mm-1659 You don't even hint at what it is you're trying to prove. So how could anyone tell whether you're right or wrong? -- Mike Hardy -- Ooops! Sorry! I forgot one essential line: The complete task was: Let n be an integer such that n*n is divisible by 3. Prove that n also is dividible my 3. What I meant was that is the sum of its digits, call it sd was dividible by \ 3, then (sn)^2 also would be. Sorry! :-) -- Ronny Mandal Prove this: Let n_1, n_2, ..., n_k be k integers and p a prime if p divides n_1*n_2*....*n_k then p divides at least one of the n_i. The result you seek readily follows by putting p = 3, k = 2, n_1 = n_2 = n. Note that by talking about the sum of n's digits you are obscuring the real question which is How does a prime divide into a product of integers? For which the answer is By dividing into one of those integers because it cannot split with part of it dividing into one integer and part of it dividing into another (or others). Here split means factor non-trivially and part means one of those non-trivial factors. The particular case with k = 2, but n_1 and n_2 possibly distinct, is due to Euclid. A rigorous proof of Euclid's theorem (which the answer above is not) can be found in Hardy & Wright. The general result can be proved by writing n_1 n_2 n_3 ... n_{k-1} n_k as ((...((n_1 n_2) n_3) ...) n_{k-1}) n_k and applying Euclid's theorem first to (...) n_k, then to (...) n_{k-1}, etc. I.e. it is a proof by descent. You're committing one of the most frequent errors: making a simple problem complicated. Don't do it by thinking about sums of digits. -- Mike Hardy days. My association with the Department is that of an alumnus. Except that this doesn't work! You seem to be saying that if the sum of the digits of n is equal to s, then the sum of the digits of n^2 will be equal to s^2. But this is false, even for multiples of 3: the digits of 6 add up to 6, but the digits of 6^2 = 36 add up to 9, which is not equal to the square of 6. Where exactly did you use the sum of the digits [of n] is divisible by 3 in the argument? Nowhere! Your actual argument is if n is divisible by m, then n*n is also divisible by m (which, really, is what you are trying to prove, for the special case of m=3; you are invoking a more general fact to prove a simpler one). You are not using the sum of digits to conclude anything about n^2, probably because it is difficult to write down what the sum of the digits of n^2 is in terms of the sum of the digits of n. Much better to simply prove your assertion that if n is divisible by m, then n*n is also divisible by m, and then apply it for the case m=3. I showed you how to prove that in an earlier response. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu Two minor technical problems with this approach: 2. The opposite is not generally true, you can't use any m, it has to be prime (or at least square free). 4|2^2 but not 4|2. I know these are only typos on your part ... but the OP may not realise this. Prove the contrapositive instead. Suppose n is not divisible by 3. Then n = 3k+1 or n = 3k+2. If n = 3k+1, then n^2 = 9k^2+6k+1 and then n^2 = 3(3k^2+2k)+1. If n = 3k+2, then n^2 = 9k^2+12k+4 and then n^2 = 3(3k^2+4k+1) + 1. So, n^2 leaves a remainder of one on division by 3 and is not divisible by 3. can anyone help. I'm using a text called algebra and trig by larson hostetler i'm getting stuck in understanding the steps used to simplify the following the steps provided are can anyone explain this in more basic steps? _If_ one had a rational expression with, let's say, (x-1) raised to the power -1/2 on the bottom then one could see a great deal of sense in multiplying top and bottom by (x-1) raised to the power 1/2 for these reasons: * multiplying the top and the bottom of the expression by anything (other than 0) won't change it's value, so it is a legitimate thing to do, and * multiplying X^Y by X^{-Y} gets rid of the power, so it is a useful thing to do. For example, _if_ the rational expression was (x-1)/(x-1)^{-1/2} one would get [(x-1)(x-1)^{1/2}] / [(x-1)^{-1/2}*(x-1)^{1/2}] which is (x-1)^{3/2}. Sadly your expression isn't (x-1)/(x-1)^{-1/2}. Your expression, x - 1/(x-1) - 1/2, seems to be simple enough as it is. Btw, there's an altogether quicker way to deal with (x-1)/(x-1)^{-1/2}: * move (so to speak) the term with the negative power from the bottom to the top, and * while it is moving (so to speak) change the power's negative sign to a positive sign. Thereby getting (x-1)(x-1)^{1/2} = (x-1)^{3/2}. (x-1)/(x-1)^(-1/2) The easiest way to simplify the expression is to use the rule: If an exponent is negative, it becomes positive when we move the expression from the numerator to denominator or visa versa. (x-1)/(x-1)^(-1/2) = (x-1)/1 * 1/(x-1)^(-1/2) = (x-1)/1 * (x-1)^(1/2)/1 = (x-1)^(1)*(x-1)^(1/2) = (x-1)^(1+1/2) = (x-1)^(3/2) We need to get rid of the negative exponent. For example, y^(-1/2)*y^(1/2) = y^0 = 1. If we just look at the denominator of (x-1)/(x-1)^(-1/2), we can do the same thing as in the example when we multiply the denominator by (x-1)^(1/2). To do, that we also need to multiply the numerator by (x-1)^(1/2), keeping the fraction as it was before. So we multiply by (x-1)^(1/2)/(x-1)^(1/2). But (x-1)^(1/2) = sqrt(x-1). [Standard JSH .] The world will never conform itself to your infantile fantasies, Harris. How many mores hundreds of times do you have to observe that, before it sinks in to you? Your pathetically inept fiction has never even deceived a newsgroup. Get help, Harris. with For *years* you have been wrong, one time after another. You are wrong again Harris You have got nothing Harris. Nihil ex nihilo. Wake up Harris you have got nothing. James.... can you really not see what a total idiot you are? What a liar you \ are? Can you now really wonder why *everyone* thinks you are a fool? