mm-129 David Ullrich says: And yes, identity is in _fact_ re呈xive. To> refute that statement you need to give an> example of something which is not identical> to itself. The idea that there is something> which is _not_ identical to itself is simply> ludicrous: ThatOs what identity _means_: A> thing is identical to itself and to nothing For a contrasting standpoint, see> ************************************************************* *> David Ullrich asks: WhatOs an example of something thats not identical ************************************************************* *> David Ullrich dares: Exhibit of proof of Ex~(x=x) from> C1-C4 and someone will point out the error.>C1 AxAy[x=y -> Az(z in x <-> z in y)] LL1>>C2 AxAy[Az(z in x <-> z in y) -> Az(x in z <-> y in z)] LL2> >>C3 EyAx[x in y <-> Et(x in t) & A] (with y not free in A)>>Classi'cation> >>C4 AxAy[Az(z in x <-> z in y) -> {Et(x in t & y in t) <-> x=y}]> Weak Would someone be kind enough help David out with a proof?> ************************************************************* > David Ullrich remonstrates: I OblunderO by saying that equality is re呈xive by de'nition?> Huh. Do you have any idea what the word de'nition means? Homework for David Ullrich: 1) What philosopher said: ...de'nitions are available only for transforming> truths, not for founding them. 2) In your own words, explain why (or why not) you think> this is true. --John Because IOm stupid, can anyone tell me whatOs the point of this discussion? Because youOre stupid, why would anyone want to bother? Because, under certain situations, like the one you are involved,> stupidity suf'ces in providing the answer. > True, the provability of Ex~(x=x) will vary from one system to> the next. Nevertheless, there is more to truth than> Otruth-in-a-modelO;> and just as the truth of Ex~(x is red) depends on how things stand> with individuals and redness so the truth of Ex~(x=x) depends on> how things stand with individuals and identity. Because IOm stupid, can you offer an example where Ex~(x=x) is true? IOll provide not one but THREE examples. The 'rst> depends on a (very simple) proof that DAVID ULLRICH COULDNOT HACK! A) Take any OpureO 'rst order logic, that is, any FOL with no> singular terms other than variables (just to keep things simple). B) To your FOL add this formation rule;> > If a and b are variables, a=b is an atomic formula. and this axiom scheme: Let be C and D be wffOs which differ only in that a occurs free> in C where b occurs free in D. If a=b, then C <-> D. C) Call the resulting logic FOL+. In FOL+, identity is symmetric and transitive and identicals are> indiscernible, but neither Ax(x=x) nor ~Ax(x=x) is a thesis. So,> FOL+ is a subtheory of FOL= (because every thesis of FOL+ is> also a thesis of FOL=), but not conversely (because Ax(x=x)> is a thesis of FOL= but not of FOL+). Example 1: Set Theory Add to FOL+ the NBG axiom scheme, C3, and CorreyOs principle of> extensionality, C4: C3 EyAx[x in y <-> Et(x in t) & A] (with y not free in A) Classi'cation> > C4 AyAx[Az(z in y <-> z in x) -> {(set y & set x) <-> y=x}]> (Equi-membered classes are identical iff these are sets.) > 1) EyAx(x in y <-> Et(x in t) & ~(x in x)) C3 Hence 2) Ax(x in r <-> Et(x in t) & ~(x in x)) 1,EI and 3) r in r <-> (Et(r in t) & ~(r in r)) 2,UI so that 4) ~Et(r in t) 3 and 5) ~(set r) 4 and 6) ~(r=r) 5,C4 so that 7) Ex~(x=x) 6,EG To be continued. --JohnGood. WhatOs your thoughts on this:I believe Aristotle de'ned identity as (x --> x) and not as (x = x).DonOt you loose the transitive property if you use the formerde'nition?Then your proof breaks down.What about that?As far as IOm conserned, identity means x --> x and not x = x, as thelatter de'nition leads to paradoxes. Anyway, IOm trying to callAristotle on his mobile phone but itOs out of cell reach...:) > A) Take any OpureO 'rst order logic, that is, any FOL with no>> singular terms other than variables (just to keep things simple).>> B) To your FOL add this formation rule;>> >> If a and b are variables, a=b is an atomic formula.>> and this axiom scheme:>> Let be C and D be wffOs which differ only in that a occurs free>> in C where b occurs free in D. If a=b, then C <-> D.>> C) Call the resulting logic FOL+.>> Crass formalism.Using the symbol = to denote something other than equality/identitydoesnOt make equality/identity intransitive.-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) >>> A) Take any OpureO 'rst order logic, that is, any FOL with no>>> singular terms other than variables (just to keep things simple).>>>> B) To your FOL add this formation rule;>>> >>> If a and b are variables, a=b is an atomic formula.>>>> and this axiom scheme:>>>> Let be C and D be wffOs which differ only in that a occurs free>>> in C where b occurs free in D. If a=b, then C <-> D.>>>> C) Call the resulting logic FOL+.>>>Crass formalism.>>Using the symbol = to denote something other than equality/identity>doesnOt make equality/identity intransitive.Indeed. How many legs does a dog have if you call the tail a leg?************************David C. Ullrich >>Using the symbol = to denote something other than equality/identity>>doesnOt make equality/identity intransitive. Indeed. How many legs does a dog have if you call the tail a leg?> I was going to say four, calling a tail a leg doesnOt make atail a leg but then I remembered that IOve occasionallyseen three-legged dogs. :-)-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.html The League of Gentlemen A) Take any OpureO 'rst order logic, that is, any FOL with no>> singular terms other than variables (just to keep things simple).>> B) To your FOL add this formation rule;>> >> If a and b are variables, a=b is an atomic formula.>> and this axiom scheme:>> Let be C and D be wffOs which differ only in that a occurs free>> in C where b occurs free in D. If a=b, then C <-> D.>> C) Call the resulting logic FOL+.> > Crass formalism. Using the symbol = to denote something other than equality/identity> doesnOt make equality/identity intransitive.YouOve far more talent for dancing on Pertti LounestoOs gravethan you have for logic:******************************************************* ***************> I have received the following message concerning> a once-frequent participant in sci.math. -- Bertfried.Fauser@uni-konstanz.de>> THIS IS WITH GREAT REGRETS THAT WE LET YOU KNOW THAT > PERTTI LOUNESTO HAS DIED WHEN SWIMMING IN CRETE ON JUNE 21. > HE WAS A FRIEND AND INSPIRATION OF MANY OF US. > HE WILL BE MISSED. > CONDOLENCES 40tntech.edu&output=gplain > Pertti Lounesto> - born in Finland> - invented quadratic nature of triality ..[1]> in Finland> - will die in Finland I am sorry to hear that he has been falsi'ed in such a way :-(> -- Robin Chapman =[of Robin Chapman]> YouOve far more talent for dancing on Pertti LounestoOs grave> than you have for logic:Nobody was dancing. The *only* thing that happened was that youmisread. And there was even a frownie to guide you! Are youstupid or something?In any case, this is irrelevant to the current discussion and itis tasteless of you to bring it up at all, which is why I donOtmind insulting you....>> Pertti Lounesto> - born in Finland> - invented quadratic nature of triality ..[1]> in Finland> - will die in Finland>> I am sorry to hear that he has been falsi'ed in such a way :-(> -- Robin ChapmanAmen. >[of Robin Chapman]>>> YouOve far more talent for dancing on Pertti LounestoOs grave>> than you have for logic:>>Nobody was dancing. This has been explained to him many times. HeOs immune tothings like rational explanations of why heOs simply wrongabout something.>The *only* thing that happened was that you>misread. And there was even a frownie to guide you! Are you>stupid or something?>>In any case, this is irrelevant to the current discussion Of course itOs relevant! The poor guy canOt even get acceptedbe the Mega Foundation (and they let _Harris_ in) - the onlyway heOs going to get his genius recognized is to convincethe world that people with radical notions like everythingis equal to itself are evil.>and it>is tasteless of you to bring it up at all, which is why I donOt>mind insulting you.>>...>>>>> Pertti Lounesto>> - born in Finland>> - invented quadratic nature of triality ..[1]>> in Finland>> - will die in Finland>>>> I am sorry to hear that he has been falsi'ed in such a way :-(>> -- Robin Chapman>>Amen.************************David C. Ullrich = Because IOm stupid, can anyone tell me whatOs the point of> this discussion? >> So, what is going on here is fairly> straightforward. John falls into that group of people who> understand the identity predicate within that topological> framework. He is trying to defend his ideas in the place> where everyone else thinks the expertise lies.> I havenOt the faintest idea what you are talking about.--John = >> Because IOm stupid, can anyone tell me whatOs the point of> this discussion?>>> So, what is going on here is fairly> straightforward. John falls into that group of people who> understand the identity predicate within that topological> framework. He is trying to defend his ideas in the place> where everyone else thinks the expertise lies.>>> I havenOt the faintest idea what you are talking about.>> --JohnOf that, I have little doubt. But that does not mean that I am incorrect, here.However, I am certainly mistaken if you are a different John--different from the one who,in explained haeccity to Immortalist with:The most straightforward de'nition I havefound is from Garth KemerlingOs Dictionary ofPhilosophical Terms and names(http://www.philosophypages.com/dy/index.htm):haecceity {Lat. haecceitas}Thisness; the property that uniquely distinguisheseach individual thing from others of its kind.Introduced by Duns Scotus as a name forthe individuating essence of any particular, the termhas been used more recently in connection with the viewthat rigidly designated individuals can exist in eachof many possible worlds.Thus, (1) is a theorem of all standard set theories: AyAx(y=x <-> y in {x}).Accordingly, granted that membership in {x} is bothnecessary and suf'cient for identity-with-x, {x}is (arguably) a haecceity of x: if you belong to{x} you are identical with x, and if you do notbelong to {x} you are not. The passages you citethe Ometaphysically robustO notion of *haecceity*:And, the quote above follows what was written in the original post for that thread. Thatis, in the post objection one, who (like myself) takesidentity to be nonre呈xive, has a non-standardresponse--to wit, that the usual axiom ofextensionality (which makes identity re呈xive) isnot indispensable: it can be supplanted by C4.C4 AxAy[Az(z in x <-> z in y) -> {Et(x in t & y in t) <-> x=y}]For from (C4) it follows that sets are self-identical, but that proper classes (like quanta?)are not.in some of the things that David Lewis has to say about singletons, and about what themereological and mereotopological advocates are saying.If I am wrong, and you are not that individual, I apologize for having tread where I shouldnot have.By the way, no one bothered to critique your proof. You made a mediate assumption betweenthe steps2) y in y <-> Et(y in t & ~(y in y))3) ~Et(y in t)That is, you assumed ~(y in y). At no point in your proof did you discharge thisassumption.:-)mitch Because IOm stupid, can anyone tell me whatOs the point of> this discussion?