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Prime Obsession
Bernhard Riemann came to the University of Goettingen in 1846 at the age of 19, originally to study theology. The University, however, was home to Carl Friedrich Gauss, "the greatest mathematician of his age and possibly of any age," and the impressionable young Riemann, succumbing to the privilege of Gauss's presence and following his already blossoming interest in mathematics, refocused his studies on the area in which he would soon attain distinct immortality. As early as 1851 he was impressing even Gauss with the results of his doctoral dissertation and in 1859 was appointed a corresponding member of the Berlin Academy. To this honor, Riemann responded with his most famous paper, entitled "On the number of prime numbers less than a given quantity," containing therein what became known as the Riemann Hypothesis.
At the heart of the RH is the Zeta function which, in its basic form, looks like this: Z(s)=1 + 1/2^s + 1/3^s + 1/4^s + ... and which, through some simple algebraic manipulation as demonstrated by the mathematically gifted journalist Derbyshire, can be given in the form (1 - 2^-s)^-1 * (1 - 3^-s)^-1 * (1 - 5^-s)^-1 * (1 - 7^-s)^-1 * ... And it is in this second form which Derbyshire calls "The Golden Key" where the non-mathematician gets the first glimpse of the Zeta function's relationship with prime numbers.
But where this Golden Key appears as this "novel's" turning point--its central conflict-- it is not until Prime Obsession's climax when the Key is at last turned and the Zeta function's true relationship to the prime counting function pi(x)--the number of primes less than a given x--is at last made clear. Along the way, from the introduction of the Zeta function to the final explanation of its relevance to prime numbers (the turning of the Key), Derbyshire enlightens us with clear, mostly English language descriptions of the mathematics involved, as well as plentiful anecdotes that give readers a sense of the life and work of the major figures in the history surrounding the RH from Euler, Gauss and Dedekind in the late 18th century through Riemann's 1859 paper, and from 1859 onward to recent advancements in the '80s and '90s.
The Riemann Hypothesis states that "all nontrivial zeros of the Zeta function have real part one-half." Understanding the statement of the hypothesis is Derbyshire's first mission for the reader. In short, most functions with a dependent variable, say f(x)=x^2-2x+1, have a value for which if you replace x with this value, the function returns zero. In the example given, it is at the value x=1 where f(x)=0. The Zeta function has an infinite number of these zeroes and an infinite number of these is "non-trivial." The non-trivial zeroes come from complex number values. Riemann's guess, his hypothesis, is that the real part of each of these non-trivial zeroes is equal to one-half. The imaginary part can be anything.
Derbyshire explains all of the mathematics in very readable language. It's unlikely that anyone who did well in high school mathematics will not be able to follow Derbyshire's mathematics (and it's unlikely that those who didn't do well will pick up a 400-page book on this topic). The Zeta function is explored from a number of angles--numerically, graphically, algebraically, statistically, and there's even a link between the non-trivial zeroes of the Zeta function and quantum physics! By a larger margin, however, Prime Obsession's intrigue lies in Derbyshire's expositions on Riemann, Hilbert, Turing, Gauss, et al, as well as those modern mathematicians he's interviewed personally. The line between the mathematical half of the book and the historical is clearly defined; the odd-numbered chapters are devoted to the former, the even to the latter.
Those fans and foes of Derbyshire's most public line of work as a journalist/editorial writer for National Review will be comforted to know all political polemics have been set aside. John Derbyshire gives a virtuoso performance as an informed journalist and maintains his stance as a personable and careful guide through a sometimes difficult terrain. Anyone with some interest in the topic will find it hard to put down Derbyshire's book once begun. If we are lucky (hint, hint, JD) perhaps Derbyshire's next book will cover the newly-proven Poincare Conjecture ...
You can purchase Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, carefully read the book review guidelines, then visit the submission page.
Who isn't obsessed with the leader of the Autobots, Optimus Prime?
It may be a fine book, but I see no reason to do anything to help line the pockets of John Derbyshire. If I decide to read it, I'll get it from the library. Vote with your feet.
Ummm...what would its peers be? Just how many "classic" math books does the lay-person have now?
Could it be that the lay-person wouldn't be interested in any book about math, no matter how well written?
I dunnnoooo...almost sounds completely probable.
Superior mathematician.
The answer? 42.
The question? What is 6 times 9.
