I’m sure you all know by now that Arafat has died. I won’t pretend to mourn because I think that the Palestinians would have been much better off both materially and spiritually if he had not been their leader for my entire lifetime. But with his passing, I think there may finally be some chance to make progress in the Israeli/Palestinian conflict.
Andrew Sullivan comes in with what may be the conventional wisdom on the topic:
<blockquote>
If a less noxious Palestinian leader emerges, will Bush use the shift to become more engaged in the Israel-Palestinian conflict as a means to encourage the U.N. or other European leaders to play a more conciliatory role in Iraq? Will he tilt against Sharon? Again I doubt it very much. The great mystery now is whether this president will use a second term to moderate somewhat or to forge ahead to the right. My bet is on the latter.
</blockquote>
I’ll assume that a less noxious Palestinian leader emerges, though that isn’t a given by any means. It would certainly be wise for the US to use leverage on the conflict to convince Europe to play along in the rest of the Middle East. As for tilting against Sharon, that might have been necessary for the Sharon who was elected immediately after Arafat started up the second intifada. But I’m not sure a huge tilt is needed now. Sharon has unilaterally acted to begin removing the settlements which are claimed to be the worst irritant. He has created a wall which many Palestinians hate, but which has had the effect of dramatically reducing the number of Israeli’s killed by suicide bombers. This is giving Israel the breathing room to think about settlement again. That wouldn’t be possible if Sharon hadn’t been able to dramatically reduce the killing of his people.
The Palestinians may have their best opportunity in a generation sometime in the next year or two. Let us hope that they don’t live up to the description of Palestinians as a people who never miss an opportunity to miss an opportunity.
Off the top of your head, without using Google, who would you recommend to the Palestinians as a leader that lives in Palestine and has fought unceasingly for the cause of a Palestinian nation for the last 30 years?
And as a second question, can you point me to any post of yours extolling the praises of any leader that meets such criteria?
minor correction: it seems Arafat is not quite dead – yet
Don’t think I’m making more of this than it is, or even really an on-point critique, but it’s a handy fact for broasd discourse on the situation: Sharon has lightened the killing of Israelis, not “people.” Killings of Palestinians this month were sky-high, apparently the most since April 2002. I think the fact that, both numerically and especially as a proportion of the population, Palestinians have had far more deaths than the Israelis doesn’t factor into public consciousness more because it has been associated with a reflexive, Palestinians-can-do-no-wrong position, which is rightfully rejected. I don’t see it that way at all; those who are responsible for the conflict (and there are many varying responsibilities placed on both sides) are also responsible for each of these deaths on both sides in some ways. It should inform discourse, not kill it.
Yes, but is Francisco Franco still dead?
There are many errors in Sebastian’s post, aside from the issue of Arafat still firing off a few brain synapses. It’s a tired refrain: the Palestinians are to blame, those awful Europeans are to blame, Arafat is to blame.
The fact is Arafat hasn’t had any significant power in the I/P conflict for nearly 5 years. Whatever ‘power’ has been assigned Arafat is very largely symbolic.
Additionally, to pretend Sharon has reduced the violence against his people is looking at a very narrow window. It’s akin to looking at yesterday’s market results and claiming the Dow will no doubt soon hit 36000.
Sharon has lightened the killing of Israelis,
This meme is simply untrue. From 1994 to Sept of 2000, 120 Israelis died in attacks. From Oct. 2000 to Sept. 2004, 478 Israelis were killed in attacks, with about 3000 wounded.
Your point about Palestinian civilian deaths is well-taken.
I’m not going to try and keep up with the folks on the list about the ins and outs of the I/P conflict, as there is a lot of knowledge that I don’t really have. What I’m interested in is whether Bush can take advantage of this opportunity, and if so, what can/will he do? It’s interesting because I imagine that Blair, who is supposedly pushing for more involvement, has probably earned the ire of the admin because of his wife’s recent remarks. I think this will be a useful test of whether the Bush administration will pursue a logical strategy or will continue to be the Mayberry Machiavellis.
Well-taken, Jadegold. He was talking about a narrower, recent timeframe, which may have problems just from being a narrow sample, but is a different argument than saying deaths declined under Sharon in general, which they of course did not.
I think this will be a useful test of whether the Bush administration will pursue a logical strategy or will continue to be the Mayberry Machiavellis.
That is, of course, the $64,000 question.
