Ken, here are several related comments. Any skill at writing that I have is due to James P. Duffy, who taught us sentence diagramming (like Chomskian Phrase Structure) when we were 15. Then there's the great Fritz Steinhardt of CCNY, from whom I learned Calculus Done Right, i.e. by starting from 0,1,2,...and constructing all other kinds of numbers from there, and then doing limits and continuity properly. These two items were developed in the 19th century, and are no longer treated in most (all?) Western classrooms. They are too unrelated---supposedly---to those "skills" that are now taught as a substitute for acquisition of knowledge.
Duffy and Steinhardt would be sacked too, but they'd be called "elitists" first. That's all the justification the sackers would need these days in several countries I'm familiar with. losing all that knowledge is a disgrace that I shall refrain from describing in the terms it deserves.

By  George Berger, at Saturday, June 13, 2009 1:53:00 pm  

"Calculus Done Right, i.e. by starting from 0,1,2,..."

Oh, no, no, no!

You should start with naive set theory and construct a set of things satisfying Peano's axioms for non-negative integers using that. As I recall, you define 0 as the empty set { } and the successor operation S by S(x) = {x, {x}}. Then the set of non-negative integers is the intersection of all sets that contain 0 and are closed under S.

By  P.M.Lawrence, at Sunday, June 14, 2009 2:03:00 pm  

Yes, you can do that. But I studied calculus from 60 to 62, before the new math set in. We started with the natural numbers. See Edmund Landau's 1929 'Foundations of Analysis' (Chelsea, 1st English ed. 1951). Goes up to the complex numbers and Dedekind's Theorem. The translator from the German (Grundlagen der Analysis) was none other than Steinhardt himself! He made it seem very simple indeed. Your way is mathematically 'purer,' but probably harder to teach. It's done your way in many texts on set theory. Landau, BTW, was a victim of the Nazi death camps. Sad.

By  George Berger, at Sunday, June 14, 2009 2:38:00 pm  

The period in Germany from Unification (first!) through the Nazi coup in 33 was one of the two periods in the West when education was considered a public good, to be heavily supported by the State. I read that in 'The Closing of the American Mind.' Not quite correct. At least in the States there was the period 1945-about 79. It started as a percveived need in the Cold War and ended when the Chicago School and Maggie gained too much influence. But whatever the ideology, education was free, except for books (then cheap) and a small administrative fee of about $16 per semester in NYC. So I got a fantastic education for four college years for less than $100 total! Today we read about 'fees', loans, etc., and students are fooled into thinking that they are getting a good deal, i.e. Value for Money. That's pure nonsense and kids should know how it was and can yet be. This pisses me off no end.

By  George Berger, at Sunday, June 14, 2009 3:02:00 pm  

P.S. I meant to say that the period from Unification through 33 was the SOLE PERIOD in.....

By  George Berger, at Sunday, June 14, 2009 3:19:00 pm  

But if we were to make good quality higher education accessible to the masses without binding them in debilitating debt in the process, we would run the risk of creating an intelligent and creative population that is not forced into excessive preoccupation with income generation. Just think of the kinds of trouble such a free and capable bunch could cause for the powers that be.

By  M. Huw Evans, at Sunday, June 14, 2009 10:00:00 pm  

Ilorien, even I never thought of that. At present I can say something about UK and the Netherlands. The governments there have it both ways. They charge you an arm and a leg to get even some basic higher ed (and in the UK have the gall to talk of Top-Up Fees) and then give you a lousy, dumbed-down education. My main example is 'media studies.' The result is, I strongly believe, just what the Rulers want: a stupified population that's incapable of adequately assessing and responding to current events, and income from these poor, duped folk. With this in place, Our Masters can do whatever they want with near-impunity. Well, if that sounds cruel, I'm sure that's exactly what it is. Intentional too.
There's another aspect involved. Our high-tech societies don't need very many highly skilled and highly educated workers. So the governments consider education not worth spending too much money on (and they lower taxes anyway). So they cut back a lot, even close whole departments at universities. For a politico to admit this in public would be political suicide (and might give the game away). So these creeps erect smokescreens by talking about 'efficiency,' 'modernization,' 'planning for the future', etc. ad nauseam. The result is a duped, partly unemployable public whose members often believe such trash and talk about 'diminished expectations' instead of protesting at what's really going on. Parliamentary blah blah complaints are literally part of this game.It's downright criminal.

