that you are a great singer but have panic to sing in public. Aritotle is saying that to overcome your fear what you need to do… is to sing in public; you need to practice. You cannot just say, “wait, I have not overcome my fears yet, I must wait until I have actually managed to do so before going on stage”, or in other words “I want to wait to have the capacity of singing in public before doing so”. Singing in public is not an ability that comes by nature, it needs to be learned by doing, there needs to be a struggle.

Aritotle says that the capacity is acquired through habit (practice) and that good qualities come from good habits. Aristotle is telling us a good habit towards learning: we need to understand that we need to practise, that we need to struggle. No complains like “I should know this”, “I do not know how to do that”. Better say “I do not know this yet“, “I do not know how to do that yet” (see the Ted talk below by Carol Dweck on this topic). Remember that  (good) struggle means that we are getting better.  No need to avoid it, useless to try to go directly to results. Enjoy the process.

In conclusion, if we want to improve our lifes, we have to put an effort in our work, in our relationship with others, in our relationship with ourselves. If you are shy and want to stop being so, you have to practice and accept the struggle. It is not going to work the first times, because you are learning, but if you practice, you will keep improving. Stop saying to yourself “I should not be shy”. Denying yourself will not only make you unhappy,  it will decrease the love you feel for yourself. Accept the fact that you are shy, understand its implications and go with it (cf. Krishnamurti).

If you want to learn mathematics, do not start with “I am supposed to be intelligent, why I cannot do this?”, because you need to practice; because you need to struggle first. Through struggle (the right struggle, though) you will bet better, you will get more intelligent. Never mind the people that try to impress, after all, we are in a very competitive culture focused on results, so people have to show results. That may be the right focus to get a scholarship or position, but not to acquire the skills.

If you want to learn a new language, do not wait to know everything until you start talking it, it is not going to happen because you will never feel that you are ready! You need to practise, you need to make mistakes, you need to talk. If you want to write a novel, start writing.

And so on.