The part he didn't tell you is that the question/answer machine was devised by a group of aliens that had 13 fingers. They wouldn't count in base 10, they would count in base 13, naturally.
6 x 9 does in fact equal 42. In base 13.
Check out the best P2P sharing website: MEDIACHEST.COM
Why is it, that if you have studied math that people get you these books for Christmas, etc. People say, "Wow, he's into math, I'm sure he'd like that", when books like this are written for the lay person, as a fun introduction to the subject. People don't get Literature majors "Shakespeare for Dummies".
Rhymes that keep their secrets will unfold behind the clouds.There upon the rainbow is the answer to a neverending story
One man's propaganda is another man's editorial opinion.
Why must we use such slanted terms to describe the views of people we disagree with?
perhaps I just answered my own question.
There's a Mercedes gap too. I want one and can't afford one, but it's not government's job to do anything about it.
You might check out my current MD5hash Challenge. Some people have told me that it is impossible to solve, some have said that mathematically it is solveable.
Not quite related to primes, but close and can certainly create an obsession. Also, look behind the scenes for something simpler to solve.
The line between the mathematical half of the book and the historical is clearly defined; the odd-numbered chapters are devoted to the former, the even to the latter.
It's been a long time since I read Douglas Hofstadter's "Godel, Escher, Bach", but didn't it use the same kind of formula, alternating between dialogs and discussion chapters? I really loved that book. I've heard a lot of criticism of it from mathematicians and musicians, but that noise always sounded like so much professional nitpicking to me.
ISBN 0452285259 = 3 * 1009 * 149417
The author must be sad.
I really don't know a thing about the guy. What is repugnant about him?
Try Mathematics for the Million by Hogben - it's fantastic, and the most coherent Calculus explanation I've ever encountered.
Need Geek Rock? Try The Franchise!
Let serve as motivation the fact that anyone who can actually proof (but not disproof) the Riemann Hipothesis will won a prize of US$ 1E6 (i.e, US$ 1000000.00)!
First: the guy is from Long Island NY.
Second: Here is a definition of the word propagandist.
-Hope that makes you feel less stupid now.
Definition of propaganda: information, facts, or opinions that you don't agree with. Therefore, you want them belittled or censored.
Mathematics And Sex (2004)
Pi: A Biography of the World's Most Mysterious Number (2004)
Chance: A Guide to Gambling, Love, the Stock Market and Just About Everything Else (2004)
Entanglement: The Unlikely Story of How Scientists, Mathematicians, and Philosphers Proved Einstein's Spookiest Theory (2003)
The Mathematical Century : The 30 Greatest Problems of the Last 100 Years (2003)
The Golden Ratio : The Story of PHI, the World's Most Astonishing Number (2003)
When Least Is Best : How Mathematicians Discovered Many Clever Ways to Make Things as Small (or as Large) as Possible (2003)
The Honors Class: Hilbert's Problems and Their Solvers (2001)
An Imaginary Tale (1998)
e: The Story of a Number (1998)
Just to pick some recent examples (i.e. not including the masterpieces of Martin Gardner and other recreational mathematicians in the 1960s and 70s, and apologies if I left off your favorite). I would agree, however, that good pop-math books are a great deal more rare.
Tiller's Rule: Never use a word in written form that you've only heard and never read. You will end up looking foolish.
http://www.amazon.com/exec/obidos/tg/detail/-/0309 085497/qid=1103745016/sr=8-1/ref=sr_8_xs_ap_i1_xgl 14/104-9691547-0499969?v=glance&s=books&n=507846
Slashdot's vendetta against Amazon is rediculous. Freedom of choice is more important than silly patents. You may click the link in the article to buy it from B&N, or this link to buy it from Amazon.
Why would you want to post: "I'm ignorant, and I want everyone to know it!"?
...as long as it's our (Slashdotters) choice.
It's called white space. Look into it. Humans parse on it much faster then they parse on operators.
I currently have no clever signature witicism to add here.
After working at Initech for a year and not using any of my math skills, this was a welcome dip in the math kiddie pool.
I would probably need to do a few laps before I could go playing around near the high-dive again or anything. I don't think this speaks to my grasp of the subject or my intelligence, but to my complete abandonment of study for a long period.
This wouldn't be a book to get someone that works in a heavily mathematical field, but its a great choice for the coder in your live that likes math but has to write boring code all day to pay the bills.
And here I was a book about Samus Aran... Ah well.
