Archive for February 2010
For future reference, reminded by a recent webcomic:
- There is no ‘t’ in Cauchy–Schwarz. It is named after Hermann Schwarz (1843–1921), who rediscovered it in 1888. His other work includes some stuff in complex analysis: Schwarz lemma, Schwarz–Christoffel mapping, a theorem about symmetry of second derivatives, etc.
- All other (mathematical) Schwar(t)zes have ‘t’s.
- There’s Jack Schwartz (1930–2009), mathematician–and–computer scientist, who was Gian-Carlo Rota’s advisor and co-wrote the monumental three-volume work on Linear Operators (“Dunford and Schwartz”). And he’s also the name in the Schwartz-Zippel lemma (“Or the Schwartz-Zippel-DeMillo-Lipton Lemma.”)
- There’s Laurent Schwartz (1915–2002), who was at ENS, worked on the theory of distributions, and won the Fields Medal in 1950. (“Schwartz space”)
Those are the major ones, I think.
Bunch of people making the same point (of course we knew it already and didn’t need to wait for the iPad, but the iPad is the harbinger of the coming gloom):
Aaron S: “Is Apple Evil?”
Mark Pilgrim: “Tinkerer’s Sunset”
The iPad is the iPrius: Your Computer Consumerized
Geomblog: Could the IPad make computer science obsolete ?
Of course, we always knew this was going to happen, and I have seen people before my time talk about PEEK and POKE on their Commodore 64s, but still…
[I had some thoughts, but I didn't write anything here and this turned into one of those drafts lost in time. At least it's a dump of two links for now.]
Found today Doron Zeilberger’s What About “Quarter Einsteins”?, written in 1967 (emphasis mine):
There is yet another kind of talented students, whose natural curiosity lead them, already from a young age, to read and look at more advanced material, in order to satisfy their natural curiosity.
When such a student enters high school (and in fact, already in the higher grades of elementary school) he sees that the material that he has already studied on his own presented in a different way. The learning is induced through severe disciple (all the system of examinations and grades), and the material is taught the same way as in animal training. The fascinating science of Chemistry turns into a boring list of dry formulas, that he has to learn by heart, and the threats and the incentives practiced in school badly offend him. As though out of spite, he does not listen to the commands of his teachers, but instead studies on his own material that is not included in the curriculum. Obviously, even the most talented student can not learn from just sitting in class, (and even during class he often studies other material), and so starts the “tragedy” described in your article.
[Einstein] managed somehow to find his way in life (but it wasn’t easy, even for him). But besides him there are “half and quarter Einsteins”, and just plain talented students that had the potential to contribute to society, but [...] flunked out of high school and their “genius” did not help them find their proper place in modern society [...].
Mark Tarver wrote a post in 2006 called the The Bipolar Lisp Programmer, which many readers found to be a frighteningly accurate description. (Reproduced below.) Again, please ignore the remarks about “outstanding brilliance” etc. That is not the point; the point is the tragedy of talented (even if only very moderately so) students failing to cope with the system.
The Bipolar Lisp Programmer
Any lecturer who serves his time will probably graduate hundreds, if not thousands of students. Mostly they merge into a blur; like those paintings of crowd scenes where the leading faces are clearly picked out and the rest just have iconic representations. This anonymity can be embarrassing when some past student hails you by name and you really haven’t got the foggiest idea of who he or she is. It both nice to be remembered and also toe curlingly embarrassing to admit that you cannot recognise who you are talking to.
But some faces you do remember; students who did a project under you. Also two other categories – the very good and the very bad. Brilliance and abject failure both stick in the mind. And one of the oddest things, and really why I’m writing this short essay, is that there are some students who actually fall into both camps. Here’s another confession. I’ve always liked these students and had a strong sympathy for them.
Now abject failure is nothing new in life. Quite often I’ve had students who have failed miserably for no other reason than they had very little ability. This is nothing new. What is new is that in the UK, we now graduate a lot of students like that. But, hey, that’s a different story and I’m not going down that route.
No I want to look at the brilliant failures. Because brilliance amd failure are so often mixed together and our initial reaction is it shouldn’t be. But it happens and it happens a lot. Why?
Well, to understand that, we have to go back before university. Lets go back to high school and look at a brilliant failure in the making. Those of you who have seen the film “Donnie Darko” will know exactly the kind of student I’m talking about. But if you haven’t, don’t worry, because you’ll soon recognise the kind of person I’m talking about. Almost every high school has one every other year or so.