> >> So, what is going on here is fairly> straightforward. John falls into that group of people who> understand the identity predicate within that topological> framework. He is trying to defend his ideas in the place> where everyone else thinks the expertise lies.>>> I havenOt the faintest idea what you are talking about.>> --John Of that, I have little doubt. But that does not mean that I am> incorrect, here. However, I am certainly mistaken if you are a different John--> different from the one who, in haeccity to Immortalist with: The most straightforward de'nition I have> found is from Garth KemerlingOs Dictionary of> Philosophical Terms and names> (http://www.philosophypages.com/dy/index.htm): haecceity {Lat. haecceitas}> Thisness; the property that uniquely distinguishes> each individual thing from others of its kind.> Introduced by Duns Scotus as a name for> the individuating essence of any particular, the term> has been used more recently in connection with the view> that rigidly designated individuals can exist in each> of many possible worlds. Thus, (1) is a theorem of all standard set theories: AyAx(y=x <-> y in {x}). Accordingly, granted that membership in {x} is both> necessary and suf'cient for identity-with-x, {x}> is (arguably) a haecceity of x: if you belong to> {x} you are identical with x, and if you do not> belong to {x} you are not. The passages you cite> the Ometaphysically robustO notion of *haecceity*: > And, the quote above follows what was written in> the original post for that thread. That is, in the post objection one, who (like myself) takes> identity to be nonre呈xive, has a non-standard> response--to wit, that the usual axiom of> extensionality (which makes identity re呈xive) is> not indispensable: it can be supplanted by C4. C4 AxAy[Az(z in x <-> z in y) -> {Et(x in t & y in t) <-> x=y}] For from (C4) it follows that sets are self-> identical, but that proper classes (like quanta?)> are not. > then you might be>quite interested in some of the things> that David Lewis has to say about singletons, and about what> the mereological and mereotopological advocates are saying.I am that John, but I am not interested in what David Lewishas to say about singletons, nor am I interested in what DavidLewis has to say about what the mereological and mereotopologicaladvocates are saying. If I am wrong, and you are not that individual, I apologize> for having tread where I should not have.Apology accepted. By the way, no one bothered to critique your proof. You made> a mediate assumption between the steps 2) y in y <-> Et(y in t & ~(y in y))> 3) ~Et(y in t) That is, you assumed ~(y in y). At no point in your proof> did you discharge this assumption. :-) mitch > So, what is going on here is fairly> straightforward. John falls into that group of people who> understand the identity predicate within that topological> framework. He is trying to defend his ideas in the place> where everyone else thinks the expertise lies. > I havenOt the faintest idea what you are talking about.> Well, *I* would translate...: [...] John falls into that group of people who understand _identity_ in a very special way. [...]Not meant as an insult, just as a clari'cation (if so).F. =Does anyone know where I can 'nd the proof of the fact thatif X is a random variable, then f(X) is a random variable using the abstractde'nitions,i.e. borel sets, borel measurable, etc.where f is a function from R to R?Preferably if there is a proof online somewhere? Does anyone know where I can 'nd the proof of the fact that> if X is a random variable, then f(X) is a random variable using the abstract> de'nitions,> i.e. borel sets, borel measurable, etc.> where f is a function from R to R? Preferably if there is a proof online somewhere? > De'nition: X:S->R is a random variable if the inverse image of any Borel subset of R is measurable in S.De'nition: f:R->R is Borel measurable if the inverse image of any Borel set is a Borel set.(Actually the 1st de'nition is often stated as something like the inverse image of (a,in'nity) is measurable for all a, but since the sets (a,in'nity) generate the Borel sets, the de'nitions are equivalent.)-- Stephen Montgomery-Smithstephen@math.missouri.eduhttp:// www.math.missouri.edu/~stephen Does anyone know where I can 'nd the proof of the fact that> if X is a random variable, then f(X) is a random variable using the abstract> de'nitions,> i.e. borel sets, borel measurable, etc.> where f is a function from R to R?> I donOt think that this is generally true. For example, f(x) could be constant.Markus Triska. Does anyone know where I can 'nd the proof of the fact that> if X is a random variable, then f(X) is a random variable using theabstract> de'nitions,> i.e. borel sets, borel measurable, etc.> where f is a function from R to R?>>> I donOt think that this is generally true. For example, f(x) could be> constant.>> Markus Triska.>Essentially the original poster is asking whether given a Borel set B in R,is the inverse image in Omega ie {omega: f(X(w)) in B} an element of thesigma algebra on Omega.If itOs constant it certainly is a random variable, but if f is anon-measurable function.... = > Essentially the original poster is asking whether given a Borel set B in R,> is the inverse image in Omega ie {omega: f(X(w)) in B} an element of the> sigma algebra on Omega. If itOs constant it certainly is a random variable, but if f is a> non-measurable function.... Yes. I readhttp://www.math.tau.ac.il/~tsirel/Courses/Prob99/abs5. psand apparently, I misunderstood the term random variable - sorry.The paper also mentions the lemma, but contains no proof.Markus Triska. =IOm sorry I meant to say that f is a borel function.> Does anyone know where I can 'nd the proof of the fact that> if X is a random variable, then f(X) is a random variable using theabstract> de'nitions,> i.e. borel sets, borel measurable, etc.> where f is a function from R to R?>>> I donOt think that this is generally true. For example, f(x) could be> constant.>> Markus Triska.> =|> A plate of mass M has the form of a disc of radius R. Given that the mass|> density of the plate varies directly as the distance from a point P on the|> boundary of the plate, locate the center of mass|> |> How can I get delta, the density function, in terms of one variable which is|> somewhat friendly? Can I assume that P = (R,0) ? If P = (R, 0) then I got|> delta (x) = k sqrt (2R^2-2XR). Then things get extremely messy from there.|> Any hints would be appreciated.|> Steven|> |> I would use a polar representation for the circle, with the originon the point P. Then the circle is represented byrho = 2R cos(theta), with -pi/2 <= theta <= pi/2 if youchoose to put the center of the circle at (rho= R, theta = 0)-- a recommended choice, by the way, since you know bysymmetry considerations that the center of mass lieson the line from P to the point diametrally opposite to Pon the density/distance to P,you have to compute(int_{-pi/2}^{pi/2} ( int_0^{2R cos(theta)} rho rho d rho ) d theta)/(R^2 pi)where the 'rst rho corresponds to the density, and therho d rho d theta to the area of a small element of the disk(an explanation rather physical than mathematical, IOm afraid),and the division by (R^2 pi) comes from the area of the diskBut integrating the inner part is easy : (8 R^3 /3) cos(theta))^3and then integrating cos^3(theta) between -pi/2 and pi/2 isroutine, owing to 4 (cos(theta))^3 = cos(3 theta) + 3 cos(theta)-- Charles Delorme tous les m.8egalomanesLRI ont une signaturecd@lri.fr .88 .8etages =The 'sher discriminator is very easy to compute when the pool covariance matrix S is not degenerate, namely inv(S) * (m1+ m2).Strange enough, none of my references handles these cases.What can be done for very simple cases like in the following example,X1 = {(1,-1), (1,0), (1,-1)} and X2 = {(-1,-1), (-1,0), (-1,-1)} ? =How is this inequality solved:2x > x + 10 > -xAnswer: x > 10Brett How is this inequality solved:>>2x > x + 10 > -x>>Answer: x > 10>You have two inequalities combined; split them:x + 10 < 2x- x < x + 10Find a possible x range for each inequality. DRAW A NUMBER LINE and graph eachsolution onto this same number line. Pick some value in each interval betweenstarting and stopping points; here, more speci'cally, points around negative5 and positive 10.Does a point less than negative 5 work?Does a point between negative 5 and positive 10 work? Does a point greater than positive 10 work?Substitute these trial points into the original inequalities to see if a truestatement occurs. One note: remember that if you multiply or divide by negative 1, this reversesthe inequality relation sign.G C How is this inequality solved: 2x > x + 10 > -x Answer: x > 10 Brett First inequality: 2x > x+10add -x to both sides: x>10.Second inequality: x+10 > -xadd -x to both sides: 10 > -2xmultiply both sides by -1/2: -5 < xBoth inequalities together: x>10 and x>-5: result x>10. be a 'xed positive integer and e be NapierOs constant .A sequence (Y_n)_{n>=0} satisfying i) Y_n= n*Y_{n-1} -n^p , for all n=1,2,... , ii) lim_{n-->infty} Y_n/n! = 0 ,is considered.ItOs true that Y_0 = e*B(p) where B(p) is a positive integer ?Find a recursion relation between numbers B(1),B(2),...,B(p),.. . ItOs possible to write B(p) as a sum of Stirling numbers of second kind ? recommend a Liapunov function that might helpcontrol this plant represented by a nonlinear differential equation:y(t) = x(t) * ( 1 - F(s) * (|x(t)|^2) )here F(s) = K/(1+sb), represents a 1st order low pass 'lter(convolution with Kexp(-bt)) with time constant 1/b, and K is asmall positive number, so y is nearly x but not exactly; both b andK are unknown although I have a good idea of their value within afactor of 2.