mm-1139 === Subject: Re: Yet another math problem I dont understand! > This is the problem I can not figure out how to work. > The path of a diver is given by y= -4/9x^2 + 24/9x + 12 where y is > the height in feet, and x is the horizontal distance from the end of > the diving board in feet. > a) What is the maximum height of the dive? b) How high is the diving board? ~Hillarie I am not now, nor have I ever taken calculus. I am taking basic college algebra. I have given this problem thought and tried to work it by treating is a a quadratic equation but that did not work. Other than treating it like a quadratic equation I dont know how to begin to complete this problem. ~Hillarie === Subject: Re: Yet another math problem I dont understand! Hillary returns after comments: >I am taking basic >college algebra.>> {original equation given: y=-4/9x^2 + 24/9x + 12} Your required concepts are likely in the course. Unclear is, what exactly you mean by basic college algebra. Does this mean Introductory Algebra? Does this mean the PreCalculus College Algebra? The current date seems a bit early in the semester for dealing with quadratic equations; this being late september. > I have given this problem thought and tried to work >it by treating is a a quadratic equation but that did not work. Other >than treating it like a quadratic equation I dont know how to begin to >complete this problem. y=-(4/9)x^2 + (24/9)x + 12 If that is truly what you are trying to express, then certainly that is a quadratic equation and it is easily factorable; the points on the x-axis will be plainly obvious. What values of x will satisfy the 0=-(4/9)x^2 + (24/9)x + 12 (but in the factored form, of course).? G C === Subject: Re: Yet another math problem I dont understand! > Hillary returns after comments: >I am taking basic >college algebra.>> > {original equation given: y=-4/9x^2 + 24/9x + 12} > Your required concepts are likely in the course. Unclear is, what exactly you > mean by basic college algebra. Does this mean Introductory Algebra? Does > this mean the PreCalculus College Algebra? The important thing about the question Are you studying for calculus is the specific suggestions we offer (if any) will depend greatly on the answer. Since it has been clarified this is algebra (the particular course doesnt really matter) as opposed to calculus, then obviously we are not going to be performing any differentiation (a tool by which similar problems are solved in calculus.) I second the motion of the other poster. Wheres your work, OP? Do you (original poster) simply want the answer and dont care how it is obtained, which would explain the repeated lack of showing any real attempt despite the requests, or would you like to know the general method for solving these kinds of problems? Im still undecided which is the case, so Ill meet you half way. If truly interested in the method, all will be revealed. If you just want the quick answer, then what follows will probably not make much sense so no harm no foul on my part. It will look like work and you will probably ignore it. Or you will prove me wrong, read and understand the following (which is probably also in your book), and apply it to your specific problem. > I have given this problem thought and tried to work >it by treating is a a quadratic equation but that did not work. The second part (b) has been thourougly addressed. For part a, understand that a parabola with vertical axis of symmetry will have vertex that is either the highest point on the graph (y is maximal) occuring when the parabola opens downward, *or* the vertex is the lowest point on the graph (y is minimal) occuring when the parabola opens upward. In this case you are asked, in essence, to state the maximal y-value of a downward opening parabola. IOW, state the y-coordinate of the vertex. Now the work: For a quadratic equation in standard form, y=ax^2+bx+c with a<>0, the coordinates of the vertex can be derived from completing the square: y = ax^2 + bx + c Divide by a... (y/a) = x^2 + (b/a)x + (c/a) Subtract c/a... (y/a)-(c/a) = x^2 + (b/a)x Add (b^2)/(4a^2)... (y/a)-(c/a)+(b^2)/(4a^2) = x^2 + (b/a)x + (b^2)/(4a^2) Combine terms on left and factor on right... (y/a) + [(b^2-4ac)/4a^2] = [x + (b/2a)]^2 Get y term alone... (y/a) = [x + (b/2a)]^2 - (b^2-4ac)/(4a^2) Multiply by a... y = a[x + (b/2a)]^2 + (4ac-b^2)/(4a) Now, given that a quite common equation of such a parabola is... y = a(x - h)^2 + k ...where (h,k) is the vertex ...we rewrite this, to fit this form, as... y = a[x - (-b/2a)]^2 + (4ac-b^2)/(4a) A similar method can be used to describe the coordinates of the vertex of a parabola with horizontal axis of symmetry (opening left or right.) -- Darrell === Subject: Re: Yet another math problem I dont understand! > I have given this problem thought and tried to work >it by treating is a a quadratic equation but that did not work. What do you mean, that did not work? What _specifically_ did you try? Show us your work; otherwise its impossible to help you see where you went wrong. The single most annoying form of trouble report is It didnt work. Surely people are not so foolish as to think thats an adequate explanation! What is someone supposed to do when hearing or reading such a statement, except ask for more details? If people asking for help thought for even a moment, they would realize that more information was necessary to diagnose the problem. Live conversations are one thing, where the helper can ask follow-up questions. But when one is posting to asynchronous media like e-mail or Usenet, its quite useless to fail to provide all relevant information in the first trouble report. The only thing more amazing is to see someone fail to provide that information in the _second_ trouble report. -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com surely reduces the number of useful answers you get. http://www.cs.tut.fi/~jkorpela/usenet/laws.html === Subject: total variation norm Define the total variation norm || || of a function on the line to be ||f|| = sup( sum over all j |f(x_{j+1})-f(x_j)| ). How do you show that, if u(x,t) is the solution to the heat equation u_t=u_{xx}, u(x,0)=f(x), then u satisfies ||u(.,t)|| <= ||f|| ? I know that u(x,t) = 1/sqrt(4 pi t) int(-oo,oo) exp( -(x-y)^2/(4t) ) f(y) dy, but with the x in the exponent I havent been able to make ||u(.,t)|| look like anything I can start writing inequalities withany suggestions? === Subject: Re: total variation norm >Define the total variation norm || || of a function on the line to be >||f|| = sup( sum over all j |f(x_{j+1})-f(x_j)| ), _where_ x_1 < x_2 < ... < x_n. >How do you show that, if u(x,t) is the solution to the heat equation >u_t=u_{xx}, u(x,0)=f(x), then u satisfies >||u(.,t)|| <= ||f|| ? >I know that u(x,t) = 1/sqrt(4 pi t) int(-oo,oo) exp( -(x-y)^2/(4t) ) >f(y) dy, but with the x in the exponent I havent been able to make >||u(.,t)|| look like anything I can start writing inequalities >withany suggestions? Make a change of variables, to show that u(x,t) = 1/sqrt(4 pi t) int(-oo,oo) exp( -y^2/(4t) ) f(x-y) dy . Use the fact that 1/sqrt(4 pi t) int(-oo,oo) exp( -y^2/(4t) ) dy = 1. ************************ David C. Ullrich === Subject: Re: total variation norm Hmmm...I see why making the change of variables makes sense, but now I cant proceed from ||u|| = sup (sum) |1/sqrt(4 pi t) INT(-oo,oo) e^(-y^2/(4t))[f(x_{i+1}-y)-f(x_i-y)] dy|. If f was in L^1, it seems like I could use some sort of Cauchy-Schwarz inequality in the integral, but its still a mystery how to end up comparing ||u|| to ||f|| rather than ||INT(-oo,oo) f||... > >Define the total variation norm || || of a function on the line to be > >||f|| = sup( sum over all j |f(x_{j+1})-f(x_j)| ), _where_ x_1 < x_2 < ... < x_n. > > >How do you show that, if u(x,t) is the solution to the heat equation >u_t=u_{xx}, u(x,0)=f(x), then u satisfies > >||u(.,t)|| <= ||f|| ? > >I know that u(x,t) = 1/sqrt(4 pi t) int(-oo,oo) exp( -(x-y)^2/(4t) ) >f(y) dy, but with the x in the exponent I havent been able to make >||u(.,t)|| look like anything I can start writing inequalities >with?any suggestions? Make a change of variables, to show that u(x,t) = > 1/sqrt(4 pi t) int(-oo,oo) exp( -y^2/(4t) ) f(x-y) dy . > Use the fact that 1/sqrt(4 pi t) int(-oo,oo) exp( -y^2/(4t) ) dy = 1. > ************************ David C. Ullrich === Subject: Re: total variation norm >Hmmm...I see why making the change of variables makes sense, but now I >cant proceed from >||u|| = sup (sum) |1/sqrt(4 pi t) INT(-oo,oo) >e^(-y^2/(4t))[f(x_{i+1}-y)-f(x_i-y)] dy|. >If f was in L^1, it seems like I could use some sort of Cauchy-Schwarz >inequality in the integral, but its still a mystery how to end up >comparing ||u|| to ||f|| rather than ||INT(-oo,oo) f||... Well Ill just do it then - make certain to mention my name when you hand it in: |u(x_1, t) - u(x_2, t)| + ... <= 1/sqrt(4 pi t) INT(-oo,oo) e^(-y^2/(4t)) (|f(x_1-y)-f(x_2-y)| + ...) dy <= 1/sqrt(4 pi t) INT(-oo,oo) e^(-y^2/(4t)) ||f|| dy = ||f|| . >> >>Define the total variation norm || || of a function on the line to be ||f|| = sup( sum over all j |f(x_{j+1})-f(x_j)| ), >> >> _where_ x_1 < x_2 < ... < x_n. >> How do you show that, if u(x,t) is the solution to the heat equation >>u_t=u_{xx}, u(x,0)=f(x), then u satisfies ||u(.,t)|| <= ||f|| ? I know that u(x,t) = 1/sqrt(4 pi t) int(-oo,oo) exp( -(x-y)^2/(4t) ) >>f(y) dy, but with the x in the exponent I havent been able to make >>||u(.,t)|| look like anything I can start writing inequalities >>with?any suggestions? >> >> Make a change of variables, to show that >> >> u(x,t) = >> 1/sqrt(4 pi t) int(-oo,oo) exp( -y^2/(4t) ) f(x-y) dy . >> >> >> Use the fact that >> >> 1/sqrt(4 pi t) int(-oo,oo) exp( -y^2/(4t) ) dy = 1. >> >> >> ************************ >> >> David C. Ullrich ************************ David C. Ullrich === Subject: integrate implicitly?? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8MCbhA31840; Hi all, I wonder if it is possible to integrate implicitly ? i dont know have i use implicitly correctly, what i meant was : integrate f(x,y) w.r.t x, where y = f(x) but we dont know what form is the f(x). eg f(x,y) = 2x + siny I thought of this question because If y and x are independent, then to integrate f(x,y) w.r.t x, treating y as a constant. eg integral 2yx+ siny = yx^2 + F(y) Ahaey === Subject: Re: integrate implicitly?? >I wonder if it is possible to integrate implicitly ? >i dont know have i use implicitly correctly, what i meant was : >integrate f(x,y) w.r.t x, where y = f(x) but we dont know what form >is the f(x). I dont know whether there is a term for what youre talking about, but the general answer is No, you cant integrate a function of x and y with respect to x when y is also a function of x -- you must first re-express the integrand as a function of x. When you proceed to further calculus (usually third semester), you will meet multiple integration. There you integrate a function of x and y with respect to x -- but only when both and y are independent variables. -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com surely reduces the number of useful answers you get. http://www.cs.tut.fi/~jkorpela/usenet/laws.html === Subject: Re: mean by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8MCc1231859; >I am working on trying to find the estimated mean for grouped data >The problem reads: What is the age distribution for adult shop >lifters. A random sample of 895 incidents of shop lifting gave the >following age distribution: age range 1)21-30 2) 31-40 3)41 and over >number of shoplifters 1)260 2)348 3)287 >And I need to estimate the mean age, sample variance, sample standard >deviation for the shoplifters. For the class 41 and over use 45.5 as >the class midpoint I dont understand why you would be doing a problem like this when you seem to be telling us you have no idea what to do. If this is a homework or text problem. They should have the formulas in the text. In any case, the point of grouped data is to treat all of the values in a group as if it were the midpoint. You have a total of 895 people, 260 of whom you are taking to be age 25.5, 348 of age 35.5, and 287 of age 45.5. If you added all those together, you would get 260(25.5)+ 348(35.5)+ 287(45.5)= 32042.5. Thats an average age of 32042.5/895= 35.8. To find variance, subtract that average, 35.8, from each midpoint age, square and average the resulting numbers. 25.5- 35.8= -10.3 (-10.3)^2= 106.09 35.5- 35.8= - 0.3 (-0.3)^2= 0.009 45.5- 35.8= 9.7 ( 9.7)^2= 94.09 The average of these, again taking into account the number in each group is (260(106.09)+ 348(0.009)+ 287(94.09))/894= 54590.362/894 = 61. (Notice the 894 instead of 895-basically thats to make the variance a little larger to allow for the fact that this is only a sample. Consult your text book or teach on that.) Finally, the standard deviation is simply the square root of the variance. === Subject: No need to be a jerk by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8MEBLg05456; Listen Pal, this forum is for discussion and learning. I saw somewhere where this was the case, apparently it doesnt apply to my case or I interpreted the problem incorrectly, which is could be the case. In the future try to show some class, which apparently you are in short supply of. === Subject: I beg to difffer by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id h8N0C0B15489 by home.