Generally what we’re talking about here is a student of outstanding brilliance. Someone who is used to acing most of his assignments; of doing things at the last minute but still doing pretty well at them. At some level he doesn’t take the whole shebang all that seriously; because, when you get down to it, a lot of the rules at school are pretty damned stupid. In fact a lot of the things in our world don’t make a lot of sense, if you really look at them with a fresh mind. And generally our man does have a fresh mind and a very sharp one.
So we have two aspects to this guy; intellectual acuteness and not taking things seriously. The not taking things seriously goes with finding it all pretty easy and a bit dull. But also it goes with realising that a lot of human activity is really pretty pointless, and when you realise that and internalise it then you become cynical and also a bit sad – because you yourself are caught up in this machine and you have to play along if you want to get on. Teenagers are really good at spotting this kind of phony nonsense. Its also the seed of an illness; a melancholia that can deepen in later life into full blown depression.
Another feature about this guy is his low threshold of boredom. He’ll pick up on a task and work frantically at it, accomplishing wonders in a short time and then get bored and drop it before its properly finished. He’ll do nothing but strum his guitar and lie around in bed for several days after. Thats also part of the pattern too; periods of frenetic activity followed by periods of melancholia, withdrawal and inactivity. This is a bipolar personality.
Alright so far? OK, well lets graduate this guy and see him go to university. What happens to him then?
Here we have two stories; a light story and a dark one.
The light story is that he’s really turned on by what he chooses and he goes on to graduate summa cum laude, vindicating his natural brilliance.
But that’s not the story I want to look at. I want to look at the dark story. The one where brilliance and failure get mixed together.
This is where this student begins by recognising that university, like school, is also fairly phony in many ways. What saves university is generally the beauty of the subject as built by great minds. But if you just look at the professors and don’t see past their narrow obsession with their pointless and largely unread (and unreadable) publications to the great invisible university of the mind, you will probably conclude its as phony as anything else. Which it is.
But lets stick to this guy’s story.
Now the big difference between school and university for the fresher is FREEDOM. Freedom from mom and dad, freedom to do your own thing. Freedom in fact to screw up in a major way. So our hero begins a new life and finds he can do all he wants. Get drunk, stumble in at 3.00 AM. So he goes to town and he relies on his natural brilliance to carry him through because, hey, it worked at school. And it does work for a time.
But brilliance is not enough. You need application too, because the material is harder at university. So pretty soon our man is getting B+, then Bs and then Cs for his assignments. He experiences alternating feelings of failure cutting through his usual self assurance. He can still stay up to 5.00AM and hand in his assignment before the 9.00AM deadline, but what he hands in is not so great. Or perhaps he doesn’t get into beer, but into some mental digression from his official studies that takes him too far away from the main syllabus.
This sort of student used to pass my way every now and then, Riding on the bottom of the class. One of them had Bored> as his UNIX prompt. If I spotted one I used to connect well with them. (In fact I rescued one and now he’s a professor and miserable because he’s surrounded by phonies – but hey, what can you do?). Generally he would come alive in the final year project when he could do his own thing and hand in something really really good. Something that would show (shock, horror) originality. And a lot of professors wouldn’t give it a fair mark for that very reason – and because the student was known to be scraping along the bottom.
Often this kind of student never makes it to the end. He flunks himself by dropping out. He ends on a soda fountain or doing yard work, but all the time reading and studying because a good mind is always hungry.
(Rest of essay follows, with the Lisp parts gratuitously excised, but you can read the original post.)
[...] the peculiar strengths and weaknesses of the brilliant bipolar mind (BBM).
[...] He can see far; further than in fact his strength allows him to travel. He conceives of brilliant ambitious projects requiring great resources, and he embarks on them only to run out of steam. Its not that he’s lazy; its just that his resources are insufficient.
[...] not just the strengths but also the weaknesses of the BBM.
One of these is the inability to finish things off properly. The phrase ‘throw-away design’ is absolutely made for the BBM [...]
[...] And he is, unlike the rank and file, unprepared to compromise. And this leads to many things.
And this brings me to the last feature of the BBM. The flip side of all that energy and intelligence – the sadness, melancholia and loss of self during a down phase. The intelligence is directed inwards in mournful contemplation of the inadequacies [...]. The problems are soluble [...], but when you’re down everything seems insoluble. [...]
So what’s the problem with Lisp? Basically, there is no problem with Lisp, because Lisp is, like life, what you make of it.