( By F(s) * (|x|^2) is meant the square of x(t), x(t)^2, is low pass'ltered by F(s).)I need a control law x = C[u, y],for positive u>0, such that thetracking error |y-u| is small. =two multi-precision integers. Numerical Recipes in C suggests usingthe Fast Fourier Transform. Then, they go on to state that the problemcan be worked using integer arithmetic (rather than doubles) viamodular arithmetic, but doesnOt supply a reference in the sameparagraph. At the end of the section, among other references, I 'ndFast Fourier Transform and Convolution Algorithms by Nussbaumer,1982. Apparently, this book is OOP and dif'cult to 'nd, so IOll getit via Interlibrary Loan. My question is: Does anyone know of any = two multi-precision integers. Numerical Recipes in C suggests using> the Fast Fourier Transform. Then, they go on to state that the problem> can be worked using integer arithmetic (rather than doubles) via> modular arithmetic, but doesnOt supply a reference in the same> paragraph. At the end of the section, among other references, I 'nd> Fast Fourier Transform and Convolution Algorithms by Nussbaumer,> 1982. Apparently, this book is OOP and dif'cult to 'nd, so IOll get> it via Interlibrary Loan. My question is: Does anyone know of anyDo you really want to reinvent everything already present in GMP(GNU Multiple Precision Arithmetic Library http://www.swox.com/gmp/ )or the work of George Woltman in OpenPFGW( http://www.primeform.net/openpfgw/ )Hugo Pfoertner = two multi-precision integers. Numerical Recipes in C suggests using> the Fast Fourier Transform. Then, they go on to state that the problem> can be worked using integer arithmetic (rather than doubles) via> modular arithmetic, but doesnOt supply a reference in the same> paragraph. At the end of the section, among other references, I 'nd> Fast Fourier Transform and Convolution Algorithms by Nussbaumer,> 1982. Apparently, this book is OOP and dif'cult to 'nd, so IOll get> it via Interlibrary Loan. My question is: Does anyone know of any Do you really want to reinvent everything already present in GMP> (GNU Multiple Precision Arithmetic Library http://www.swox.com/gmp/ )> or the work of George Woltman in OpenPFGW> ( http://www.primeform.net/openpfgw/ )Not necessarily. I am interested in 'nding the most ef'cient way ofdoing the work. I was also aware that some Multiple Precision softwareexists. But I did not know what the best/most up-to-date librarieswere. I want my software to be ported to both Windows and *nixsystems, and thus am hoping to 'nd source 'les rather thanassembly-optimized libraries. Furthermore, I am curious to 'nd outout.Brett> Hugo Pfoertner > two multi-precision integers. Numerical Recipes in C suggests using>> the Fast Fourier Transform. Then, they go on to state that the problem>> can be worked using integer arithmetic (rather than doubles) via>> modular arithmetic, but doesnOt supply a reference in the same>> paragraph. At the end of the section, among other references, I 'nd>> Fast Fourier Transform and Convolution Algorithms by Nussbaumer,>> 1982. Apparently, this book is OOP and dif'cult to 'nd, so IOll get>> it via Interlibrary Loan. My question is: Does anyone know of any>>Do you really want to reinvent everything already present in GMP>(GNU Multiple Precision Arithmetic Library http://www.swox.com/gmp/ )>or the work of George Woltman in OpenPFGW>( http://www.primeform.net/openpfgw/ )>IsnOt that how one learns?By your reasoning, math should not be taught in elementary schools,since calculators have made it obsolete.Besides, the more choices the better, in my opinion.To the original poster, i donOt have any information on the mostrecent advances on the subject, but then the twenty-year-oldtexts may have the basic information that you need as well. Do youhave access to a university mathematics library?The links that Hugo posted will also help, since reading the sourcecode will certainly help, and one hopes that there are referencesincluded.-- -johnFebruary 28 1997: Last day libraries could order catalogue cardsfrom the Library of Congress. > two multi-precision integers. Numerical Recipes in C suggests using>> the Fast Fourier Transform. Then, they go on to state that the problem>> can be worked using integer arithmetic (rather than doubles) via>> modular arithmetic, but doesnOt supply a reference in the same>> paragraph. At the end of the section, among other references, I 'nd>> Fast Fourier Transform and Convolution Algorithms by Nussbaumer,>> 1982. Apparently, this book is OOP and dif'cult to 'nd, so IOll get>> it via Interlibrary Loan. My question is: Does anyone know of any>>Do you really want to reinvent everything already present in GMP>(GNU Multiple Precision Arithmetic Library http://www.swox.com/gmp/ )>or the work of George Woltman in OpenPFGW>( http://www.primeform.net/openpfgw/ )> IsnOt that how one learns? By your reasoning, math should not be taught in elementary schools,> since calculators have made it obsolete. Besides, the more choices the better, in my opinion. To the original poster, i donOt have any information on the most> recent advances on the subject, but then the twenty-year-old> texts may have the basic information that you need as well. Do you> have access to a university mathematics library?No. But, I can use I.L.L. to get nearly anything I need.> The links that Hugo posted will also help, since reading the source> code will certainly help, and one hopes that there are references> included.Brett >> two multi-precision integers. Numerical Recipes in C suggests using>> the Fast Fourier Transform. Then, they go on to state that the problem>> can be worked using integer arithmetic (rather than doubles) via>> modular arithmetic, but doesnOt supply a reference in the same>> paragraph. At the end of the section, among other references, I 'nd>> Fast Fourier Transform and Convolution Algorithms by Nussbaumer,>> 1982. Apparently, this book is OOP and dif'cult to 'nd, so IOll get>> it via Interlibrary Loan. My question is: Does anyone know of any>>Do you really want to reinvent everything already present in GMP>(GNU Multiple Precision Arithmetic Library http://www.swox.com/gmp/ )>or the work of George Woltman in OpenPFGW>( http://www.primeform.net/openpfgw/ )> IsnOt that how one learns?Agreed, I have learned a lot by re-inventing existing methods.However it is sometimes helpful to know which methods exist. By your reasoning, math should not be taught in elementary schools,> since calculators have made it obsolete.Maths is a little bit more than calculators can do ... Besides, the more choices the better, in my opinion. To the original poster, i donOt have any information on the most> recent advances on the subject, but then the twenty-year-old> texts may have the basic information that you need as well. Do you> have access to a university mathematics library? The links that Hugo posted will also help, since reading the source> code will certainly help, and one hopes that there are references> included.Unfortunately the source code of the mult functions is mostly Assemblerand poorly commented, at least in the GMP source. --> -johnAn excellent starting point is Chapter 4.3.3 How fast can we multiply?in Donald E. Knuths The Art of Computer Programming Vol. 2, 3rdEditionPages 294-318, (C. Discrete Fourier transforms). Knuth alsogives the references to the key papers of Strassen, Schoenhage andPollard.See also http://members.tripod.com/careybloodworth/ntt.htm giving somematerial and links to the Number Theoretical or Pollard TransformHugo multi-precision integers. Numerical Recipes in C suggests http://members.tripod.com/careybloodworth/ntt.htm giving some> material and links to the Number Theoretical or Pollard TransformA better link is Carey BloodworthOs Multiplication page:http://members.tripod.com/careybloodworth/ multiplication.htmand his well documented example programs, download via:http://members.tripod.com/careybloodworth/downloads.htm Hugo =What is the use of parametric equations ?When to use them (in 2D , or 3D, other ) ?When to use them instead of cartesian equations ?Anthony = > What is the use of parametric equations ?They are handy when you want to model the path of a moving object, as opposed to modeling a static set of points.For example, x^2 + y^2 = 1 represents the unit circle in the plane.The parametric equations x = cos ty = sin tt in [0, 2pi)represent the same set of points . . . so far no difference.Butx = cos 2ty = sin 2tt in [0, 2pi)models a point traveling around the unit circle twice in the same amount of time that the previous object traveled only once around the circle.In other words the parametric equations give more information than the static x-y equation. The parametric equations not only describe the set of points in the plane that are traversed, but also how fast the object travels. When to use them (in 2D , or 3D, other ) ?> When you want to represent the path of a moving object, as opposed to a static set of points. Also, sometimes itOs just more convenient to use them.> When to use them instead of cartesian equations ?When itOs more convenient, or when you need to describe motion through a set of points. =The 'rst clear de'nition I foundHave you some good (clear :-)) sitesto advise meorbooks ?>>>> What is the use of parametric equations ?>> They are handy when you want to model the path of a moving object, as> opposed to modeling a static set of points.>> For example, x^2 + y^2 = 1 represents the unit circle in the plane.>> The parametric equations>> x = cos t> y = sin t> t in [0, 2pi)>> represent the same set of points . . . so far no difference.>> But>> x = cos 2t> y = sin 2t> t in [0, 2pi)>> models a point traveling around the unit circle twice in the same amount> of time that the previous object traveled only once around the circle.>> In other words the parametric equations give more information than the> static x-y equation. The parametric equations not only describe the set> of points in the plane that are traversed, but also how fast the object> travels.>>>> When to use them (in 2D , or 3D, other ) ?>>> When you want to represent the path of a moving object, as opposed to a> static set of points. Also, sometimes itOs just more convenient to use> them.>>>> When to use them instead of cartesian equations ?>> When itOs more convenient, or when you need to describe motion through a> set of points. =-- -[Original message quoted below due to length]Another reason for using parametric equations is that the equations in Cartesian coordinates are either very messy or impossible to write down in terms of elementary functions. The parametric form gives a clearer picture of what the curve is. The prototypical example is the cycloid and related curves.Ballou, Analytic Geometry.>The 'rst clear de'nition I found>>Have you some good (clear :-)) sites>to advise me>or>books ?>>>>>>>>> >>>>> >>>>>>>>>>>What is the use of parametric equations ?>>> >>>>>They are handy when you want to model the path of a moving object, as>>opposed to modeling a static set of points.