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: \ 1.9 primary) id j1MDVgh15578; 1. Assume f(x, y) is a differentiable function in two variables and P is a plane, such that the tangent plane at any point on the surface z = f(x, y) is parallel with P. Show that there exists numbers a, b, c such that f(x, y) = ax + by + c for all x, y. the curvature of the curve given by x = cos(t), y = sin(t), z = t^n has constant curvature. 3. If u , v , w are three vectors in space, show that with equality if and only if all vectors have the same lenght and they are perpendicular to each other. Geometrically this implies that for the parallelepiped having one vertex at the origin and three of its edges the vectors u, v , w and say, volume one, the total lateral area is at least 6 with equality achieved only if the parallelepiped is a cube. moving in a plane. 5. Assume that S is the surface given implicitly by a(x^2) + b(y^2) + c(z^2) + dxy + eyz + fzx = 1 for some real numbers a, b, c, d, e, f. Show that if the intersection of S with any plane is the empty set, a point or a circle, then S is a sphere centered at 0. + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + And would you like some fries with the solutions? Aristotle Polonium + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + Justin, There's some protocol and etiquette here of which you may not be aware. When posting to math newsgroups (and may be a.m.undergrad in particular), subscribers usually won't answer a list of hw questions dumped in a post. Instead, say more about the progress you've made on each problem and what your difficulty is, and other posters will usually offer you a solid hint (or even a solution that has some holes that need to be filled in). Travis --Lynn Yes, very nice indeed. -- -- Geo. Michael Henry No! Bad dog! I said sit! anonymous by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: \ 1.9 primary) id j1MDVfh15569; Does anyone know the equation of the graph that makes an M with the middle point on the origin and the sides approaching negative infinity? i could use some help :) Did you really want the sides approaching -infinity, or just to have very steep slopes? If you really want the asymptotes, how about something like x^2/(x^2 - 1) + 30 * | x |, where you can change the 30 for aesthetic reasons. --Lynn There are lots of functions that will do the trick, assuming that there's some leeway in the interpretation of 'makes an M', but the simplest is a quartic (fourth-degree) polynomial. Since the sides have to go down, the leading coefficient (coeff. of x^4) will have to be negative. You want it to be tangent to the x-axis at the origin, so 0 will have to be a double root. You also want it to cross the say at -1 and 1. Can you write down a quartic that has -1, 0, 0, and 1 as its roots? Brian by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: \ 1.9 primary) id j1MGA4h30563; give p(x)= (9^x)/(9^x+3) find p(1/2001)+p(2/2001)+p(3/2001)+...+p(2000/2001) Calculate p(t) + p(1 - t). Can you see how that helps? (I confess that this trick took a while to find.) Ken Pledger. by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: \ 1.9 primary) id j1MGA4v30587; I know that I can use the Laplace-transform to solve linear differential equation, by transforming the equation, solve it, and then use the inversion-formula. My question is; why does this work? transforms g(s) is a 1-1 transformation. It has the fortuitous property that the transform of a derivative is essentially multiplication of the transform by s. So differentiating in the original function space corresponds roughly to multiplication in the transform space. Solving for the solution of a D.E. is a calculus problem, whereas solving for the transform g(s) of the solution in the transform of the D.E. is an algebra problem. But since L is a 1-1 transform, if we can figure out the inverse of g(s) which we have found algebraicallly, that inverse must be the solution to the original D.E. Clear as mud? --Lynn I'm James!!! are you pretending to be me??? the Mail-To-News-Contact: abuse@dizum.com A multivalued function is a function that assumes two or more distinct values in its range at least one point in its domain, also known as a multiple-valued function (Knopp 1996, part 1 p. 103). While these functions are not functions in the normal sense of being one-to-one or many-to-one, the usage is so common that there is no way to dislodge it. I did not add the scare quotes; they're in Mathworld's original text. This is not quite the ringing endorsement of your position that you make it out to be. -- Michael F. Stemper Visualize whirled peas! listed above. 1) If The state of being positive or being negative can only be intuitively [whatever that means] applied to numbers in the real domain, and i is not in the real domain, then how can you claim that i is positive? 