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.4 nullclient) id h8N0Bwi16703; >Listen Pal, this forum is for discussion and learning. I saw >somewhere where this was the case, apparently it doesnt apply to my >case or I interpreted the problem incorrectly, which is could be the >case. In the future try to show some class, which apparently you are >in short supply of. Heres a heads-up Matt - Im not your Pal. You saw somewhere that sin(3 - 3) = sin(0) = 1??? Which apparently doesnt apply in your case??? I would be amazed if you could find *any* case where sin(0) = 1 did apply. Good god - at what level are you attempting to study at? I stand by my earlier post. Ill try to show some class if you try to show some brains, Matt. (And I wont even make any cracks about *your* short supply) === Subject: Re: I beg to difffer >>Listen Pal, this forum is for discussion and learning. I saw >>somewhere where this was the case, apparently it doesnt apply to my >>case or I interpreted the problem incorrectly, which is could be the >>case. In the future try to show some class, which apparently you are >>in short supply of. >Heres a heads-up Matt - Im not your Pal. There seems to be a rash of people posting follow-ups as new threads. your software for follow-up, not for posting a new thread. Discussions are impossible to follow when people fragment them as you and others have done. And changing the subject lines just makes it worse. -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com surely reduces the number of useful answers you get. http://www.cs.tut.fi/~jkorpela/usenet/laws.html === Subject: Re: I beg to difffer > >>Listen Pal, this forum is for discussion and learning. I saw >>somewhere where this was the case, apparently it doesnt apply to my >>case or I interpreted the problem incorrectly, which is could be the >>case. In the future try to show some class, which apparently you are >>in short supply of. > >Heres a heads-up Matt - Im not your Pal. > There seems to be a rash of people posting follow-ups as new > threads. > your software for follow-up, not for posting a new thread. > Discussions are impossible to follow when people fragment them as > you and others have done. And changing the subject lines just makes > it worse. Let me get this straight----its fine to ßame, so long as the format is proper? Ha! === Subject: integration-please help by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8MIXFL24351; I have the following problem relating to a life table function X exp(-S 1/1600 u du ) 0 where S is definite integral. How do I multiply out of this to get a solution for the life table function? Please help!! D === Subject: Re: integration-please help >I have the following problem relating to a life table function > X >exp(-S 1/1600 u du ) > 0 >where S is definite integral. How do I multiply out of this to get a >solution for the life table function? You dont multiply out; you evaluate the integral. Did you actually mean the integrand to be 1/1600u, which is what you and the first one isnt much harder. If youre truly stuck after looking at this a second time, post again and SHOW US WHAT YOU TRIED. -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com surely reduces the number of useful answers you get. http://www.cs.tut.fi/~jkorpela/usenet/laws.html === Subject: Questions on Calculus by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8MLgAX06095; A.How do you prove? 1. lim f(x)=2 if f(x)= 4-2x, x<1 B.Show by example that the following statement is wrong: 1. The number L is the limit of f(X) as X approaches Xo if f(X) gets closer to L as x approaches Xo. Explain why the function in your in your example does not have the given value of L as a limit as X-->Xo 2.The number L is the limit of f(x) as x approaches Xo if given any epsilon>0, there exists a value of x for which |f(x)-L|Xo C.Find the limits 1.lim (X3-3x+2)/(X3-2x2) note:x cube -3x +2 divided by x cube -2 x square when the limit is a)X-->0+ b)X-->2+ c)X-->2- d)X-->2 e)what can be said about the limit as x--->0 D.Theory and examples 1.Once you know lim x-->a+ f(x) and lim x-->a- f(x) at an interior point of the domain of f, do you then know lim x-->a? Giv resons for your answer. 2.If you know lim x-->c f(x) exist, can you find its value by calculating lim x-->c+ f(x)? Give reasons for your answer 3.Suppose that f is an odd function of x. Does knowing that lim reasons for your answer E.Formal definitions od one -sided limits 1. Given epsilon >0 find an interval I = (5, 5.5+delta), delta>0,such that if x lies in I, then square root of (x-5)0 , find an interval I = (4-delta , 4), delta>0, such that if x lies in I, then square (4- x) A.How do you prove? > 1. lim f(x)=2 if f(x)= 4-2x, x<1 > x->1 6x-4, x > and = 1 Do the right side and the left side limits separately. > B.Show by example that the following statement is wrong: > 1. The number L is the limit of f(X) as X approaches Xo if f(X) gets > closer to L as x approaches Xo. How is 1 different than 2 other than 1 is less exact? > Explain why the function in your in your example does not have the > given value of L as a limit as X-->Xo > 2.The number L is the limit of f(x) as x approaches Xo if given any > epsilon>0, there exists a value of x for which > |f(x)-L| Explain why the function in your example does not have the given value > of L as a limit as x-->Xo Huh? Youre asked to find a function and a number L for which lim(x->x0) f(x) /= L ? If thats whats being asked, its most easy. > C.Find the limits > 1.lim (X3-3x+2)/(X3-2x2) > note:x cube -3x +2 divided by x cube -2 x square The proper way to write that is (x^3 - 3x + 2)/(x^3 - 2x^2) > when the limit is > a)X-->0+ > b)X-->2+ > c)X-->2- > d)X-->2 > e)what can be said about the limit as x--->0 > 1 Define g(3)ina way that extends g(x) = (x2 -9)/(x-3) to be > continuous at x = 3 Do you mean (x^2 - 9)/(x - 3) = x + 3 ? Thats a lot of homework for you to do and you havent even show any attempts at doing any of it. Seems you dont want any help but only somebody to do your homework for you. === Subject: typo by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8MLnb506437; my e-mail is ohyes_tw@yahoo.com === Subject: What is y=f(x) by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id h8N0BwB15486 by home.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.4 nullclient) id h8N0BvH16699; I know the basic concept of y equals a function of x. But can someone give a beeter explanation of this funciton? === Subject: Re: What is y=f(x) >I know the basic concept of y equals a function of x. But can someone >give a beeter explanation of this funciton? Which part of the basic concept are you having trouble with? Otherwise youre just asking us to take shots in the dark, and any improvement on whats in your textbook would be a matter of luck. -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com surely reduces the number of useful answers you get. http://www.cs.tut.fi/~jkorpela/usenet/laws.html === Subject: function by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8NDArA00566; hi, i saw the briefexplanation of function at this page http://mathforum.org/library/drmath/view/51453.html hope its useful to you. =) extract from Implicit Functions === Subject: Implicit functions --------- In order to be a *function*, of course, given a value of the independent variable, there must be a *unique* value of the dependent variable which makes the equation true. If there is more than one, you dont have a function, but something called a relation. For the sake of clarity, consider x to be the independent variable, and y the dependent variable. For x = y^2, y is *not* a function of x, because for each positive value of x, there are two values of y which work: y = Sqrt[x] and y = -Sqrt[x] === Subject: Why was my message posted twice? by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id h8N0C2B15492 by home.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.4 nullclient) id h8N0C0m16707; Although I know what Sin(0) is, I sure havent been able to figure out how to post on this forum without creating all kinds of silly little Anyway, sorry for the clutter. === Subject: riddle by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) with ESMTP id h8N0C9B15529 by home.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.4 nullclient) id h8N0C8716727; You can find us in darkness but never in light. We are present in daytime but absent at night. In the deepest of shadows, We hide in plain sight. What am I? === Subject: Re: riddle > You can find us in darkness but never in light. > We are present in daytime but absent at night. > In the deepest of shadows, We hide in plain sight. > What am I? A shadowy character. === Subject: Proving monotonous functions. by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8N5Yi307332; question: Prove by (1) a calculus approach and (2) an algebra approach That f(x)=arctan(x) is 1-1 for x between (-pi/2, pi/2). Hint for (2) be careful you dont say; arctan(a)=arctan(b) -> a=b - you will need the identity arctan(x)-arctan(y) = arctan((x-y)/(1+xy)). Any help would be appreciated. === Subject: Re: Proving monotonous functions. > question: > Prove by (1) a calculus approach > and (2) an algebra approach > That f(x)=arctan(x) is 1-1 for x between (-pi/2, pi/2). Likely you made mistake about the range of x. Are you trying to indicate arctan is the pricipal value? Show f(x) is positive and use mean value theorem. > Hint for (2) be careful you dont say; > arctan(a)=arctan(b) -> a=b - you will need the identity > arctan(x)-arctan(y) = arctan((x-y)/(1+xy)). > Any help would be appreciated. tan arctan x = x === Subject: Re: Proving monotonous functions. >question: >Prove by (1) a calculus approach > and (2) an algebra approach >That f(x)=arctan(x) is 1-1 for x between (-pi/2, pi/2). >Hint for (2) be careful you dont say; >arctan(a)=arctan(b) -> a=b - you will need the identity >arctan(x)-arctan(y) = arctan((x-y)/(1+xy)). Have you thought carefully about the hint? To prove that a function is 1-1 you need to prove that f(a)=f(b) if a=b and f(a)<>f(b) if a<>b. But f(a)=f(b) is the same as f(a)-f(b)=0. You are given f(a)- f(b) in convenient form. As for the calculus method, you should have learned a theorem about monotonic functions being 1-1. -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com surely reduces the number of useful answers you get. http://www.cs.tut.fi/~jkorpela/usenet/laws.html === Subject: Using a delta/epsilon argument to show continunity by support1.mathforum.org (8.11.6/8.11.6/The Math Forum, $Revision: 1.9 primary) id h8NDCUH00698; Hey, any used a delta/epsilon argument to prove a limit? Q: Using a delta, epsilon argument show that f(x) = x^2+x+1 is continuous at x=a. The basis for doing this is , given e>0, there is d>0 such that if |x-a|Q: Using a delta, epsilon argument show that f(x) = x^2+x+1 is >continuous at x=a. >The basis for doing this is , given e>0, there is d>0 such that if >|x-a|With my question I cant get my |f(x)-f(a)| to sometihng in terms of >|x-a|, so Im kinda stuck. Why not? f(x) = x^2+x+1; f(a) = a^2+a+1. f(x)-f(a) = x^2-a^2 + x-a = (x-a)(x+a+1). -- Stan Brown, Oak Road Systems, Cortland County, New York, USA http://OakRoadSystems.com surely reduces the number of useful answers you get. http://www.cs.tut.fi/~jkorpela/usenet/laws.html === Subject: Re: Uniqueness of gcd(a,b) = as + bt > Hi everyone, > > It is well known that gcd(a, b) = as + bt for some integers a, b, s, t, > with > a > b > 0. What I need to know is whether s and t are unique. Any hints? > > Bernd Rationale behind search for counterexample (or proof): > Suppose they arent. Suppose p,q do the job too. Then; > as + bt = gcd(a, b) = ap + bq > a(s-p) = b(q-t) > So how about letting; > s-p = b => p = s-b > q-t = a => q = a+t > So; > gcd(a, b) = ap + bq = a(s-b) + b(a+t) = as + bt > as required. > I hope. (Getting practice in before term starts...!) So p and q are not unique. Which isnt surprising, since ma + nb = 0 has infinitely many solutions. Jon Miller === Subject: Re: Uniqueness of gcd(a,b) = as + bt >> Hi everyone, It is well known that gcd(a, b) = as + bt for some integers a, b, s, t, >> with >> a > b > 0. What I need to know is whether s and t are unique. Any >> hints? Bernd >> Suppose they arent. Suppose p,q do the job too. Then; >> as + bt = gcd(a, b) = ap + bq >> a(s-p) = b(q-t) >> So how about letting; >> s-p = b => p = s-b >> q-t = a => q = a+t The argument is bogus. Why not let s - p = q - t = 0. Then p = s, q = t > and ap + bq = as + bt as desired. Wrong! The argument is spot on! >> So; >> gcd(a, b) = ap + bq = a(s-b) + b(a+t) = as + bt >> as required. >> I hope. (Getting practice in before term starts...!) === Subject: Desire for fame is a bitch I thought I was set. With a high I.Q. group set to publish my paper on factoring polynomials into non-polynomial factors I figured that now certainly I could push my agenda to fame and fortune. I was wrong. So here I am back again, humbled yet again, as theres no escaping it, there is no way Ill get anywhere pissing off mathematicians. So here are some concessions. If mathematician wish to dismiss my prime counting function. Ok. Im not conceding any of that wacky bull like that its just Legendres Method as any idiot can look at the two and see theyre different, but its not worth arguing over as Ive figured out people dont give a damn about counting prime numbers anyway. And as for Fermats Last Theorem, its not worth the effort arguing about it. If you want to believe Wiles proved it, then Im not interested in arguing with your need. If youve personally traced out his work and are certain based on your own intellect then...GOOD FOR YOU!!! So quit the lying you dark evil people as Im not out here claiming to have a proof of Fermats Last Theorem and Im not out here claiming to have found THE prime counting function. Take down all those webpages attacking me, and quit with the posts calling me a crank. Im finally tired of being called a crank. I want to go legit. Um, there is that little problem with algebraic integers to discuss though; however, Im open-minded and willing to consider *proof* that Im wrong. Lets get back to it folks. No FLT. NO ING PRIME COUNTING!!! But finally I want some straight answers on the ring of algebraic integers. Thats all thats on the table. And theres no website