I HAVE RETURNED! Hide the women and children. Well, maybe not thewomen…………..

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After a disappointing year of graduate school, I’ve returned at the close of summer and the beginning of my last semester (I HOPE) of schoolwork in my life. Flecks of premature grey adorn my beard as the analogous summer of my life ends and the chill of winter slowly but inevitably approaches-and a PHD still nowhere in sight due to the collapse of the American empire.

I will develop my observations on this matter in depth in future posts.
But forget the barbarians being at the gate: The guard was their all-too-willing accomplices as they walked right in and enslaved the entire kingdom under the pretexts of “free market economy“ and “lobbying“.

I fear for the future of this country. The Radical Red Staters are poised to take advantage of 2 generations of steadily degenerating education of our citizens to polarize and divide this nation, so that it’s no longer a battle of liberal and conservative ideas. Rather, it’s now between thinking, logical, scientifically objective people and obsessively tribal, dogmatic, racist, exclusionary Christian fundamentalist extremists-with the latter group being frighteningly agitated into a frenzy by a paradoxically self righteous and simultaneously self-servingly duplicitous leadership who blasts their inflammatory beacons on the internet and talk-radio.

And just think: All it took was the election of the first African-American president-and the first real attempts at social progress in over a decade as a logical response by his administration to the worst economic disaster in our history-for the populace of the US to revert socially to the 1930’s. Socialism. Illegal aliens. Doubts over evolution being forcibly imposed in school textbooks by a few concerned educators in Texas.

Somewhere in Hell, Adolf Hitler, Joseph Stalin and Joseph McCarthy are laughing their asses off. I see the cliff coming and no one seems to want to slam on the brakes before we go over………

Again-MUCH more on this in future posts. But I can’t justify or contextualize this first post’s purpose without some preamble of the desperation felt by my aging self as the world I knew as a teenager slips away-to be replaced by a darker jungle of uncertainty.

The wake of my father’s death-now 4 years distant-has financially crippled what remains of my family. My father’s 18 year battle with cancer-which he ultimately lost-has now left us with a debt that barely allows my mother to buy food. I know-we’re hardly alone in that. But this has taken it’s toll on my career. I’ve had to take 3 graduate courses in the last year just to maintain my eligibility for health insurance as well as student loans to PAY for that insurance. (Of course, this being America, you’d think this would be the primary place for free health care for all it’s citizens. Of course, we don’t live in a logical or moral reality, do we?)

That alone would make struggling through these courses hard enough. But then in a moment of desperation-I made a very foolish choice regarding my health. I really can’t get into the specifics here-I hope to do so in a future post in connection to a larger issue.
I will say this: I’ve officially learned the hard way that if you have no other available methods of controlling psychological illnesses other then drugs and someone tells you to go off them cold turkey and “you’ll feel so much better, all you need is to man up!”-then if you actually listen to them, the REAL imbecile in the conversation is YOU.

As you can imagine, the long term result was somewhat less then expected. I rectified the result, but the damage was done. And now I’m stuck with 3 subpar grades in courses I didn’t even fucking WANT. It’s entirely possible now my dreams of an Ivy League PHD programs-unless I solve the Riemann Hypothesis-are out the door and my career ends here with a Master’s degree and a future as a high school teacher.

The wonderful destiny awaits of dying of cardiac complications from prostate cancer when I’m 75-face down in puddle of cold decaf tea grading high school algebra papers from student who can barely read.

So it goes.

I haven’t given up yet. I can’t. Why not? That’s what a rational person of my intelligence would do.

Well, we’re all going to die of something. I lost my youth long ago-sacrificed it for my family. I think I’ve finally made my peace with that. It hurts like hell what I lost. But we’re all losing so much as the second decade of the 21st century opens. Parents losing their children in 2 pointless wars that have bankrupted the country the survivors are coming back to. PHDs mopping floors because those educated in other nations or of higher pedigrees are preferred for the vanishingly small number of jobs available.

Again, the cliff approaches for all but the top 1% of us.

I dunno about all of you, but I’d rather go off the cliff screaming my rage at this pointless, Godless reality and fighting with my last breath against the dying of the light.

Which is why I’m taking the initiative and beginning my own online business. (Nice segway, huh?)

I began this Ebay store on whim. I’ve been selling textbooks online for nearly 8 years on and off for pocket cash-and all told, it’s worked out pretty well. But “working out” has meant what’s basically chump change by selling second hand books and cannibalizing my own library.
So I started thinking: What kind of cash can I make with a REAL inventory of books to sell?

So one thing lead to another and viola! Parthenon Academic Books.

Actually, it wasn’t that simple. History never is.

So what’s the scoop behind it?

I’d love to tell you guys, but I’m passing out at almost 3 am. So it’ll have to wait-along with several other things-for the next post.

After all, how can you build a following to a blog without good cliffhangers?

TO BE CONTINUED!!!
Be back soon,same blogsphere plane and frequency.

Beware, Citizens...........


Update 7/4/2015 : Parthenon Academic Books was a complete disaster. It may still exist in some virtual shell sense, with the original page and listings in some remote corner of the net, like an aborted fetus left to rot by some spoiled sociopathic teenage mother (EW, nice image) , but that's all it is now. An  aborted dream. My dearest hope is that my latest and far larger effort at www.tuloomath.com succeeds in far greater fashion. Check it out and let me know.

Re: arXiv:The Modern Cure For B.A.D Mathematicans?

This'll be a short one. But hopefully something I'll comment on more in the future.

I've found a terrific article by Professor Melvin Henriksen published in The Mathematical Intelligencer in 1993 and republished online at the Topology Atlas by him. Henriksen-if you're unfamiliar with him-is currently Professor Emeritus at Harvey Mudd College and he's one of the few remaining active-sort of-mathematicians in one of my favorite areas of mathematics:point set topology. He's also published quite a bit in algebra,has been very active in historical aspects of mathematics and is currently one of the major overseers of the mammoth virtual site Math Forum supported by Drexel University.

The elitism in mathematics is nothing new-nor,sadly,is it unique to mathematics among academic endeavors. Henriksen-never one to keep his opinions to himself-summed up the situation-and the reasons behind it-beautifully and informatively,in this article:

http://at.yorku.ca/t/o/p/c/10.htm



If anything,the situation has worsened since he wrote this article.

When you mention certain branches of mathematics at some unmentionable universities that believe only the half a dozen places on Earth called "Ivies" are where civilized humans exist and everywhere else is untamed jungle with blood drinking,grunting barbarians with pieces of paper masquerading as educated humans-you actually get audible laughter. They don't even try to be kind about it. Why should they? Anyone who can't see that they're right is a fool and won't get promoted anywhere. At least,not if they have anything to say about it-and sadly,they do.