Unfortunately, the answer is not encouraging judging by past performance. Increased European participation is not necessarily useful or helpful–unless that participation (like the US) is seen as an honest broker. And the US is not likely to participate as an honest broker because to do so would come at some political cost.
Given the options of doing what’s right or scoring political points, this appointed administration will never hesitate to take the political road.
It’s a sign from God.
Wednesday: Bush wins reelection.
Thursday: Arafat in coma.
However, the meaning is as yet unclear.
Jadegold, I think comparing deaths in the pre-intifada period to the intifada period isn’t really very helpful. Sharon gained power with the intifada in full swing, it got worse, and then since he has forced settlements to be removed and more importantly since he has built the wall, Israeli deaths have dramatically declined.
I don’t think I made the mistake about people’s deaths. I said: “This is giving Israel the breathing room to think about settlement again. That wouldn’t be possible if Sharon hadn’t been able to dramatically reduce the killing of his people.” If I was going to complain about those sentences I would complain about the use of the ambiguous ‘settlement’ when I mean “resolution”.
My point was that the Israeli’s weren’t going to be thinking seriously about resolving the conflict (other than through crushing the Palestinians) while their sons and daughters were getting blown up in pizza joints twice a week. Sharon and the wall have created a situation where there are few enough Israeli’s being murdered each week that Israel can think about the long-term future. The Palestinians have not been able to do so under Arafat because his interest was in the continuation of the conflict which keeps European millions flowing directly into his hands. The Palestinians may have the opportunity to make a real settlement now that their terrorist leader is out of the picture (or well on his way out.)
Jadegold, I think comparing deaths in the pre-intifada period to the intifada period isn’t really very helpful. Sharon gained power with the intifada in full swing, it got worse, and then since he has forced settlements to be removed and more importantly since he has built the wall, Israeli deaths have dramatically declined.
Wait a minute; it’s not helpful to compare two periods–one covering about 6 years and the other 4–but it’s useful to take a small period of several months as definitive evidence?
Since most people think Sharon was largely responsible for provoking the infitadah, I’m not going to give him a whole lot of lee-way for not having been officially in power during the first few months of its existence.
This is why God gave us derivatives, I think.
Icon driven strategies are always a bust. Remember when catching Uday and Qsay was going to stop the insurgency? Then it was Saddam the king pin. Then it was Sadhr (whoops!). Likewise with Arafat. The people waiting to fill the vacuum are going to be even worse, and another cycle will start.
But of course Sebastian will come up with a rather intricate explanation as to why it’s not the US’s or Israel’s fault that it got worse. After all, who could have predicted it?
I cannot imagine a legitimate (for Palestinians), credible(to Israelis & Americans) negotiating partner for peace. In any case, whatever the Palestinians may want, I don’t believe the Arab League wants peace in I/P, and with financing and moral support of the radical groups, can prevent a effective settlement.
Sorry.
Since most people think Sharon was largely responsible for provoking the infitadah
And he did that how? Sure, he committed one somewhat provocative act, but to claim that this provoked the intifadah is going many miles too far.
More realistically, it was a handy excuse.
I doubt Bush will do much of anything until Sharon implements his Gaza pullout.
Sebastian –
just curious, and willing to be convinced either way –
what is the evidence that the wall has been responsible for the downswing in suicide attacks? In my lifetime, these attacks have waxed and waned, surged, then receded, often with no particular cause ascribable (that I was aware of). Are there hard data on increased arrests, interdictions, etc., made possible by the bottlenecks created by the wall, or some other data? Or are you drawing conclusions from the (admittedly very suggestive) correlation in timing?
“Since most people think Sharon was largely responsible for provoking the infitadah”
I have difficulty believing that is anything other than a joke. Before the second intifada it was generally believed that Sharon’s political career was over. Israeli’s who were willing to negotiate with Arafat were ascendant. He had been relegated to a bit player in Israeli politics. He didn’t start gaining support again until after the intifada was in full swing–and as a response to the idea that Israel was sick of attempting to appease the Palestinians if they were just going to get repaid for their overtures with more and more blood. That is the factual timeline of Sharon’s re-ascent to power.
I also note that his ‘provacative’ act was to go to the Temple Mount–the holiest site in Judaism. It isn’t as if he snuck into the Kabba.
This is why God gave us derivatives, I think.
Does that mean that integration is the Devil’s work?