>>>>For example, x^2 + y^2 = 1 represents the unit circle in the plane.>>>>The parametric equations>>>>x = cos t>>y = sin t>>t in [0, 2pi)>>>>represent the same set of points . . . so far no difference.>>>>But>>>>x = cos 2t>>y = sin 2t>>t in [0, 2pi)>>>>models a point traveling around the unit circle twice in the same amount>>of time that the previous object traveled only once around the circle.>>>>In other words the parametric equations give more information than the>>static x-y equation. The parametric equations not only describe the set>>of points in the plane that are traversed, but also how fast the object>>travels.>>>>>> >>>>>When to use them (in 2D , or 3D, other ) ?>>>>>> >>>>>When you want to represent the path of a moving object, as opposed to a>>static set of points. Also, sometimes itOs just more convenient to use>>them.>>>>>>>> >>>>>When to use them instead of cartesian equations ?>>> >>>>>When itOs more convenient, or when you need to describe motion through a>>set of points.>> >>>>> >-- Stephen J. Herschkorn herschko@rutcor.rutgers.edu = What is the use of parametric equations ? When to use them (in 2D , or 3D, other ) ? When to use them instead of cartesian equations ?TheyOre often useful for problems in which the equation[s]relate the variables implicitly, in other words are notreadily or simply expressable as y = function of (x).In situations like this a parametrization is a useful wayof OuntanglingO the equation into equivalent equations which,even collectively, are often more tractable, and, likely asnot, also more illuminating of what the equation represents.As just one example, people often post requests here forhelp in 'nding the four points of intersection of twoellipses, and plowing into this directly, using Cartesiancoordinates, results in a horrendous mess. But if you pluginto one ellipse a parametrization of the other, then theresulting quartic condition is much simpler, with itscoef'cients simple linear combinations of those of theoriginal ellipses.- --John R Ramsden (jr@aNdOsSlPaAtMe.com) A stockbroker is someone who invests your money until itOs all gone. Woody Allen boundary=-=_NextPart_000_001F_01C37F89.230F7AD0 =-- - If I have the following Example Data Set:14, 29, 32, 38, 41, 45, 68, 71, 74, 83, 86, 87, 94, 99How would I 'nd the 'rst quartile of that data set? What is the procedure?Mark =If I have the following Example Data Set:14, 29, 32, 38, 41, 45, 68, 71, 74, 83, 86, 87, 94, 99How would I 'nd the 'rst quartile of that data set?What is the procedure?Find the median = 69.5Then 'nd the median of the lower half,which is 38, the 'rst quartile. =Any thoughts?Mark> If I have the following Example Data Set:> 14, 29, 32, 38, 41, 45, 68, 71, 74, 83, 86, 87, 94, 99> How would I 'nd the 'rst quartile of that data set?> What is the procedure?>> Find the median = 69.5> Then 'nd the median of the lower half,> which is 38, the 'rst quartile.>>> =I need help on this question:Find the maximum and minimum values of f(x1,x2) = x1^2 -2x1x2 + 1 overD= (x element R^2: ||x||<=1}Now I know critical points occur where the gradient is 0. So Icalculated the gradient and found it is 0 at (0,0). Now I also know Ineed to check the boundary of D for max/min value aswell. I trieddoing this, but I am stuck. Can some one show me how I can check theboundary for max/min values?? = I need help on this question: Find the maximum and minimum values of f(x1,x2) = x1^2 -2x1x2 + 1 over> D= (x element R^2: ||x||<=1} Now I know critical points occur where the gradient is 0. So I> calculated the gradient and found it is 0 at (0,0). Now I also know I> need to check the boundary of D for max/min value aswell. I tried> doing this, but I am stuck. Can some one show me how I can check the> boundary for max/min values??> The equation for ||x||=1 is x1^2 + x2^2 = 1. Given this, there are twoattacks IOm familiar with. Solve for x2 and plug it into f(x1,x2) fora function of x1 alone and use ideas from 1d calculus to 'nd themaximum/minimums on that line. Secondly, if the gradient is orthogonalto the slope of the line tangent to ||x||=1 at any particular point,you know something about the value of the function at that point.YouOve found a point on the circle at which the value of the functionis not increasing/decreasing on either side of that point. = I need help on this question: Find the maximum and minimum values of f(x1,x2) = x1^2 -2x1x2 + 1 over> D= (x element R^2: ||x||<=1} Now I know critical points occur where the gradient is 0. So I> calculated the gradient and found it is 0 at (0,0). Now I also know I> need to check the boundary of D for max/min value aswell. I tried> doing this, but I am stuck. Can some one show me how I can check the> boundary for max/min values??> The boundary, ||x|| = 1, consists of the circle x1^2 + x2^2 = 1,so 'nd the max and min of g(t) = f(cos(t),sin(t)) boundary=-=_NextPart_000_0056_01C37F8E.ECB71190 =-- - Any thoughts?Mark> If I have the following Example Data Set:> 14, 29, 32, 38, 41, 45, 68, 71, 74, 83, 86, 87, 94, 99> How would I 'nd the 'rst quartile of that data set?> What is the procedure? Find the median = 69.5> Then 'nd the median of the lower half,> which is 38, the 'rst quartile. > > Any thoughts?> > Mark> > Nat Silver If I have the following Example Data Set:> 14, 29, 32, 38, 41, 45, 68, 71, 74, 83, 86, 87, 94, 99> How would I 'nd the 'rst quartile of that data set?> What is the procedure?>> Find the median = 69.5> Then 'nd the median of the lower half,> which is 38, the 'rst quartile.I agree with Nat that 38, the median of the lower half, is the 'rst quartile. I have heard about computer packages giving different answers before. For example, Excel (the least trustworthy for statistics) says 38.75! Got me how the packages come up with these.-- Stephen J. Herschkorn herschko@rutcor.rutgers.edu =THE INCH AND ROD METHODThe Speed of Light and PhiTo calculate the speed of light:Measure with the rod to the inch by the extreme and mean,the light speed, exact to the centimeter, is then obtainedfrom the shen and three cubed and squared.Here is the working out, ROD 1 37 3701 R+O+D = 37 1 37 3702 I+N+C+H = 34 2 74 7403 P+H+O+T+O+N = 88 3 111 11105 1+1+2+3+5+8+13+21+34 = 88 5 185 18508 ROD ~ (1) a light detecting eye cell 8 296 29613 (2) a unit of length measure 13 481 48121 INCH~ (1) a unit of length measure 21 777 77734 729 ~ the cubesquare of lightINCH 34 1258 125855 10^7 ~ hieroglyph shen = 55 (light circling earth) THE INCH AND ROD METHODc = 125855/77734 x 729 x 10^7 in/sec = 125855/77734 x 729 x 10^7 x 2.54 cm/sec = 1.619047... x 729 x 10^7 x 2.54 cm/sec = 29979245800 cm/s (nearest centimeter)To recall the reckoning note that the ROD is the name of a lightdetecting cell in the human eye. The ROD is also a measuring rule.Thus the word ROD links light to measurement and, visa versa,measurement to light.Then using gematria, A=1, B=2, C=3,..., etc.., obtain the numericalvalue for the ROD as measuring unit = R+O+D = 18+15+4 = 37.The extreme and mean, otherwise known as the golden mean ratio,is the ratio of two consecutive elements on the 'bonacci sequencetaken to the limit. But weOre using the ROD as the unit, soconstruct a 'bonacci seq using the number 37 as the starting unitinstead of the usual 1.And rather than go all the way to in'nity, we go up only to the INCH,that is, the word INCH = I+N+C+H = 19+14+3+8 = 34, and so we stop atthat number in the standard 'bonacci sequence to obtain the twoelements for the phi ratio.As a check, note that the sum of these 'bonacci elements gives us thenumber of the PHOTON = 88 = 1+1+2+3+5+8+13+21+34. Thiscon'rms the mark in the sequence corresponding to the INCH as the placewhere the light or photon measure is to be obtained.Now we add the two 'bonacci sequences together, the standard sequenceand the sequence with the ROD as unit, but in such a way that the RODnumbers donOt interfere with the standard 'bonacci numbers, so we needto multiply the ROD column by 100 before adding the standard 'bonnacisequence to it. Another way to think of this is to consider the ROD asthe 10Os and the standard numbers as the 1Os, but in a centennial systemusing 100 numbers instead of decimal system with 10. The only trickto remember is that we adjust the 'bonacci numbers by 1 row before weadd them to the ROD column. In other words, the 'nal sequence is notjust a multiple of the standard 'bonacci sequence, it really is acombination of two sequences. We can think of one sequence as the extremeand the other as the mean, where the extreme is the higher ROD numbers,while the mean is the usual standard 'bonacci counts. As we walk downthe two 'bonacci sequences weOve got one foot in front of the other,so to speak.Well, having stopped at the INCH, we calculate the ratio125855/77734which we then scale by two multipliers. The 'rst scale factor is 729,the cubesquare of 3, i.e., the number 3 cubed, 3*3*3 = 27, then squared,27*27 = 729. This is PlatoOs magic number for measuring the intervalbetween extremes. [See PlatoOs Republic, Book 9]. Note also that thisnumber is a cubesquare like the Horus Eye number 64, which the Egyptiansused for establishing a system of measuring fractions 1/2,1/4,..,1/64,and so on. But being that the Human eye sees 3 basic colors, having 3different cone cells to detect light, we refer to the sixth power of 3as the cubesquare of light. Recall that the cubesquare is the numberthat allows cubic volumes to be partitioned into the same number of partsas square areas, and thus enables ef'cient mapping of 3-d space to 2-dsurfaces like the back of the retina, etc..so the eye numbers are allcubesquares; the 'rst, 64, is used for the divided Horus Eye, theeye Seth destroyed and was re-constructed by Horus. Peet mentions in histranslation of the RMP that thereOs a belief that the EgyptianOs alsohad a system of 1/3, 1/9, ..but the evidence is inconclusive.However, we can remember the 729 factor by recalling that the eye seeslight by using both RODs and cones, and the RODs see the intensity,while the cones see the colors by detecting and combining 3 basic colors.The ratio 125855/77734 obtained from the ROD calculation, then needsthat cone factor 3^6 = 729 to modify it. ThatOs probably easier toremember than looking up Plato anyway.The other factor is the shen = 10^7. Now the OshenO is the ancientEgyptian number that measures the extremes again, just like PlatoOsextreme number. However, this time itOs the light going around theBut there are two such horizons, the rising sun in the east and thesetting sun in the west, and these are opposites, and extremepositions of the sun in the sky. This is the largest number in theto represent it, so itOs an extreme number in their