2) i is not defined as the solution which returns the positive square root of negative one - such a definition would be absurd in light of your comments; see (1). i could be defined as one solution, arbitrarily chosen, to the solution x^2 = -1. Better would be to define the complex numbers as ordered pairs of reals (a,b) with (a,b) + (c,d) = (a+c,b+d) and (a,b) * (c,d) = (ac - bd,ad + \ bc) and then define i = (1,0). Matt On the contrary, it shows the problem you have with mathematics quite clearly. night, algebraic again, redoing to divisible themselves, My theory is that Harris indulges in 'magical thinking'. It resembles the cargo-cult thinking in south Pacific islands, where people would construct little models that looked like airplanes in the hope that the airplanes would return again and bestow various goodies as they had done during the war. Harris constructs what looks to him like mathematics. He has faith that whatever that I think goes back to his junior high days when he was identified as 'gifted' and given special treatment, and then again when he got a scholarship to Vanderbilt - he concluded that because of his gift, he didn't need to work hard like other people - his ideas were just automatically golden. Perhaps it's an example of the downside of labelling people as 'gifted'. It has something in common too with the thinking of compulsive gamblers. The big win is always just about to happen. I met such a guy once in Las Vegas - he had just had a few wins, and he was quite seriously convinced that he was on a 'hot streak', and he was going to play it for all it was worth. The gambler has this sense that he is someone special, that destiny wants him to win. He throws the dice with the same kind of indomitable confidence that Harris has when he 'throws his ideas out there' - then when he goes bust, he thinks it is because the fates somehow inexplicably turned against him just when he was about to clean up, and if he had had just a few more dollars, it would have turned around again. Or he thinks he was cheated somehow. After a while he forgets all the bad parts and losses, and just remembers the thrill of almost having it in his grasp, and he starts over again. He has this since that because of his gift, he is OWED success - it is an injustice when he is denied - against God's will, even. When people oppose him they are acting against the will of Fate, they are cheating and lying, and righteous indignation and fantasized smiting of enemies of almost Old Testament proportions ensues. And of course, like the gamblers and the cargo-cult believers, and maybe the believers in voodoo dolls and talismans, he doesn't have to WORK for his just deserts - he thinks of all of modern math as just so much meaningless abstract structure which has lost touch with the basics of number theory - he doesn't need to learn that stuff - he has the gift, he can see through to the simple, obvious things that the modern pretentious ivory-tower snobs have overlooked - he can even see basic errors that they have not noticed because they are too busy with abstract theory, which, of course, just makes your head ache and gets in the way of infallible instinct and the gift of his special insight. I think I am saying much the same as what you said. In fact maybe we all have a little of this faith in us that we are something special - not as much apparently as Harris has, and most of us know that nothing is going to happen without a lot of hard work - it's as if Harris heard what Edison said about inspiration and perspiration, but got the proportions confused. And more and more now, he is dwelling on fantasies of triumph and revenge, he is turning away from the people who tell him the truth, and living out his internal delusions. It cannot end well. Nora B. At the risk of being offensive--and please believe me I don't intend to be--do you think that Harris is suffering from a mental condition that a clinician could put a name to and perhaps even cure? I ask because I find his posts so unpleasant. It's not so much his incompetence at mathematics that bothers me (that would be a case of the pot calling the kettle black) but his exceedingly nasty remarks about the people who try to help him. It would be nice to think that his unpleasantness might some day be cured--if it is curable. The funny thing is that Harris himself has put a name to his problems cowardly behavior when he embarrasses himself, he deleted it from the Google archives. But it's still available elsewhere. For instance, see: http://mathforum.org/discuss/sci.math/m/468612/468612 to read, in his own words, a description of his real situation. It's one of the few bits of clear thinking he's ever demonstrated here -- though it still reeks of self-pity. -- Wayne Brown (HPCC #1104) | When your tail's in a crack, you improvise fwbrown@bellsouth.net | if you're good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock to that a I am no expert in psychology or psychiatry, and certainly not a devotee of Freud, e.g., but Freud did say one thing that I think rings true. He said that the definition of mental disease is that the person is unable to love or to work. We actually don't know much about Harris on either of those factors - he has worked as a programmer, and he may still be doing so now - I have no idea about