That would actually explain a lot, I think…
Must be that faith-based calculus so popular in the red states.
“There are many errors in Sebastian’s post, aside from the issue of Arafat still firing off a few brain synapses. It’s a tired refrain: the Palestinians are to blame, those awful Europeans are to blame, Arafat is to blame.
The fact is Arafat hasn’t had any significant power in the I/P conflict for nearly 5 years. Whatever ‘power’ has been assigned Arafat is very largely symbolic.”
There’s more than symbolism: there’s missed opportunities, from the Carter-Sadat-Begin talks to the Clinton-Barak Camp David talks, ‘cos Arafat preferred to keep the fantasy of Arab victory over Israel than risk becoming the Palestinan David Trimble. Whatever the Palestinans will get out of future talks, it will be a shittier deal for them than they could have achieved in the late 1970s or late 1990s.
I don’t agree with Sebastian very often, but Arafat kicking the bucket is A Good Thing.
“This is why God gave us derivatives, I think.”
Didn’t know God incarnated as Isaac Newton/Karl Leibnitz/Archimedes (yup, old Archy came up with the calculus, only some idiot dark ages monk used the only existing copy as a palimpest.)
Ah, it must be Humor Deprivation Day. I forgot to check my calendar this morning.
“Ah, it must be Humor Deprivation Day. I forgot to check my calendar this morning.”
No, just I don’t think God should be blamed or credited for the works of Man’s reason (or lack thereof).
Also, I wanted to get in the trivia point that Archimedes discovered the calculus, but unfortunately it fell into obscurity for over a 1 1/2 millenia. Imagine what different paths history could have taken if the Roman world had had the calculus as a tool?
Having a bit more than a grazing acquaintance with the wonderful world of mathematics, let me once again assure you that my remark was intended humorously. If it seemed a bit blasphemous to you, my apologies, but I can nearly guarantee you it won’t be the last time.
(yup, old Archy came up with the calculus, only some idiot dark ages monk used the only existing copy as a palimpest.)
To be fair, all we know is that Archimedes came up with a notion of quadrature (specifically quadrature of the parabola, IIRC, but possibly for some slightly more general functions). To the best of my knowledge, Archimedes didn’t possess either a true notion of differentiation — which, to be fair, had to wait until the 19th century — or, more importantly, the Fundamental Theorem of Calculus, without which you can’t really do “calculus” per se.
“Having a bit more than a grazing acquaintance with the wonderful world of mathematics,”
Having learned second-order differential equations & group theory in High School, I assure you I can dick-wave with the rest of the math nerds.
“let me once again assure you that my remark was intended humorously. If it seemed a bit blasphemous to you, my apologies,”
Quite the opposite. I was trying to stick up for us creatures of clay against the Transcendent. Which may be out of style these days, as faith seems to have a full house while reason is sweating on a pair of fours.
I was going to bring that up, Anarch, but again, far too lazy.
I was just idly wondering how our friend Archy came up with the notion of continuity, and did he really also come up with limits? But then laziness kicked in.
Plus, were functions even a distinction back then?
To the best of my knowledge, Archimedes didn’t possess either a true notion of differentiation — which, to be fair, had to wait until the 19th century — or, more importantly, the Fundamental Theorem of Calculus, without which you can’t really do “calculus” per se.
(a HREF=”http://www.pbs.org/wgbh/nova/archimedes/about.html”>Ddid you see this PBS Nova programme. My impression from it was that he wasn’t far off from where Newton & Leibnitz were.
Ah bugger. Let’s try that link again:
Did you see this PBS Nova programme?
I think you’re overdoing it here, a bit. An understanding of calculus is just the first baby step beyond high school algebra. No dick-waving is wanted or needed.
“I was just idly wondering how our friend Archy came up with the notion of continuity, and did he really also come up with limits?”
To take one, his method of estimation of pi shows some understanding of the idea of a limit, if in more geometrical terms than we’re used to.
“An understanding of calculus is just the first baby step beyond high school algebra.”
In other countries, calculus comes a fair bit earlier than college, though. We first learned calculus at 14.
“No dick-waving is wanted or needed.”
My apologies. I assumed that:
“Having a bit more than a grazing acquaintance with the wonderful world of mathematics,”
Was the first sign of a zipper being pulled down.
To take one, his method of estimation of pi shows some understanding of the idea of a limit, if in more geometrical terms than we’re used to.