number system too.The hieroglyph of the sun on the horizon is just a simple circlesitting on a straight line segment that it bisects and which touchesthe circle as a tangent.In a sense this also suggests the idea of a circle curvilinear measurebeing contrasted to a straight rectilinear line measure, hinting at therecti'cation of the circle, or squaring the circle, of the ancientphilosophers. And the shen obviously suggests a connection to lightagain, since it uses the sun. Moreover, squaring the 10^7 gives thenumber of wavelengths of light that we see best which 'ts around thecircumference of the earth. That is to say, the human eye is bestadapted to see light in the region of green light, and such light haswavelength that, if used to measure the circumference of the earth,would produce a number with order of magnitude 10^14. The square rootof this is 10^7, the same shen number used by the Ancient Egyptiansfor their largest number and represented by light circling the earthin the form of the sunOs apparent motion. So the 10^7 factor is indeeda light measure number. But here it is indicative of the extremescale of the universe, being that it numbers the measurement on thepath of RA the sun god, about our world earth, etc..Now we combine all our extreme numbers which relate to lightin various ways, to determine the speed of that light. The PHIratio is also an extreme number being that it is the limit of theratio of two consequtive 'bonacci numbers, and PHI represents themean growth of a good many natural processes too, being then a kindof central limit that natural phenomena tend to gravitate towards.And light, of course, is the extreme speed limit on the highwayof kinematic transport, so weOve got a convergence of extremes.Combining the ROD and Cone numbers with this Scale factor gives us thespeed of light. And since we stopped at the INCH, in the 'bonaccisequence, the unit of length in the lightspeed is British Inches, andlight is therefore in inch/sec units.c = 125855/77734 x 729 x 10^7 in/secBut, as we said, our calculation is exact in centimeters. (So thatwe donOt forget the important French contributions to the world ofscience.) It is not an approximate result. So, we convert inches tocentimeters and round to the nearest whole centimeter to obtain ourexact result. There are exactly 2.54 centimeters in 1 inch. So,c = 125855/77734 x 729 x 10^7 x 2.54 cm/sec = 29979245800 cm/s (nearest centimeter)neat huh?pmj THE INCH AND ROD METHOD> The Speed of Light and Phi>>> To calculate the speed of light:>> Measure with the rod to the inch by the extreme and mean,> the light speed, exact to the centimeter, is then obtained> from the shen and three cubed and squared.>> Here is the working out,>>>> ROD> 1 37 3701 R+O+D = 37> 1 37 3702 I+N+C+H = 34> 2 74 7403 P+H+O+T+O+N = 88> 3 111 11105 1+1+2+3+5+8+13+21+34 = 88> 5 185 18508 ROD ~ (1) a light detecting eye cell> 8 296 29613 (2) a unit of length measure> 13 481 48121 INCH~ (1) a unit of length measure> 21 777 77734 729 ~ the cubesquare of light> INCH 34 1258 125855 10^7 ~ hieroglyph shen 55 (light circling earth)>> THE INCH AND ROD METHOD>> c = 125855/77734 x 729 x 10^7 in/sec> = 125855/77734 x 729 x 10^7 x 2.54 cm/sec> = 1.619047... x 729 x 10^7 x 2.54 cm/sec> = 29979245800 cm/s (nearest centimeter)>>> To recall the reckoning note that the ROD is the name of a light> detecting cell in the human eye. The ROD is also a measuring rule.> Thus the word ROD links light to measurement and, visa versa,> measurement to light.>So who decided Cones donOt count? =David C. Ullrich pushed brie囤 to theto the shed door:^ >I suspect he is remembering the following quote from^ ><3f5e5c01.11252651@news.global.net.uk>:^ >| ^ Corollary?^ >| ^ >| Ooooh, me, Sir, ME!^ >| ^ >| Why does JSH keep hearing from Dave The Rave Ullrich? Because DTRU has^ >| got nothing better to do than correspond with crackpots.^ >| ^ >| Do I win 'rst prize?^ Actually that was his second post recently about Dave The Rave.^ Seems like he was disappointed when I didnOt reply to his 'rst:^ ^ group:sci.math&hl=en&lr=&ie=UTF-8&selm=3f5b5bdf.^ 246312921%40news.global.net.uk&rnum=2^> ^ >Trying to reason with Dave the Rave is also useless, unfortunately.^ >Perhaps he is mentally ill too. He certainly canOt seem to get his^ >head round the idea that a mentally ill person like James is simply^ >not susceptible to having the obvious pointed out. God bless him, heOs^ >been plugging away pointing out the obvious to him, in various ways^ >from condescending to sarcastic, for a few years now, and never seems^ >to tire of it. One has to conclude that he really does do it for his^ >own amusement.Just in case youOre under any illusion about Dave The Rave being mycreation, this seems like the right place to point out that actually Ijust took amused note when someone else used it quite a while ago.Bill Taylor, I think. I donOt know if he coined it or borrowed it inturn from someone else. In the end, your own obsessive behaviour,alternating between decrying JSH Os own deluded obsessiveness andhinting about the more dangerous extremes of irrational behaviour,got suf'ciently under my skin again that it seemed like a good timeto re-invite you to examine the mote in your own eye.It has been quite a long time since I last got tempted to poke fun atyou in public, though, hasnOt it? It is very tiresome when two peoplepersist in a public slanging match that should be carried out viasent you at the time. Had you done so, I doubt we would be persistingin public slanging now.^ It does make his statement as far as I recall, I have never ^ stated that such behaviour is inappropriate sort of interesting.^ I suppose I should apologize for incorrectly paraphrasing^ what he said - he never said such behavior was inapproriate,^ just that it might be symptomatic of mental illness.Incorrect paraphrasing is a forte of yours. This is a second example.Not only did I never say such behaviour was inappropriate, I alsonever said that it might be symptomatic of mental illness. I was quiteexplicit that my criticism was aimed not at participation per se, butat overly perseverative participation, of which you are the #1 primeexponent. The distinction is either lost on you, or you choose tooverlook it. Bearing in mind the notion that insanity is expectingdifferent results from repeating the same behaviour, you really oughtto think more carefully before presuming to advise anyone else aboutthe state of their mental health. ^ >I thought it was just a joke and you didnOt really^ >intend any serious criticism, but it wasnOt aimed at me.^ ^ DonOt get the wrong idea - regardless of how it was intended^ it was nothing but amusing at this end (because itOs been^ clear the guy has a bug up his ass since the thread a while^ ago where he insisted on making a _pompous_ fool of^ himself over CLT (pompous referring to his repeated ^ statements that the reason he understood the issues better^ than his stat friend was he was a mathematician, when^ in _fact_ he was totally wrong about the whole thing and^ his stat friend had things straight.))Yup, hands up there. I made a complete arse of myself. DidnOt I wearthe hair shirt for long enough to satisfy you at the time? ISTR beingpretty open about admitting having been a twat.Not the 'rst time IOve behaved like a twat, not even on sci.math andcertainly not on Usenet, and it certainly wonOt be the last. At leastmy twattishness is con'ned to occasional outbursts, though. IMO, YMMVetc.Andy-- sparge at globalnet point co point uk In a sense do we not all have psychological or pharmaceutical crutches forming our bridges to the stars? (or our gangplank across lifeOs mud吧ts) .97.96, uk.rec.sheddizen >> Mega moniker of the real high IQ group Mega Society that sued his ass>>> for>>> IP theft.>>>> http://www.polymath-systems.com/intel/hiqsocs/megasoc/ judgment.html>>>> Harris got picked up by a pack of scam artists. Huh. This judgement, dated March of this year, orders him to stop> publishing his Noesis Journal. But isnOt that the name of the thing> that James got published in?Despite its web addresscontaining the word noesis, itOs now renamed itelfas Noeon.So thatOs all right then :-)-- Robin Chapman, www.maths.ex.ac.uk/~rjc/rjc.htmlNeedless to say, I had the last laugh. Alan Partridge, _Bouncing Back_ (14 times) > Mega moniker of the real high IQ group Mega Society that sued his ass>>> for>>> IP theft.>>>> http://www.polymath-systems.com/intel/hiqsocs/megasoc/ judgment.html>>>> Harris got picked up by a pack of scam artists. Huh. This judgement, dated March of this year, orders him to stop> publishing his Noesis Journal. But isnOt that the name of the thing> that James got published in? Despite its web address > containing the word noesis, itOs now renamed itelf> as Noeon. So thatOs all right then :-)Hmm. Skirting a thin line, I guess. The judgement mentionsNoesis and Mega Society and variations, and also prohibitsuse of any of the infringed trademarks in a DOMAIN anyway. Cost of doing businessfor a scammer, right? - Randy = question> that people in colleges, academia, and sciences will encounter. Why> are there> so many disproportionate number of jews in sciences? Is it because> they are> a superior race and conversely lending truth to racism and thus> ShockleyOs> fallacy that blacks are inferior? Do the jews have greater stamina> than> others? They have Jewish mothers. Read PortnoyOs Complaint by Philip Roth. > Chinese mothers are equally lethal and man-hating. That Jews from the> off the bottom 90% of the bell curve for European Jews doesnOt hurt> either - evolution is a hoot if you are one of the survivors. The> best of the best emigrated to the New World and were scythed again by> anti-Semitism. The survivors are intellectually superior in every way> (on the average). Selective breeding works the other way, too. The absolutely most> stupid Blacks in West Africa were captured by their marginally more> intelligent and vicious brethren, then sold to Arabs who in turn sold> them to the Triangular Trade and New World slavery. Uppity Darkies> were weeded out. The result is US Inner Cities as celebrations of> ethnic diversity.