his personal life - he mentions his family on rare occasions. What I like about Freud's criteria is that they lead to relatively straightforward, down-to-earth questions that you can answer in real life, and every now and then you can even answer them on your own behalf. But in Harris's case we don't have enough information. I think Harris has been depressed at times, and I think he drinks and some of his most vicious rants derive from this, but drinking is not a sole criterion for diagnosing mental illness as far as I know. the He is vicious, no question. However I don't think viciousness or mean-spiritedness are criteria for 'mental conditions' either. As for people trying to help him: everyone acts out of selfish motives. When we try to prove someone wrong, to some degree we are not trying to help them, but rather polishing our own apple, showing that we are smart gals and guys too. Our motives are not so high and morally pure. My usual motive with Harris is (1) to try to figure out the correct math, (2) to try to figure out where his thinking has gone wrong - that is one of the fun things about teaching math, trying to see how students fall off the logical tightrope and how to get them back on it again, (3) to explain what I think is right in the simplest possible way, and (4) to crush Harris underfoot like the disgusting pillbug that he is. Not entirely facetious, that last bit. I think not. Being unpleasant is not a disease. The question is really how deep his delusions run - does he really believe what he says, deep down - at some point they will become so entrenched that being forced to give them up would be unbearable and would plunge him into serious depression, at which point Freud's criteria would start to take hold. He keeps moving in that direction but may not be there yet. Nora B. days. My association with the Department is that of an alumnus. [.snip.] I've commented on this before. E.g., I commented some months ago that you seem to think that terminology and definitions are like magic spells and incantantions: you do not need to understand them, you just need to say the words in the right order with the right inflection, and all your problems will disappear like magic. (My guess: James thinks that definitions are magic spells: if you can come up with the correct definition, it will protect you against harm. The first part of the definition, about units, is his attempt at I won't have to worry about f being a unit, because I know it is not a unit in the integers; that will show the bastards who argued against me before; the second part of his definition is his attempt at I won't have to worry about divisibility, because I'm ensuring that 'a divides b' will be true everywhere if it is true anywhere; that willshow the bastards who kept pestering me about what 'factor' meant. [)] The problem, James, is that you are dealing with definitions as if they were magic spells. You think that if you can just come up with the right combination of words, everything will get fixed magically. But nowhere on your page do you ever use explicitly any properties of objects or object rings, and the only place where you use them implicitly (in the factorization) is a big huge gap. It is based on your incorrect conclusion that such a factorization need not exist for algebraic integers. You don't know what you want, you don't know why you want it, so it is small wonder you cannot give a correct definition. There also seems to be a bit of the same kind of approach as Alexander Abian used to take: he'll come up with the grand ideas, everyone else will do the grunt work and work out the details for him (while preserving ultimate glory and rewards for the one who came up with the grand idea, of course). Refereee reports are expected to point out specific errors, and to explain how to fix any such and make the argument right. Any gaps are to be filled by others, and simply pointing them out is not valid. Finally, there is an utter incomprehension of how mathematics is taught and learned once one gets beyond lower division calculus and related courses. I've commented on this before as well, though I can't seem to find the right phrases to find one of those posts in presented and so on make it painfully obvious that he believes math instruction occurs in the same general format as in calculus: certain rules and theorems are stated but not proven, and students are asked to take them for granted (for example, the Intermediate Value Theorem is seldom proven in lower division courses in the U.S., or the Extreme Value Theorem; they are merely asserted and students are asked to take them on faith and use them). The notion that in an upper division course the normal process is to state theorems and give proofs in detail, and students are asked, nay, required to make sure every single line is clear and valid, seems completely foreign to him. It could be part of that same labeling you mentioned (having taken advanced courses before finishing high school, for example). -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu and his true if huge small Actually Arturo, I think there is a shade of difference between what you are saying and what I have in mind, and maybe it is the difference between the cargo-cult guy and the compulsive gambler. The cargo-cult guy thinks that magic spells and such