Whoever stated that signature sizes should be limited to one hundred and twenty characters can just go ahead and kiss my
Sense of humor turn on
Does it hurt to hear them lying? Was this the only world you had?
My favorite book on math is The Mathematical Tourist by Ivars Peterson.
It's very readable, and has chapters on interesting stuff like knot theory, cellular automata and primes.
I highly recommend it. It isn't going to turn anyone into a math professor, but it is very interesting reading.
I've heard a lot of criticism of [Hofstadter's "Godel, Escher and Bach"] from mathematicians and musicians..
Of course mathematicians and musicians will criticize the book. It challenges the very logical foundations upon which their theories are based. Perhaps the most dogmatic disciplines outside of Christian fundamentalism are the sciences. It's the age old case of man believing his logic is impenetrable, where in reality it amounts to nothing more than the finger pointing to the moon. The sciences may have theory-this and theory-that, but they will never in an infinite amount of lifetimes be able to run the full course of reality with their tools. And that's a fact that mathematics itself asserts.
I once ran into an old friend of mine I knew back in middle school. He has a twin brother that, over ten years since he left highschool is still in university plugging away at some mathematics doctorate. I silently asked myself. What are his aims, his purpose? To solve the universe? It was clear he was always a brilliant student; I'm sure his I.Q. is off the chart, but ambitious mathematicians have to learn to let go. All their combined knowledge amounts to one drop in the Pacific ocean of reality.
If you take a liking to esoterics and esoteric knowledge, you will notice there's a smooth transition between scientists and esoterics; that is, there is the complete scientist who deems it worthless to search for truth in the unseen and the non-constant -- that the only universe worth pursuing is the visible and measurable universe. Then you have the transition scientists (Godel, Heisenberg) who through experiments of their own come to the realization that the sciences are not adequately equipped to be able to completely ascertain truth and that there must be more -- another form of reasoning perhaps outside the realm of postulation and thought where paradox becomes perfectly logical, but they may at the same time reserve making any definite statement about one or the other, effectively taking up the agnostic position.
Finally you have the esoteric, who acknowledges science as a method for ascertaining some degree of truth, though a limited portion of it, but through experience is assured that complete truth is to be found outside the dualistic disciplines of science and philosophy. Zen masters, enlightened sufis or Christian mystics might fall into that category. Due to their highly honed awareness, they are able to acertain more in a ten minute period about the laws of life than ten scientists could over the course of a hundred years. These, quite rightfully are higher order human beings. I imagine it's the same sort of higher order, perhaps to a somewhat lesser degree, that allows the idiot savant to blast through hundreds of years of perpetual calendars or calculate ridiculously large numbers in their heads almost instantaneously. Savants appear to have a firm, instinctual understanding of computational causality. They may very well be solving our mathematics from some other conscious plane the rest of humanity haven't yet achieved, a plane that allows them to blaze logical trails in parallel and from a figurative bird's eye view, through our "world." The same thing goes for enlightened men. Though we may plug along attempting to understand the unverse with 4-bit effectiveness, they do it from a conscious vantage point that may exceed a figurative 1024-bits or more. They simply know.
- IP
I know very few mathematicians and math students who aren't familiar with the Riemann Hypothesis (largely due to the million dollar prize associated with its proof), so a book exclusively on such a topic probably wouldn't interest too many people. What makes this book interesting, at least to me, is the Math History covered in it. In particular, the author goes into great depth into the personality and character of each of the principle figures in this book: the anecdote regarding Hilbert's torn pants, Gauss's (perhaps justified) arrogance, and Riemann's quiet nature. All of these aspects of the book add a lot more depth to the people behind this problem, and I find that to be far more valuable, as a mathematician, than yet another essay on the Riemann Hypothesis.
I agree with the reviewer's sentiment that the book is well written, and it is very enjoyable. The author writes in a very audience-centric fashion, even going as far to discuss the "scaffolding" of the book itself (all of the "hard math" stuff is found in odd chapters, the author had debated putting this information in only the "prime" chapters, but then said "there is such a thing as being too cute.")
Anywho, if you have a math friend you need to buy a gift for, definitely consider this book.
I have discovered a truly remarkable sig which this margin is too small to contain.
Those interested in his other writings should check out John Derbyshire's homepage.
These comments do express the opinions of my employers, and, personally, I think they're complete rubbish.
Oh excuse me
Warning: The following post requires Humour 2.1 or higher
Was that review English?