I'm currently investigating the possible role of general topology in additive number theory. To be honest,if arXiv-simply called "Archive" by most of us-didn't exist,I doubt I could publish it anywhere. This remarkable tool has changed publishing forever through open access and free publishing in mathematics and physics with no formal refereeing-and therefore no monkey business. Any attempts to shut it down or seriously regulate it should be met with savage resistance. Such attempts at regulation has already begun in the form of the vote in 2004 by the Archive board to allow only preprints-presumably because copyright issues could arise that could jeapordize corporate profits. The bottom line is that it's begun-the attempts to control it.

(The copyrighting of concepts as property is a terrifying phenomenon that I hope to tackle in depth another time.Suffice to say this is a Pandora's Box that threatens all original thinking if it's not strictly controlled.)

It's a wonderful reality we live in currently in this regard- free publishing. Let's not let the B.A.D. crew and their wealthy allies wreck it like they've wreaked whatever doesn't serve their purposes.

In other words,business as usual on Planet Earth.

A Brief (Partial) Apology For Speaking out of Turn: Calculus, CirriculaAnd Constudents...............

I'm not usually one to apologize when I feel someone is being a dick.

Anyone that knows me knows that.

But my guilt has gotten the better of me and I think I need to make amends for my last post.
Namely,my swipe at McMasters' University professor James Stewart.

I think I was angry at the decaying civilization around me and I took it out on him.


I'm really apologizing just for one small part of the rant that I felt was beneath me. It was simply untrue and would be very unfair for me to say about someone I've never even heard lecture or speak once.I referred to Stewart as a "grotesquely overpaid hack without an ounce of mathematical talent".


Well,that was completely untrue and unfair:Professor Stewart is actually a very fine teacher and mathematician from what I know of him. (It turns out he's the mathematical grandson of the famous Oxford mathematician E.C.Titchmarsh. I didn't know that and found that kind of interesting in and of itself.)


I dug out my copy of the third edition of his textbook to act physical evidence in this trial of my conscience.I also borrowed a copy of the 6th edition.

He's made a lot of improvements in the text since I used it-a lot more pictures, the exponential and logarithmic functions are introduced and discussed MUCH earlier (in the first chapter,in fact),and in general a lot more explicit focus on the overall process of problem solving,which was only indirectly stated in the edition I'm familiar with. Stewart was a graduate student of George Polya before moving on to get his PhD-the influence of the Stanford problem solving master is all over this textbook in both editions. Stewart approaches calculus as a problem solving enterprise first and foremost-such an approach is bound to be pragmatic and will intentionally sacrifice rigor where it obscures understanding.


In short, Stewart is trying to teach his students how to become intelligent problem solvers above all else. As teachers (and speaking for myself as an aspiring teacher at the college level), discouraging the good intentions behind such an approach is the last thing we should want to do. It's easy to forget how confusing calculus and physics is when one first seriously tackles it as a college undergraduate-or for the more fortunate and/or talented, high school. As a result, it's easy to get on your high horse and badmouth a text like this from the viewpoint of someone who's mastered a good portion of rigorous mathematics. Stewart offers to take the student by the hand and walk him or her step by step through the fog-showing them tricks of the trade along the way and tried-and-true methods of attacking problems in ways that not only obtain solutions,but a complete understanding of the MEANING of what's being asked of them. "What do they want from you?What will satisfy the question?" This is what Stewart is trying to teach with his book.

It's really informative in this regard to read Stewart's own comments on the text from an interview done by the MAA on July 6th,comparing it to the texts he used as a student at Stanford University and The University Of Toronto in the 1960's:

IP: How have mathematics textbooks changed over the years?
JS: Compared with the textbooks that I had as a student, textbooks are so much better now. I don’t know how kids learned from these old books. There was no motivation. It was very austere. You can go too far in the other direction, but the state of the exposition of mathematics is just so much better than it was three decades ago.
As an author of the high school textbooks in the 70s, I kept my eye on trends in education. The new math had been well ensconced by then. But what I observed and decried was the waves, the extremes, the pendulum going back and forth from the new math back to basics. You still see this, especially in the U.S., especially at the high school level, where it is much more virulent. At that time, I longed to get hold of that pendulum and stop it somewhere in a sensible middle. People get too dogmatic.

Even more insightful into Stewart's thinking is his comments on teaching and what he's doing lately:

IP: Are you still teaching?
JS: Although I am Professor Emeritus at McMaster, a year ago I was appointed professor of mathematics at the University of Toronto, and I have twice taught first-year calculus. Although I don’t teach fulltime anymore, I love teaching. Being an author is a pretty solitary, sedentary occupation, so I miss the social aspect—which is teaching. I do it partly to keep in touch with kids, because it brings out the best in me, and to give me new ideas for new editions of my books. This fall I am introducing a new course at the University of Toronto on problem solving. I introduced such a course at McMaster quite some time ago. When I was a graduate student at Stanford I fell under the spell of George Polya, who was retired but used to come in and give these problem-solving talks. He had all of us—teachers and students alike—literally sitting on the edges of our seats with mathematical excitement, presenting data, asking us to make conjectures. The idea is: Suppose you’re faced with a problem that you have never seen before. How do you get started? The first few lectures introduce some basic principles of problem solving. The remaining lectures start with a “problem of the day.” How would you solve it? What strategy would you use? What about trying a special case or solving a simpler problem first? It’s my favorite course to teach.I’m doing that this fall, working with some of the faculty at the University of Toronto so that they can carry on after me. It will be a kind of capstone course. You’re drawing on everything that you’ve learned up to that point, putting it together. There’s no new content whatsoever. But once you take a problem out of the context of a specific course, it becomes harder.

Now that's a book I'd love to read-a problem solving textbook by Stewart that emerges from that course!


But sadly,Stewart seems to miss that the problem with this approach to calculus which has made his book so successful is also why it's damaging to students used by itself.The result of the "practical" nature of the text is that the fact that it's a book on calculus becomes completely incidental.

He never asks the all important "why" questions that brought the real number system and the structure of real analysis into focus for mathematicians in the 19th century.Everything's given a name-Sum Rule,Product Rule,Method of Secants,etc.-which makes them tailor-made for memorization rather then learning.He gives quite good "geometric" explanations-such as a good discussion of motivating the definition of the derivative as the limit of a sequence of secant lines to a point on a curve.But such a discussion is completely independent of the definition of a derivative as a limit.It might as well appear in a book on physics or geometry. As a result, it's all completely mechanical-the fact that it's a book on calculus almost become irrelevant!

And this is the problem he fails to see:To most of today's students,it is irrelevant.You may as well be teaching them how to play checkers and they memorize the rules.


Sure, a few students will really look at the very nice geometrical arguments and walk away really learning something.