Archimedes’ estimates of pi are completely rigorous AFAIK, but limited by a “nice” geometric realization. I was a tad too dismissive earlier — I forgot that he’d done quadrature of simple cubics as well — but I’m not sure whether he’d even have recognized an abstract quartic, let alone an abstract polynomial, let alone a continuous function, let alone the Fundamental Theorem. Heck, it took until Descartes to figure out how to graph a function and thence showcase the algebraic and geometric duality we take for granted today; while I’m not sure how advanced Archimedes’ understanding of algebraic geometry was, I’m fairly sure it was not at 16th century levels.
Which in no way whatsoever diminishes Archimedes’ accomplishments — hell, I couldn’t actually ascertain the first three continued fraction approximants to pi from purely geometric reasoning, and I’m a 21st century mathematician! — but I think it’s important to keep them in perspective.
Having learned second-order differential equations & group theory in High School, I assure you I can dick-wave with the rest of the math nerds.
Can I really, really, REALLY suggest we not get into a dick-waving contest? I mean, that in general, but a phallomathematical competition is just so not what this country needs after the election…
“This is why God gave us derivatives, I think.”
You should also meditate upon the phrase ‘small sample size’.
In other countries, calculus comes a fair bit earlier than college, though. We first learned calculus at 14.
Which country, may I ask?
Am I the only one who found calculus about 3 times easier to grasp than trig?
I do not know math, but I tell you as a Christian Lebanese that we all want peace. We know there is no peace when there is no justice. The comment that Arabs do not want peace for Palestine and Israelis because Europe sends us money is absurd and cynical and had no point in reality. You must think all Arab people are greedy, but your comment unfortunately says more about yourself than Arabs.
Sharon is a bad man. Believe me when I tell you that he is using the USA.
The Palestinian situation is very bad for all Arab countries. In Lebanon especially so. We were invaded twice- once by the Palestinians, and again by the Israelis chasing them. We had to have the Syrians save us and now they do not leave. All of this because of the Israeli situation continues.
Am I the only one who found calculus about 3 times easier to grasp than trig?
You, me, and about forty of my students this semester.
“In other countries, calculus comes a fair bit earlier than college, though. We first learned calculus at 14.
Which country, may I ask?”
Northern Ireland. Was in standard Additional Mathematics O-level syllabus as of the 1980s. During the paralyzingly-terrifying “revision periods”, we’d all stand up, our math teacher would go down the class making us differentiate an equation, and if you got it wrong, if was two whacks with the strap. (Yes, it was a Catholic school, now you mention it.)
Now they’ve changed the system (O-levels to GCSE) they might have moved introducing calculus to A-level. From what I’ve seen of e.g. E.European countries and Singapore, other countries might even be more aggressive.
“Am I the only one who found calculus about 3 times easier to grasp than trig?
You, me, and about forty of my students this semester.”
Have you thought about frightening the crap out of them with the threat of physical abuse as an aid to learning?
“Heck, it took until Descartes to figure out how to graph a function and thence showcase the algebraic and geometric duality we take for granted today; while I’m not sure how advanced Archimedes’ understanding of algebraic geometry was, I’m fairly sure it was not at 16th century levels.”
Catch the NOVA programme on Archy if you can; you might be surprised how much we now think in the lost manuscript of “The Method”. It does make it seem even more of a shame that when the Romans sacked Syracuse, that they didn’t specify more clearly “try not to kill old guys doodling circles in the sand; we need them as valuable siege engineering consultants”.
I guess the more puzzling thing is why there was so much time between Archy and Descartes.
Regarding the title of this post:
He’s still alive. I know there’s not much love lost for the man, but isn’t at least an update warranted? Just a bit premature to be shoveling the dirt onto his coffin.
No, just an indication that I’ve been around the block a time or two. I’ve got way too much regard for those who’re actually proficient in maths to claim that I’m one of them.
Last I heard he is braindead. I wouldn’t be surprised if they keep is heart beating so his attorney can get easier access to the bank accounts until they figure out what the heck is going to happen with the hundreds of millions in the Swiss banks.
What’s hard about trig beyond keeping secant and cosecant etc straight? And is my experience of finding real analysis at least an order of magnitude more difficult than PdiffEqs and topology and algebra typical, in the sense that everything’s easy until you get out of your depth and then it’s impossible?
I will find all of your mathpeens to be of miniscule size until you can explain for me the topology of the microdimensions in string theory.