"I use a Mac because I'm just better than you are."
He'll do this for a few more years, and then, in a fashion like manic-depression he'll waffle to the right again.
" am not of the opinion that anyone who disagrees with me is just spreading proaganda " Yet, that is exactly how you came across. Vicious opinion by Brock is "truth", but vicious opinion by NR is "propaganda". You have once again made use of the real definition of the word "propaganda": information that I do not agree with.
... if you don't know (immediately), how can you expect them to know?
Z
The arrogance of your comment was compounded by the atrocious spelling.
I'm in charge in Moria!!
Don't blame Durga. I voted for Centauri.
Which ones specifically are rubbish? I checked a few of his opinions, and they were quite well rooted in fact.
People get those gifts because they try. They don't understand math at all, but they know that you do "something mathy".
Exactly right. They are trying to get you something that they think you might like even though they don't know very much about math. Instead of the grandparent getting all hot under the collar that his family and friends dare insult his grant intellect by purchasing him a "Math for Dummies" book (as he seems to think this historical work is), he should feel gratified to know that he family cares enough about him to actually put forth some effort to getting something that attempts to match his interests. There are lots of people who simply buy generic gifts for family like socks or shit like that. Isn't this book a lot better than a gift like that?
Reading the grandparents rant, I was reminded of an article in The Onion awhile back about some film snob getting all upset because his family -- damn their incompetance! -- dared buy him the widescreen edition of one of the Matrix sequels when he actually wanted the letterboxed edition (opportunity for karma whoring here if someone can link to it). For chrissake, your family and friends are trying their goddamned best and you get your panties in a bunch over details? That's so incredibly childlike, I can hardly believe this above "rant". Christmas isn't really about getting exactly what you want -- at least once you're an adult it's not. Christmas is just an opportunity to get together with loved ones and exchange gifts as a token of affection. It doesn't have to be the "perfect gift"; as long as it's somewhere in the ballpark you should feel happy that your family is at least aware of your interests.
GMD
watch this
BTW, this Bourbaki guy is very interesting. Especially since he is not a real person. It was just a joke invented by a group of famous mathematicians. Under this name they wrote a number of very good books on methematics. A Wikipedia link.
Z
I just started reading
The Music of the Primes : Searching to Solve the Greatest Mystery in Mathematics
which covers also covers the Riemann Hypothesis.
Other books I've read in the genre include:
The Golden Ratio : The Story of PHI, the World's Most Astonishing Number
In Code: A Mathematical Journey
Fermat's Enigma : The Epic Quest to Solve the World's Greatest Mathematical Problem
Euclid's Window : The Story of Geometry from Parallel Lines to Hyperspace
Haven't Read this one yet but I own it:
Gödel, Escher, Bach: An Eternal Golden Braid
read the link in the parent's post, then go to his website and read a few of his editorials... He's more concerned about men being "manly" than most straight men I know. Is he hiding something about himself?
I read this book about six months ago and greatly enjoyed it -- it's one of the best 'popular' explanations of a math topic I can recall.
.
And it was the only time I'd heard of John Derbyshire. When I saw a political blogger slag him off a couple of weeks ago, I thought "this can't be the same guy who wrote the Riemann book!"
Maybe I should get out more. .
whats special about the prime chapters of the book?
Why not cite his own explaination of his homophobia?
These comments do express the opinions of my employers, and, personally, I think they're complete rubbish.
Just what I said
The lucky part about that would be that someone had finally proved it, and that a consensus of mathematicians accepted the proof. To the best of my knowledge, the current state is that one man claims to have proved it but that the verdict's still out.
Dewey, what part of this looks like authorities should be involved?
"n.
1.The systematic propagation of a doctrine or cause or of information reflecting the views and interests of those advocating such a doctrine or cause.
2. Material disseminated by the advocates or opponents of a doctrine or cause: wartime propaganda. "
Seems the usage was correct.
The revolution will NOT be televised.
Claiming that anti-homosexual bigots are really secretly homosexuals makes as much sense as claiming that anti-African-American bigots are secretly Black. Tell that to Jesse Helms or Robert Byrd.
Don't blame Durga. I voted for Centauri.
His book might be good but make no mistake about it, John Derbyshire is a creepy right-wing bigot.
You can read his weird daily posts over at National Review's blog The Corner.
Check out this article here where he hints at the long standing right-wing fantasy that white caucsians are, in fact, smarter than the rest of the world.