of mine, so no way to claim that Im NOT dropping FLT and THE prime counting you evil bastards. LETS GET BACK TO BUSINESS!!! James Harris === Subject: Re: Desire for fame is a bitch >I thought I was set. With a high I.Q. group set to publish my paper >on factoring polynomials into non-polynomial factors I figured that >now certainly I could push my agenda to fame and fortune. I was >wrong. Tee-hee. The rest of us mathematicians are stuck publishing in plain old low-IQ mathematical journals. Curious how you cant get your stuff published there... >So here I am back again, humbled yet again, as theres no escaping it, >there is no way Ill get anywhere pissing off mathematicians. >So here are some concessions. >If mathematician wish to dismiss my prime counting function. >Ok. >Im not conceding any of that wacky bull like that its just >Legendres Method as any idiot can look at the two and see theyre >different, but its not worth arguing over as Ive figured out people >dont give a damn about counting prime numbers anyway. >And as for Fermats Last Theorem, its not worth the effort arguing >about it. >If you want to believe Wiles proved it, then Im not interested in >arguing with your need. If youve personally traced out his work and >are certain based on your own intellect then...GOOD FOR YOU!!! >So quit the lying you dark evil people Tee-hee. A second ago you said youd realized that theres no way youll get anywhere pissing off mathematicians. And now youre back referring to us as dark evil liars. You should give up math and go with your strength: start a seminar on how to win friends and inßuence people. >as Im not out here claiming to >have a proof of Fermats Last Theorem and Im not out here claiming to >have found THE prime counting function. So this is the end of cycle n+1: the retraction. I guess n+2 is starting soon, eh? >Take down all those webpages attacking me, and quit with the posts >calling me a crank. Im finally tired of being called a crank. >I want to go legit. >Um, there is that little problem with algebraic integers to discuss >though; Oops, I was wrong, n+1 is not quite over yet. >however, Im open-minded and willing to consider *proof* that >Im wrong. Um, first you have to state coherently exactly what the supposed problem _is_. Last I recall the problem was that the algebraic integers were incomplete, but in spite of repeated requests you declined to define incomplete. Tired of being called a crank, then define your terms - insisting on Truths involving terms you refuse to define makes you a crank. >Lets get back to it folks. No FLT. NO ING PRIME COUNTING!!! >But finally I want some straight answers on the ring of algebraic >integers. Answers to what? You havent shown that there are any problems. The algebraic integers are incomplete is meaningless until you give that definition, and all the _specific_ assertions youve made about funny stuff in the algebraic integers are easily seen to be simply false. Exactly what is the question you want straight answers to? >Thats all thats on the table. >And theres no website of mine, so no way to claim that Im NOT >dropping FLT and THE prime counting you evil bastards. Hmm. Not just dark evil liars, were evil bastards. But you dont want to piss people off. Huh. HINT: Today you say youre no longer claiming to have a proof of FLT. You should also include an apology to all the people youve called various names (incompetent liars, etc) for stating that the Proof was wrong. >LETS GET BACK TO BUSINESS!!! >James Harris David C. Ullrich ************************** As far as Im concerend youre trying to wait until I die, so I figure maybe you should die instead. How about that, eh? Wouldnt that be a better twist? You refuse to follow the math, so the great Powers that control reality and *speak* in mathematics decide to kill you instead of me. So what do you think about that, eh? Oh, cant hear Them talking? Well, I guess thats because you dont really understand Mathematics, the true language, which is THE language. Theyre talking about you now, and They agree with my assessment, and will not penalize me as They allowed the others like Galois and Abel to be penalized. They will kill you instead. James Harris speaking on Weird factorization, genius === Subject: Algebraic Integers In sci.physics, James Harris > I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. So here I am back again, humbled yet again, as theres no escaping it, > there is no way Ill get anywhere pissing off mathematicians. So here are some concessions. If mathematician wish to dismiss my prime counting function. Dismiss, no. Blow away, yes. Christian Bau did a remarkably good job with his implementation at the higher numbers, although he had help from Meissel and Lehmer. :-) And you still havent proved that Z[1/2] = R, either. Or for that matter Q. (Is 1/3 in Z[1/2]? No.) But I for one can let that slide for now, as discussions thereon will probably lead us far astray into the transfinite realm. [snippage] > But finally I want some straight answers on the ring of algebraic > integers. Thats all thats on the table. And theres no website of mine, so no way to claim that Im NOT > dropping FLT and THE prime counting you evil bastards. LETS GET BACK TO BUSINESS!!! > James Harris Fine. Whats the issue regarding algebraic integers? Its a ring, not a field, first off; both 1 and 2 are algebraic integers, but 1/2 is not. Neither pi nor e are algebraic integers -- or even algebraic numbers. If a number x != 0 satisfies an equation x^n + a_{n-1} * x^{n-1} + ... + a_0 = 0, as required by the definition of an algebraic integer, then its reciprocal y = 1/x satisfies the equation a_0 * y^n + a_1 * y^{n-1} + ... + 1 = 0. This means that x is an algebraic unit if a_0 = 1 or -1. (Not sure how to prove the only if part, mostly because y could satisfy some alternate equation -- although its highly unlikely if the equation defining x is irreducible over Q.) I suspect part of the reason one can uniquely factor any nonzero integer in the ring of integers into primes (otherwise known as the fundamental theorem of arithmetic), is because there are only two units in the ring of integers: +1 and -1. This is certainly not true in the algebraic integer ring; 4 - sqrt(15), for instance, is a unit, as it is defined by the equation x^2 - 8x + 1; the other root 4 + sqrt(15) is also a unit, and the reciprocal to boot. This also means units are not confined to the unit circle on the complex plane; from the looks of it theyre scattered all over the place. (Does anyone know if the ring of algebraic integers is a principal ideal ring? Its clear that the algebraic integers, like their namesake the integers, form an integral domain. I doubt that the set of algebraic integers however is a principal ideal ring, since 2, 3, 6, and sqrt(6) are all algebraic integers (2 and 3 being prime in the integer ring), yet 6 = 2 * 3 = sqrt(6) * sqrt(6). Hardly unique.) -- #191, ewill3@earthlink.net Its still legal to go .sigless. === Subject: Re: Algebraic Integers > In sci.physics, James Harris > > I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. So here I am back again, humbled yet again, as theres no escaping it, > there is no way Ill get anywhere pissing off mathematicians. So here are some concessions. If mathematician wish to dismiss my prime counting function. Dismiss, no. Blow away, yes. Christian Bau did a remarkably good job with > his implementation at the higher numbers, although he had > help from Meissel and Lehmer. :-) Thats false. All Christian Bau even claimed was that he was rehashing old work and I never claimed to have the fastest prime counting algorithm. So youre caught in a falsehood as its impossible for my position to have been blown away by someone putting up someone elses work when my position was never the one that you imply. However, someone naive who actually *trusted* you might have believed you and the implication, which is that Christian Bau actually did something, versus copy from what other researchers found, and that my position was that I had the fastest prime counting algorithm, when that was not my position. But now they can put you in their list of sources not to be trusted. who looks for targets to attack to bring attention to yourself. You probably figured I was a good and easy target, so you trotted out your bogus claim. James Harris === Subject: Re: Algebraic Integers Visiting Assistant Professor at the University of Montana. [.snip.] >Thats false. All Christian Bau even claimed was that he was >rehashing old work and I never claimed to have the fastest prime >counting algorithm. You did insinuate it many times (or at least, said that you ->thought<- you did) early on: (May 26, 2002) Um, I have a feeling that record will fall VERY soon. I think that the actual prime counting function will allow for counted all the primes up to 10,000,000 in 12.8 seconds (program has been posted). But you did in fact make it explicit you were not claiming that it was ->necessarily<- the fastest around: (May 29, 2002) Not surprisingly the function in its purest form is not necessarily the *fastest* form, which is something that comes up repeatedly in mathematics. Though of course once again you left wiggle room about how fast you could make it: For those of you who more focused on speed and records (like the current prime counting record of 10^29) the method can be optimized *greatly*. How that would work is where you see loops where the program currently using the pi function to determine if a number is prime, instead find all of the primes below the square root of the max, and then loop using them. The fastest way to do that is to use a sieve. The speed should surprise you and put a few records within reach. (May 29, 2002) Again, I suspect the current prime counting record will be broken in a few days. (June 29, 2002) Its actually kind of scary because I could probably blow away the 10^22 record on my pc, this afternoon. You seem to have backed away from such claims shortly after that. (Posts found by searching James Harris prime counting record group:sci.math author:James author:Harris [Gabriele Rossetti] has left a vast body of writings... in which he has attempted to prove the truth of his unorthodox interpre- tation of medieval literature. They present a formidable record of unsystematic research in which we see an enthusiast plunging farther and farther and farther from the logic of facts and good sense until truth is lost in the dreadful nightmare of an idee fixe. There is no real evolution of the Theory although it grows and expands until it embraces ever wider horizons. The numerous inaccuracies of deduction, mis-statements of historical fact, and self-contradictions...have caused critics to turn away from them in disgust... [...] It is impossible to read far... without realizing that we have to deal with a work of faith and imagination rather than of reasoning. There is an appearance of reason, for the author is set on proving by logic the truth of what he already believes by intuition. The truth is plain to him and he cannot comprehend why others do not immediately accept it, but as they desire demonstration he has multiplied his proofs. It is the redundancy and confusion of a prophet expounding by a familiar method the truth revealed to his own simple soul in a ßash of inspiration... In such work as this... it is idle to look for the calm reasoning of a scholar; we do not find it, and there is little or no advantage in attacking the obvious inconsistencies and absurdities that abound. -- E.R. Vincent, _Gabriele Rossetti in England_, quoted in _The Shakespearan Ciphers Examined_, by William F. Friedman and Elizebeth S. Friedman Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Algebraic Integers Ive been reading this list for years. Im an amateur/hobbyist mathematician that studies number theory in his spare time (lately Ive had a lot of that). There are people on this list that know way more than I do, I hope at some point I can become as well versed. If youre so convinced in your findings then go find people who will listen to you. Obviously the 100k -> 1M+ people who read usenet groups havent gratified your needs, so why are you still here trying to convince them? You cant still be typing away because you think you can regain your credibility with them. All youve managed to do is undermine any possibility that if you do actually figure something out they wont listen to you. And in your wake of burining bridges have now moved on to disparaging people not even in the argument with you. Ive seen people post here and get positive feedback and others not. You didnt get the accolades you were looking for, tough - thats the way life is. Now move on. P- > In sci.physics, James Harris > > I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. > So here I am back again, humbled yet again, as theres no escaping it, > there is no way Ill get anywhere pissing off mathematicians. > So here are some concessions. > If mathematician wish to dismiss my prime counting function. Dismiss, no. Blow away, yes. Christian Bau did a remarkably good job with > his implementation at the higher numbers, although he had > help from Meissel and Lehmer. :-) Thats false. All Christian Bau even claimed was that he was > rehashing old work and I never claimed to have the fastest prime > counting algorithm. So youre caught in a falsehood as its impossible for my position to > have been blown away by someone putting up someone elses work when my > position was never the one that you imply. However, someone naive who actually *trusted* you might have believed > you and the implication, which is that Christian Bau actually did > something, versus copy from what other researchers found, and that my > position was that I had the fastest prime counting algorithm, when > that was not my position. But