actually and specifically work. The gambler may carry around his lucky rabbit's foot or wear his lucky underwear (boxer shorts with shamrocks, e.g.) but I think that is mostly empty symbolism and the gambler knows this; but he still thinks that one's life is determined by Fate or Destiny or something real called 'Luck' or whatever, and that Somebody Up There wants him to win [though gamblers are not particularly religious, I think they do believe in Fate or Destiny or Luck]. Harris now and then tries to dress up his writing by invoking words that he either doesn't understand or just barely understands - that is not, I think, for magical purposes,but because he thinks that is the kind of thing that convinces us that what he is saying makes sense and that he can sling the lingo just like the rest of us when he wants to. He has hunches, intuitions - like some other people I know (esp. system programmers), once he has a hunch, he falls in love with it and goes to bed with it and hangs onto it until it is absolutely, totally proven wrong and is beaten to death (and as far as I know, he has never accepted a disproof of one of his claims unless it was reduced to just plain brute arithmetic, like 2 + 2 = 5). His intuition is erratic but on average very weak, and mostly he cannot get beyond what he learned in high school level math. The 'magical' part for him is the feeling that whatever he dreams up is basically correct, even though maybe wrong in detail - the idea that he has this special gift for seeing things that the rest of us pedestrian plodders with our limited imaginations - stunted by overexposure to modern math and abstraction - cannot. His ideas are poorly thought out, half-baked - he really avoids revisiting vulnerable parts that he whips past, once he has written them down. That is why APF went through several versions and recompositions over the course of a year before it was discovered that there was an egregious misprint which rendered the conclusion nonsense (on top of the more basic central error). So, yes, he parrots [you have used this word too in describing I think he thinks of it not as magic, but as a necessary nuisance to convince mathematicians that he knows what he is talking about. He does not understand the discipline of rigorous proof and thinks that his own overpowering intuitions (Surrogate factoring MUST work. After all, I thought it up, and I am Gifted ... I just need to get the details right ... almost got it ... it's a simple idea, really, but no one else has ever thought of anything like it ... it's HUGE ...) are really the same thing as what mathematicians call proof. Alexander the I don't know Abian, but yes, Harris very definitely wants to play the role of the idea man, where everyone else picks up what he has started and develops it. That is CLEARLY what he wanted to happen with his partial-difference / partial differential equation idea from the 'prime counting function' - his lightning-bolt intuition there was that the limiting case of the partial-difference equation was a partial differential equation, and if you could solve that, you would get the Riemann zeta function representation of the distribution of the primes. Of course he had not the faintest idea how to solve it - nor did anyone else - it was the ugliest differential equation ever, possibly - but he thought someone else who knew DE's (Ullrich, possibly???) would snatch it up and prove it and he would sit back and reap the credit for having the HUGE idea that started it all. can't the asked Maybe I don't quite agree here either. I think he has looked a little bit at journals and books and he doesn't understand what he reads, so he assumes it is meaningless gibberish or pointless formalism. He thinks modern mathematicians have gotten out of touch with the basics. He assumes that what he doesn't know is not worth knowing. If he hasn't seen it before, it doesn't exist and he is the first person in the world to ever think of it. He thinks the basic errors in teaching math are specific to his work in polynomial factorization, i.e., specific to algebraic number theory and Galois theory. The teaching of calculus may well be suboptimal, but I don't think Harris is criticizing that at all. Such are my views on the Harris phenomenon - he has indeed achieved legendary fame, though not how he wanted it to happen - Greatest Crank in the history of sci.math. Nora B. days. My association with the Department is that of an alumnus. [.snip.] I agree with this, but then I would say that this is not really relevant to the cargo cult analogy. My understanding is that when one talks about cargo cult in the context like the one you used, what one usually refers to is the aping of the form, coupled with a lack of understanding of the substance, in the hopes of obtaining the same results. Often, but not necessarily, this hope resides in the notion that there is something mystical about the form being aped. In that respect, I completely agree that James engages in cargo-cult mathematics; part of this cargo cult is mystical, part is not, but it all still revolves around the aping of forms without understanding or knowledge of the substance. This also manifests in the tiresome comparisons with Galois and other figures of the past. A developing nation that lowers its interest rates to the same level