But most students-who make up most of today's colleges and whom the university administrators are aiming to sell calculus to-couldn't care less.

I call such students constudents-a hybrid of conmen and students. They aren't interested in learning-in fact, like thieves excited about stealing and not getting caught or cheating husbands who call their wives to tell them they're going to be late while getting oral sex from their mistress-getting an A while never learning a damn thing is exciting to them.

I know what some of you are thinking: "Come on-that's human nature,there's always going to be students like that!"

Sure,of course.

But the big advantage of the rigorous calculus texts of the past was that it was almost impossible for such students to con their way to a good grade-the fact that rigorous mathematics was an essential part of the structure of the course ensured they actually had to learn something to do reasonably well. And the course acted to ensure that students with impure motives who didn't even try didn't get good grades.

Books like Stewart's have eliminated this fail-safe altogether.

I remember as a premed sitting around with a number of students taking calculus using Stewart and the discussion of the exam was like they were talking about a football game and how they were going to "beat" the exam. They came up with codes,mnemonics,word games-not a single theorem or concept or proof. I made the idiotic mistake of asking if anyone actually learned the material and the whole table erupted with laughter. The President of the Student Medical Association smiled at me like The Grinch.

"Winning is about APPEARING to know what you're doing,not actually doing it.Don't worry-you can always work taking out the trash in my office on 5th avenue."


Our society rewards this kind of behavior.Why?Because letting these monsters use Stewart and get thier A's without learning anything is good for business,that's why. The university gets to pack the classes with 200 paying students by making this a required course,the students get thier A's which the college can use to improve it's ranking standing so that administrators get promoted for making so much money and helping public relations and off they go to Ivy League medical schools thinking urea is made in the kidney-and worse,not giving a shit.
And 5 years later they're killing and crippling patients left and right and being acquitted at malpractice trials because the only one in the room who's a better liar then they are is the son of a bitch defending them.

A book like Stewart's ENABLES this kind of system.

I have no problem with Stewart wanting to make the book of a problem solving nature-as I've said,this leads to the book having many positive qualities.My problem is that including mathematical rigor need not be contrarian to this intention and for someone claiming to be so devout to teaching, Stewart refuses to acknowledge this.

Sadly, I think he's too smart not to see this. I think his position is one of willful ignorance in a corrupt academic culture that's made him not only very wealthy for his occupation, but very famous. I doubt anyone outside of McMaster would have ever heard of him without this text.

And I stand by my earlier criticism of Stewart of his ridiculous excess with his own concert hall.

He loves music, fine. Bless him. But spending more on his hobby then 5 families spend on their homes is nauseating and he should be ashamed of himself.


Of course,he's hardly alone in that in this day and age.

But he's an academic. He should know better.

Frankly,I think he does and his own words betray this:

When I started writing my first book, I had no idea you could make any money writing books. That was not a motivation at all. It was a surprise, but it enabled me to build this house. And I’ve got to continue to work to pay for the house. The house’s cost [$24 million] is double the original estimates.


It sounds like he has a very strong motivation for continuing to enable the sharks. Amazing what people are able to justify to themselves.

I hope Dr.Stewart keeps making money and succeeds in paying for his house so his heirs have the proceeds from using it as a tourist trap when he passes away. I hope all his kids and grandkids go to Harvard from it and maybe follow in his footsteps as a teacher instead of becoming criminal defense attorneys and bankers as the later generations usually do when the first generation creates a fortune for them. And I hope a lot of teachers of calculus use it as a supplementary reference or secondary source for their calculus courses and as the main text in high school courses.

I just hope one day someone has the balls to challenge the American way someday and writes the text that replaces Stewart by combining mathematical rigor with his teaching skills to give us a calculus text for students and not con-students.

And I hope I and my loved ones are never at the mercy of the enabled MDs in a hospital with their lawyers' number constantly in their back pocket.


Welcome To The Twilight Jungle.

Abandon All Honesty And Integrity Ye That Enter Here.................

A Brief Ode To Stewart's Calculus-NOT.........................

I just read a really funny post at Ars Mathematica and had to share it with all of you with commentary. Apparently, the question's come up with what McMaster's University's self-made gazillionare James Stewart did with all his royalites from the famous/infamous-depending on how much you care about mathematics-calculus book every other university's department uses.
Apparently, he built a gigantic house with his own personal concert hall in the middle of it. You don't believe me? See for yourself :



http://online.wsj.com/article_email/SB123872378357585295-lMyQjAxMDI5MzA4NDcwMjQzWj.html



This was so he-a trained violinist-could perform with his friends in the privacy and comfort of his own mansion. Talk about hubris worthy of being struck down by the Gods with the Ceres asteroid.

Apparently the only way Stewart's fragile self esteem could make it as a violinist in a concert hall was to have one built for himself where he'd be the star of the show every single night.

    Sigh.


Only in America would that seem like a logical action and not a gigantic excess of self-centered indulgence. I recently passed-on my way to the bus-a recently homeless family of 4 living in their car with their 4 year old daughter crying to the mother, "Mommy,what happened to my bed?"

Meanwhile, this grotesquely overpaid hack without an ounce of mathematical talent is spending 3 times what these poor people's former house was worth because he doesn't want to embarrass himself in public with his violin playing.................



     But be that as it may-I was honestly asked:How bad is Stewart's book and what are some of your favorite texts?What would you use to teach calculus given the chance?

Well,sadly,since I was a complete imbecile in high school and didn't know grades mattered in life-and my parents being laborers,well,they didn't know either-I ended up at The City University Of New York instead of a real college.(I made many friends there and learned a lot-but let no one be deceived my lack of pedigree and relatively advanced age will give me a huge battle ahead for any degree of success.)

So my first exposure to calculus was Stewart.


In all fairness,I was being a bit disingenuous up to this point. It's not as bad as many people make it out to be. The real positive about the book is the immense number of exercises with complete solutions.

Unfortunately,that's a double edged sword and it's the main reason it's completely unpalatable for mathematicians:It reduces calculus to a step-by-step, plug-and-chug bag of techniques without any real mathematical insight or thinking. Anything that requires more thought then a baboon is either completely omitted,put in rushed optional sections or shunted to a mythical "advanced calculus" course.

The students don't have to do any real thinking at all. Which is why most students-particularly the non-science majors-love it,of course.

Let's face it-that's why the bottom feeding universities buy it every year-so the premeds,accounting students,actuaries,pre-law and all the rest of the master cheaters that form the vast majority of bodies filling the enormous lecture halls of the average 200 student calculus course can program the solutions of all their exams into their programmable calculators.

"This is Anerica. Let the Japanese waste their time thinking and just give me my f***ing A so I can go out and screw people over for 6 figures a year working for Goldman-Sachs,geek."