“Can I really, really, REALLY suggest we not get into a dick-waving contest? I mean, that in general, but a phallomathematical competition is just so not what this country needs after the election…”
Mah opponet, Jahn Karri, would allow the Unnidded Nashuns a veetoo over the preempuv waving of falloma- fallo-…geometrical private parts to ‘ntimate our enymies. Ah will never need a permission slop from the S’cretary Genural of the YouEnn to protect the security of the Urnited Stades against math nerds waggling their peepees at our great nashun.
Gawd Bless Amurkier.
“What’s hard about trig beyond keeping secant and cosecant etc straight? And is my experience of finding real analysis at least an order of magnitude more difficult than PdiffEqs and topology and algebra typical, in the sense that everything’s easy until you get out of your depth and then it’s impossible?”
I don’t know why I had so much trouble with trig, but I found the concepts of calculus and even partial differential equations much easier than learning trig many years earlier. You may be right about everything being easy until you get out of your depth. All through calculus I could check my work against the graph of what I knew the answer should be in my head–even if multi-dimensional. But I never got a good conceptual hook to use for real analysis. It was what caused me to drop the math side of what started out as a math/english double major.
“I don’t know why I had so much trouble with trig, but I found the concepts of calculus and even partial differential equations much easier than learning trig many years earlier.”
Personally, it was the eigenvectors and fourier analysis which made me decide to switch physics for chemical engineering in the hope to get away from all the math getting in the way of understanding the physical concepts. Which was like deciding to leave the artillery and join an infantry division because you don’t like all the loud bangs going off.
Calculus I,II,III and IV, Differential Equations 1-2, plus a couple more for my Mechanical Engineering Degree and heed my warning!
If you don’t use it you WILL lose it! I can’t remember any of that stuff anymore!!
Should I cry or cheer? That is the question?
“If you don’t use it you WILL lose it! I can’t remember any of that stuff anymore!!”
Naw, it’s just when off the boil. Give yourself a day or two with it and it’d come back.
Mind you, I’ve worked as an engineer for 15 years, and have used calculus exactly once.
I think in my three years in the blogosphere, this is the farthest I’ve seen a thread has go off topic. Submit this somewhere for recognition.
Mind you, I’ve worked as an engineer for 15 years, and have used calculus exactly once
May I ask what kind of engineer?
I use calculus pretty frequently; for a number of years, I used spherical trig on a daily basis.
bob, it’s probably also the least contentious thread containing the name “Arafat” on a non-partisan blog…
USA, aka Tom: Northern Ireland. Was in standard Additional Mathematics O-level syllabus as of the 1980s. During the paralyzingly-terrifying “revision periods”, we’d all stand up, our math teacher would go down the class making us differentiate an equation, and if you got it wrong, if was two whacks with the strap. (Yes, it was a Catholic school, now you mention it.)
Heh. I took O levels/GCSE meself (they were switching over when I took my GCSEs so while I did the GCSE exams, we revised using the old O levels) and did the A Pure & Applied, Further Maths and S level Maths in Hong Kong.
Have you thought about frightening the crap out of them with the threat of physical abuse as an aid to learning?
Yeah, but those damn librul gummint sons o’ bitches up in Washington won’t let a public university TA like me kick some ass. Plus, really? I don’t have the heart to hurt them any more than the material and their shoddy backgrounds already conspire to.
Catch the NOVA programme on Archy if you can; you might be surprised how much we now think in the lost manuscript of “The Method”.
If the Nova webpage is anything to go by, I’m still not convinced. As I said before, geometric quadrature — though indeed a powerful Method — is a long way away from the Fundamental Theorem, the sine qua non of calculus.
Personally, it was the eigenvectors and fourier analysis which made me decide to switch physics for chemical engineering
Basic Fourier analysis I found really easy; it was moving into delicate convergence questions about convolution integrals that finally broke my back.
“Can I really, really, REALLY suggest we not get into a dick-waving contest? I mean, that in general, but a phallomathematical competition is just so not what this country needs after the election…”
I know I’m quoting myself but… you know you’ve been reading too much ObWi when you read this and suddenly have this image of two buff, oiled studs wrestling over a blackboard with the legend “Enjoy Math Responsibly”.
rilkefan: What’s hard about trig beyond keeping secant and cosecant etc straight?