now they can put you in their list of sources not to be trusted. who looks for targets to attack to bring attention to yourself. You > probably figured I was a good and easy target, so you trotted out your > bogus claim. > James Harris -- ############# Imagination is more important than knowledge - A. Einstein === Subject: Re: Desire for fame is a bitch I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. So here I am back again, humbled yet again, as theres no escaping it, > there is no way Ill get anywhere pissing off mathematicians. Let alone getting the mathematics wrong! So here are some concessions. If mathematician wish to dismiss my prime counting function. Ok. Im not conceding any of that wacky bull like that its just > Legendres Method as any idiot can look at the two and see theyre > different, but its not worth arguing over as Ive figured out people > dont give a damn about counting prime numbers anyway. And as for Fermats Last Theorem, its not worth the effort arguing > about it. If you want to believe Wiles proved it, then Im not interested in > arguing with your need. If youve personally traced out his work and > are certain based on your own intellect then...GOOD FOR YOU!!! So quit the lying you dark evil people as Im not out here claiming to > have a proof of Fermats Last Theorem and Im not out here claiming to > have found THE prime counting function. Take down all those webpages attacking me, and quit with the posts > calling me a crank. Im finally tired of being called a crank. I want to go legit. Um, there is that little problem with algebraic integers to discuss > though; however, Im open-minded and willing to consider *proof* that > Im wrong. Lets get back to it folks. No FLT. NO ING PRIME COUNTING!!! But finally I want some straight answers on the ring of algebraic > integers. Thats all thats on the table. And theres no website of mine, so no way to claim that Im NOT > dropping FLT and THE prime counting you evil bastards. LETS GET BACK TO BUSINESS!!! James Harris === Subject: Re: Desire for fame is a bitch I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. So here I am back again, humbled yet again, as theres no escaping it, > there is no way Ill get anywhere pissing off mathematicians. Let alone getting the mathematics wrong! Ah, but you see, I know I do NOT have the math wrong as I explained the argument in my paper to a Professor McKenzie at Vanderbilt University *in person* and used a lot of chalkboard space while doing it. Heres a link to Vanderbilts page on him: http://sitemason.vanderbilt.edu/site/czXIYM He even shot down the objections of Magidin who intriguingly enough went to a school where Professor McKenzie spent some time--Berkeley. Yes, I mentioned the objections raised by people on the sci.math newsgroup. However, Professor McKenzie began claiming my work is algebraic geometry which is out of his field. So I explained the entire thing over more than an hour, having driven up four hours from Atlanta metro, and he tells me its out of his field. I checked with a Professor Kovaks at University of Washington and he tells me its not algebraic geometry, but is algebraic number theory. Worse, I specifically told Professor McKenzie that I was interested in explaining my work, and would appreciate any help from my alma mater. He claimed no one at Vanderbilt had the expertise, but a Professor Kalman pointed out to me in an email that theres a Professor Megibben at the school who does. So at this point theres no doubt about the correctness of the paper Advanced Polynomial Factorization. James Harris === Subject: Re: Desire for fame is a bitch > Ah, but you see, I know I do NOT have the math wrong as I explained > the argument in my paper to a Professor McKenzie at Vanderbilt > University *in person* and used a lot of chalkboard space while doing > it. Heres a link to Vanderbilts page on him: > http://sitemason.vanderbilt.edu/site/czXIYM He even shot down the objections of Magidin who intriguingly enough > went to a school where Professor McKenzie spent some time--Berkeley. Yes, I mentioned the objections raised by people on the sci.math > newsgroup. However, Professor McKenzie began claiming my work is algebraic > geometry which is out of his field. So I explained the entire thing > over more than an hour, having driven up four hours from Atlanta > metro, and he tells me its out of his field. I checked with a Professor Kovaks at University of Washington and he > tells me its not algebraic geometry, but is algebraic number theory. Worse, I specifically told Professor McKenzie that I was interested in > explaining my work, and would appreciate any help from my alma mater. > He claimed no one at Vanderbilt had the expertise, but a Professor > Kalman pointed out to me in an email that theres a Professor Megibben > at the school who does. Yeah, my old advisor also had a crank file. Whenever hed get a call Mr. so-and-so, I was intrigued by the clear exposition on your letter, unfortunately this topic seems slightly outside my own field but I have a *good colleague* who has been working on similar problems for a while and his address is ... and thereby effectively short-circuiting the kooks with each other. He claimed he had never heard back from any of them. This was before email or the internet. > So at this point theres no doubt about the correctness of the paper > Advanced Polynomial Factorization. So how long exactly do people have to give you the run-around before you get the hint? === Subject: Re: Desire for fame is a bitch So at this point theres no doubt about the correctness of the paper > Advanced Polynomial Factorization. Youve been blown off repeatedly and this is your conclusion? Well you deleted out the part where I pointed out explaining the paper *in person* and yes for those who wonder Professor McKenzie did challenge me repeatedly at points. Luckily the argument is simple as I could meet each and every such challenge and show how each step followed logically, and therefore correctly. > Btw, you do realise that some of the people that are responding to you > here have very similar credentials to the ones you talk to in real life? > Why would you believe the one and not the other? Its not about believing any of you but about your willingness or unwillingness to accept correct mathematics. What I verified is my suspicion that others besides posters on sci.math, who might feel safe because of the medium, could see the explanation, see that it is correct, yet still just *decide* to not accept the importance of the mathematics. After all, I have repeatedly answered objections put forward on sci.math but found that posters would just lie and then no one would catch them on lies!!! Later theyd toss out the same objections that Id refuted and that includes posters like Magidin and Nora Baron. What my meeting with Professor McKenzie also confirmed for me is that a professional mathematician wouldnt accept their primary objection, which confirms to me that they were deliberately lying, as its nonsensical to believe that factors of f vary as functions or as dependents on m, which Professor McKenzie didnt even seriously consider as a possibility. It seems to me that many of you are quite willing to lie on Usenet, and now I have the proof. At least Professor McKenzie didnt toss out wacky lies like Magidin repeatedly did. So as I said there is no doubt about the correctness of the paper Advanced Polynomial Factorization. What I have clearly verified is that certain posters who *are* mathematicians, like Magidin, have been lying about the mathematics, and lying repeatedly with objections that a professional mathematician quickly rejected. If the poster Victor Eijkhout wishes to challenge that directly then I suggest he point out an error in the paper and if he doesnt have it, Id be happy to send it. I have nothing to hide. Its mathematicians like Magidin who are being now caught in deliberate and hurtful lies which are against mathematics. James Harris === Subject: Re: Desire for fame is a bitch >> >> I thought I was set. With a high I.Q. group set to publish my paper >> on factoring polynomials into non-polynomial factors I figured that >> now certainly I could push my agenda to fame and fortune. I was >> wrong. >> >> So here I am back again, humbled yet again, as theres no escaping it, >> there is no way Ill get anywhere pissing off mathematicians. >> >> Let alone getting the mathematics wrong! >Ah, but you see, I know I do NOT have the math wrong as I explained >the argument in my paper to a Professor McKenzie at Vanderbilt >University *in person* and used a lot of chalkboard space while doing >it. Huh? The fact that you explained it shows its not wrong? >Heres a link to Vanderbilts page on him: >http://sitemason.vanderbilt.edu/site/czXIYM >He even shot down the objections of Magidin who intriguingly enough >went to a school where Professor McKenzie spent some time--Berkeley. Again: Did he shoot down _verbatim_ _quotations_ of Magidins objections, or was he dealing with your _paraphrases_ of Magidins objections. It matters, because it happens really a lot that you say someone said something that turns out to bear almost no resemblance to what he actually said. In any case, you say elsewhere that he blew you off. You seem to be implying that he agreed your work was correct - given that its very hard to figure out what you mean by saying he blew you off... >Yes, I mentioned the objections raised by people on the sci.math >newsgroup. >However, Professor McKenzie began claiming my work is algebraic >geometry which is out of his field. So I explained the entire thing >over more than an hour, having driven up four hours from Atlanta >metro, and he tells me its out of his field. >I checked with a Professor Kovaks at University of Washington and he >tells me its not algebraic geometry, but is algebraic number theory. Of course its not algebraic geometry. Anyone who thought it was is really not a very reliable source... >Worse, I specifically told Professor McKenzie that I was interested in >explaining my work, and would appreciate any help from my alma mater. >He claimed no one at Vanderbilt had the expertise, but a Professor >Kalman pointed out to me in an email that theres a Professor Megibben >at the school who does. >So at this point theres no doubt about the correctness of the paper >Advanced Polynomial Factorization. One of the most bizarre things youve ever said. The fact that there exists someone at Vanderbilt who knows something about some field shows that your work is correct? Heres a question: Supposing for the sake of argument that you found a professional mathematician who says your work is correct. Its not clear from what youre saying today whether or not youre even claiming that thats happened, but never mind, suppose its happened. You know that there exist many professional mathematicians who say your work is nonsense, or rather that the better parts of it are nonsense, while most of it is not clear enough to qualify for that label. Since the pros saying youre wrong dont prove youre wrong, _why_ do the hypothetical pros saying youre right prove youre right? Just curious. >James Harris David C. Ullrich ************************** As far as Im concerend youre trying to wait until I die, so I figure maybe you should die instead. How about that, eh? Wouldnt that be a better twist? You refuse to follow the math, so the great Powers that control reality and *speak* in mathematics decide to kill you instead of me. So what do you think about that, eh? Oh, cant hear Them talking? Well, I guess thats because you dont really understand Mathematics, the true language, which is THE language. Theyre talking about you now, and They agree with my assessment, and will not penalize me as They allowed the others like Galois and Abel to be penalized. They will kill you instead. James Harris speaking on Weird factorization, genius === Subject: Re: Desire for fame is a bitch Visiting Assistant Professor at the University of Montana. > > I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. > > So here I am back again, humbled yet again, as theres no escaping it, > there is no way Ill get anywhere pissing off mathematicians. > > Let alone getting the mathematics wrong! >>Ah, but you see, I know I do NOT have the math wrong as I explained >>the argument in my paper to a Professor McKenzie at Vanderbilt >>University *in person* and used a lot of chalkboard space while doing >>it. >Huh? The fact that you explained it shows its not wrong? No, its the fact that he used a lot of chalkboard space while doing it that shows its not wrong. Duh. [.snip.] >>Heres a link to Vanderbilts page on him: >>http://sitemason.vanderbilt.edu/site/czXIYM >>He even shot down the objections of Magidin who intriguingly enough >>went to a school where Professor McKenzie spent some time--Berkeley. Yes, he did. I know him, though he probably does not remember me. I used to play spades and bridge with a couple of his graduate students while I was a graduate student. >Again: Did he shoot down _verbatim_ _quotations_ of Magidins >objections, or was he dealing with your _paraphrases_ of Magidins >objections. >It matters, because it happens really a lot that you say someone >said something that turns out to bear almost no resemblance to >what he actually said. >In any case, you say elsewhere that he blew you off. You >seem to be implying that he agreed your work was correct - >given that its very hard to figure out what you mean by saying >he blew you off... Well, theres another point. One of the problems with his Advanced Polynomial Factorization is that it is not clear what it is he is saying; and as many have pointed out over several months, he could be saying true things, or he could be saying false things. However, as many others have pointed out as well, the true