It's also why Stewart would never have become so absurdly wealthy writing a book that is the very pinnacle of mediocrity in any other academic system but America's.

It's why a piece of crap like Charmed was on for 7 years while great shows like Farscape vanish, why Transformers:The Revenge Of The Fallen-with a mindless plot and racist "black" Autobots-is the #1 film in America at this writing.

It's why we sold our blood won freedoms to a stupid evil Texan from a rich family we elected king for the illusion of safety while Americans lost the entire Bill of Rights for 8 years.

"Americans aren't stupid!"


Really? You must be living in a different USA then I am.


So it goes.

My favorites? Well,when anyone tells you Micheal Spivak's Calculus
is the best calculus book ever-ever-it's really hard to argue. It's incredibly beautiful and a model of clarity. But much more then that,with every word,picture and exercise, Spivak asks the reader to think about the concepts before him or her before setting the task of doing it. Really THINK about it.

Is it too hard for the average student?

Well,depends on what you mean by the average student.

The average student cheating their way through every homework and test and sleeping with TAs to get a 4.0 to get into Harvard medical school,sure.

But if you're talking about a typical smart and curious undergraduate student-not necessarily a mathematics or natural science student-who reads everything with a real effort,wonders and asks real questions even if they don't understand or particularly like it because they're there to learn something?

I think they can.

Yes,it would be a struggle-particularly in learning how to calculate with epsilonic limit arguments for the first time. But with a good,patient teacher by their side, they could definitely get through it.In the process,they'd learn an enormous amount-not only about calculus, but logical thinking and problem solving. Which is useful in all walks of life, not just the sciences-and they'd be all the better for it.

For the mathematically talented, the book will become a treasured keepsake for a lifetime.The chapter on infinite series alone is worth photocopying and keeping.

I refuse to recommend soft,"applied" books.To me,the pure/applied mathematics distinction is a symptom of the problem above. There is no pure math or applied math-there is only mathematics. If you don't realize that,you're not part of the solution,you're part of the problem. That being said-the main problem with using Spivak is that he has virtually no applications-just one lame application of vector algebra to celestial mechanics late in the book. The main point of calculus is to calcul-ATE. Theory is important and all well and good, but teaching calculus as real analysis completely devoid of application is a little like teaching music students the complete mechanics of writing scores and symphonies,but never teaching them how to play!!!!

A book that fascinates me and I'd love to try using for a basic calculus course one day is Donald Estep's Practical Analysis In One Variable
. Estep,a numerical analyst, teaches a basic real analysis course combined with a basic calculus course, using numerical methods to motivate the rigorous development of the real numbers via Cauchy sequences of rationals and epsilon-delta arguments-with dozens of actual real-world examples from chemistry and physics!!! It's precisely the kind of book I wish there were more of-a book that combines application and fully careful mathematical development. I'd be a little scared to use the book,though-Estep makes a couple of really strange choices. The biggest one is deciding not to discuss infinite series. To Estep, infinite series is best done with complex variables,so he decides to omit them altogether. Huh?!? I hope there's a second edition where he adds a chapter on infinite series. Still, it's a relatively minor flaw in an altogether marvelous book that should be in everyone's library who loves calculus.

My favorite all around calculus book is a nearly forgotten one by a legendary teacher-Calculus by Edwin E.Moise.
It's based on both the regular and honors versions of the course in calculus that Moise taught for many years at Harvard and won several awards for. It's completely rigorous, yet beautifully intuitive with many,many pictures and geometric insight motivated using Euclidean geometry such as lines,planes and conic sections, as well as many physical applications. It's not quite as rigorous as Estep or Spivak,but it is considerably more careful then the average calculus book.

It breaks my heart this book is out of print and I'd love to republish it myself one day. This is the book I would use to teach my children calculus.Go to the library and check it out for yourself if you're disappointed with the ton of fluff the departments are trying to push on you to teach calculus with.

You'll thank me later,I promise.

Stewart and his private concert hall.Yet another example we are living in the era of the barbarians at the gate. It's so frustrating-with no address,you can't even drive by and throw a firebomb through his window to burn it down...........LOL

Re:The Vampires Of American Medicine And WTF Does "Well Defined" Mean?!?

So much for posting regularly at this blog.I may as well just shut it down and start again.

But I won't. I WILL keep trying to post on a regular basis for the rest of the summer until the blog catches on. Or it doesn't. A blog is for the author,no one else.Anyone else reads it,that's a plus.

I AM hoping it does catch on,though. I have a lot of thoughts on many things ongoing-but now's not the time. If anything, small posts will begin appearing regularly.

This summer-my last one before applying to PHD programs has not gone well. Sleep has eluded me for the better part of a month-stolen by gut pain combined with frequent urination. And the wonderful health care system of America has assured my internest can't see me.

I don't have a right to live according to the AMA, you see-not enough money to buy good health.


That's why they let my father die of agonizing prostate cancer at the end-they crunched the numbers and thier profits simply outwieghed my dad's treatment. So they gave us the bullshit story that "There's nothing more we can do." The cancer metastisized througout his bones over his last few weeks, giving him a death you wouldn't wish on Bernie Madoff.

Meanwhile, if he was a drug kingpin who dropped off 5 million in CASH,I wonder if a miraculous treatment they suddenly remembered about would have appeared and extended his life by 5-10 years. Since corporations now control the publication of most medical research as well as the mass media, we'd never know if one existed no matter how much you researched.

I can get fully into this here, but I WILL say this: The fact that Yale Medical School considered seriously adding ACTING CLASSES to it's required cirriculia for the M.D. for all students entering after 2011 to "improve maximally productive patient-practitioner interaction"(translation:to make the doctors the best con-artists possible) speaks volumes of the age of medicine we live in-and why I turned my back on that world years ago. I consider myself VERY lucky to have good and trustworthy doctors-but I can't tell you how hard my family searched to find them.
100 monsters for every one like them.