as developed nations because thinks it can achieve economic growth by having low interest rates (developed nations have low interest rates, right) is engaging in a kind of cargo cult, even though there is no real magical thinking in the sense of spells and spirits behind it. Argentina engaged in cargo-cult when it simply declared the peso to be the equal of the dollar and thought this would fix the economy. An attempt at aping the form without understanding of the substance, hoping that it will produce the same results. Classic cargo cult. Whether this cargo cult is rooted in honest-to-goodness magical thinking, or in the feeling that he must garb himself in the trappings of academia in order to reap its rewards, does not really seem to distinguish it. I mean, I don't believe he thinks that definitions are magic spells in the sense of Advanced Dungeons and Dragons! But he treats them as meaningless collections of words, because that's what he sees when he reads a textbook. Alexander Abian used to have this quote at the end of all his posts: IF IT EXISTS IT IS MASS TIME IS MASS. ABIAN MASS-TIME EQUIVALENCE FORMULA T=(10^18)Log(1-m/Mo) SECONDS. ALTERING EARTH'S ORBIT AND TILT - STOPPING GLOBAL DISASTERS AND EPIDEMICS. ALTERING THE SOLAR SYSTEM. REORBITING VENUS INTO A NEAR EARTH-LIKE ORBIT TO CREATE A BORN AGAIN EARTH When asked about actually making his ideas work, he would often reply with a quote from Einstein (IMAGINATION IS BETTER THAN KNOWLEDGE), preceded with one of his own making ( IMAGINATION IS THE ESSENCE THE REST ARE DETAILS ). His role was coming with the ideas... I must be showing my net.age. His is the name that pops into my head when I discuss that sort of attitude... Yes. But read his comments about students and about mathematicians teaching wrong mathematics. Read his comments about how mathematicians are taught not to question. They all make perfect sense if you imagine that all mathematics classes have the same sort of format as a calculus class; they are nonsense when you know what an advanced mathematics course is like. His assumption of gibberishness and pointless formalism is something separate from this, I think. You are correct, in other words, but it is not what I'm refering to. I think you misread me. I wasn't saying James is complaining about how we teach calculus. I think he believes that we teach all math courses like calculus is taught, and so assumes that students are taught to accept, not to question, etc. That theorems are stated but not proven. This is how he can explain why the errors would not be found except by researchers (who of course would have to try to prove these results to one another; but then it would be easy to hide inconsistencies). When you next feel utterly bored, go back and read his comments on unquestioning students and the like. Then think of the person saying it as having no experience with a math class beyond the calculus level. At least to me, they all make sense from that viewpoint, i.e., someone who thinks that the way we teach calculus in the US is the way all math is taught at all levels to everyone. -- It's not denial. I'm just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu aping in Of course I am no cargo cult expert - in some ways it looks like a kind of religion - possibly when the real planes came and dispensed things of value, the local guys thought they were gods and that airplanes were their way of coming down to earth to distribute their beneficence. The little models that the cultists constructed were not present when the planes were actually arriving - they were not copying something that actually worked at the time - they are more like sacred pictures, prayer objects. There is too the question of what the cultists did and thought while they were sitting around waiting for the planes to return. Presumably every now and then a plane would be seen passing high overhead, but not landing - that would give them hope. The cultists might have been the object of derision to the other people on the island who noted that it was actually more useful to do WORK to make a living - fishing or digging clams or harvesting coconuts or growing yams or whatever - the industrious pragmatic people might have thought the cultists were effete lazy kooks. I don't know - maybe the cultists, like some holy men, lived on the charity of those who worked for a living. But they might have been derided and resented. You know. What's Daddy doing sitting out in that field? Shut up and dig your yams. What Harris has in common with the cultists is (1) a belief that what he is doing is going to work and make him rich and famous, and (2) a failure to work hard to get what he wants. Certainly he *thinks* he works hard now, but huge amounts of his time are spent not in working but in fantasizing about success and wishful thinking - he has no idea how hard real math is, how much you have to know, how deep the concentration must be, how narrow the path. His ideas are like duckweed on a pond, compared to the depths that one must go to now to contribute to modern math. He doesn't know this. I think the cultists, too, thought that their little models were pretty much the same as real airplanes - just lacking size and some kind of magic that would make them fly. They had no idea of a real airplane's complexity. about of would