> Wow...ainOt nobody that can accuse Uncle Al of excessive politicalcorrectness!Still, sad to say, what this honkey, racist curmudgeon posts has theunmistakable ring of truth!To some people, this truth is a problem. The question then is, whydoesnOt society 'x the problem rather than pretending that it doesnOtexist or justi'ng it?Teaching someone to read or speak correctively shouldnOt cost verymuch, unless the politicians get their hand into it. Similarly, basicmath skills are not very dif'cult to teach or to learn. Once peoplemaster language and mathematics skills, plus a bit of factual history,college becomes a matter of hard work...nothing else.Then too, I once in a while have to sit back and ask myself thequestion: Why is American education more poised to train workers thanto educate people? Asking such questions in a New England town meetingtends to make me very unpopular, but I donOt understand why.Then too, possibly I donOt wish to understant by, because the obviousexplanation is so very ugly. Harry C. =characterized this thread)>Teaching someone to read or speak correctively shouldnOt cost very>much, unless the politicians get their hand into it. Similarly, basic>math skills are not very dif'cult to teach or to learn. Once people>master language and mathematics skills, plus a bit of factual history,>college becomes a matter of hard work...nothing else.> >This strikes me as wrong, unless, of course, you prefer shacks forschools and not paying teachers very much.>Then too, I once in a while have to sit back and ask myself the>question: Why is American education more poised to train workers than>to educate people? Asking such questions in a New England town meeting>tends to make me very unpopular, but I donOt understand why.> >Well, the educational system I grew up in (NYC schools in the 50s) wasspeci'cally designed to train of'ce and skilled trade workers in NYC. BTW, that was the one Uncle Al pines for. If you want to tell me that it didnOt cost very much, well heck, thatwas because they were living off schools constructed in the 30s and40s and women teachers who had few other career opportunities andguys who got locked into the system during the depression. The stuffhit the fan in the 60s and 70s. Kind of reminds me of what the US is doing now, living off pastinvestment. Sooner or later the piper comes to play.josh halpern>Then too, possibly I donOt wish to understant by, because the obvious>explanation is so very ugly.>> Harry C.> > =go away, trolls.-- Mark McIntyreCLC FAQ CLC readme: > question> that people in colleges, academia, and sciences will encounter. Why> are there> so many disproportionate number of jews in sciences? Is it because> they are> a superior race and conversely lending truth to racism and thus> ShockleyOs> fallacy that blacks are inferior? Do the jews have greater stamina> than> others?>> They have Jewish mothers. Read PortnoyOs Complaint by Philip Roth.> Chinese mothers are equally lethal and man-hating. That Jews from the> off the bottom 90% of the bell curve for European Jews doesnOt hurt> either - evolution is a hoot if you are one of the survivors. The> best of the best emigrated to the New World and were scythed again by> anti-Semitism. The survivors are intellectually superior in every way> (on the average).>> Selective breeding works the other way, too. The absolutely most> stupid Blacks in West Africa were captured by their marginally more> intelligent and vicious brethren, then sold to Arabs who in turn sold> them to the Triangular Trade and New World slavery. Uppity Darkies> were weeded out. The result is US Inner Cities as celebrations of> ethnic diversity.>>> Wow...ainOt nobody that can accuse Uncle Al of excessive political> correctness!>> Still, sad to say, what this honkey, racist curmudgeon posts has the> unmistakable ring of truth!>> To some people, this truth is a problem. The question then is, why> doesnOt society 'x the problem rather than pretending that it doesnOt> exist or justi'ng it?>> Teaching someone to read or speak correctively shouldnOt cost very> much, unless the politicians get their hand into it. Similarly, basic> math skills are not very dif'cult to teach or to learn. Once people> master language and mathematics skills, plus a bit of factual history,> college becomes a matter of hard work...nothing else.>> Then too, I once in a while have to sit back and ask myself the> question: Why is American education more poised to train workers than> to educate people?Somebody has to make the donuts.......>Asking such questions in a New England town meeting> tends to make me very unpopular, but I donOt understand why.>> Then too, possibly I donOt wish to understant by, because the obvious> explanation is so very ugly.The truth is that the vast majority of the population hasa hard time keeping enough in their heads to get through thenext day much less deal with you telling them how you think theyshould go about life....>> Harry C. >> >>Wrong. The most persecuted Semitic population are the Palestinians, and>>ironically most persecuted by the Israelis.>>>> Oh great. Another bigot 吧unts himself in front of the world.>>>> The one clearly demonstrating bigotry is yourself, I have no objections to>> Jews and every objection to Israeli foreign policy. Unlike you, I am not>> so bigoted that I canOt tell one from the other.>>It would be an interesting scienti'c study to determine why>there is such aggressive, hostile reaction>to criticism that involving Israel, Jews, a Jew,>or some claimed accomplishment of a Jew,>and why critics are personally attacked,>and the issue in play is avoided and obscured.>>It is okay to demean most ethnic groups with words like>raghead, redneck, wop, wet back, chink, polock, etc.>and little is made of it, but suggest that something Jewish is negative>and the hits the fan and goes 囤ing in all directions,>mostly toward the critic.>>As this intense negative reaction is counter productive>to Jews over the long run, and harmful to the larger society,>it seems that an effort should be made to examine this problem,>and to see what causes it, and how to solve it.>>It may be that the intensive religious and ethnic indoctrination>of Jewish children, which is far more intense than that of Muslims,>Catholics, etc. is the root cause of the problem, It may be your brain not working is the root cause of yours.It is interesting to see that Lloyd ParkerOs post tends to con'rm my suggestion that many people are brainwashed to react with aggression and hostility, when exposed to ideas that con告ct with their conditioning.It would certainly be in the interests of mankind for a scienti'c study to be conducted, to see how intense religious/ethnic conditioning causes social problems.As can be seen, Jews have often been in the eye of the hurricane and at times have been drawn into the heavy winds.Most of the instigators of the class wars of the 1900Os were Jews, and most of the instigators of the religious wars of the 2000Osare Jews.The question is, does the intense ethnic/religious conditioning of Jewish children, bring them into con告ct with their communities, and other religious and ethnic groups?If so, how can this be prevented?I suggest that governments should limit the amount of time that a child can be subjected to ethnic/religious brainwashing.--Tom Potter The question is, does the intense ethnic/religious conditioning > of Jewish children, bring them into con告ct with their > communities, and other religious and ethnic groups?In the United States, Jewish children live in a peacful and law abiding way among and with their Gentile neibhbors. What con告ct? The occurence of violence and criminality is much lower among Jews, than in the country taken as a whole. What con告ct?Bob Kolker It would be an interesting scienti'c study to determine why> there is such aggressive, hostile reaction> to criticism that involving Israel, Jews, a Jew,> or some claimed accomplishment of a Jew,> and why critics are personally attacked,> and the issue in play is avoided and obscured.>> It is okay to demean most ethnic groups with words like> raghead, redneck, wop, wet back, chink, polock, etc.> and little is made of it, but suggest that something Jewish is negative> and the hits the fan and goes 囤ing in all directions,> mostly toward the critic.>> As this intense negative reaction is counter productive> to Jews over the long run, and harmful to the larger society,> it seems that an effort should be made to examine this problem,> and to see what causes it, and how to solve it.>> It may be that the intensive religious and ethnic indoctrination> of Jewish children, which is far more intense than that of Muslims,> Catholics, etc. is the root cause of the problem,>> As this creates a lot of trouble for Jews, and the larger society,> perhaps a solution would be to limit the amount of religious and ethnic> brainwashing that children can be subjected to.>> As the more intelligent Jews are not religious anyway,> they should welcome a reduction in religious indoctrination,> as this would save them time and money,> and would eliminate a major source of con告ct with the larger society.>> The world is too small,> to allow this chasm to persist> between Jews and the larger society,> as it is a major source of the worlds problems.> Tom Potter http://tompotter.us>>> [Fread]> Rather remarkably you seem to have obscured fact with opinion. The Jews> have been a rather remarkably oppressed people for well over 2000 years.> Primarily because they insist on maintaining some kind of identity of> their own. You 'nd this the ultimate sin. Wishing to remain Jews is the> same as the sin of the Christians in a pagan world wanting to maintain> themselves as Christians. Yet you 'nd this condition only unacceptable> in the case of Jews. What is it about Jews that you 'nd so offensive?> There have been a considerable number of them, quit educated and quite> willing to live within norms established by their surrounding peoples,> who were found so offensive that they too were attacked by those who> found them unacceptable. It appears that the Jew cannot be accepted> until such time as he disappears totally as a Jew. And even then there> are those who 'nd him unacceptable even after he is no longer a Jew> save for purposes of ancestry.> [hanson]> Fred, this is cool! I like that. > [Fred]> That appears to be part of the problem with people of your ilk.> You canOt forgive the stiff necked pride of those who claim> to be a chosen people. Coming in second or not even in> the race at all has made you consumed with envy. Why bother?> It is a terrible burden to have to live up to that religious claim.> Too many demands of superior performance.> FK> [hanson]> Fred, this is not cool. But, I like that too.> In your last six lines you have restated IOW exactly what> seem to bee bothering Tom Potter and many others, wherein> your envy solution may back're unto your ilk, big time. Still, ....letOem sing... ALL ofOem ... itOs a beautiful choir.