"We're coming for your money and we'll GET it all. We're the only real winners.The players don't stand a chance." -from the screenplay of Martin Scorsese's CASINO

Changing the subject to something mathematical, something on the web caught my eye yesterday and I just need to share it with the house. Ever wonder what well-defined means? It's amazing how many graduate students-particularly those working in category theory and the higher altitudes of algebra,where the phrase probably comes up most-never ask what that means. It's kind of accepted everyone "sorta" knows what it means. And for most people,that's good enough.
I remember the first time I ever wondered about it-it was in Kenneth Kramer's honors abstract algebra course a few years ago at Queens College. He was sketching the proof of Cayley's theorum on the fact that every group is the same as some group of permutations on a set (i.e. they're isomorphic). ( Actually, he wasn't proving it,he just wanted to sketch the proof because he'd rather spend the classes' time developing the theory of group actions on a set, of which Cayley's theorum is a special case-i.e. a group acting on itself. But I digress.............)
He was constructing the composition map which is the isomorphism of a group G onto it's corresponding permutation group acting on it's underlying set S -I forget what he denoted it as,call it P(S). He commented the map was clearly well-defined. I raised my hand in frustration since I'd asked the question before and never gotten a straight answer from any professor (some of them actually got annoyed with it and made unkind remarks about my age as a student)
What followed was one of the most impressionable moments of my student career as Dr.Kramer and I exchanged comments on what exactly it meant to be well-defined. "It means it's not ambiguous what the value assigned is, Andrew-that we don't get 2 values for the same arguement." "Oh, you mean the relation actually specifies a function?" "Well, not exactly-if the formula IS a function, you're absolutely right. But this may not be a function and still be a well defined mathematical object." I didn't get it. After a few minutes of him giving a few examples, no progress was made. He ultimately asked me to table the question so we don't waste any more of the classes' time.
I did so,but ultimately,it disturbed me. Dr.Kramer is a gifted teacher on all matters mathematical-an early student of John Tate's at Harvard-and usually the most pleasant and patient of people with even the stupidest of students' questions. In fact,I'll be taking a course on elliptic functions with him at the City University Of New York Graduate Center this fall. The sheer wieght of the subsequent coursework-the first 6 chapters of Herstein's classic Topics In Algebra in a VERY intensive 2 semesters,plus his own notes-prevented us from broaching the subject further. All that really got settled was that it was pretty clear what "well-defined" meant if the object under consideration was a function-in fact, it's almost redundant. But how would you describle a general mathematical object as being "well defined"?

Leave it to Tom Gowers to make everybody happy.

There are several blogs online I try so hard not to miss. Peter Woit's Not Even Wrong, Terrance Tao's, John Baez's The N-Category Cafe' , The Secret Blogging Seminar and a few others. But nothing matches Gower's blog for sheer beauty of writing and thinking about mathematics. A lot of people can do mathematics, a lot more people can teach mathematics, and even more people can talk about mathematics .(Sadly, this is whether or not they know what the fuck they're talking about or not...........)

There are so few who can do all of the above.

Elias Stien can do it (sometimes).

Melvyn Nathanson can do it.

James Stasheff can do it. Better then anyone I've ever heard.

William Thurston can do it.

But for my money, no one does it better currently and consistently then Tom Gowers. His blog should be required reading for all mathematicans and serious math students. (By the way-his old teacher at Cambridge, Bela Bollabos-is also great at all of the above. I doubt that's an accident. )
Anywho, I was reading Gowers' blog and low and behold, Gowers also wanted to know, after grading the exams for the year at Cambridge and discovering NONE of his students understood it,either-what's it mean for something to be well defined?

People who know me know I'm Socratic to a fault, to the point of making people violent. I almost NEVER agree with EVERYTHING someone says.

But this is rare occasion when I'm speechless with complete conviction and agreement with someone else's analysis. As I said, leave it to Gowers to give the perfect answer to a great question.

I'll simply let the beauty,depth and simplicity of Gowers' blogpost speak for itself-I simply have nothing to add to it. Nothing at all. Anyone asks me this question in the future, I'll simply give them a copy of Gowers' post. For all basic mathematical discussions that may come up in the future, I seriously doubt anyone can debunk this discussion.


It's THAT good.


Oh,screw the self-engratiating pontification,here's Gowers. And if you don't bookmark his blog, shame on you.

Good night to all,fellow travelers. Until next time.


http://gowers.wordpress.com/2009/06/08/why-arent-all-functions-well-defined/#more-605

Re:Crazy Days At CUNY........................

Has it really been over 3 MONTHS since my last post here?!? Jesus f***ing Christ!!! So much for my commitment to the blog. I'm hoping to be more committed to it from now on. Not that it matters-I seem to be the only one reading it. Maybe I shouldn't have posted that pic of my adorable self so fast............?


My third and hopefully final semester of Master's degree work began at the CUNY Graduate Center and Queens College nearly a month ago.It was off to a horrific start due to the usual shenanagians with the Registrar. I'll talk about that in a post later this week.Frankly, I feel like I had no summer. I spent half of it at home watching what's left of my family wither as my brothers "sort of" live there and my mother cries remembering my late father. The other half I spent trying to learn differential manifold theory from Loring W.Tu's wonderful Introduction to Manifolds. Yeah, THAT Loring Tu, the student of Raoul Bott's who coauthored his classic Differential Forms In Algebraic Topology. Requiring only a semester of real analysis and abstract algebra and rolling in at a total of 350 pages, the book is everything you want in a differential topology text and more. I needed a couple of good books for self study on the subject to teach myself differential geometry to complete the problem sets for Josef Dodziuk's course taken-and never finished-in the spring. A lot of my friends prefer John M.Lee's Introduction To Smooth Manifolds . Lee's wonderfully written, but its' HUGE and I think works better as a reference. And of course, the old timers point you towards Spivak's magum opus on differential geometry. Spivak's wonderful if you have a year and half to work through it at your leisure-which I don't. I looked at a couple of other books, but I am so glad I took a chance and plunked down 30 bucks for this softcover. Everything is clearly presented with lots of examples and pictures and with a deep mastery of the subject by the author-and good exercises,too. The thing I probably came away with more then anything besides a deep understanding of manifolds and differential forms is that the fact that manifolds are locally homeomorphic to Euclidean space is just the beginning of the story of modern differential geometry.A differentiable manifold needs to be able to support calculus on it and so much of the structure we take for granted in Euclidean space that makes that possible-the vector space structure over R or C, the norms and thier resulting metrics, the linear maps that result from the topological vector space structure-simply doesn't exist on an arbitrary manifold.Differential manifolds and thier respective structures are unique in that regard-and an enormous amount of that structure is not topological/analytic, but ALGEBRAIC-specifically all kinds of R-modules and thier related maps. Tangent spaces, derivations,smooth algebras of functions and Lie groups and algebras-without them,manifolds cannot support calculus and modern differential geometry vanishes in a flash of ectoplasm. The more modern mathematics I learn,the more I realize modern algebra is the glue that holds the whole mammoth structure together and it is taken for granted by most physicists and nonalgebraicists.................



It was eerie in the common room at the Graduate Center mathematics department for most of the summer. The room was for the most part dead with the occasional faculty or graduate student dropping in. Then a week before the semester started-boom,all the familiar faces began trickling in. Lou Thrall and Satyanand Singh (Sam to his friends), arguing low dimensional topology and sheaf theory from Sullivan's notes as usual. Pretty Jeanne Funk, splitting all her time between getting ready for her PHD thesis on algebraic geometry and working as a teacher in the shithole we sadly call the New York City school system for what little pay she gets. Gangly Schlomo Ben-Har, whom I've known for the better part of a decade on and off at Queens College and now in his second year of PHD work at the Graduate Center-what little I see of him in either school.