Identities, for those with insufficient algebraic background. Trig equations, for those who don’t really grasp the general notion of function and how to read off solutions. And, of course, the monster known as “trig integration”, for those who really want to hurt themselves.
And is my experience of finding real analysis at least an order of magnitude more difficult than PdiffEqs and topology and algebra typical, in the sense that everything’s easy until you get out of your depth and then it’s impossible?
It’s not terrible unusual, in precisely that sense. Me, I found basic real analysis and topology (both set-theoretic and algebraic) dead easy, certain kinds of algebra easy and other kinds somewhat unnatural, and PDEs downright mystifying. I mean, I get the basic idea and all, but the convolutions you have to put yourself through in order to establish results… meh, I just can’t bring myself to care.
bob: I think in my three years in the blogosphere, this is the farthest I’ve seen a thread has go off topic. Submit this somewhere for recognition.
rilkefan: bob, it’s probably also the least contentious thread containing the name “Arafat” on a non-partisan blog…
What, you think this is a coincidence? 😉
“I think in my three years in the blogosphere, this is the farthest I’ve seen a thread has go off topic. Submit this somewhere for recognition.”
What, you’ve never used USENET?
“Calculus I,II,III and IV, Differential Equations 1-2, plus a couple more for my Mechanical Engineering Degree and heed my warning!
If you don’t use it you WILL lose it! I can’t remember any of that stuff anymore!!”
That’s funny, because it really isn’t my experience at all. I helped out a friend on vector calculus a couple of months ago and hadn’t touched the stuff in almost 10 years. It took 10 minutes looking at the textbook and I was right back in the thick of it.
You may be right about everything being easy until you get out of your depth.
This was my experience. I was a math major and it was all crystal clear and I couldn’t imagine why anyone didn’t understand it. Then one day I didn’t understand it either.
I’m curious whether anyone understands this whole process of racing along and then more or less hitting a wall. It’s strange if you think about it. I can’t imagine it happening to people in other disciplines.
At the risk of insulting other disciplines, this ‘hitting a wall’ shows the difference between maths (and related disciplines like theoretical physics) and liberal arts disciplines. While I’m not going to engage in any sort of contest on maths ability (I hit my wall at a very early age) I think it is similar to any complex skill based activity like sports or martial arts as well as things like language ability. In those sorts of activities, you always hit walls, some of which you overcome, some of which you never get over. Application of effort is not always the answer. Sometimes, it is important to just leave for a while and approach it again.
christ on a crutch, are all the frequent posters here math geeks?
FDL — A.B. Dartmouth College 1986 mathematics/computer science.
whereupon i decided NOT to go work for microsoft and ended going to law school instead.
oops.
and today i couldn’t solve an integral if my life depended on it.
[but i do help keep the water flowing for people like Sebastian. not a bad tradeoff.]
Francis
It’s hard for me to remember the wall – part of may have had to due with 2nd semester senior year, part my feeling real analysis was ugly – but perhaps it’s a matter of the ability to hold a chain of abstractions in one’s mind. A fiber bundle is a mapping from an open cover of some sort of group acting on something with the following properties which you either can’t think of any example of or any counterexample and how the hell do you show it’s continuous anyway and let’s talk about iambic pentameter instead.
The point was (shout-out to whoever on this blog recommended Maker’s Mark) intended to be that at some point adding one more concept is like adding one more ball to the merry juggled array and, your mind unable to simulate one deeper level of abstraction, the whole constellation crashes to the ground.
christ on a crutch, are all the frequent posters here math geeks?
Of course. Why do you think the caliber of the discourse is so high here? 😉
A fiber bundle is a mapping from an open cover of some sort of group acting on something with the following properties…
That’s algebraic topology, actually, not real analysis. And although I unfortunately don’t remember the details of a fibre bundle, I actually found them quite natural and intuitive; they’re sort of the logical extension of covering spaces and most people have an intuitive notion of those.
[Except for the Hopf fibration. That sucks. But the homotopy of spheres is a beautiful, and to this day poorly understood, area of research.]
“I’m curious whether anyone understands this whole process of racing along and then more or less hitting a wall. It’s strange if you think about it. I can’t imagine it happening to people in other disciplines.”
I don’t know if you can consider it a discipline, but as a chess player I can put a number on mine:1920. That is not an absolute peak, but kinda a sustainable high. And it is of course, a mental/knowledge/skill activity. There is advice out there on getting past your wall that might be applicable to other “walls.”
