This section at once both interests and bothers me > The great Norwegian mathematician Niels Henrik Abel was once asked how he had > become so good at mathematics. He replied that it was “by studying the > masters, not their pupils”. The current essay is motivated by Abel’s > admonishment. As a programmer, I’m a beginner (and almost completely new to > Lisp), and so this essay is a way for me to work in detail through ideas from > masters such as Alan Kay, Peter Norvig, and Paul Graham. Of course, if one > takes Abel at his word, then you should stop reading this essay, and instead > go study the works of Kay, Norvig, Graham, and the like! I certainly > recommend taking the time to study their work, and at the end of the essay I > make some recommendations for further reading. However, I hope that this > essay has a distinct enough point of view to be of interest in its own right. > Above all, I hope the essay makes thinking about Lisp (and programming) fun, > and that it raises some interesting fundamental questions. Of course, as a > beginner, the essay may contain some misunderstandings or errors (perhaps > significant ones), and I’d welcome corrections, pointers, and discussion. >
Niels Henrik Abel wasn't asked "how did you begin to learn mathematics" he was asked how he got so good at it. I'm sure to BEGIN mathematics he learnt from someone who wasn't one of the great masters (mostly because they were not in fact likely to be alive). But I'm also sure that who he learnt from taught him not to be closed about mathematics - to search out the greater understandings, and most likely told him OF the great masters. When we are beginners, we need clear, well thought-out teachers who are ABOVE our understanding. It doesn't matter how far, only that they have a capacious understanding of what is above them themselves and not motivated by ego (and preferably are in the process of extending themselves, too and are honest about it). Ideally they don't teach us incorrect information (obviously) because that is damaging. I had this when learning martial arts. I once had a few lessons from an amazing master - the top of our entire series of schools - a grandmaster. I couldn't understand the lesson! He was teaching such advanced stuff that I wasn't sure what was and what wasn't the lesson. Here's the rub: most of the semi-advanced students in the room could have given me more than enough for me to go on with... his time would be wasted teaching me this stuff... and his basics (the maxwell equations of martial arts) were so highly advanced I didn't even understand them to be basics. What I needed was well grounded basics taught to me in a frame that I could understand. The context is incredibly important. This entire process of learning LISP and Maru has been incredibly rewarding, but do you know what else it has been? Intensely frustrating. Like... possibly one of the most frustrating things I've ever done. I *knew* there was a way through it, because it's obvious that so many people I talk to on here and read from on the internet have made their way through it... but seriously folks, this is where our pedagogical efforts are up to at the moment? There's no clear, obvious and shining path to understand this stuff. This is actually part of the work that I'm most interested in (and have been for the last decade). It's exciting and I think I might be getting to a point where I can understand enough to put some of my ideas into practice quite soon. I still feel the same way as receiving the grandmaster's lesson when given directions by Alan or Ian. I'm just not at their level yet. I can see when they give me some advice what I need to do to get to the point where I can use that advice, but I'm just not there yet. I have to literally shelve their advice, then go find something in the middle, with that advice in mind until the point where I'm able to use the advice (sometimes days or weeks later). I'm intensely grateful for the chance to be able to talk to the likes of Alan and Ian, but it's not easy for me sometimes. So... this over-humble article is actually perfectly what I needed about a month ago (maybe more?) when I began my foray into LISP. Thank you very much Andre. It's incredibly helpful. I'll continue to read now :) Amusingly, things seem to happen like this in my life. It's usually how I know I'm on the right track... I will work on something incredibly hard, and then something will appear that explains it all clear and succinct :) Also, "lispy" as referred to by the article, is great. I can't believe no one has linked to it before on here when discussing this. Mind you, I don't particularly like python, but it is quite readable and understandable. (http://norvig.com/lispy.html) Kind Regards, Julian On 13/04/2012, at 9:50 AM, Andre van Delft wrote: > FYI: Michael Nielsen wrote a large article "Lisp as the Maxwell’s equations > of software", about the famous page 13 of the LISP 1.5 Programmer’s Manual; > see > http://www.michaelnielsen.org/ddi/lisp-as-the-maxwells-equations-of-software/ > > The article is discussed on Reddit: > http://www.reddit.com/r/programming/comments/s5jzt/lisp_as_the_maxwells_equations_of_software/ > > > _______________________________________________ > fonc mailing list > fonc@vpri.org > http://vpri.org/mailman/listinfo/fonc
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