Faculty we don't see too much of outside of classes and the seminars here-at least,not in the early going. Dennis Sullivan-the invisible god here at the CUNY Grad Center-makes his presence felt by his impact on the serious topology students like Lou and Sam who've associated with him closely enough to freely call him "Dennis" in open conversation-and speak of him in hushed tones. John Terilla-one of my mentors among the younger staff at Queens and a student of James Stasheff-speaks of him in the same hushed tones. I'll be sitting in on Sullivan's class this semester-hopefully becoming a regular. I dunno if I'll be attending the string theory seminar Dr.Sullivan runs this semester. Depends on if a certain well-known geometer is attending.The person in question currently teaches at Columbia and that's as specific as it gets here. I had one run-in with her at the string theory seminar last year. We broke for lunch. I introduced myself to her,she smiled-we had what I thought was a nice conversation going for a few minutes,telling her about myself and what she thought of the seminar,etc. Smiling,she suddenly tells me,"Excuse me,you're just a very annoying person and you're boring me-could you please stop talking to me?" All with a smile. I smiled back,politely excused myself and went to mingle with others. Honestly, I was too stunned to be offended.I don't know if I caught her on a bad day or what-the whole episode still mystifies me. Anyway,after that I put her on my "avoid if possible" list.
I just wished at that moment my father had been alive and bore witness to it. At that moment, she crystalized the very significant distinction between being bluntly honest and being wantonly cruel-blunt honesty is done for a higher purpose and never without consideration for its effects. What she did is done randomly,capriciously and strictly for the affector's own pleasure. That distinction was one I could never make my father understand while he was alive.....................

I'm taking the deformation theory seminar at the Graduate Center this semester headed by John Terilla and Thomas Tradler. It's so exciting to be learning living mathematics-not something that was done and buried by World War II. I really need to brush up on my tensor algebra, though. I'll also be reading a ton of papers on the subject-particularly Gerstenhaber's original papers,which the lectures will be leaning on heavily. Taking graph theory with Christopher Hanusa and probability theory with Stefan Ralescu, both at Queens this semester-and it looks like a full slate.

I hope to finally begin research this semester on a topic I made a couple of false starts on-the p-adic topologies, a family of topologies named on the integers by Kevin Broughan.The first such instance of a p-adic topology was used by Harry Furstenberg over 40 years ago to give a topological proof of the infinity of primes. I was talking with Lou the other day and he told me to stop talking about it,just pick up a paper and do it. Research is the currency of mathematical careers-anyone serious has to begin it as soon as possible. I doubt anything earth shaking will come of it-but if I could just produce one or 2 publishable papers-it will go a long way towards cementing my place in the order of things.And maybe I don't have to settle for the CUNY graduate center for a PHD.

My bed is calling me.I have 72 hours beginning tomorrow to learn 4 weeks of deformation theory. I hope the Gods of Logic And Inspiration are with me.

Until next time.........................

Dealing In Triangles Part Deux: Revenge Of The Sugarman

When last we left my humble post, I’d attempted to do the student community a favor by making more widely known the short proof by Moran and Doyle of the existence of a triangulation for a compact 2 manifold. Feeling proud of the service I performed, I went back to my studies and pathetic excuse for a life until my friend JS (his name is being withheld to protect the innocent from harm-namely ME) brought up during a discussion about a possible student conference we’re discussing for Queens College that the matter was quite a bit murkier then it initially looked. Quote from the math society message board:
That's interesting. I was confused because I heard that all surfaces are compact and I believed it without looking at any proofs. Also when I looked at it on wikipedia, they were unclear as to whether or not the surfaces had to be compact.I imagine that since every 2-manifold has a differentiable structure, and every manifold that has a differentiable structure has a piecewise linear triangulation you should be able to triangulate every surface regardless of whether or not it is compact.I could be wrong about a lot of things though, since I don't know the proofs for any of these things and I haven't even glanced at the papers. It would be awesome if you could clarify all this stuff for me and even more awesome if you could talk about it in August.

Leave it to JS to point out the gaping hole in the ceiling. He was right,though-I’d seen Rado’s proof stated for noncompact and compact surfaces, something clearly wasn’t clear here. Does an arbitrary surface admit a triangulation or not? It turns out it depends on what you call a surface-and mathematicians are not of a single mind on this.
This is the definition of a manifold I was always taught: An n dimensional manifold is a Hausdorff topological space that is locally homeomorphic to an open subset of R n . That definition clearly does NOT require n dimensional manifolds to be compact: consider the very simple example of a hyperplane in R n . This is clearly a manifold of dimension n-1, but it’s not compact. It turns out the necessary condition for 2-manifolds to be triangulable is that they must be 2nd countable (i.e. have a countable basis). This in turn implies that the spaces are separable (i.e. has a countable dense subset). If the surface is 2nd countable, then every surface is triangulable by the aforementioned VERY lengthy proof by Rado. ( Yes, to make sure, I DID read Rado’s original proof. There is an excellent statement and discussion of the proof in Zieschang, Vogt and Coldewey’s Surfaces And Planar Discontinuous Groups, Springer-Verlag, 1980). The proof hinges on a decomposition of the surface into disjoint closed regions which are then separated using carefully selected arcs and the Jordan-Shoenflies theorem. It turns out without second countability, there are counterexamples to this construction, namely the so-called Prufer surface, which is a seperable but NOT second countable and therefore non-triangulable complex surface. (Note that for a manifold, second countability implies separability but not vice versa.) A terrific discussion of this counterexample can be found in the paper linked HERE:
http://arxiv.org/PS_cache/math/pdf/0609/0609665v1.pdf
(It turns out this surface is also nonmetrizable ,which has deep consequences for both the general theory of Riemann surfaces and homotopy group of an associated CW complex, namely it doesn’t HAVE one. )
So all we have to do is assume all manifolds are second countable and end of problem, right? WRONG. It turns out differential geometers always define manifolds to be second countable partly to avoid this problem and algebraic topologist and algebraic geometers usually drop the condition since the counterexamples such as a Prufer surface is useful to them. (I’m too damn tired at this point to answer why, just trust me, they like the wacko manifolds……….) So as usual in mathematics-context, context ,context. This is why we need to DEFINE everything carefully people. Since most of us are a lot more interested in the geometry of manifolds then their topology per se-I’m inclined to give them all countable bases and be done with it.
By the way, the geometers have found there’s an even better reason to assume all manifolds are 2nd countable spaces: Since manifolds that are not 2nd countable are not necessarily seperable, the result is that the smooth structure on said manifold MAY NOT BE UNIQUE. That kind of ruins your day if you plan to do differential geometry on them, doesn’t it………….?
Off to bed. Discuss this among yourselves and no need to thank me………………..