> hansonI suggest that what hanson asserts is cool is not cool at all.As can be seen, fkasner makes the mistake of equating maintaining some kind of identity with oppression.The question, what is oppression, and who is and has been oppressed and why?No doubt, at times, various nations and peoples have oppressed Jews, but the key questions are:Why did they do this?How can this be prevented?For example, during the 1900Os many nations oppressed Jews because a small group of Jews were instigating class warfare all over the globe, and Jews in many nations were giving moral and 'nancial support to the terrorists.And note that today, many Jews are instigating religious warfare, and they have placed America and Americans right in the middle of their religious wars, at the cost of 911, the Iraqi war, loss of American markets, loss of American allies, dollar 告ght, hatred of America, etc.and no doubt this will create great hostility toward Jews and eventually active government oppression as the masses begin to take note of the cost of the religious wars in terms of lives, limbs and dollars.The world is too small to allow this chasm to exist between Jews and other groups. I suggest that the root cause of the chasm is that many Jews are brainwashed intently and they react to their conditioning rather than to actual reality.I suggest that the solution to the problem is for governments to limit the amount of time that children can be brainwashed to religious and ethnic dogma. NOte thjat Jews are conditioned more intently than Muslims, Catholics, idol worshippers, etc. and this no doubt is the source of the problem.People who live together should not be conditioned to set themselves apart from other folks, and to put their religion and ethnitity above their welfare of the community they live in.And regarding fkasner assertion that Jews are oppressed, I dare say that many Palestinians, Muslims, Blacks, Poles, Irish, Indians, Asians, etc, would gladly swap their oppression with the Jews over an extended period of time and space.--Tom Potter And note that today, many Jews are instigating religious > warfare, and they have placed America and Americans > right in the middle of their religious wars, > at the cost of 911, the Iraqi war, loss of American markets, Our dependence on middle east oil has nothing to do with this, of course. And the fact that fanatical Moslems attack our people and property both at home and abroad have nothing to do with this, of course.It is only Jewish activism that creats the Moslem terror, right?The Wahabite who have been fulminating since the 18-th century long before the creation of the State of Israel, have nothing to do with this, right?I would propose to you that Moslem fanatics have more to do with our current woes, than pro Zionist Jews.Bob Kolker = ... snip ... > It would be an interesting scienti'c study to determine why> there is such aggressive, hostile reaction> to criticism that involving Israel, Jews, a Jew,> or some claimed accomplishment of a Jew,> and why critics are personally attacked,> and the issue in play is avoided and obscured. It is okay to demean most ethnic groups with words like> raghead, redneck, wop, wet back, chink, polock, etc.> and little is made of it, but suggest that something Jewish is negative> and the hits the fan and goes 囤ing in all directions,> mostly toward the critic. As this intense negative reaction is counter productive> to Jews over the long run, and harmful to the larger society,> it seems that an effort should be made to examine this problem,> and to see what causes it, and how to solve it. It may be that the intensive religious and ethnic indoctrination> of Jewish children, which is far more intense than that of Muslims,> Catholics, etc. is the root cause of the problem, As this creates a lot of trouble for Jews, and the larger society,> perhaps a solution would be to limit the amount of religious and ethnic> brainwashing that children can be subjected to. As the more intelligent Jews are not religious anyway,> they should welcome a reduction in religious indoctrination,> as this would save them time and money,> and would eliminate a major source of con告ct with the larger society. The world is too small,> to allow this chasm to persist> between Jews and the larger society,> as it is a major source of the worlds problems. --> Tom Potter http://tompotter.us Rather remarkably you seem to have obscured fact with opinion. The Jews > have been a rather remarkably oppressed people for well over 2000 years. > Primarily because they insist on maintaining some kind of identity of > their own. You 'nd this the ultimate sin. Wishing to remain Jews is the > same as the sin of the Christians in a pagan world wanting to maintain > themselves as Christians. Yet you 'nd this condition only unacceptable > in the case of Jews. What is it about Jews that you 'nd so offensive? > There have been a considerable number of them, quit educated and quite > willing to live within norms established by their surrounding peoples, > who were found so offensive that they too were attacked by those who > found them unacceptable. It appears that the Jew cannot be accepted > until such time as he disappears totally as a Jew. And even then there > are those who 'nd him unacceptable even after he is no longer a Jew > save for purposes of ancestry. That appears to be part of the problem > with people of your ilk. You canOt forgive the stiff necked pride of > those who claim to be a chosen people. Coming in second or not even in > the race at all has made you consumed with envy. Why bother? It is a > terrible burden to have to live up to that religious claim. Too many > demands of superior performance.> FKIt is interesting to see that fkasner equates insist on maintaining some kind of identity with being oppressed.It is also interesting to see that fkasner obscures fact with opinion with his statements:1. You 'nd this the ultimate sin.2. you 'nd this condition only unacceptable in the case of Jews.3. That appears to be part of the problem with people of your ilk.4. You canOt forgive the stiff necked pride of those who claim to be a chosen people.5. Coming in second or not even in the race at all has made you consumed with envy.As can be seen, fkasner has been severly conditioned, to think that he is superior, and the folks who doubt this to be inferior, and he parrots the conventional boilerplate, and uses the conventional tactic of attacking the messenger, rather than addressing the message in a rational, logical, intelligent, MORAL way.As can be seen from fkasnerOs conditioned response, he, like many brainwashed people, is unable to discuss certain issues in a rational, intelligent way, and note that like most brainwashed people, he strikes out at the messenger in an effort to prevent discussion of the issue.My position is that the root cause of the problem is too much religious and ethnic brainwashing, and the solution is for governments to limit the amount of time a child can be exposed to ethnic and religious brainwashing. A good government should require that all citizens put the nation and itsO mores 'rst, and ethnic and religious mores second.fkasnerOs position is that people should attack the folks interested in 'nding the root cause, and the cure for this problem.(Con告ct between Jews and the other folks in the world.)A 'nal note.Note that fkasnerOs response to my post clearly reveals that my premise that many people are brainwashed to react in an aggressive, hostile way to the discussion of certain issues, is correct.--Tom Potter http://tompotter.us >My position is that the root cause of the problem >is too much religious and ethnic brainwashing, >and the solution is for governments to limit the amount >of time a child can be exposed to ethnic and religious >brainwashing. A good government should require that all >citizens put the nation and itsO mores 'rst, and recommendation would violate Constitutional rights regarding freedom of speech, assembly, etc.2. You apparently have not recognized that the US Goverment IS a religion. It has every attribute of a religion. a. Advocates belief in and assumes there is a God as evidenced by phrases on coins, prayers in Congress, etc. b. Has sacred texts: Bill of Rights, Constitution, etc. c. Has high priests: Supreme Court d. Has sacred places: White House, Arlington National Cemetery e. Exists so as to preserve the group (Americans)I spent a words and found, e.g., this:So basically, Tom you want to replace the traditional religionswith the new nation-state religions like Americanism. Thisis a very old story Tom. Looks like you are a nation-statefundamentalist!--Marshall So basically, Tom you want to replace the traditional religions>with the new nation-state religions like Americanism. This>is a very old story Tom. Looks like you are a nation-state>fundamentalist!>>--MarshallAbove, I described Tom as being a nation-state fundamentalist.Please except my appologies Tom (IOm sleep deprived.) for thatis a personal attack. Better that I should have writtenthat Tom is advocating nation-state fundamentalism. --Marshall My position is that the root cause of the problem> is too much religious and ethnic brainwashing,> and the solution is for governments to limit the amount> of time a child can be exposed to ethnic and religious> brainwashing. A good government should require that all> citizens put the nation and itsO mores 'rst, and> ethnic and religious mores second.In that respect, there is not that much difference between pious Jews andArabs. They both are intolerant, not only of each other but of themselves.This is also true of other fundamentlist religions, including ChristianityThe solution is to make people valuable. This can be accomplished by meansof nuclear war. The Human species would not be harmed if the worldpopulation were pruned down to 100,000,000. Life would be harder, but notthreatened. It will only be rough on the people trimmed off or those whoinsist on luxuries.Bill The solution is to make people valuable. This can be> accomplished by means of nuclear war. The Human species> would not be harmed if the world population were pruned> down to 100,000,000. Life would be harder, but not> threatened. It will only be rough on the people trimmed> off or those who insist on luxuries.You really need to get together with David Polewka, whohangs out in alt.anagrams. Blind mass-murderous sociopathicnutcases need a support group like anyone else.xanthian, former nuclear weapons maintainer, who wants toremark that if you think you can titrate nuclear weapons tokill off 59/60ths but not 60/60ths of the human population,you need a science education desperately.xanthian.-- > >>>The solution is to make people valuable. This can be>>accomplished by means of nuclear war. The Human species>>would not be harmed if the world population were pruned>>down to 100,000,000. Life would be harder, but not>>threatened. It will only be rough on the people trimmed>>off or those who insist on luxuries.