people. That's the difference, I think. The cultists probably believed in the magic. They were trying to *charm* the airplanes into landing, rather than trying to *fool* them into landing. Harris however does not think using the big words was magic - he thought that this was a necessary chore to placate real mathematicians - he could fool us into thinking he knew what he was doing, and that was good enough - he knew that he had the right idea, it's just a matter of saying it right. Very often he complained that other people seemed to believe what I said rather than what he said, and he thought that was because I was just better with the lingo of math, I was good with words, not because I actually had the better argument. So often of course he (and the rest of us, it must be said) were playing to a more or less imaginary gallery - he thought that the mathematicians succeeded because they knew how to say things better than he did, not because they were right. It wasn't a matter of magic at all. It was just part of the evil conspiratorial injustice that kept denying him due recognition. Approximately true, I think. Certainly any time he tried to construct a definition of his own, it was as if he had never read an actual rigorous definition. The object ring for example - it went on for many months, a hopelessly inadequate definition, rightly and accurately criticized, but he refused to fix it. He knew he had a correct underlying idea which he knew was good enough, but he just didn't know how to write it down. Another unfairness that we imposed. else out T=(10^18)Log(1-m/Mo) Whoa. I would say he was definitely in the deep end of the pool there. Harris may have some ways to go after all. The name sounds familiar (of course it sounds a little too much like 'A. Adrian Albert', the famed 'A-Cubed of the University of Chicago). Did Abian ever do creditable work at some time in the past? and math certain asked sure example). an I would not be surprised if the 'advanced placement' classes that he might have taken in high school, or the honors classes, tried to teach calculus at the epsilon-delta level - and might not have succeeded, at least not with Harris. I still maintain that his problem is with teaching that he hasn't actually experienced, at the graduate level - Galois theory, for example - he claimed as recently as yesterday that he had disproved basic stuff that undermined Wiles' proof of the Taniyama conjecture - stuff that he thinks has been taught without question to grad students for the last 150 years. Of course it's also true that he addresses a lot of his posts to alt.math.undergrad - he hopes to teach these young still uncorrupted minds to question modern math and to get to them before their brains are stunted in graduate courses. And I must say, this part has nothing to do with magical thinking. how found Yes - he may assume that - but first, he may actually have been exposed to some pretty good math teaching as an undergrad at Vanderbilt - it might not all have been rote learning. He might not have learned it much - there are some hints that he wasn't a very good student - but that doesn't mean it was badly taught. Second, if you asked him what was wrong with math teaching, I think he would answer very narrowly that graduate courses dealing with algebraic integers are the really central problem. He has never complained about differential equations, for example - knows they are useful in physics, hasn't really thought much about them. saying way I recognize that he thinks that - mostly though I think he is referring to the lurkers in sci.math and alt.math.undergrad who just lap up whatever we dish out without question, who never speak up to defend him because we have them totally fooled with our convincing but superficial mastery of the secret language. Yesterday he said people were committing fraud simply by not speaking up when they knew of his revelations of the flaws in the algebraic integers. You can evidently go to jail just by not saying anything. Right, lurkers? You just believe anything we say just because we make the right incantations and sound like we know what we are talking about, right ? I was thinking earlier today - Harris of course thinks I am a total liar and hypocrite bent on suppressing his genius - and what does he think now of Arturo Magidin? He went into battle with you over and over again, and many, many times he called you a liar and worse - but he knew, he knew, and he didn't ignore you like he did, say, others who cast aspersions but didn't take his math seriously - I won't name names - and does he still think you too are a liar and cheat who was jealous of his discoveries? He knew, too, that if he ever convinced you of anything, ever painted you into a corner that you couldn't get out of, ever got you to agree that he was basically right, he was halfway to the glory that he craved. And though I cannot think of a single instance in which you lied, and very very few instances in which you even made a mistake, does Harris still think you are a primarily a liar? I would guesss so. Or is it some combination of liar and venerable (truth-telling) oracle? If, as he believes, math is a kind of magic, is Magidin a master magician, or an evil cynical jealous fake ? something published confers magic as well. Once it gets into print, it has been