Dealing in Triangles:A Little Known Short Proof Of The Existence of A Triangulation Of A Compact Surface And Other Matters Mathematical...........

Holla. Back on the chain gang with my girl bitching I'm broke ass and wondering why she gives me the time of day. OoOoOoO,I can't wait until she's in England next year getting her Master's. She thinks she's going to go to class and work part time since "school is so much easier then working."I can't wait until she calls me at 3 am long distance crying..................LOL

Before we get to the first mathematical post of the blog-I should introduce myself formally. My name is Andrew L. As for the rest:

Name: Oh,wouldn't you like to KNOW..............
Location:The City That Never Sleeps And Hates King George For Letting 9/11 Happen..................
Age:As old as my tongue and a little older then my teeth.

Gender:Male
Marital Status::If you can ask,you've never seen a picture of me.......................
Hobbies & Interests:Just about EVERYTHING,really-with particular emphasis on anything mathematical or in the hard sciences.(I don't distinguish between pure and applied mathematics and to me,EVERYTHING other then theoretical mathematics is just applied math-biology,physics,chemistry-EVERYTHING.Sue me............) Studying(naturally),Research;tall,curvaceous girls with brains and hearts (a rare commodity to be sure,but worth the search);writing,debating,compassionate friend to the ungrateful masses and whatever else I can accomplish in this meaningless existence to fill up my time until I join the dinosaurs.
Favorite Gadgets:The internet on whatever PC I can steal...............
Occupation: WAS a double major in mathematics and biochemistry-have since entered Queens College of The City University Of New York as a pure mathematics Master's student and hoping to use it as a new beginning to an Ivy League PHD after wrecking my career caring for my late father.Studying topology with Dennis Sullivan next semester if all goes well,that should get me off on the right foot...............
Personal Quote:"God doesn't exist.GET OVER IT..........."

To that,I'd like to add 2 things:
a) I'm learning this career path is MUCH harder then I could have imagined without coffee, which I can't drink anymore. IBS be damned............
b) This past semester,I relearned my love of philosophy under the tutelege of the legendary Saul Kripke in his philosophy of mathematics lectures at the Graduate Center of the City University Of New York.
To expand on these endeared memories-I remember the first day.I showed up with my friend Joey-probably the department's most talented mathematics major-to hear the giant speak. (Check that-I dunno if I'd go so far as to say Joey's the most TALENTED.We have a half a dozen really talented students in our mathematics club. But he's certainly the most advanced of us in his studies and research-and none of us are as dedicated or focused as he is.) Dr.Kripke went on about matters I remembered little about from my philosophy days in his unique,soft spoken and sometimes halting manner-he would stop to think about what he wanted to say and when it did come out,it was amazingly profound. It was clear to me this was a man who cared not only about what he was saying,but took time to stop himself and make sure he got it right.
Joey didn't agree-he looked at me perplexed and disappointed in Kripke's style-and he left and never came back. It was his loss. I'll talk more about it in future posts-but Joey, you missed an experience in this course. Dr.Kripke is giving a second semester by popular demand next semester-sadly,it's at the same time as the deformation theory research seminar myself and several others are already committed to. Unless it can be moved to a half-hour earlier, I'll have to make some hard choices before the fall. It will agonize me to not attend the second semester. But I am a mathematics graduate student and my heart must follow that path for now. I'm torn between my past love and my current path. The fork in the road will have some of my heart's blood on it either way I choose.
Today, I was engrossed with algebraic topology,a subject I swore a blood oath to conquer this summer before I went back. I raced through it last time trying to make a deadline for completion the department forced on me-and ended with a less then stellar grade of B+. Under the circumstances,though-I really should be estatic with it.Considering I crammed most of homology theory in in ONE WEEK,I should be thanking all the Fates and giving my professor John Terilla a kiss for that grade. I'm mad at myself because I know I can do better. Be that as it may-I was looking over Massey's presentation proof of the classification theorum of surfaces. I've always thought it was a beautiful tour-de-force: An incredibly deep result (all compact orientable surfaces(2-manifolds) are homeomorphic to either a) a connected sum of tori ,b) a connected sum of spheres or c) the projective plane) proved with "bare hands" by folding, glueing and pasting carefully selected edges and points on the surface S and showing the resulting quotient spaces have to be equivelent to one of those three. This proof is pretty long-it takes up most of chapter 1 of Massey's Algebraic Topology:An Introduction ( or A Basic Course In Algebraic Topology, the first half of the second book is basically the first with the useless last chapter removed). But it always intrigued me that this proof relies on a fact most topology books take for granted-the fact that all compact surfaces have at least one triangulation. Classically,a trangulation of a surface was exactly that-a homeomorphic decomposition of the surface into a set of oriented disjoint triangles. This step is critical for the classical proof of the classification theorum-there's literally nowhere to begin without it. As I usually do when something mystifies me-I dig into history to see how a concept evolved. Apparently the idea of busting a surface up into a mass of triangles originated with the first rigorous "combinatorial" definition of a surface in the plane by Dehn and Heergard in 1907; they defined a surface S as a simplexical complex where each edge is incident with 2 triangles and each fixed vertex is incident on a set of ordered vertices where each vertex in the set and the fixed vertex define a unique edge of a triangle in S. ( Aren't you glad you're not a topologist living back then?) Classical topology then proceeded on this assumption until mathematicans began to question if the definition was valid i.e. can every surface be covered with edge-pairwise disjoint triangles? The answer turned out to be yes,as was shown by Tibor Rado in 1925-but the proof had 2 major drawbacks: First, it was LONG. 23 PAGES long to be exact. Not exactly the kind of thing you can do in a classroom in a few lectures. The other and much more serious problem was that Rado's proof showed that although a surface can be covered by a set of triangles defined as above, the set need not be finite. Indeed, some mathematicans had already succeeded in producing infinite triangulations of some surfaces before Rado's proof.
It's because of all this BS that modern topologists have come to define triangulations in a much more abstract way: A triangulation of a topological space X is a simplicial complex K, homeomorphic to X, together with a homeomorphism h:K to X. Unsurprisingly,even with this definition, most topologists have been reluctant to directly decompose manifolds like they did in the old days;most stick with homology group(or for those sharper tools in the shed. groupoids) based analyses and call it a day. Still-it would be fascinating to have a short,clear proof of the fact to convince oneself that the classification of surfaces isn't mere combinatorial slight of hand.