>> >>>>You really need to get together with David Polewka, who>hangs out in alt.anagrams. Blind mass-murderous sociopathic>nutcases need a support group like anyone else.>>xanthian, former nuclear weapons maintainer, who wants to>remark that if you think you can titrate nuclear weapons to>kill off 59/60ths but not 60/60ths of the human population,>you need a science education desperately.> >HavenOt heard that one, but I have always paid attention toKruechevOs remark that after a nuclear war the living wouldenvy the deadjosh halpern>xanthian.>>> > > The solution is to make people valuable. This can be> accomplished by means of nuclear war. The Human species> would not be harmed if the world population were pruned> down to 100,000,000. Life would be harder, but not> threatened. It will only be rough on the people trimmed> off or those who insist on luxuries.>> You really need to get together with David Polewka, who> hangs out in alt.anagrams. Blind mass-murderous sociopathic> nutcases need a support group like anyone else.>> xanthian, former nuclear weapons maintainer, who wants to> remark that if you think you can titrate nuclear weapons to> kill off 59/60ths but not 60/60ths of the human population,> you need a science education desperately.>> xanthian.ThereOs a much easer way to prune.. CanOt remember thename of the island off hand but thereOs a volcanic islandin the paci'c and along the main ridge line thereOs a faultline.. If that fault line were to shear it would drop ahunk of land about 20 miles long and 4 miles wide into thepaci'c... ThatOs estimated to send a 70 foot open waterwave across the east coast of US, all of the east coast ofSouth America, Mexico, England to the west andall the Populated countries around the paci'c..That would mean once the wave hits the shallow watersof the land masses the wave would rise to around 700 feetand wiping a pretty good hunk of the human infestation ..A set of 3 or 4 small nukes along the fault line and itwould slide... Heck... its unstable now and could gonext week for no apparent reason anyway....Then thereOs drilling into the center of Yellow Stoneand setting a string of charges all the way to the magmachamber below.. once you pop that cork you can saygood bye to at least 3/4 of the earths population...It already has a 700mm rise in the uplift dome since1895..... Even 2 or 3 earth penetrate nukes would dothe trick.... Timed to detonate just as the re呈ctiveshock wave meets the impact point of the 'rst device.A mind is a terrible thingPaul R. Mays --Some where within the Quantum StateHttp://Paul.Mays.Comhttp://paul.mays.com/resume.htmlAll truth passes through three stages:First, it is ridiculedSecond, it is violently opposedThird, it is accepted as self-evident. - Arthur Schopenhauer It is okay to demean most ethnic groups with words like> raghead, redneck, wop, wet back, chink, polock, etc.> and little is made of it, but suggest that something Jewish > is negative and the hits the fan and goes 囤ing in ,> all directions mostly toward the critic.>PotterOs observation and opinion is very wide spread and valid.Furthermore, Tom believes that this Jewish knee-jerk reaction can be traced back to excessive brainwashing by their religious doctrineor establishment, resulting them to scream bigot and Anti-Semite upon the slightest drop of a hat, when they donOt like something.Of course such Jewish overreaction only aggravates the situation & thefallout avalanches, resulting in the forced conclusion (right or wrong)that Jews themselves are the cause, source and origin of bigotryand Anti-Semitism. An underlaying, collective cultural pathology may also play a role in this, in that Jews have an unnaturally excessive desire, craving, need and demand to be praised, loved and adored.....whencompared to Non Jews, with the exception that this very same phenomena can be seen, in different colors, on the exactly the same level, for the same reasons, from/in the White Power, Heil, the Black isBeautiful or the La RazaOs all for me none for you......(nice company)Along these same lines, there is an even more unfathomable JewishMO, which back 'res on them constantly and in告cts damage ontotheir fellow Jews. ItOs their because I am Jewish gag, which they do announce incessantly, almost in a tourette-style fashion .......whenever they tell a good joke, when they get rich because they worked hard , when they publish, produce or invent something outstanding.....Jews seldom to never say:I worked very hard for it, or I was at they right time at the right place.......but they often to always attribute their successes to the fact:because I am Jewish.It may be true that Jews have objectively an above average IQ becausethey have a superior communal/religious edu system, because they studywith more intensive interest, work harder at a task, .....may that be as is, but then they it up, diminish or destroy the fruits of their labor by advertising loudly that all their accomplishments happened because they are Jewish.It is an old human adage, that if you walk around and tell everybody thatyou are smarter, richer, bigger, better, catholic, protestant, Muslim, orJewish, or atheist, etc.....eventually the vast majority who is not so smart, not so rich, not so big, not so good, not catholic, not protestant, not Muslim, or not Jewish, or not atheistetc.........they will get jealous, angry and if you keep up with constantly self-anointing yourself in front of themthey will kick your ass.In case of the Jews, history shows that they havenOt leaned this lesson forin/their 5700 years of history. Actually, it appears that they love it, thatthey prefer and work very hard to invite such backdrafts, so that they can cry and whine bigot and Anti-Semite, producing a never ending viscous circle for themselves, between suffering in KZOs and then enjoying the industrial style extraction of $Billions over the murdered corpses of their kinfrom the grandchildren and great grandchildren of their tormentors ........and to boot........they fully expect these innocent children to love them.........ahahahaha.........ahahahah..... if Jews are really 5.5 times smarter,as Robert Kolker has posted them to be...then what good did it bring them?ahahahaha..........ahahahahanson = [racist drivel] Groups that are over-represented in any 'eld of endeavor, from mugging> to astrophysics, probably work harder to participate in those 'elds. ItOs called merit, something racists fail to 'nd lacking in> themselves, but all the rest of the world notices easily by its omission> in their works. xanthian.I think that is better to invoke some more intelignent anti-Semites.I will quote the philosopher Cioran (The Temptation to Exist, Paris Gallimard, 1956. pp. 91-92), in his autobiographical remorsals.<>Anti-Semitic behavior usually compensates some de'ciency, thereforeas a friendly I would advice these people to look for someprofessional help.bandika >>>>>>>>>> Oh, for heavensO sake. Children of that age not only can, but will >>>count>>>>>> for themselves, if only because itOs so much fun going Seven-three!>>>>>> Seven-three! Neener, neener!. All these people trying to be nice >for>>>>>> the sake of the chiillldruuunnn are stupid for not realising (or,>>>>>> indeed, remembering) how un-nice children themselves can be.>>>>>>>>>>And who should, as a reminder, read GoldingOs Lord of the Flies.>>>>>>>>>Yes, yes.>>>>>>>>>Besides, I think that competitiveness just prepares the kids for the >real >>>>>world...>>>>>>>>Exactly. This is what the purpose of all play is, preparation for the >>>>real world. The modern enlightened educational approach, though, is >>>>based on keeping kids as sheltered from the real world as possible >>>>till they reach 18, then expect them to magically turn into adults at >>>>this date. Then everybody is surprised why there are so many immature valedictorian rituals>>>because all the other kids might feel bad. The gal who>>>lost out proposed that athletic letters anyone?>>>>:-))>>>Yep. That gal had spunk. SheOll do well if she continues with>the attitude.>I hope she does. We need more like her.Mati Meron | When you argue with a fool,meron@cars.uchicago.edu | chances are he is doing just the same >>>>>>>> Oh, for heavensO sake. Children of that age not only can, but will >>count>>>>> for themselves, if only because itOs so much fun going Seven-three!>>>>> Seven-three! Neener, neener!. All these people trying to be nice for>>>>> the sake of the chiillldruuunnn are stupid for not realising (or,>>>>> indeed, remembering) how un-nice children themselves can be.>>>>>>>>And who should, as a reminder, read GoldingOs Lord of the Flies.>>>>>>>Yes, yes.>>>>>>>Besides, I think that competitiveness just prepares the kids for the real >>>>world...>>>>>>Exactly. This is what the purpose of all play is, preparation for the >>>real world. The modern enlightened educational approach, though, is >>>based on keeping kids as sheltered from the real world as possible >>>till they reach 18, then expect them to magically turn into adults at >>>this date. Then everybody is surprised why there are so many immature valedictorian rituals>>because all the other kids might feel bad. The gal who>>lost out proposed that athletic letters That gal had spunk. SheOll do well if she continues withthe attitude./BAH =In equation (1) can someone 'nd the rational x, rational y on this quartic?There are the roots, of course, x = +/- 10423*sqrt(18289), and x = +/-221563225/sqrt(18289), with y=0, and the point x=0, y = +/-2309353494175*sqrt(18289), but I need a rational point with nonzero y.I am fairly certain that there is one around height of slightly less than 36that does exist, but IOve not been able to pry it loose using the mwrankprogram.(1) 18289*x^4 - 85428628717705634*x^2 + 97537313918194915089082200625 = y^2Randall boundary=-=_NextPart_000_003C_01C37FA6.22532980 =-- - Why do you think that the algorithms in these computer packages differ?Why arenOt they universal?Any thoughts or comments?Mark> > Any thoughts?> > Mark> > Nat Silver If I have the following Example Data Set:> 14, 29, 32, 38, 41, 45, 68, 71, 74, 83, 86, 87, 94, 99> How would I 'nd the 'rst quartile of that data set?> What is the procedure?>> Find the median = 69.5> Then 'nd the median of the lower half,> which is 38, the 'rst quartile.I agree with Nat that 38, the median of the lower half, is the 'rst quartile. I have heard about computer packages giving different answers before. For example, Excel (the least trustworthy for statistics) says 38.75! Got me how the packages come up with these.-- Stephen J. Herschkorn herschko@rutcor.rutgers.edu