4 February 2012

And now that I mentioned unlearning...

...let me also point out this posting by Eliezer Yudkowsky and this one by Ben Casnocha who mentions three things that one has to unlearn from school [the non-italicized comments are mine]:
  1. The importance of opinion: An opinion is the lowest form of human knowledge; it requires no accountability and no understanding. Schools, apparently, emphasize the role of students' opinions. "Tell me John, what is your opinion of the validity of Quantum Mechanics in the macroscopic world?" Or: "What is your opinion, Mary, about the solution of this equation?" Of course, we all have opinions, but we don't start learning by having them. Opinions are (should be) formed after a well-thought procedure.
  2. The importance of solving problems: Schools teach us to be clever, great problem solvers, something that makes us arrogant about our abilities. What schools do not emphasize is that the problems we learn how to solve have been solved by others first. And what they don't tell us is that formulating a problem is just as important as solving it. What they do to us is convince us that solving a problem is the end of any effort. And often, we become so good at problem solving of one kind that we underestimate our stupidity in solving problems of other kinds.
  3. The importance of earning the approval of others:  That grade that you get at school is presented to us as being something of such a value that even money cannot buy (or does it, sometimes?)We seek to get good grades so that we can be approved by friends, parents, the society, the employers... We seek their approval. Is the approval of others something that really proves our, say, understanding of Physics? Damn the teachers who tell us that the exam is what we should care about. Instead of trying to earn the approval of others, why don't we focus on those people who disapprove of us, people whom we cannot easily please? 
Unlearning is as important as learning (correctly).


  1. Nice, I will share these with my 12 year old son. Thanx

    I too have learned these, but I wonder if it involves the paradox that "in order to learn these points well, we must have learned their opposites first."

    Or perhaps some variant of that. All to say, the principle of "readiness of learning" and "stages of development". Maybe we can't skip over some mistakes.

  2. You are welcome. My comments are based on the things I found on the linked web site (which I found through a nadder...). And I modified them slightly to suit my ideas :-)

    Hm... I am not sure I agree with the method of learning the opposites first. At least not always. Certainly, one claims to have reached an "advanced" stage of learning (postgraduate degree, say) and maintains he or she has done so quite painlessly, having "fun" all the way along, then he or she is a liar, a bullshitter, or, simply, someone who is not what he or she thinks he or she is... There is no royal path...



What measure theory is about

It's about counting, but when things get too large.
Put otherwise, it's about addition of positive numbers, but when these numbers are far too many.

The principle of dynamic programming

max_{x,y} [f(x) + g(x,y)] = max_x [f(x) + max_y g(x,y)]

The bottom line

Nuestras horas son minutos cuando esperamos saber y siglos cuando sabemos lo que se puede aprender.
(Our hours are minutes when we wait to learn and centuries when we know what is to be learnt.) --António Machado

Αγεωμέτρητος μηδείς εισίτω.
(Those who do not know geometry may not enter.) --Plato

Sapere Aude! Habe Muth, dich deines eigenen Verstandes zu bedienen!
(Dare to know! Have courage to use your own reason!) --Kant