things he could be saying are not applicable to the situation he wants to apply them to, and the things which are applicable are not true. So it is entirely possible (even likely) that someone could say that what James says in Advanced Polynomial Factorization is correct; that does not mean that it is what James thinks he is saying is correct. [Gabriele Rossetti] has left a vast body of writings... in which he has attempted to prove the truth of his unorthodox interpre- tation of medieval literature. They present a formidable record of unsystematic research in which we see an enthusiast plunging farther and farther and farther from the logic of facts and good sense until truth is lost in the dreadful nightmare of an idee fixe. There is no real evolution of the Theory although it grows and expands until it embraces ever wider horizons. The numerous inaccuracies of deduction, mis-statements of historical fact, and self-contradictions...have caused critics to turn away from them in disgust... [...] It is impossible to read far... without realizing that we have to deal with a work of faith and imagination rather than of reasoning. There is an appearance of reason, for the author is set on proving by logic the truth of what he already believes by intuition. The truth is plain to him and he cannot comprehend why others do not immediately accept it, but as they desire demonstration he has multiplied his proofs. It is the redundancy and confusion of a prophet expounding by a familiar method the truth revealed to his own simple soul in a ßash of inspiration... In such work as this... it is idle to look for the calm reasoning of a scholar; we do not find it, and there is little or no advantage in attacking the obvious inconsistencies and absurdities that abound. -- E.R. Vincent, _Gabriele Rossetti in England_, quoted in _The Shakespearan Ciphers Examined_, by William F. Friedman and Elizebeth S. Friedman Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Desire for fame is a bitch > > > I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. > > So here I am back again, humbled yet again, as theres no escaping it, > there is no way Ill get anywhere pissing off mathematicians. > > Let alone getting the mathematics wrong! Ah, but you see, I know I do NOT have the math wrong as I explained >>the argument in my paper to a Professor McKenzie at Vanderbilt >>University *in person* and used a lot of chalkboard space while doing >>it. > >Huh? The fact that you explained it shows its not wrong? No, its the fact that he used a lot of chalkboard space while doing > it that shows its not wrong. Duh. [.snip.] Well, rationally, one would suppose that in explaining a math argument a person has to go step-by-step, which reveals all the logical links. >>Heres a link to Vanderbilts page on him: >>http://sitemason.vanderbilt.edu/site/czXIYM He even shot down the objections of Magidin who intriguingly enough >>went to a school where Professor McKenzie spent some time--Berkeley. Yes, he did. I know him, though he probably does not remember me. I > used to play spades and bridge with a couple of his graduate students > while I was a graduate student. I didnt give your name as it wasnt relevant. However, youve given the information that you know of him, and he IS your senior. He dismissed the objection youve used so often, and in fact, thats not surprising as it never made any sense to think that f divided off P(m) as some function of m or dependent on m, as its just not mathematics. Ive called it voodoo math. >Again: Did he shoot down _verbatim_ _quotations_ of Magidins >objections, or was he dealing with your _paraphrases_ of Magidins >objections. > >It matters, because it happens really a lot that you say someone >said something that turns out to bear almost no resemblance to >what he actually said. > >In any case, you say elsewhere that he blew you off. You >seem to be implying that he agreed your work was correct - >given that its very hard to figure out what you mean by saying >he blew you off... Well, theres another point. One of the problems with his Advanced > Polynomial Factorization is that it is not clear what it is he is > saying; and as many have pointed out over several months, he could be > saying true things, or he could be saying false things. However, as > many others have pointed out as well, the true things he could be > saying are not applicable to the situation he wants to apply them to, > and the things which are applicable are not true. So it is entirely > possible (even likely) that someone could say that what James says in > Advanced Polynomial Factorization is correct; that does not mean > that it is what James thinks he is saying is correct. A math professor senior to Magidin when presented with the objection Magidin has given for months, quickly dismissed it. Rather than simply tell the truth, Magidin now backs away from his original position, I guess now claiming that Professor McKenzie didnt understand what I was discussing. The conclusion of the paper Advanced Polynomial Factorization is that for the factorization 65x^3 - 12x + 1 = (a_1 x + 1)(a_2 x + 1)(a_3 x + 1) where the as are all algebraic integers, one of them is coprime to 5. The mathematics is mostly basic algebra with some basic algebraic manipulations. There simply isnt a lot of room for confusion. What some of you need to realize is that Magidin lied to you. You apparently wanted to believe the lie, so you accepted it *against* the math. Well I went and talked to a math professor in person and verified what I already knew, and it plays better so that now you see that Magidin stands against the discipline of mathematics. James Harris === Subject: Re: Desire for fame is a bitch Visiting Assistant Professor at the University of Montana. [.snip.] >Well, rationally, one would suppose that in explaining a math argument >a person has to go step-by-step, which reveals all the logical links. You would think so. Ive explained step by step why your claims about the roots of x^3+3x-2 are false. Did you look at it? [.snip.] >However, youve given the information that you know of him, and he IS >your senior. Surely thats irrelevant? I thought it wasnt about who had what degree, but about the math? (Yes, he is my better, by far. Hes a world-renowned expert in Universal Algebra, he solved the Tarski Problem a few years back, he invented Tame Congruence Theory, and has a significant number of accomplishments under his bel) >He dismissed the objection youve used so often, and in fact, thats >not surprising as it never made any sense to think that f divided off >P(m) as some function of m or dependent on m, as its just not >mathematics. Apparently, he dismissed what you think or what you told him was my objection. Your track record is clear: you have great difficulty in correctly paraphrasing other peoples objections. We have no way of knowing if what you told him was an accurate representation of my view, other than your say so. And you have been wrong on this subject pretty much every time youve tried to state what my objection is. But, tell you what: state my objection in full context, and provide a link to a post where I made it. Its not that f divided off P(m) as some function of m or dependent on m because I have never used the words divided off, so thats your paraphrase. And it depends very much on just what the heck f and P(m) are supposed to be. So, go ahead. Provide the complete statement, well see how accurate you were in reporting it. >Ive called it voodoo math. Yes. Youve also said that saying that something is a parameter is rejecting algebra. Did this professor also agree with you on that point? [.snip.] >>In any case, you say elsewhere that he blew you off. You >>seem to be implying that he agreed your work was correct - >>given that its very hard to figure out what you mean by saying >>he blew you off... >> >> Well, theres another point. One of the problems with his Advanced >> Polynomial Factorization is that it is not clear what it is he is >> saying; and as many have pointed out over several months, he could be >> saying true things, or he could be saying false things. However, as >> many others have pointed out as well, the true things he could be >> saying are not applicable to the situation he wants to apply them to, >> and the things which are applicable are not true. So it is entirely >> possible (even likely) that someone could say that what James says in >> Advanced Polynomial Factorization is correct; that does not mean >> that it is what James thinks he is saying is correct. >A math professor senior to Magidin when presented with the objection >Magidin has given for months, quickly dismissed it. Non sequitur. By your own standards, seniority is irrelevant, but let that be as it may. I have absolutely no problems admitting that Ralph McKenzie is way smarter than I am. However, there is not an iota of evidence that what you presented to this professor was an accurate report of my objection. >Rather than simply tell the truth, Magidin now backs away from his >original position, What was my original position? >I guess now claiming that Professor McKenzie didnt >understand what I was discussing. No, I did not make that claim. What I said, as shoudl be clear from a simple reading of the above, is that your Advanced Polynomial Factorization is unclear, and many statements are ambiguous. That certain interpretations of those statements lead to absolutely correct statements, which are not applicable in the situation you are trying to apply them (your FLT argument); and that certain interpretations of the ambiguous statements lead to absolutely false statements. Which interpretation did you present? >The conclusion of the paper Advanced Polynomial Factorization is that >for the factorization > 65x^3 - 12x + 1 = (a_1 x + 1)(a_2 x + 1)(a_3 x + 1) >where the as are all algebraic integers, one of them is coprime to 5. And that conclusion is false. Weve gone over it, in detail. But here it is again, just for you. Tell me which step you think is wrong. (Original calculations done by Dale Hall): 1. Let q1 = 8 (a_1)^2 - 76 (a_1) - 185 r1 = 8 (a_1)^2 - 4 (a_1) - 45 s1 = 4 (a_1)^2 - 37 (a_1) - 104 Since a_1 is an algebraic integer, each of q1, r1, s1 are algebraic integers. 2. Likewise, let q2 = 8 (a_2)^2 - 76 (a_2) - 185 r2 = 8 (a_2)^2 - 4 (a_2) - 45 s2 = 4 (a_2)^2 - 37 (a_2) - 104 and q3 = 8 (a_3)^2 - 76 (a_3) - 185 r3 = 8 (a_3)^2 - 4 (a_3) - 45 s3 = 4 (a_3)^2 - 37 (a_3) - 104 Each of q2, r2, s2, q3, r3, s3 are algebraic integers. 3. We have that q1*r1 = [8(a_1)^2 - 76(a_1) - 185][8(a_1)^2 - 4(a_1)-45] = 64(a_1)^4 - 32(a_1)^3 - 360(a_1)^2 -608(a_1)^3 + 304(a_1)^2 + 3420(a_1) -1480(a_1)^2 + 740(a_1) + 8325 = 64(a_1)^4 - 640(a_1)^3 - 1536(a_1)^2 + 4160(a_1) + 8325 Since (a_1)^3 - 12(a_1)^2 + 65 = 0, we have that (a_1)^3 = 12(a_1)^2 - 65 (a_1)^4 = 12(a_1)^3 - 65(a_1) = 12( 12(a_1)^2 - 65) - 65(a_1) = 144(a_1)^2 - 780 - 65(a_1) = 144(a_1)^2 - 65(a_1) - 780, so q1*r1 = 64(a_1)^4 - 640(a_1)^3 - 1536(a_1)^2 + 4160(a_1) + 8325 = 64 [144(a_1)^2 - 65(a_1) - 780] - 640 [12(a_1)^2 - 65] - 1536(a_1)^2 + 4160(a_1) + 8325 = 9216(a_1)^2 - 4160(a_1) - 49920 - 7680(a_1)^2 + 41600 -1536(a_1)^2 + 4160(a_1) + 8325 = 41600+8325-49920 = 5. Since (a_2)^3 - 12(a_2)^2 + 65 = 0 and (a_3)^3 - 12(a_3)^2 + 65 = 0, we also have q2*r2 = 5. q3*r3 = 5. 4. Using the same definitions, we have: r1*s1 = ( 8(a_1)^2 - 4(a_1) - 45) * (4(a_1)^2 - 37(a_1) - 104) = 32(a_1)^4 - 296(a_1)^3 - 832(a_1)^2 - 16(a_1)^3 + 148(a_1)^2 + 416(a_1) - 180(a_1)^2 +1665(a_1) + 4680 = 32(a_1)^4 - 312(a_1)^3 - 864(a_1)^2 + 2081(a_1) + 4680 = 32( 144(a_1)^2 - 65(a_1) - 780) - 312( 12(a_1)^2 - 65) - 864(a_1)^2 + 2081(a_1) + 4680 = 4608(a_1)^2 - 2080(a_1) - 24960 - 3744(a_1)^2 + 20280 - 864(a_1)^2 + 2081(a_1) + 4680 = (a_1) + 20280 + 4680 - 24960 = a_1 And so we also have r2*s2 = a_2 r3*s3 = a_3. 5. Since r1, s1, q1 are algebraic integers, r1*q1 = 5 and r1*s1 = a_1, it follows that r1 is a common algebraic integer factor of a_1 and 5. 6. Since r2, s2, q2 are algebraic integers, r2*q2 = 5 and r2*s2 = a_2, it follows that r2 is a common algebraic integer factor of a_2 and 5. 7. Since r3, s2, q3 are algebraic integers, r3*q3 = 5 and r3*q3 = a_3, it follows that r3 is a common algebraic integer factor of a_3 and 5. 8. We claim that r1, r2, and r3 are roots of the polynomial: f(x) = x^3 - 969 x^2 + 315 x + 5. To verify this, plug in the value of r1, and use the following identities: (a_1)^3 = 12(a_1)^2 - 65. (a_1)^4 = 144(a_1)^2 - 65(a_1) - 780. (a_1)^5 = (a_1)^3(a_1)^2 = (12(a_1)^2-65)(a_1)^2 = 12(a_1)^4 - 65(a_1)^2 = 12(144(a_1)^2 - 65(a_1)-780) - 65(a_1)^2 = 1728(a_1)^2 - 780(a_1) - 9360 - 65(a_1)^2 = 1663(a_1)^2 - 780(a_1) - 9360. (a_1)^6 = (a_1)^4 (a_1)^2 = (144(a_1)^2 - 65(a_1) - 780) (a_1)^2 = 144(a_1)^4 - 65(a_1)^3 - 780(a_1)^2 = 144 (144(a_1)^2 - 65(a_1) - 780) - 65(12(a_1)^2 - 65) - 780(a_1)^2 = 20736(a_1)^2 - 9360(a_1) - 112320 -780(a_1)^2 + 4225 -780(a_1)^2 = 19176(a_1)^2 - 9360(a_1) - 108095. Same for r2 and r3, replacing a_1 for a_2 and a_3, respectively (omitted for space). 9. f(x) is monic, primitive, and irreducible over Q. For the latter, the polynomial is reducible over Q if and only if it has a root over Q, since it is degree 3. The only possible rational roots, by the p/q test, are 1, -1, 5, and -5, and f(1) = -648 f(-1)=-1280 f(5) = -22520 f(-5)=-25920. 10. r1 is an algebraic integer unit if and only if 1/r1 (its multiplicative inverse) is also an algebraic integer. But 1/r1 is a root of the polynomial we obtain from f(x) = x^3 - 969 x^2 + 315 x + 5. by plugging in 1/x, setting equal to 0, and solving, that is, 1/r1 is a root of g(x) = 5x^3 + 315x^2 - 969x + 1 which is a primitive, non-monic, irreducible polynomial over Q. Therefore, none of its roots are algebraic integers. So 1/r1, a root, is not an algebraic integer. So r1 is not an algebraic integer unit. 11. Neither r2 nor r3 are algebraic integer units, since they are also roots of g(x). 