*blaring of trumpets in the background in anticipation of startling revelation*


Such a simple 2 PAGE proof HAS in fact been found-it was published by P.H. Doyle and D.A. Moran,then both of Michigan State, in an obscure journal in 1968. It's like most good things in life, pretty simple mathematically-and it relies on a very easy generalization of the Jordan curve theorum to convert a covering of 2-cells (open disks) of a surface S into a countably infinite set of simplexical complexes.(Note,though,sadly it hasn't reduced the triangulation to finitely many complexes.Oh well.) I am proud to present the link to the proof,which I have found posted online. It shocks me that this proof is not more commonly known-most mathematicans I've asked referred me with pained expressions to Rado's proof when I asked about taking triangulations on faith. The only mathematican I was able to find in the textbook literature refer to it was James R.Munkres in his book.
So the mystery is no longer so intractable,students! Go forth and add this beautiful result to your toolbox-we no longer need to take this fact on faith! Spread the word, that this momentously practical result can now be shared by all!

http://www.digizeitschriften.de/contentserver/contentserver?command=docconvert&docid=374534

Andrew L.
The Mad Mind

Re: A Brief Apology................

I needed to take a minute or so out to apologize to Dr.Fernando Gouvea for posting the small excerpt of his email at my blog. It was done VERY innocently to make a point-nothing private or personal is present in the selection. But I was just alerted by a friend-who's much more internet savvy then I am-that such is grounds for a lawsuit since an email is private communication. I was always under the impression emails, like everything else on the internet, was in principle accessible in the public domain by computer experts. I want to heartily apologize to Dr.Gouvea for my innocent error; the post will be edited appropriately and the excerpt removed.
Again,I'm so VERY sorry.
Next time,meaningful blogging (I HOPE).......................
Andrew L.

We Interrupt The Misery Of Human Existence For This Insignificant Blog To Light Meaning In The Darkness Of Mere Being..............

Yello, Netdwellers.
Welcome to my world-such as it is.Who am I? Good question. The answer will slowly emerge on this blog-along with many,many other things. What is this blog going to be about? Well, it'll be about MANY things. That my opinions will be part of the fabric of this place is nothing new-any jackoff with access to a keyboard or touchpad has a blog these days where they rant about everything What makes it unique besides the place where the mathematical sciences live and breathe through my voice. My voice is that of a first year graduate student in pure mathematics-with many issues,ideas and peeves.I decided if the imbeciles who believe George Bush is The Voice Of God and that price of gas is a conspiracy by environmentalists to wean America off gas and take thier precious SUVs from them could have blogs,why not me?
Actually,there was more to it then that. I've never really been a big fan of blogs. Yeah,they're useful for whining in public when no one else gives a damn what you're saying,but they have a tendency to become self-serving and obsessive. So why the sudden 180?
Blame Fernando Q. Gouvêa.
For those who don't know,Dr.Fernando Gouvêa is a professor of mathematics at Colby College in Maine,probably best known for writing the standard introductory text on p-adic analysis. Much more relevant to me,as I've been a native New Yorker all my life and wouldn't know Colby if you dropped me from a chopper into its main walkway-he's the editor,among other things,of the Mathematical Association Of America's Mathematical Sciences Digital Library
webpage. I've been writing for Professor Gouvêa's book review section for almost a year now. Among the books I've reviewed 5 textbooks to date, including Walter Rudin's Principles Of Mathematical Analysis and David Watkin's Topics In Commutative Ring Theory. For the most part, these reviews have gone pretty smoothly, with the exception of the usual grammar (which I don't care about) and me screwing up my facts (which I DO care about,but I'm not above admitting a screw up). He and I didn't really have a major issue until I tried to submit a review about Dover's wonderful new reissue in cheap paperback of Kenneth Hoffman's Analysis In Euclidean Space. I thought such a review would be a wonderful place for me to rant about the criminal cost of scientific textbooks in academia. I submitted the review. A few days later, I got an email from Dr. Gouvêa basically telling me that my review was no place for such commentary and that it exposed the MAA to litigation from the insulted parties i.e. the book publishers. (He DID offer to publish my comments in another forum intended for such commentary,such as FOCUS.)
I was livid and made my displeasure felt in no uncertain terms. In retrospect, I feel somewhat guilty about it. Dr. Gouvea was just doing his job-which,like it or not, it partly to protect the website from legal retaliation over an opinion. But the fact that this was even a real concern is truly tragic in what is supposed to be the Land Of The Free. To make a long story short, after a brief but somewhat heated exchange between us,I revised the review,removed all the commentary and the "safe" version was posted at the website.
I don't blame Professor Gouvea for the incident-he was doing the responsible thing for the website. It's the fact that he felt he HAD to that burned me. In the Land Of King George, Creationist Science, the Patriot Act and the most corrupt administration in our generation's lifetime, freedoms are what they say it is. I remember going to a diner with my late father a few weeks after 9/11-the diner owner was a Middle Eastern immigrant. The guy was practically in terror of any American coming through-he had the place loaded with American flags and said "God bless America" with every other sentence. His eyes looked like he was begging people not to call the police-and meanwhile, people were looking him up and down like he was wearing a .45 Magnum. I remember an Afgani friend of mine running for his life from a group of students throwing rocks at him for 4 blocks in Manhattan at about the same time. I also remember shopping in my local grocery store and a report coming over the radio of them shutting down JFK and beating the crap out of some guy who looked-and I quote-"vaguely Arabic". The time of Red State Rule finally is showing real resistance in the form of the Obama Movement (not so much the man, but the ATTITUDE that's made him the Democratic nominee) . But in the face of all this,the fears of intellectuals voicing thier opinions is a real threat.
We are not free anymore. We Are Property Of The Wealthy. So I can't feel anger towards my editor. Like I said, it's his job to protect the MAA from the dictatorship and the ignorance of those who worship them. As I've said-there's a very real sense of anger-driven change in the air-driven by homeless middle class people who can't heat thier homes and keep burying thier children before thier 25th birthday in a senseless war about ego and power. But change will not come if those who rage against the dying of the light stay silent.
Hence this blog. All opinions here are entirely mine. There is no fact here except those I identify, only passion and opinion, without which there can be no freedom. A change is trying to come. Whether or not it will actualize depends on what Bill Maher so beautifully called The Moron Factor in America. The Moron Factor saddled us with 4 more years of rule this planet will be paying for for centuries. Whether it dooms the Earth with ANOTHER 4 years is a story that will play itself out in the next 5 months.
Hence, the Beginning. There will be more-much more-here in the coming months. Next time-I'll formally introduce myself in a little more detail-and hopefully get to matters mathematical.
And of course,please feel free to contribute to the blog anything you want. And I mean ANYTHING. (Well, not porno, but you get the idea.................)
Ciao,all. A propo, I close with a quote from Kevin Smith:
" Don't have a belief-have an IDEA........................"
Andrew L.