For those who are not into chess, the scale is roughly logarhythmic: a 2000 player is ten times as good as a 1900. (Or is it only twice as good)
I’ve been an engineer for over 20 years, and I use it nearly every day. But there’s a rather wide gulf between theory and applications; the theory guys know their maths inside out and sideways; I just know enough about it to be able to use it for problem-solving. But since everyone else whipped theirs out: Ordinary Diff Eqs, PDEs, Complex Variables (which ought to have preceded ODEs, only didn’t), abstract algebra, numerical analysis, special functions, perturbation theory, advanced calculus (generalization to multivariate calculus). Most of which was fascinating but likewise most of which I don’t use. With the exception of ODEs and perturbations, which I use almost daily. Numerical methods I use less frequently. Complex variables I mostly use when I can’t remember some of my trig identities and have to rederive them.
And once again I’d like to stress that although I’ve got a bit more advanced training than average (maybe not for this group, though) I’ve got less theoretical rigor than I’d like to have. I think Anarch has my ass kicked rather thoroughly. Rilkefan probably does, too. I’m an applied math guy, so I’m not as strong on the theory as others might be.
My wall was in ODEs, which I had to take twice. Once I learned what the big deal was all about (in essence, ODEs was merely a collection of solutions to classes of ODEs, and what to do when there are boundary conditions) I got an A. PDEs was the second wall; first time through I got a C. There wasn’t a second time, because I never had the time to retake it. You know that you’re in trouble when two-thirds of the class is auditing and there’s only one prof that teaches it.
“At the risk of insulting other disciplines, this ‘hitting a wall’ shows the difference between maths (and related disciplines like theoretical physics) and liberal arts disciplines.”
Well, ‘cos things tend to build on each other, and I my case, you were hurtling through the material at an ungodly pace (‘cos the physics department wanted to kill off 75% of the first year class), and once you hit a bump, it was hard to catch up and the material quickly became Not Very Much Fun At All, because the rapid pace was interfering with getting a deeper understanding of the underlying concepts.
And, unlike the more modular US courses, you couldn’t slow down the pace by deciding to lower your courseload – you were pretty much train-tracked, three years and then out.
bob, I think chess is sufficiently knowledge-based as to be susceptible to steady progress – you learn more openings, you finally submit to the need to understand rook-and-pawn endgames, you go over your middlegames with a strong program and find out what you’re doing wrong, you devote time on the clock to planning. 100 points advantage means you expect to score 70%. For people who haven’t really worked at chess I’d guess doing so is worth more than that. I never put that sort of effort into a math class, but I suspect one usually can’t climb the wall that way. (Of course for people with real talent at chess you’re right, they have something different going on in their heads than you or me.)
Back on topic, Abu Abbas, come on down!
Seems like a reality-based kind of guy.
I had a faint twinge of hope for Mahmoud Abbas for the couple months he was PM. Here’s hoping it’s him up next, with as little bloodshed as possible.
Well. I am not a math geek, though I did all the math geek things in high school. The moment when I realized, after one semester of Calc2 in college, that I did not have to take math any more since I was no longer in high school, I felt overwhelmed by joy: it had not occurred to me until that moment that it was conceptually possible not to take math.
There are walls in philosophy, by the way. But it’s not a standard humanities discipline, being sort of math-y in its way.
I never really hit my wall, but I looked at it and said, “nah.” Linear and multivariable calc were doable, but I wasn’tabout to go further.
Incidentally, if you pluralize “math,” does that make you smarter? If so, count me in.
Bring on the maths, b*tches!
At traffic school today (91 in a 65), i remembered my wall.
there’s a proof which involves creating a list of equations, then circling the first term in the first equation, the second in the second, etc. It’s called a something square, maybe? i think kdrum posted about it a while back?
anyway. that proof was in a class i took, and i never came close to understanding what the hell was going on.
any help?
Francis
Yet more math.
Since Arafat died on Friday, if he dies AGAIN on Sunday, does that mean he was arisen for three days?
Then what happens?
fdl, you’re likely talking about Cantor’s diagonal proof that the real numbers are a bigger set than the integers. You associate each integer with a real then generate a new real by changing (for the nth integer) the nth decimal place of its corresponding real.
Check out the last graph – I live in the spike.
Hmm. Try this link.
Ok, on sober reflection that’s surely just someone trying to use excel to do an analysis, never mind.
btw, now he’s dead.