There is much more where that came from. Feel free to read his archive here.
If I were a conservative, I wouldn't want Derbyshire's misogyny and homophobia associated with my beliefs. There are good conservative values, but those aren't among them.
In any case, when I read Derbyshire's weak attempts at arguments to support his prejudices, I find it difficult to imagine he could write anything worth reading. At least my prejudices operate on the individual level, rather than condemning an entire gender. It doesn't surprise me to read that he's not very good at math; he's not very good at logical argument, objectivity, or understanding of the human condition. He's taken a personal psychological hangup and dressed it up as though it were a political position.
I happen to have studied enough mathematics for MSU to grant me a master's degree and I didn't find Derb's book the equivalent of "Shakespeare for Dummies."
It was more like the nuts and bolts of how the Bard lived while he was writing Hamlet and how various folks who have come after have interpreted the parts.
To be quite honest, after doing all those fun maths in school, my career has generally involved little more than algebra. It was a rare pleasure to solve an order 360 polynomial using a secant method gradient descent. Then, sadly, to hand the algorithm to another guy to code up. Something my high school senior daughter did last year in AP Calc.
Thus the popular math book provides a math-mitty (as in Walter) to remember when he ran with the big dogs.
To anyone familiar with calc and number theory, the notion of bringing the two together is a mind-boggling coolness. When mathematicians see such things the response is akin to worship.
mmmm pie
In fact the odds are close to 60% against.
Consider a set of size n (with n fairly large) and a random function f from that set back to itself. How many pairs (x,y) are there with f(x)=y and f(y)=x?
Well the number of pairs in the set is n*(n-1)/2 which is approximately n^2/2. Each pair has odds 1/n^2 of satisfying the condition. It turns out that pairs are not perfectly independent in satisfying/not satisfying (if (x,y) satisfies the condition then (x,z) cannot for any other z), but in a detailed analysis it is close enough to independent for what I'm going to say next to still be true.
The situation that we have here is that we are observing a large number of unlikely possible events, with a ratio between the number and the probability indicating that we expect to see a fixed amount on average (in our case 0.5 since the number of pairs is n^2/2 and the probability of a given pair satisfying our condition is 1/n^2). How many do we deserve? Assuming that the number is large, probability says that the distribution that we see is well-approximated by the Poisson Distribution, which says that the odds of seeing k occurances is exp(-lambda)*lambda^k/k! with lambda being the expected number of occurances.
Therefore the odds of our seeing 0 occurances are exp(-0.5)*0.5^0/0! = 0.60653065971263... - hence my claim that they are 60% against.
If you had only one finger, in which number
system would you naturally count?
The answer is: base 2. (Think: computer)
Given N fingers, the "natural" number system is
base N+1, not N.
Hasn't the genius of John Woo taught us all that single bullets can stop freightliners in their tracks?
His writing style is horrible. He needs an editor desperately. Prime Obsession does contain some interesting mathematical tidbits and some interesting historical anecdotes but overall it's just a really dull read.
"sweet dreams are made of this..."
While you are reading this book, put your computer to work helping to prove the hypothesis in the Zetagrid project (see my short summary of the project here). If your computer can run Java applications, it can run the small ZetaGrid client. In the 3.3 years the project has run, participants have discovered almost 1 trillion "nontrivial zeros of the Riemann zeta function."
You are talking about Perelman who seems to have given an outline of a proof of the Thurston Geometrization Conjecture which, I think, contains the Poincaré Conjecture as a special case. So he has allegedly proved something much more general than Poincaré.
"sweet dreams are made of this..."
People like him do make me a little sick to my stomach... but I'll still read his book. I'll buy it used or borrow it from the library.
The modular division used to make a check digit on the end of ISBN numbers is fascinating. I learned all about it in my number theory class I took last fall. I would explain it here, but...
...I don't really remember how it works.
Sorry.
-Tim
Interesting.... wonder if they still use French to describe the moves.
Also good of him to appreciate the very urban use of "Word!" as a greeting. "datanauts" are always cooler when they're into 20 yr old black expressions.
The revolution will NOT be televised.
I noticed the book sitting on the downstairs couch, and gave it a read. Personally, once I realized that the Derbyshire who wrote the book was, indeed, the Derbyshire of Andrew Sullivan's Derbyshire Award, I was impressed at the lack of disgusting bigotry in the book. He doesn't even take a single cheap shot at Alan Turing.