By  George Berger, at Monday, June 15, 2009 2:59:00 am  

George Berger -
I'm sad (though not terribly surprised) to hear that despite some more progressive outward forms, the UK and Western Europe suffer from similar maladies to those of the US.

Most of my observations are within the medical field, but I think they're likely to apply to other professions to varying degrees. We have a shortage of physicians in the US (though relative to such shortages in other parts of the world, we are ridiculously well endowed). In particular, we are short on primary care physicians (family practice, internal medicine, pediatrics, and obsetrics/gynecology). The majority of students start medical school planning to go into primary care; when the reality of accumulating $100-250K of debt (not to mention the $50K-150K of undergraduate student loans) sets in, however, far too many of them feel pressed to go into a more lucrative specialty or subspecialty. By the time they've emerged from their mountain of debt, they've gotten very good at generating, accumulating, and protecting wealth, and it's hard to break the habit -- or even recognize anything problematic about it. Physicians who've made it through 8+ years of training and another 8+ years of loan repayment tend to feel a bit entitled... and tend to be far more conservative (politically and economically) than they were when they started in on the process. The AMA encourages these tendencies with propoganda that portrays physicians as an uber-noble breed of over-worked, self-sacrificing servants who are continually burdened with such horrors as inadequate compensations from medicare/medicaid and the growing threat of that all-feared monster: a government-sponsored universal health plan. The AMA does not tend to mention their own financial ties to private health insurance companies, nor the fact that they purposely limit the number of new physicians in order to promote the demand that results in maintenance of salaries.

Forgive my rambling digression there. My main point is that the financial pressures on young (potentially idealistic and possibly even relatively selfless) doctors is instrumental in transforming them into the self-protecting, fear-fettered physicians who oppose any reform in national health care or in medical education that might pose a threat to their lofty position.

Hmmm... now how do I avoid that treacherous path myself?

By  M. Huw Evans, at Monday, June 15, 2009 5:07:00 pm  

Hi ilorien---Your report from my Old Country---I was born in NYC---rings all too true. My confidante Vivian tells me daily such things as you just wrote. To make matters worse, healthcare is one of my chief hobby-horses. In fact, one reason I moved to Amsterdam from NY State was my perception that European healthcare was altogether more humanely and rationally organized, financed, and distributed than in the States. That was largely true in 1972. In the Netherlands of 79 things began to deteriorate so badly that when the rot impacted a friend of mine I seriously began speaking of illcare. Things got so bad that when I was seriously affected by this crap I fled the Netherlands for good, and wound up in Uppsala Sweden. I'm not exaggerating when I tell you that this seemingly batty act saved my life---with the help of course of top physicians who DO NOT fit your description above of American medical people. Starting today I had to start referring to the Dutch model not as illcare but as deathcare: for that's exactly what it is if you are 65+. All my attempts to publish this greed-based outrage failed, thanks to self-censorship in the Dutch and UK media. I fear that I must stop right here, for fear of getting a stroke. I'd be more than glad to send you my take on this matter, which I am now distributing widely, to good effect I'm glad to say. I'm at bergergeorgeATyahooDOTcom.

By  George Berger, at Monday, June 15, 2009 9:07:00 pm  

This might be of interest (though you'll need a login and if you've got one will probably have read it already, I suppose)

By  ejh, at Tuesday, June 16, 2009 1:42:00 am  

Good morning Ken. I'd like to thank you once again for the opportunity of getting my various analyses online.

By  George Berger, at Tuesday, June 16, 2009 7:07:00 am