12. So r1 is (a) an algebraic integer; and (b) a common factor of a_1 and 5 in the ring of algebraic integers; and (c) not a unit. Therefore, r1 is a non-unit common factor of a_1 and 5 (in the ring of algebraic integers). 13. By the same reasoning, r2 is a non-unit common factor of a_2 and 5 (in the ring of algebraic integers). 14. By the same reasoning, r3 is a non-unit common factor of a_3 and 5 (in the ring of algebraic integers). 15. Two algebraic integers x and y are not coprime (in the ring of all algebraic integers if and only if there is a common non-unit factor of x and y in the ring of all algebraic integers. [This is the definition you are using, and it is equivalent for this ring to the standard one] 16. Therefore, a_1 is not coprime to 5, a_2 is not coprime to 5, and a_3 is not coprime to 5. 17. Therefore, the claim that one of them is coprime to 5 is false. >The mathematics is mostly basic algebra with some basic algebraic >manipulations. The mathematics is basic algebraic manipulations, together with a basic theorem of algebra (roots of non-monic, primitive, irreducible polynomials with integer coefficients are not algebraic integers) which you have agreed. >There simply isnt a lot of room for confusion. >What some of you need to realize is that Magidin lied to you. You have never managed to justify this. It is nothing but your (false) assertion, made over and over again. It is libel. >Well I went and talked to a math professor in person and verified what >I already knew, and it plays better so that now you see that Magidin >stands against the discipline of mathematics. Whatever. Interesting that you now start claiming that professional standing ->is<- important. Why is it important that one professor, who did not say you were correct (the best you can say is he did not find an error), is my senior, but it is ->completely irrelevant<- that I am ->your<- senior in mathematics? Just curious. Why do you take so much trouble to expose such a reasoner as Mr. Smith? I answer as a deceased friend of mine used to answer on like occasions - A mans capacity is no measure of his power to do mischief. Mr. Smith has untiring energy, which does something; self-evident honesty of conviction, which does more; and a long purse, which does most of all. He has made at least ten publications, full of figures few readers can critize. A great many people are staggered to this extend, that they imagine there must be the indefinite something in the mysterious all this. They are brought to the point of suspicion that the mathematicians ought not to treat all this with such undisguised contempt, at least. -- A Budget of Paradoxes, Vol. 2 p. 129 by Augustus de Morgan Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Desire for fame is a bitch > And theres no website of mine, so no way to claim that Im NOT > dropping FLT and THE prime counting you evil bastards. Mr. Harris, that should have been you evil mathematical bastards! Oh, and thank you for such kind words regarding the folks in this group and mathematicians all over the world. You missed us didnt you! Hey! === Subject: Re: Desire for fame is a bitch > I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. > Didnt you go away? === Subject: Re: Desire for fame is a bitch >> I thought I was set. With a high I.Q. group set to publish my paper >> on factoring polynomials into non-polynomial factors I figured that >> now certainly I could push my agenda to fame and fortune. I was >> wrong. >Didnt you go away? I *knew* we couldnt trust him to get lost and stay lost. Id hoped, though, that it might take longer for him to come back this time since hed at least found some people he could *pay* to listen to him. -- Wayne Brown | When your tails in a crack, you improvise fwbrown@bellsouth.net | if youre good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock === Subject: Re: Desire for fame is a bitch I thought I was set. With a high I.Q. group set to publish my paper > on factoring polynomials into non-polynomial factors I figured that > now certainly I could push my agenda to fame and fortune. I was > wrong. The High IQ group is the same kind of jackass stunt you are, Harris. It is discredited as being a psychotics personal fetish. Said psychotic has been successfully sued to cease and desist. Here, Harris, go look at your sorry self, http://w0rli.home.att.net/youare.swf http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html -- Uncle Al http://www.mazepath.com/uncleal/eotvos.htm (Do something naughty to physics) === Subject: Professor McKenzie, problem with ring of A.I. I know you undergraduates have been frustrated with my continuing proclamations when I tend to go out of my way to piss off mathematicians. Ok, yeah, I admit it. Ive said some nasty stuff about mathematicos, but Ive recognized that pissing off mathematicians will NOT get me anywhere as hey, Im talking mathematics!!! In any event, I went back to my alma mater and talked to a Professor McKenzie. Heres a link to Vanderbilts page on him: http://sitemason.vanderbilt.edu/site/czXIYM And yes, Im very happy in one thing as finally sitting down with an actual mathematician I explained my entire paper Advanced Polynomial Factorization and he couldnt find anything wrong with it. He even shot down the objection that Magidin and others have used for so long dismissing it almost on sight. Then he said it was out of his area and thought it was algebraic geometry. So I contacted a Professor Kovacs at the University of Washington who happens to specialize in algebraic geometry. Heres what he said: James, %> If nothing else can you evaluate for me his claim that this paper is %> in the field of algebraic geometry? I looked at your paper, and actually, although related, this is not algebraic geometry. It belongs to algebraic number theory, as in general the study of algebraic integers does, as well as for example Galois Theory. Number theory connects to algebraic geometry through arithmetic geometry, but this is still not arithmetic geometry, either. Your professor was not far though as algebraic geometry studies solutions of polynomials. However, those solutions are generally regarded in a field and not among algebraic integers. -SK Well then that established that Professor McKenzie had been off, but was he really just toying with me? Its a good question. Then again I drove over FOUR HOURS to get to Nashville from here to talk to him. Sure hed said come by next time I was in Nashville, but what choice did I have? Im called a crank all over the web, desperate to get some kind of official recognition, so I drove up. Heres his invitation: If you are ever in Nashville, drop by my office (with some advance email notice so I can be sure to be there). If you can present these ideas to me for about an hour in a setting where I can ask a jillion questions, I imagine either I will come to understand what you are doing and possibly be able to show you some tricks for explaining it to other, or maybe I can be helpful even if it remains a mystery to me. Ralph McKenzie So I tried to get him to let me call him on the phone. Here was his reply: Sorry, over the phone will not work. Blackboard, time, two people present is the minimum requirement to accomplish anything. So I did it. I drove back to Vanderbilt, which was my first visit in over 12 years. I explained to Professor McKenzie, answered ALL objections, and he blew me off. Im a loser. ING super math discovery, a ING ERROR thats over a hundred years old and I ING piss off the only people who can help me. Screw with my alma mater Vanderbilt and all because I cant seem to work with people. But youre so dumb!!! Why cant any of you just accept mathematics? Why do you listen to proven liars like Magidin? Im screwed. Mathematicians dont accept mathematics. What can you do? Whats wrong with freaking mathematicians??!!! Whats wrong with you??!!! James Harris === Subject: Re: Professor McKenzie, problem with ring of A.I. James Harris: not only you seem to have a slanted understanding of mathematics (at best), but you also seem to have a lack of understanding of reason and implication. Furthermore, why do you think that misjudging the field where your nonsense might belong is toying with you? If you had seen the smallest glimpse of mathematics, you would appreciate the fact that it is sometimes hard to tell where a particular paper belongs to, especially, if 1) the paper does not make much sense, 2) the possible area is not ones expertise. These professors you are so ready to criticize and accuse devoted you. They gave you a respectable chance. Then they tried to give you their opinion in the most gentle way possible. They could have been much harsher on you. Instead of appreciating their efforts to protect your feelings, you come back with empty accusations. By the way, I am also a mathematician, so I am evil, too... Complete Moron === Subject: Re: Professor McKenzie, problem with ring of A.I. > I know you undergraduates have been frustrated with my continuing > proclamations when I tend to go out of my way to piss off > mathematicians. Ok, yeah, I admit it. Ive said some nasty stuff > about mathematicos, but Ive recognized that pissing off > mathematicians will NOT get me anywhere as hey, Im talking > mathematics!!! > In any event, I went back to my alma mater and talked to a Professor > McKenzie. > Heres a link to Vanderbilts page on him: > http://sitemason.vanderbilt.edu/site/czXIYM > And yes, Im very happy in one thing as finally sitting down with an > actual mathematician I explained my entire paper Advanced Polynomial > Factorization and he couldnt find anything wrong with it. > He even shot down the objection that Magidin and others have used for > so long dismissing it almost on sight. > Then he said it was out of his area and thought it was algebraic > geometry. > So I contacted a Professor Kovacs at the University of Washington who > happens to specialize in algebraic geometry. > Heres what he said: > > James, > %> If nothing else can you evaluate for me his claim that this > paper is > %> in the field of algebraic geometry? > I looked at your paper, and actually, although related, this is not > algebraic geometry. It belongs to algebraic number theory, as in > general the study of algebraic integers does, as well as for example > Galois Theory. > Number theory connects to algebraic geometry through arithmetic > geometry, but this is still not arithmetic geometry, either. > Your professor was not far though as algebraic geometry studies > solutions of polynomials. However, those solutions are generally > regarded in a field and not among algebraic integers. > -SK > > Well then that established that Professor McKenzie had been off, but > was he really just toying with me? > Its a good question. Then again I drove over FOUR HOURS to get to > Nashville from here to talk to him. Sure hed said come by next time > I was in Nashville, but what choice did I have? Im called a crank > all over the web, desperate to get some kind of official recognition, > so I drove up. > Heres his invitation: > > If you are ever in Nashville, drop by my office (with some advance > email notice so I can be sure to be there). If you can present these > ideas to me for about an hour in a setting where I can ask a jillion > questions, I imagine either I will come to understand what you are > doing and possibly be able to show you some tricks for explaining it > to other, or maybe I can be helpful even if it remains a mystery to > me. > Ralph McKenzie > > So I tried to get him to let me call him on the phone. Here was his > reply: > > Sorry, over the phone will not work. Blackboard, time, two people > present is the minimum requirement to accomplish anything. > > So I did it. I drove back to Vanderbilt, which was my first visit in > over 12 years. I explained to Professor McKenzie, answered ALL > objections, and he blew me off. > Im a loser. ING super math discovery, a ING ERROR thats > over a hundred years old and I ING piss off the only people who > can help me. Screw with my alma mater Vanderbilt and all because I > cant seem to work with people. > But youre so dumb!!! Why cant any of you just accept mathematics? > Why do you listen to proven liars like Magidin? > Im screwed. Mathematicians dont accept mathematics. > What can you do? > Whats wrong with freaking mathematicians??!!! Whats wrong with > you??!!! > James Harris Maybe, you should stick to nursing in the Army Reserves James. Lurch === Subject: Re: Professor McKenzie, problem with ring of A.I. > Im screwed. Mathematicians dont accept mathematics. > What can you do? > Whats wrong with freaking mathematicians??!!! Whats wrong with > you??!!! You know, when everyone tells you youre wrong, that does NOT mean that youre wrong. On the other hand, in that case you should at least consider the possibility. I might add that when you ask such questions as Whats wrong with you? you are acconplishing little more than assuring that you have an unsympathetic audience. If you have something valid to say, it should stand on its own merits, this is true. It shouldnt matter whether anyone likes you. However, thats not how things really work. Especially in a matter that requires training and thought, few people are going to exert themselves much to review your work, or even to glance at it if youve pissed them off. Asking someone whats wrong with you? is very likely to piss them off. Rather than just trying to fix blame on people, I think youd be better served simply showing them your work and asking for their professional opinion. Otherwise, youll very likely remain a voice crying in the wilderness. And Ill add that you should be open to the possibility that there may be errors in your work, lest you end up persisting in error