Certified as True, for All Time. Never mind that errors are published all the time and papers are retracted, and lots more errors are never caught. He wanted publication so bad he could taste it - I really think he would have declared total victory if he had ever succeeded in publishing something which he knew to be wrong - he was willing to cheat to achieve it. He accepted publication as an infallible imprimatur of Truth. And similarly he never understood that mathematical proof is not objectively defined - he thinks it is some kind of absolute, that proof exists independent of human beings - he has never understood that mathematical proof, for all its mystique of rigor and logic, is basically just one guy convincing another guy that he is right - that mathematics is (gasp!) inherently a SOCIAL ACTIVITY - there is no absolute. He thinks we suppress him for social reasons, indeed, but he actually underestimates, I think, how deeply social and human mathematicians actually are. It is not a solitary game. Being a good mathematician is partly a matter of being smart, but partly also a question of character and integrity. An honest hardworkding dullard may be more likely to be a good mathematician than a flashy habitual liar. You have to be honest with yourself to know when you have or don't have a valid proof. Nor is proof something with magical powers; it is told like a joke or anecdote or good story by one human to another. Getting a paper published is NOT a guarantee of truth. In a sense it is even worse than Harris thought. We ARE social creatures. Galois gave the ultimate proof of that, trying to leave a legacy the night before he was to die, in case anyone had doubts. The tragedy! Nora B. break doesn't work that complicated so, drive that he in claim ain't what state. polynomials will number I'm in total agreement with you. However there is something lacking in your analysis; Harris' very ugly and very real evil side. There is the Ullrich incident, the student he would preclude from graduating, his turning against those most kind to him. All that emphasised by his ever more nasty fantasies about punishment and revenge against mathematicians and his detractors in general. I think one tends to oversee this when conmiserating the sad looser he actually is, but It's important to keep it in mind. last when the than wild guys not stood be algebraic Testament in the ever It's Guenther, This is true. I did vaguely allude to it when I said I mentioned his 'righteous indignation' and his sense of being OWED credit for what he has done, etc.. There is no question that he is a nasty, devious, and even ruthless person, resentful and embittered by years of failure and rejection, all this on top of the magical thinking and the self-delusion. If he were not so mean-spirited one would feel sympathy. I don't. Nora B. Cargo-cult mathematics. I like it. Gib If dx/dy=(2x+cosx)^(-1) then, using the chain rule, is the second differential with respect to y (not x) d2x/dy2=(-1)*((2x+cosx)^-2)*(2-sinx)*(dx/dy) and, using the dx/dy = x', notation can you rewrite this as x''=(-1)((x')^2)*(2-sinx)*(x') which further simplifies to x''= (-1)(x')^3(2-sinx) or am I misunderstanding something? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: \ 1.9 primary) id j1MNkrv08014; I need help on my pre-Algrebra problems that i have to do tonight for home work because i have math 2 priod tomorrow i hope some one can help me tonight please??? I am in 8th grade so next year i am going to be a freshman next year so please can some one help me tinight please?? Sorry, my crystal ball's in the shop. What problems are you having trouble with? Show us what you did on each one. -- Stan Brown, Oak Road Systems, Tompkins County, New York, USA http://OakRoadSystems.com/ How can we help with your homework unless we know what it is? Do you want help with your English as well? Erm typical, don't acually understand laws of chance or probabilty. Saying something 'Generally' is NOT something you can use as proof. What is that? : slightly more than 50% (usually the case in this sort of crap when the word 'generally' is applied) of the 466 that cuts it down to around 250. Balance this up with the people who weren't prayed for and you have a very average figure well within the laws of chance. He of course doesn't say whether these patients were picked at random or were all located in the same ward etc. Something that combines wooley conditions with praying for two different things - congestive heart faliure increases the risk of heart attack (which throws another variable) is NOT any sort of proof. Anyway this is a games newsgroup - resident evil 4 rocks!!! D Hi Everyone, I am having some trouble setting up the integral for this question and am wondering if anyone could help me with it: -x e -------- _____ V y Find the average temperature in the region bounded by the cylinder y = x^2, the plane y = 1, and the plane z = 2y. Its really the second part that is being a pill. One idea is: 0 <= x <= 1, 0 <= y <= x^2, 0 <= z <= 2y Does anyone else think this is right? Elizabeth Why do you have 0 <= x <= 1 instead of -1 <= x <= 1 ? Hmmm - then y = x^2 would be like a cup extending along z in both directions. In that case: -1 <= x <= 1 , x^2 <= y <= 1, 0 <= z <= 2y That image makes more sense. Does that sound more like it? -Elizabeth