Now there's a man who knows how to separate his two personas.
--grendel drago
Laws do not persuade just because they threaten. --Seneca
Nice to see you ripping him from behind a AC post. Derb's one of the more entertaining writers around these days, and it's refreshing to find someone with multiple interests in such divergent fields.
But of course, he's on the other side of the political spectrum from you, Mr. Coward, so none of that matters. Tell me, what makes him a "creepy bigot", Mr. Coward? Is it that he opposes gay marriage? So do I, comrade. Better pencil me in for the next re-education camp. Or maybe it's his belief that perhaps we should be focusing more on Arabic and Muslim suspects at airports than old ladies? Well, count me in on this one too. God, I'm so insensitive. Maybe you're referring to his criticism of the left for their undying support of terrorists like Yassar Arafat while considering Israel the focus of evil in the Middle East? Once again, I'm with the creepy right-wingers on this one. See, I agree that these people are old fashioned Jew-Haters, wrapped in a respectable leftist cloak of political correctness. Anti-Semitism is so passe anyway, eh?
Slashdot NEEDS a little more balance in its political coverage.
Life is hard, and the world is cruel
Thanks, I'd seen many that pointed out slashdot's 120 character limit on sigs, and I thought "Hmm, how can I take that idea, and nerd it up." This is what I came up with ;)
Your sig is a remarkably amusing send-up of a tantializingly short note by a famous mathematician concerning one of the major mathematics problems of all time, whereas my sig just makes a pun on the simple physics equation "f = ma" and a quote from an old SF movie.
Surely your karma will soon exceed mine by a long shot. I'm not worthy, I'm not worthy...{sorry, another old movie quote}
Tag lost or not installed.
Chomsky DOES get away with it...the fact that you've reasonably pointed this out, and got an absolute karma-reaming proves that Chomsky would love this place. The way things are going, you have to wonder how long it is until Democratic Underground and Slashdot start some sort of editorial collaboration.
Life is hard, and the world is cruel
You're thinking of the hat-check problem. That is the question of what the odds are of a bijection from a set back to itself having an element mapping to itself. That is a different problem.
First the minor quibble: we don't know that it is a bijection (well it might be, but I don't know that). This is a quibble though, because for bijections and regular functions the answer turns out to be the same (but the convergence to that answer is different).
Now the major one, here we are looking for 2 distinct elements, one of which maps to the other and the other of which maps to the first. That is a more complex arrangement, and significantly reduces the odds.
If you're going to refer to Derb as a "Propogandist", then please have the courtesy to apply the same standards to liberal and leftist writers. If you reference Michael Kinsley or Noam Chomsky, please refer to them as propogandists as well.
Derb writes for National Review. It's a conservative opinion magazine. Does that make it propoganda? Then, is The New Republic or Slate propoganda as well?
So, is all political opinion propoganda then? Or just right-wing political opinion?
Life is hard, and the world is cruel
Anyway, Derbyshire's opinions can be annoying if you're a democrat (and I am, BTW), but he's generally an entertaining writer, on whichever topic he chooses to write about, and he has a math puzzle at the end of each of his Diary entries (see his website)!
I say, if you're worried about supporting Derbyshire's opinions by way of buying his book, keep in mind who he writes for in his editorials (generally conservatives who already agree with him) and remember he's getting a paycheck as well. The Derbyshire I know from Prime Obsession may be the 'real' Derbyshire :) This theory reminds me of a Kurt Vonnegut book called 'Mother Night,' where the main character becomes a fierce Nazi propagandist (not that I in any way would compare Republicans with Nazis; the ideas which I'm relating are the only similarity) purely for professional reasons. I'm assuming he's really conservative, but I'll bet he could write better opinion peices if he wrote for other than the National Review...
There are lots of people who simply buy generic gifts for family like socks or shit like that. Isn't this book a lot better than a gift like that?
No. There are a lot of people who like to say "it's the thought that counts", but what poor gifts show is a lack of real consideration. Think about it. Do I really show I'm thoughtful if I get someone a shitty MP3 player because I heard they like music? Or rather do I show that I simply can't grok their specialized needs, and instead of admitting that their devotion to music is so far beyond my grasp that I have no better choice but to give them cash (or some generic gift that everyone needs)? Personally, I prefer to be surrounded by friends with abilities I can't touch in fields of expertise I barely know. None of that "I know you're a nurse, so I got you some cotton balls because that's the limit of my ability to understand nursing" bullshit. Nobody should pretend to know what the other needs in their specialty. That's the thought that really counts.