and becoming more of a pariah. Just some thoughts... === Subject: Re: Professor McKenzie, problem with ring of A.I. Visiting Assistant Professor at the University of Montana. >He even shot down the objection that Magidin and others have used for >so long dismissing it almost on sight. He did? Did he shoot down my (single?) objection? Did he read ->my<- words, or was it something you, ehr, explained to him? Because you have a track record of just not getting what the objection is. It is interesting that I do not see anything in your correspondences below with Ralph McKenzie or anyone else that even mentions me, though. Its not denial. Im just very selective about what I accept as reality. --- Calvin (Calvin and Hobbes) Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Professor McKenzie, problem with ring of A.I. >I know you undergraduates have been frustrated with my continuing >proclamations when I tend to go out of my way to piss off >mathematicians. Ok, yeah, I admit it. Ive said some nasty stuff >about mathematicos, but [i] >Ive recognized that pissing off >mathematicians will NOT get me anywhere >as hey, Im talking >mathematics!!! >In any event, I went back to my alma mater and talked to a Professor >McKenzie. >Heres a link to Vanderbilts page on him: > >http://sitemason.vanderbilt.edu/site/czXIYM [ii] >And yes, Im very happy in one thing as finally sitting down with an >actual mathematician I explained my entire paper Advanced Polynomial >Factorization and he couldnt find anything wrong with it. >He even shot down the objection that Magidin and others have used for >so long dismissing it almost on sight. >[...] [ii] > I drove back to Vanderbilt, which was my first visit in >over 12 years. I explained to Professor McKenzie, answered ALL >objections, and he blew me off. >Im a loser. ING super math discovery, a ING ERROR thats >over a hundred years old and I ING piss off the only people who >can help me. Screw with my alma mater Vanderbilt and all because I >cant seem to work with people. [iv] >But youre so dumb!!! Why cant any of you just accept mathematics? >Why do you listen to proven liars like Magidin? >Im screwed. Mathematicians dont accept mathematics. >What can you do? >Whats wrong with freaking mathematicians??!!! Whats wrong with >you??!!! We have serious problems with consistency here. [ii] says youre happy that McKenzie shot down Magidins objections (just curious: did you show him some _verbatim_ _quotes_ of Magidins objections, or did he shoot down your _paraphrase_ of Magidin? See, it happens a lot that you misrepresent peoples positions...) and then in [iii] you say he blew you off. Dont get it - he agreed that youre right about everything but also explained why youre all wrong? Then theres the apparent inconcistency between [i] and [iv]... Hint: if you dont want to piss people off then a good start would be to refrain from calling them dumb liars. >James Harris David C. Ullrich ************************** As far as Im concerend youre trying to wait until I die, so I figure maybe you should die instead. How about that, eh? Wouldnt that be a better twist? You refuse to follow the math, so the great Powers that control reality and *speak* in mathematics decide to kill you instead of me. So what do you think about that, eh? Oh, cant hear Them talking? Well, I guess thats because you dont really understand Mathematics, the true language, which is THE language. Theyre talking about you now, and They agree with my assessment, and will not penalize me as They allowed the others like Galois and Abel to be penalized. They will kill you instead. James Harris speaking on Weird factorization, genius === Subject: Re: Professor McKenzie, problem with ring of A.I. > Im a loser. ING super math discovery, a ING ERROR thats > over a hundred years old and I ING piss off the only people who > can help me. Screw with my alma mater Vanderbilt and all because I > cant seem to work with people. > But youre so dumb!!! Why cant any of you just accept mathematics? > Why do you listen to proven liars like Magidin? > Im screwed. Mathematicians dont accept mathematics. > What can you do? > Whats wrong with freaking mathematicians??!!! Whats wrong with > you??!!! Maybe mathematics is not what you think it is. Dirk Vdm === Subject: Re: Professor McKenzie, problem with ring of A.I. > Im a loser. ING super math discovery, a ING ERROR thats > over a hundred years old and I ING piss off the only people who > can help me. Screw with my alma mater Vanderbilt and all because I > cant seem to work with people. So post this discovery for all to see. Sure there are naysayers whos only job in life is to make sure no one knows anything they dont already understand. A few naysayers are capable of disproving things, and so can be used to find problems with a theory. Problems that might be interesting to solve. There are also explorers here, people interested in the interesting. So post away === Subject: Re: Professor McKenzie, problem with ring of A.I. Im a loser. ING super math discovery, a ING ERROR thats > over a hundred years old and I ING piss off the only people who > can help me. Screw with my alma mater Vanderbilt and all because I > cant seem to work with people. So post this discovery for all to see. Sure there are naysayers whos only job in life is to make sure no one knows > anything they dont already understand. A few naysayers are capable of > disproving things, and so can be used to find problems with a theory. > Problems that might be interesting to solve. There are also explorers here, people interested in the interesting. So post > away Ive posted it before as I found a way using *non* polynomial factors of a polynomial to show a problem with the ring of algebraic integers. Id be happy to explain again in detail in this thread. However, you might want to check out the following link where Ive gone into detail at a site that takes LaTeX, so it looks prettier: http://mathdb.math.cuhk.edu.hk/forum/e_show.php?msg=759 Hope that works. Tell me if it doesnt. I call using non-polynomial factors to factor a polynomial, non-polynomial factorization. James Harris === Subject: one-sided limits Suppose f is bounded, measurable on R. How do you show Lim (t -> 0) 1/(4 pi t) INTEGRAL( -oo , oo ) exp[ -(x-y)^2 / (4t) ] f(y) dy = [ F_l(x) + F_r(x) ] / 2 where F_l(x) = lim f(y) as y goes to x from the left and F_r(x) = lim f(y) as y goes to x from the right (assuming of course that these one-sided limits exist for f)? If both limits are equal, I have no problem showing Lim (t -> 0) 1/(4 pi t) INTEGRAL( -oo , oo ) exp[ -(x-y)^2/(4t) ] f(y) dy = f(x) using real analysis methods and things like this, but what to do when the limits dont necessarily agree? === Subject: Re: one-sided limits > Suppose f is bounded, measurable on R. How do you show Lim (t -> 0) 1/(4 pi t) INTEGRAL( -oo , oo ) exp[ -(x-y)^2 / (4t) ] > f(y) dy = [ F_l(x) + F_r(x) ] / 2 where F_l(x) = lim f(y) as y goes to x from the left and > F_r(x) = lim f(y) as y goes to x from the right (assuming of course that these one-sided limits exist for f)? If both limits are equal, I have no problem showing Lim (t -> 0) 1/(4 pi t) INTEGRAL( -oo , oo ) exp[ -(x-y)^2/(4t) ] f(y) > dy = f(x) using real analysis methods and things like this, but what to do when > the limits dont necessarily agree? I assume t > 0 in the above. WLOG, x = 0. Define g = 1 to the right of 0, g = -1 to the left of 0. Then the result holds for g, because exp(-y^2/t) is even. If f has limit R from the right and limit L from the left, consider f + [(L-R)/2]*g; this function has the same limit from left and right. === Subject: Talk to a mathematician (Op-Ed) Obviously Im rather gleeful at having managed to talk over my work which reveals that wacky problem with algebraic integers with an actual, real-live mathematician, and not a possibly fake one that just posts a lot on Usenet!!! Yes I used chalk and went over it all on the chalkboard and even talked over some of the math history like talking about Dedekind. What I verified is that oddity that you CAN talk to a mathematician, give a correct math argument, go over each and every point step-by-step, yet have that mathematician simply dismiss you. In this case the professor claimed it was out of his area, and gee, guess what? According to him no one else at Vanderbilt University had the necessary expertise. Basically he was blowing me off, but not because I was wrong. Remember, Id gone over each and every point step-by-step. It seems to me that clearly he *knew* he could simply reject my work because hes a mathematician, and thats what a mathematician can do. However, now at least I know that I can explain my work, refute all objections, and still face mathematicians willing to just ignore it like that professor, or lie about it on Usenet. And hey, you all knew that, right? You knew that people on Usenet like lie all the time and that even mathematicians who post will lie. Well Ill give that professor one bit of praise, at least he didnt claim my work was incorrect. And he dismissed the objection that certain lying mathematician posters have used repeatedly, I guess because they know that most of you are too stupid to catch them. The professor trashed it in an instance. Too bad other mathematicians who have posted a lot on Usenet werent smart enough at least not to lie about my work, but hey, they know they can lie to most of you, now cant they? And I dont really think its that youre all too stupid to catch the lies, as I think you just *want* to believe. After all, its a simpler world where Im just a nut, instead of a major discoverer who found an over hundred year old error in core mathematics, right? James Harris === Subject: Re: Talk to a mathematician (Op-Ed) >Obviously Im rather gleeful at having managed to talk over my work >which reveals that wacky problem with algebraic integers with an >actual, real-live mathematician, and not a possibly fake one that just >posts a lot on Usenet!!! >Yes I used chalk and went over it all on the chalkboard and even >talked over some of the math history like talking about Dedekind. >What I verified is that oddity that you CAN talk to a mathematician, >give a correct math argument, go over each and every point >step-by-step, yet have that mathematician simply dismiss you. Fascinating. He did in fact dismiss your work, but nonetheless this fills you with glee. >In this >case the professor claimed it was out of his area, and gee, guess >what? According to him no one else at Vanderbilt University had the >necessary expertise. >Basically he was blowing me off, but not because I was wrong. Of course not. No matter how many people, usenet posters, journal editors, famous mathematicians you pester with email, mathematicians you visit in person, no matter _how_ many of them say youre wrong, its simply not possible that the reason theyre all saying that is that youre _wrong_. >Remember, Id gone over each and every point step-by-step. It seems >to me that clearly he *knew* he could simply reject my work because >hes a mathematician, and thats what a mathematician can do. >However, now at least I know that I can explain my work, refute all >objections, and still face mathematicians willing to just ignore it >like that professor, or lie about it on Usenet. >And hey, you all knew that, right? You knew that people on Usenet >like lie all the time and that even mathematicians who post will lie. >Well Ill give that professor one bit of praise, at least he didnt >claim my work was incorrect. And he dismissed the objection that >certain lying mathematician posters have used repeatedly, I guess >because they know that most of you are too stupid to catch them. The >professor trashed it in an instance. Answer the question. Youve been asked at least four times by now: Did he refute a _verbatim_ _quote_ of Magidins objections, or your paraphrase of them? >Too bad other mathematicians who have posted a lot on Usenet werent >smart enough at least not to lie about my work, but hey, they know >they can lie to most of you, now cant they? >And I dont really think its that youre all too stupid to catch the >lies, as I think you just *want* to believe. After all, its a >simpler world where Im just a nut, instead of a major discoverer who >found an over hundred year old error in core mathematics, right? >James Harris ************************ David C. Ullrich === Subject: Re: Talk to a mathematician (Op-Ed) > >Obviously Im rather gleeful at having managed to talk over my work >which reveals that wacky problem with algebraic integers with an >actual, real-live mathematician, and not a possibly fake one that just >posts a lot on Usenet!!! > >Yes I used chalk and went over it all on the chalkboard and even >talked over some of the math history like talking about Dedekind. > >What I verified is that oddity that you CAN talk to a mathematician, >give a correct math argument, go over each and every point >step-by-step, yet have that mathematician simply dismiss you. Fascinating. He did in fact dismiss your work, but nonetheless > this fills you with glee. However, the imporant point is that he couldnt find an error. There are people who *dismiss* the idea that man landed on the moon. The key issue here is mathematical correctness. My point is that I went through the math point-by-point and the professor could not find an error. >In this >case the professor claimed it was out of his area, and gee, guess >what? According to him no one else at Vanderbilt University had the >necessary expertise. > >Basically he was blowing me off, but not because I was wrong. Of course not. No matter how many people, usenet posters, > journal editors, famous mathematicians you pester with email, > mathematicians you visit in person, no matter _how_ many of > them say youre wrong, its simply not possible that the reason > theyre all saying that is that youre _wrong_. But youre now lying David Ullrich as my point is that Professor McKenzie did NOT say that I was wrong. It is such an obvious falsehood that I feel confident in calling you out here as a liar. The issue is mathematical correctness. And your implication that its so rejected is false, as in fact a key paper of mine is to be published. See http://www.megasociety.net/NoesisHighlights.html >Remember, Id gone over each and every point step-by-step. It seems >to me that clearly he *knew* he could simply reject my work because >hes a mathematician, and thats what a mathematician can do. > >However, now at least I know that I can explain my work, refute all >objections, and still face mathematicians willing to just ignore it >like that professor, or lie about it on Usenet. > >And hey, you all knew that, right? You knew that people on Usenet >like lie all the time and that even mathematicians who post will lie. > >Well Ill give that professor one bit of praise, at least he didnt >claim my work was incorrect. And he dismissed the objection that >certain lying mathematician posters have used repeatedly, I guess >because they know that most of you are too stupid to catch them. The >professor trashed it in an instance. Answer the question. Youve been asked at least four times by now: > Did he refute a _verbatim_ _quote_ of Magidins objections, or your > paraphrase of them? He refuted the assertion that f or factors in common with f can divide off dependent on m or as functions of m. He quickly dismissed it, which confirmed for me that an experienced mathematician wouldnt take it seriously, even for a moment, confirming that Magidin was, as I figured, lying. Unless you wish to claim that Magidin is incompetent. >Too bad other mathematicians who have posted a lot on Usenet werent >smart enough at least not to lie about my work, but hey, they know >they can lie to most of you, now cant they? > >And I dont really think its that youre all too stupid to catch the >lies, as I think you just *want* to believe. After all, its a >simpler world where Im just a nut, instead of a major discoverer who >found an over hundred year old error in core mathematics, right? That quick dismissal of a key objection confirmed my suspicion of a high *tolerance* of readers to lies from certain sources. Apparently, many of you decided to accept false mathematics from posters like Magidin; however, in a different context--off Usenet--an experienced mathematician quickly rejected the same objection which apparently satisfied many of you who are on sci.math for MONTHS. Magidin gave you what you wanted, where you clearly wanted to hear that I was wrong, and the mathematical truth didnt matter to you, as you so readily accepted the lies. The point is that the math didnt matter to readers on the sci.math newsgroup, or Magidins false claims would have been dismissed as quickly there, as in that professors office. The math didnt matter to you. James Harris === Subject: Re: Talk to a mathematician (Op-Ed) > The key issue here is mathematical correctness. My point is that I > went through the math point-by-point and the professor could not find > an error. The key issue here is that weve seen *many* people point out *many* errors to you, which you simply ignore. Then you post another load of tripe claiming that no one can find an error. So, Im certain this professor found errors which you refused to acknowledge, until he finally gave up and fobbed you off with that excuse about it being out of his area. (Translation: Its clear youre just wasting my time, so Im going to get rid of you however I can.) > And your implication that its so rejected is false, as in fact a key > paper of mine is to be published. > See http://www.megasociety.net/NoesisHighlights.html Yes, its being published in a vanity rag by a group of con artists who charge crackpots like yourself for the feeling of being special. -- Wayne Brown | When your tails in a crack, you improvise fwbrown@bellsouth.net | if youre good enough. Otherwise you give | your pelt to the trapper. e^(i*pi) = -1 -- Euler | -- John Myers Myers, Silverlock === Subject: Re: Talk to a mathematician (Op-Ed) [.snip.] >> Answer the question. Youve been asked at least four times by now: >> Did he refute a _verbatim_ _quote_ of Magidins objections, or your >> paraphrase of them? >He refuted the assertion that f or factors in common with f can divide >off dependent on m or as functions of m. Absent context, this statement is meaningless. >He quickly dismissed it, which confirmed for me that an experienced >mathematician wouldnt take it seriously, even for a moment, >confirming that Magidin was, as I figured, lying. Unless you wish to >claim that Magidin is incompetent. Please provide a verbatim quote of: (1) What I am alleged to have said; (2) What you said; (3) What Prof. McKenzie said; Then explain why that means that I was lying. For instance, I have never used the words divide off dependent on m, so the statement above cannot be something ->I<- said. It looks, as usual, like what you claim or think I said, based on your lack of understanding. You have accused me of lying for years now. Will you ever produce a direct quote of something I said, in context, which is a lie? Challenging your current assertion does not count, because the correctness of your current assertion is ->precisely<- the matter at issue. I could just as easily call you a liar for saying something is true when Ive said its false and given you an explanation for why it is false. >That quick dismissal of a key objection confirmed my suspicion of a >high *tolerance* of readers to lies from certain sources. I have never said that something divides off, let alone dependent on m. I have no idea what it is you think was my objection, but it is certainly not what you have just reported here. What it looks like is that you either presented something DIFFERENT from what I objected to, or you reported my objection as something DIFFERENT from what I actually said. Which would make you a...n individual confused as to the truth. >The point is that the math didnt matter to readers on the sci.math >newsgroup, or Magidins false claims would have been dismissed as >quickly there, as in that professors office. Please provide verbatim quote of me saying that something divides off dependent on m, or else admit that what may or may not have been dismissed in that office was YOUR VERSION of what I may or may not have said. [Gabriele Rossetti] has left a vast body of writings... in which he has attempted to prove the truth of his unorthodox interpre- tation of medieval literature. They present a formidable record of unsystematic research in which we see an enthusiast plunging farther and farther and farther from the logic of facts and good sense until truth is lost in the dreadful nightmare of an idee fixe. There is no real evolution of the Theory although it grows and expands until it embraces ever wider horizons. The numerous inaccuracies of deduction, mis-statements of historical fact, and self-contradictions...have caused critics to turn away from them in disgust... [...] It is impossible to read far... without realizing that we have to deal with a work of faith and imagination rather than of reasoning. There is an appearance of reason, for the author is set on proving by logic the truth of what he already believes by intuition. The truth is plain to him and he cannot comprehend why others do not immediately accept it, but as they desire demonstration he has multiplied his proofs. It is the redundancy and confusion of a prophet expounding by a familiar method the truth revealed to his own simple soul in a ßash of inspiration... In such work as this... it is idle to look for the calm reasoning of a scholar; we do not find it, and there is little or no advantage in attacking the obvious inconsistencies and absurdities that abound. -- E.R. Vincent, _Gabriele Rossetti in England_, quoted in _The Shakespearan Ciphers Examined_, by William F. Friedman and Elizebeth S. Friedman Arturo Magidin magidin@math.berkeley.edu === Subject: Re: Talk to a mathematician (Op-Ed) David C. Ullrich scribbled the following on sci.math: >>In this >>case the professor claimed it was out of his area, and gee, guess >>what? According to him no one else at Vanderbilt University had the >>necessary expertise. >>Basically he was blowing me off, but not because I was wrong. > Of course not. No matter how many people, usenet posters, > journal editors, famous mathematicians you pester with email, > mathematicians you visit in person, no matter _how_ many of > them say youre wrong, its simply not possible that the reason > theyre all saying that is that youre _wrong_. What a wonderful quote, David. Can I have your permission to print this out and put on my wall? -- /-- Joona Palaste (palaste@cc.helsinki.fi) --------------------------- | Kingpriest of The Flying Lemon Tree G++ FR FW+ M- #108 D+ ADA N+++| | http://www.helsinki.fi/~palaste W++ B OP+ | ----------------------------------------- Finland rules! ------------/ Outside of a dog, a book is a mans best friend. Inside a dog, its too dark to read anyway. - Groucho Marx === Subject: Re: Talk to a mathematician (Op-Ed) .... After all, its a > simpler world where Im just a nut, instead of a major discoverer who > found an over hundred year old error in core mathematics, right? Yes, right. Or at least, nearly so. Id replace nut with silly person who could learn some [not all that difficult] mathematics, but chooses not to. -- G.C. === Subject: Re: Talk to a mathematician (Op-Ed) .... After all, its a > simpler world where Im just a nut, instead of a major discoverer who > found an over hundred year old error in core mathematics, right? Yes, right. Or at least, nearly so. Id replace nut with silly > person who could learn some [not all that difficult] mathematics, but > chooses not to. Which defies the fact that I *explained* my mathematical argument point-by-point in person to an actual math professor. That professor did NOT find any error, but instead claimed my work was out of his area. However, given that information, you choose to claim that I am a silly person who needs to learn mathematics, which is an odd response. Oh, in case any of you are wondering, he did challenge me throughout the discussion on many points. Its just that the mathematics is rather basic and easy, so even a well-trained mathematician cant successfully challenge a *single* point of it with mathematics. What has happened on Usenet when I discuss the same argument is simple, posters have lied. When Ive called them on lies, they lie again. Strangely, on the sci.math newsgroup, these lies have simply not been challenged by other posters. If any wish to dispute that assessment, I welcome them or any of those who have disputed my argument in the past to come forward here with a *mathematical* objection and Ill explain--yet again--why its wrong or doesnt apply. James Harris === Subject: Re: Talk to a mathematician (Op-Ed) > > .... After all, its a > simpler world where Im just a nut, instead of a major discoverer who > found an over hundred year old error in core mathematics, right? > > Yes, right. Or at least, nearly so. Id replace nut with silly > person who could learn some [not all that difficult] mathematics, but > chooses not to. > Which defies the fact that I *explained* my mathematical argument > point-by-point in person to an actual math professor. That professor > did NOT find any error, but instead claimed my work was out of his > area. > However, given that information, you choose to claim that I am a > silly person who needs to learn mathematics, which is an odd > response. > Oh, in case any of you are wondering, he did challenge me throughout > the discussion on many points. Its just that the mathematics is > rather basic and easy, so even a well-trained mathematician cant > successfully challenge a *single* point of it with mathematics. Nonsense. It has not only been successfully challenged, repeatedly, but successfully refuted, repeatedly. You are in denial to the point of complete fabrication. > What has happened on Usenet when I discuss the same argument is > simple, posters have lied. When Ive called them on lies, they lie > again. Strangely, on the sci.math newsgroup, these lies have simply > not been challenged by other posters. > If any wish to dispute that assessment, I welcome them or any of those > who have disputed my argument in the past to come forward here with a > *mathematical* objection and Ill explain--yet again--why its wrong > or doesnt apply. You do not explain--yet again when confronted with dispute. You either ignore the specific challenge completely (too often to count) or simply repeat your faulty argument, over and over. Case in point: Arturo Magidins recent post with 7 specific questions requiring little more than Ôyes or Ôno answers. Shame on you. Thats not rational. -- There are two things you must never attempt to prove: the unprovable -- and the obvious. -- Democracy: The triumph of popularity over principle. -- http://www.crbond.com === Subject: Re: Talk to a mathematician (Op-Ed) Obviously Im rather gleeful at having managed to talk over my work > which reveals that wacky problem with algebraic integers with an > actual, real-live mathematician, and not a possibly fake one that just > posts a lot on Usenet!!! Hey stooopid Harris, one demonstrated disproof is death of a theory. You have been killed so many times you are rotted in place. http://w0rli.home.att.net/youare.swf http://www.mazepath.com/uncleal/sunshine.jpg http://www.you-moron.com/ http://www.apa.org/journals/psp/psp7761121.html http://insti.physics.sunysb.edu/~siegel/quack.html -- Uncle Al http://www.mazepath.com/uncleal/ (Toxic URL! Unsafe for children and most mammals) Quis custodiet ipsos custodes? The Net!