Christmas is just an opportunity to get together with loved ones and exchange gifts as a token of affection. It doesn't have to be the "perfect gift"; as long as it's somewhere in the ballpark you should feel happy that your family is at least aware of your interests.
Honestly, I've never felt that giving gifts of any kind showed real interest. I've always been happy with just the "get together" part. I'll often pay for the meal (or whatever), but I'm unlikely to show up with something hastily bought and pointlessly wrapped. And nothing I ever give comes with the assumption of an "exchange". I think it's childish to keep track of personal relationships based on who owes who what "gift".
Not too surprising that his political views aren't included in this book, seeing as how he's not a lefty.
If he were, of course, they'd have to change it to fiction.
The task specified different files. So you're looking for an element in the kernel of f^2 that is not in the kernel of f.
This matters because there are about 38% odds that f^2 has a non-empty kernel, but all elements of it are in the kernel of f.
interesting, such a long thread and no mention of david berlinski... before i got to Hofstadter's GEB, I went through 3 berlinki books that were just as great... a tour of the calculus, the advent of the algorithm and newton's gift
Can't believe nobody has mentioned this yet (maybe they have?), but this book (I think it is the same book) can be read for free online at the National Academies Press
I've started it and it is very good so far. Haven't had time to get past the first few chapters unfortunately.
Nothing disturbs me more than blind loyalism towards some unrealistic and over-idealistic notion of one's nationality.
I've read most of the book even though I don't normally read math books. I picked up this one because I was familiar with the author's political commentary and I knew his writing was easy to follow and pleasantly written.
Most of the book is pretty easy to follow, but there are some concepts near the end that are difficult to wrap your mind around even if you are able to follow the individual steps (which the author makes it easy to do).
I often don't like the choices people make, but I like the fact that people make choices. That's why I'm a conservative.
"Wherever there is a jackboot stomping on a human face there will be a well-heeled Western liberal to explain that the face does, after all, enjoy free health care and 100 percent literacy."
That essay is one of my all-time favorites.
I think you may have misread me; I didn't stop reading the book when I realized who he was, though I felt a strange cloud of duality overhanging the whole thing. I thoroughly enjoyed the book, and I found the part about the decimation of the Gottingen mathematics department in the early 1930s (a legacy handed down from Gauss, etc., to Hilbert, who watched it die), I was truly touched.
And yeah, Andrew Sullivan is a bit of a tool sometimes. I read his blog, sure, but I read Little Green Footballs, Ted Rall's column, ESR's blog and This Modern World as well.
--grendel drago
Laws do not persuade just because they threaten. --Seneca
I didn't actually purchase the book; my father did, possibly from the discount rack.
Turing's death was indeed tragic. His house was broken into, he reported the crime, his homosexuality was discovered, he offered no defense, believing that he had done nothing wrong. He was offered a choice between prison and estrogen shots. After a year or so on the drugs (which were not without their side effects), he killed himself.
The story infuriates me every time I tell it. A brilliant man, to whom we all owe a debt of gratitude for founding our field, struck down in the middle of his productive years by stupid bigotry. What a waste.
--grendel drago
Laws do not persuade just because they threaten. --Seneca
Actually, it was even more stupid: The book was asking what the total temperature was of all the stars. Averaging temperatures at least makes some kind of sense, but you won't convince me that two people put together in a room have a temperature of 72 degres Celsius.
You know, old ladies don't seem to be prime with Muslim to me...
(Yes, I'm raping the term, but comedy has its needings, folks...)
anyway i was at the bookshop and found this nice ...- /1579 550088/002-3007275-6926447?v=glance
book "A new kind of science" by wolfram.
it's about patterns
anyway check it out at:
http://www.amazon.com/exec/obidos/tg/detail/
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i think there we have a future milionair and he's
def. on the right path to proof that riemann funny
theorem. we have to stop looking "inside" a
system for a solution, e.g with math, but look at
the pattern. how we count. the keywoard is
prolly "nested".
Irony is a virus, and lots of people seem to have nortonized.
#!/usr/bin/english
Why didn't anybody else notice this?>?!?!?
free speach
Did you mean: free speech
The History of Pi by Petr Beckman.
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